Of Time and Space and Other Things
by Isaac Asimov

eversion 1.0

                          INTRODUCTION

      As we trace the development of man over the ages, it seems
      in many respects a tale of glory and victory; of the develop-
      ment of the brain; of the discovery of fire; of the building
      of cities and of civilizations; of the triumph of reason; of
      the fimng of the Earth and of the reaching out to sea and
      space.
         But increasing knowledge leads not to conquest only, but
      to utter defeat as well, for one learns not only of new po-
      tentialities, but also of new limitations.  An explorer may
      discover a new continent, but he may also stumble over
      the world's end.
         And it is so with mankind.  We are distinguished from
      all other living species by our power over the inanimate
      universe; and we are distinguished from them also by our
      abject defeat by the inanimate universe, for we alone have
      learned of defeat.
         Consider that no other species (as far as we know) can
      possess our concept of time.  An animal may remember,
      but surely it can have no notion of "past" and certainly not
      of "future."
         No non-human creature lives in anything but the present
      moment.  No non-human creature can foresee the inevita-
      bility of its own death.  Only man is mortal, in the sense
      that only man is aware that he is mortal.
         Robert Bums said it better in his poem To a Mouve.
      He addresses the mouse, after turning up its nest with his
      plough, apologizing to it for the disaster he has brought
      upon it, and reminding it fatalistically that "The- best-laid
      schemes o' mice and men / Gang aft a-gley."
         But then, in a final soul-chilling stanza (too often lost
      in the glare of the much more famous penultimate stanza
                                    7

    about mice and men), he gets to the real nub of the poem
    and says:

              "Still thou art blest compar'd wi' me!
              "The present only toucheth thee:
              "But oh, I backward cast my e'e
                    "On prospects drear!
              "An' forward tho' I canna see,
                    "I guess an' fear!"

      Somewhere, then, in the progress of evolution from
    mouse to man, a primitive hominid first caught and grasped
    at the notion that someday he would die.  Every living crea-
    ture died at last, our proto-philosopher could not help but
    notice, and the great realization somehow dawned upon
    him that he himself would do so, too.  If death must come
    to all life, it must come to himself as well, and ahead of
    him he saw world's end.
      We talk often about the discovery of fire, which marked
    man off from all the rest of creation.  Yet the discovery of
    death', is surely just as unique and may have been just as
    driving a force in man's upward climb.
      The details of both discoveries are lost forever in the
    shrouded and impenetrable fog of pre-history, but they
    appear in myths.  The discovery of fire is celebrated most
    famously in the Greek myth of Prometheus, who stole fire
    from the Sun for the poor, shivering race of man.
      And the discovery of death is celebrated most famously
    in the Hebrew myth of the Garden of Eden, where man
    first dwelt in the immortality that came of the ignorance
    of time.  But man gained knowledge, or, if you prefer, he
    ate of the fruit of the tree of knowledge of good and evil.
      And with knowledge, death entered the world, in the
    sense that man knew he must die.  In biblical terms, this
    awareness of death is described as resulting from divine
    revelation.  In the 'solemn speech in which He apprises
    Adam of the punishment for disobedience, God tells him
    (Gen. 3:19):          for dust thou art, and unto dust shalt
    thou return."
      But man struggles onward under the terrible weight of
    Adam's curse, and I cannot help but wonder how much
                                 8

      of man's accomplishment traces directly back to his en-
      deavor to neutralize the horrifying awareness of inevitable
      death.  He may transfer the consciousness of existence from
      himself to his family and find immortali    ,ty after all in the
      fact that though his own spark of life snuffs out, an allied
      spark continues in the children that issued out of his body.
      How much of tribal society is based on this?
         Or he may decide that the true life is not of the body
      which is, indeed, mortal and must suffer death; but of the
      spirit which lives forever.  And how much of philosophy
      and religion and the highest aspirations of man's faculties
      arises from this striving to deny Adam's curse?
         Yet what of a society in which the notion of family and
      of spirit weakens; a society in which the material world of
      the senses gradually fills the consciousness from horizon to
      horizon?  The nearest approach-to such a society in man's
      history is probably our own.  How, then, has the modern
      West, which has deprived itself of the classical escapes, re-
      acted to the inevitability of death?
         Is it entirely a coincidence that of all cultures, that of
      the present-day West is the most time-conscious?  That it
      has spent more of its energies in studying time, measuring
      time, cutting time up into ever-tinier segments with ever-
      greater accuracy?
         Is it entirely a coincidence that the most materialistic
      subdivision of our most materialistic culture, the twentieth-
      century American, is never seen anywhere without, his
      wristwatch?  At no time, apparently, dare he be unaware of
      the sweep of the second hand and of the ticks that mark
      off the inexorable running out of the sands of his life.
         So it is that the opening essays in this collection deal
      directly with man's attempt to measure time.  The notion
      of time creeps into a number of the other essays as well;
      in a discussion of units which turn out always to include
      the "second"; in a discussion of catalysts which squeeze
      more action into less time.  For really, time is a subject that
      cannot be entirely excluded from any; corner of science.
         When man faces death directly, then, he studies time, for
      it is by accurately handling time that he can measure other
      phenomena and find a route through science.  And through
                                     9

     science, perhaps, may come a truly materialistic defeat of
     Adam's curse.
       For my final essay in this book takes up the inevitability
     of death, and the conclusion is that though all men are
     mortal, they are not nearly as mortal as they ought to be.
       Why not?  That is the chink in death's armor.  Why does
     man live as surprisingly long as he does?  If we can some-
     day find the answer to that, we may find the answer to
     much more.
       Immortality?
       Who knows, but-maybe!

                                  10

                 Part I
          OF TIME AND SPACE
       I

                                       A

               1. THE DAYS OF OUR YEARS

     A group of us meet for an occasional evening of, talk and
     nonsense, followed by coffee and doughnuts and one of
     the group scored a coup by persuading a well-known
     entertainer to attend the session.  The well-known enter-
     tainer made one condition, however.  He was not to enter-
     tain, or even be asked to entertain.  This was agreed to.
       Now there arose a problem.  If the meeting were left
     to,its own devices, someone was sure to begin badgering
     the entertainer.  Consequently, other entertainment had to
     be supplied, so one of the boys turned to me and said,
     "Say, you know what?"
       l,knew what and I objected at once.  I said, "How can
     I stand up there and talk with everyone staring at this
     other fellow in the audience and wishing he were up there
     instead?  You'd be throwing me to the wolves!"
       But they all smiled very toothily and told me about the
     wonderful talks I give. (Somehow everyone quickly dis-
     covers the fact that I soften into putty as soon as the flat-
     tery is turned on.) In no time at all, I agreed to be thrown
     to the wolves.  Surprisingly, it worked, which speaks highly
     for the audience's intellect-or perhaps their magnanimity.
      I As it happened, the meeting was held on "leap day"
     and so my topic of conversation was ready-made and the
     gist of it went as follows:

       I suppose there's no question but that the earliest unit
     of time-telling was the day.  It forces itself upon the aware-
     ness of even the most primitive of humanoids.  However,
     the day is not convenient for long intervals of time.  Even
     allowing a primitive Iife-span of @ years, a man would
                                  13

      live some 11,000 days and it is very easy to lose track
      among all those days.
        Since the Sun governs the day-unit, it seems natural to
      turn to the next most prominent heavenly body, the Moon,
      for another unit.  One offers itself at once, ready-made-
      the period of the phases.  The Moon waxes from nothing to
      a full Moon and back to nothing in a definite period of
      time.  This period of time is called the "month" in English
      (clearly from the word "mooif') or, more specifically, the
      "lunar month," since we have other months, representing
      periods of time slightly shorter or slightly longer than the
      one that is strictly tied to the phases of the moon.
        The lunar month is roughly equal to 291/2 days.  More
      exactly, it is equal to 29 days, 12 hours, 44 minutes, 2.8
      seconds, or 29.5306 days.
        In pre-agricultural times, it may well have been that no,
      special significance attached itself to the month, which re-
      mained only a convenient device for measuring moderately
      long periods of time.  The life expectancy of primitive man
      was probably something like 350 months, which is a much
      more convenient figure than that of I 1,000 days.
        In fact, there has been speculation that the      extended
      lifetimes of the patriarchs reported in the fifth chapter of
      the Book of Genesis may have arisen out of a confusion
      of years with lunar months.  For instance, suppose Me-
      thuselah had lived 969 lunar months.  This would be just
      about 79 years, a very reasonable figure.  However, once
      that got twisted to 969 years by later tradition, we gained
      the "old as Methuselah" bit.
        However, I mention this only in passing, for this idea
      is not really taken seriously by any biblical scholars.  It is
      much more likely that these lifetimes are a hangover from
      Babylonian traditions about the times before the Flood.
      . . .But I am off the subject.
        It is my feeling that the month gained a new and
      enhanced importance with the introduction of agriculture.
      An agricultural society was much more closely and pre-
      cariously tied-to the season& than a hunting or herding
      society was.  Nomads could wander in search of grain or
                                   14

      grass but farmers had to stay where they were and hope
      for rain.  To increase their chances, farmers had to be cer-
      tain to sow at a proper time to take advantage of sea-
      sonal rains and seasonal warmth; and a mistake in the
      sowing period might easily spell disaster.  What's more, the
      development of agriculture made possible a denser popu-
      lation, and that intensified the scope of the possible dis-
      aster.
        Man had to pay attention, then, to the cycle of seasons,
      and while he was still in the prehistoric stage he must have
      noted that those seasons came fall cycle in roughly twelve
      months.  In other words, if crops were planted at a par-
      ticular time of the year and all went well, then, ff twelve
      months were counted from the first planting and crops
      were planted again, all would again go well.
        Counting the months can be tricky in a primitive so-
      ciety, especially when a miscount can be ruinous, so it isn't
      surprising that the count was usually left in the hands
      of a specialized caste, the priesthood.  The priests could
      not only devote their time to accurate counting, but could
      also use their experience and skill to propitiate the gods.
      After all, the cycle of the seasons was by no, means as rigid
      and unvarying as was the cycle of day and night or the
      cycle of the phases of the moon.  A late frost or a failure
      of rain could blast that season's crops, and since such
      flaws in weather were bound to follow any little mista e
      in ritual (at least so men often believed), the priestly func-
      tions were of importance indeed.
        It is not surprising then, that the lunar month grew to
      have enormous religious significance.  There were new
      Moon festivals and special priestly proclamations of each
      one of them, so that the lunar month came to be called
      the "synodic month."

        The cycle of seasons is called the "year" and twelve
      lunar months therefore make up a "lunar year." The use
      of lunar years in measuring time is referred to as the use
      of a "lunar calendar." The only important group of people
      in modem times, using a strict lunar calendar, are the
                                   15

     Moh  ammedans. Each of the Moharmnedan years is made
     up of 12 months which are, in turn, usually made up of
     29 and 30 days in alternation.
       Such months average 29.5 days, but the length of the
     true lunar month is, as I've pointed out, 29.5306 days.
     The lunar year built up out of twelve 29.5-day months is
     354 days long, whereas twelve lunar months are actually
     354.37 days long.
       You may say "So what?" but don't.  A true lunar year
     should always start on the day of the new Moon.  If, how-
     ever, you start one lunar year on the day of the new Moon
     and then simply alternate 29-day and 30-day months, the
     third year will start the day before the new Moon, and the
     sixth year will start two days before the new Moon.  To
     properly religious people, this would be unthinkable.
       Now it so happens that 30 true lunar years come out to
     be almost exactly an even number of days-10,631.016.
     Thirty years built up out of 29.5-day months come to
     10,620 days-just 1 1 days short of keeping time with the
     Moon'  For that reason, the Mohammedans scatter 1 1 days
     through the 30 years in some fixed pattern which prevents
     any individual year from starting as much, as a full day
     ahead or behind the new Moon.  In each 30-year cycle
     there are nineteen 354-day years and eleven 355-day
     years, and the calendar remains even with the Moon.
       An extra day, inserted in this way to keep the calendar
     even with the movements of a heavenly body, is called an
     "intercalary day"; a day inserted "between the calendar,"
     so to speak.
       The lunar year, whether it is 354 or 355 days in length,
     does not, however, match the cycle of the seasons.  By the
     dawn of historic times the Babylonian astronomers had
     noted that the Sun moved against the background of stars
     (see Chapter 4).  This passage was followed with absorp-
     tion because it grew apparent that a complete circle of the
     sky by the Sun matched the complete cycle of the seasons
     closely. (This apparent influence of the stars on the sea-
     sons probably started the Babylonian fad of astrology-
     which is still with us today.)
       The Sun makes its complete cycle about the zodiac in
                                 16

      roughly 365 days, so that the lunar year is'about II days
      shorter than the season-cycle, or "solar year." Three lunar
      years fall 33 days, or a little more than a full month be-
      hind the season-cycle.
         This is important.  If you use a lunar calendar and start
      it so that the first day of the year is planting time, then
      three years later you are planting a month too soon, and
      by the time a decade has passed you are planting in mid-
      winter.  After 33 years the first day of the year is back
      where it is supposed to be, having traveled through the
      entire solar year.
         This is exactly what happens in the Mohammedan
      year.  The ninth month of the Mohammedan year is named
      Ramadan, and it is especially holy because it was the
      month in which Mohammed began to receive the revela-
      tion of the Koran.  In Ramadan, therefore, Moslems ab-
      stain from food and water during the daylight hours.
      But each year, Ramadan falls a bit earlier in the cycle of
      the seasons, and at 33-year intervals it is to be found in
      the hot season of the year; at this time abstaining from
      drink is particularly wearing, and Moslem tempers grow
      particularly short.
         The Mohammedan years are numbered from the Hegira;
      that is, from the date when Mohammed fled from Mecca
      to Medina.  That event took place in A.D. 622.  Ordinarily,
      you nught suppose, therefore, that to find the number of
      the Mohammedan year, one need only subtract 622 from
      the number of the Christian year.  This is not quite so,
      since the Mohammedan year is shorter than ours.  I write
      this chapter in A.D. 1964 and it is now 1342 solar years
      since the Hegira.  However, it is 1384 lunar years since the
      Hegira, so that, as I write, the Moslem year is A.H. 1384.
         I've calculated that the Mohammedan year will catch
      up to the Christian year in about nineteen millennia.  The
      year A.D. 20,874 will also be A.H. 20,874, and the Moslems
      will then be able to switch to our year with a minimum of
      trouble.

         But what can we do about the lunar year in order to
      make it keep even with the seasons and the solar year?  We
                                  17

     can't just add II days at the end, for then the next year
     would not start with the new Moon and to the ancient
     Babylonians, for instance, a new Moon start was essential.
       However, if we start a solar year with the new Moon
     and wait, we will find that the twentieth solar year there-
     after starts once again on the day of the new Moon.  You
     see, 19 solar years contain just about 235 lunar months.
       Concentrate on those 235 lunar months.  That is equiva-
     lent to 19 lunar years (made up of 12 lunar months each)
     plus 7 lunar months left over.  We could, then, if we
     wanted to, let the lunar years progress as the Moham-
     medans do, until 19 such years had passed.  At this time
     the calendar would be exactly 7 months behind the sea-
     sons, and by adding 7 months to the 19th year (a 19th
     year of 19 months-very neat) we could start a new 19-
     year cycle, exactly even with both the Moon and the sea-
     sons.
       The Babylonians were unwilling, however, to let them-
     selves fall 7 months behind the seasons.  Instead, they
     added that 7-month discrepancy through the 19-year cycle,
     one month at a time and as nearly evenly as possible.  Each
     cycle had twelve 12-month years and seven 13-montb
     years.  The "intercalary month" was added in the 3rd, 6th,
     8tb, I lth, 14th, 17th, and 19th year of each cycle, so that
     the year was never more than about 20 days behind or
     ahead of the Sun.
       Such a calendar, based on the lunar months, but gim-
     micked so as to keep up with the Sun, is a "lunar-solar
     calendar."
       The Babylonian lunar-solar calendar was popular in
     ancient times since it adjusted the seasons while preserving
     the sanctity of the Moon.  The Hebrews and Greeks both
     adopted this calendar and, in fact, it is still the basis for
     the Jewish calendar today.  The individual dates in the
     Jewish calendar are allowed to fall slightly behind the Sun
     until the intercalary month is added, when they suddenly
     shoot slightly ahead of the Sun.  That is why holidays like
     Passover and Yom Kippur occur on different days of the
     civil calendar (kept strictly even with the Sun) each year.
                                  18

      These holidays occur on the same day of the year each
      year in the Jewish calendar.
        The early Christians continued to use the Jewish calen-
      dar for three centuries, and established the dayof Easter
      on that basis.  As the centuries passed, matters grew some-
      what complicated, for the Romans (who were becoming
      Christian in swelling numbers) were no longer used to a
      lunar-solar calendar and were puzzled at the erratic jump-
      ing about of Easter.  Some formula had to be found by
      which the correct date for Easter could be calculated in
      advance, using the Roman calendar.
        It was decided at the Council of Nicaea, in A.D. 325
      (by which time Rome had become officially Christian),
      that Easter was to fall on the Sunday after the first full
      Moon after the vernal equinox, the date of the vernal
      equinox being established as March 21.  However, the full
      Moon referred to is not the actual full Moon, but a fic-
      titious one called the "Paschal Full Moon" ("Paschal"
      being derived from Pesach, which is the Hebrew word for
      Passover).  The date of the Paschal Full Moon is calcu-
      lated according to a formula involving Golden Numbers
      and Dominical Letters, which I won't go into.
        The result is that Easter still jumps about    the days of
      the civil year and can fall as early as March 22 and as
      late as April 25. Many other church holidays      are tied to
      Easter and likewise move about from year to year.
        Moreover, all Christians have not always agreed on the
      exact formula by which the date of Easter was to be cal-
      culated.  Disagreement on this detail was one of the reasons
      for the schism between the Catholic Church of the West
      and the Orthodox Church of the East.  In the early Middle
      Ages there was a strong Celtic Church which had its own
      formula.

        Our own calendar is inherited from Egypt, where sea-
      sons were unimportant.  The one great event of the year
      was the Nile flood, and this took place (on the average)
      every 365 days.  From a very early date, certainly as early
      as 2781 B.C., the Moon was abandoned and a "solar calen-
                                   19

     dar," adapted to a constant-length 365-day year, was
     adopted.
       The solar calendar kept to the tradition of 12 months,
     however.  As the year was of constant length, the months
     were of constant length, too-30 days each.  This meant
     that the new Moon could fall on any day of the month,
     but the Egyptians didn't care. (A month not based on the
     Moon is a "calendar month.")
       Of course 12 months of 30 days each add up only to
     360 days, so at the end of each 12-month cycle, 5 addi-
     tional days were added and treated as holidays.
       The solar year, however, is not exactly 365 days long.
     There are several kinds of solar years, differing slightly in
     length, but the one upon which the seasons depend is the
     "tropical year," and this is about 3651/4 days long.
       This means that each year, the Egyptian 365-day year
     falls 1/4 day behind the Sun.  As time went on the Nile
     flood occurred later and later in the year, until finally it
     had made a complete circuit of the year.  In 1460 tropical
     years, in other words, there would be 1461 Egyptian years.
       This period of 1461 Egyptian yea'rs was called the
     "Sothic cycle," from Sothis, the Egyptian name for the
     star Sirius.  If, at the beginning of one Sothic cycle, Sirius
     rose with the Sun on the first day of the Egyptian year, it
     would rise later and later during each succeeding year
     until finally, 1461 Egyptian years later, a new cycle would
     begin as Sothis rose with the Sun on New Year's Day once
     more.
       The Greeks bad learned about that extra quarter day as
     early as 380 B.C., when Eudoxus of Cnidus made the
     discovery.  In 239 B.c. Ptolemy Euergetes, the Macedonian
     king of Egypt, tried to adjust the Egyptian calendar to
     take that quarttr day into account, but the ultra-conserva-
     tive Egyptians would have none of such a radical innova-
     tion.

       Meanwhile, the Roman Republic had a lunar-solar
     calendar, one in which an intercalary month was added
     every once in a while.  The priestly officials in charge were
     elected politicians, however, and were by no means as con-
                                  20

      scientious as those in the East.  The Roman priests added
      a month or not according to whether they wanted a long
      year (when the other annually elected officials in power
      were of their own party) or a short one (when they were
      not).  By 46 B.C., the Roman calendar was 80 days behind
      the Sun.
         Julius Caesar was in power then and decided to put an
      end to this nonsense.  He had just returned from Egypt
      where he had observed the convenience and simplicity of
      a solar year, and imported an Egyptian astronomer, Sosig-
      enes, to help him.  Together, they let 46 B.C. continue for
      445 days so that it was later known as "The Year of Con-
      fusion." However, this brought the calendar even with
      the Sun so that 46 B.C. was the last year of confusion.
         With 45 B.C. the Romans adopted a modified Egyptian
      calendar in which the five extra days at the end of the year
      were distributed throughout the year, giving us our months
      of uneven length.  Ideally, we should have seven 30-day
      months and five 31-day months.  Unfortunately, the Ro-
      mans considered February an unlucky month and short-
      ened it, so that we ended with a silly arrangement of seven
      31-day months, four 30-day months, and one 28-day
      month.
         In order to take care of that extra 1/4 day, Caesar and
      Sosigenes established every fourth year with a length of
      366 days. (Under the numbering of the years of the Chris-
      tian era, every year divisible by 4 has the intercalary day
      -set as February 29.  Since 1964 divided by 4 is 491,
      without a remainder, there is a February 29 in 1964.)
         This is the "Julian year," after Julius Caesar'   At the
      Council of Nicaea, the Christian Church adopted the
      Julian calendar.  Christmas was finally accepted as a
      Church holiday after the Council of Nicaea, and given a
      date in the Julian year.  It does not, therefore, bounce
      about from year to year as Easter does.
         The 365-day year is just 52 weeks and I day long.  This
      means that if February 6, for instance, is on a Sunday in
      one year, it is on a Monday the next year, on a Tuesday
      the year after, and so on.  If there were only 365-day years,
      then any given date would move through the days of the
                                   21

    week in steady progression.  If a 366-day year is involved,
    however, that year is 52 weeks and 2 days long, and if
    February 6 is on Tuesday that year, it is on Thursday the
    year after.  The day has leaped over Wednesday.  It is for
    that reason that the 366-day year is called "leap yearip
    and February 29 is "leap day."

       All would have been well if the tropical year were
    really exactly 365.25 days long; but it isn't.  The tropical
    year is 365 days, 5 hours, 48 minutes, 46 seconds, or
    365.24220 days long.  The Julian year is, on the average,
    11 minutes 14 seconds, or 0.0078 days, too long.
       This may not seem much, but it means that the Julian
    year gains a full day on the tropical year in 128 years.  As
    the Julian year gains, the vernal equinox, falling behind,
    comes earlier and earlier in the year.  At the Council of
    Nicaea in A.D. 325, the vernal equinox was on March 21.
    By A.D. 453 it was on March 20, by A.D. 581 on March
    19, and so on.  By A.D. 1263, in the lifetime of Roger
    Bacon, the Julian year had gained eight days on the Sun
    and the vernal equinox was on March 13.
       Still not fatal, but the Church looked forward to an
    indefinite future and Easter was tied to a vernal equinox
    at March 21.  If this were allowed to go on, Easter would
    come to be celebrated in midsummer, while Christmas
    would ed e into the spring.  In 1263, therefore, Roger
              9
    Bacon wrote a letter to Pope Urban IV explaining the
    situation.  The Church, however, took over three centuries
    to consider the matter.
       By 1582 the Julian calendar had gained two more days
    and the vernal equinox was falling on March I 1. Pope
    Gregory XIII finally took action.  First, he dropped ten
    days, changing October 5, 1582 to October 15, 1582.  That
    brought the calendar even with the Sun and the vernal
    equinox in 1583 fell on March 21 as the Council of Nicaea
    had decided it should.
       The next step was to prevent the calendar from getting
    out of step again.  Since the Julian year gains a full day
    every 128 years, it gains three full days in 384 years or,
    to approximate slightly, three full days in four centuries.
                                 22

     That means that every 400 years, three leap years (accord-
     ing to the Julian system) ought to be omitted..
        Consider the century years-1500, 1600, 1700, and so
     on. In the Julian year, all century years are divisible by
     4 and are therefore leap years.  Every 400 years there are
     4 such century years, so why not keep 3 of them ordinary
     years, and allow onl one of them (the one that is divisible
       by 400) to be a leap year?  This arrangement will match
     the year more closely to the Sun and give us the "Gre-
     'gorian calendar."
        To summarize: Every 400 years, the Julian calendar
     allows 100 leap years for a total of 146,100 days.  In that
     same 400 years, the Gregorian calendar allows only 97
     leap years for a total of 146,097 days.  Compare these
     lengths with that of 400 tropical years, which comes to
     146,096.88. Whereas, in that stretch of time, the Julian
     year had gained 3.12 days on the Sun, the Gregorian year
     had gained only 0.12 days.
        Still, 0.12 days is nearly 3 hours, and this means that
     in 3400 years the Gregorian calendar will have gained a
     full day on the Sun.  Around A.D. 5000 we will have to
     consider dropping out one extra leap year.,

        But the Church had waited a little too long to take
     action.  Had it done the job a century earlier, all western
     Europe would have changed calendars without trouble.
     By A.D. 1582, however, much of northern Europe bad
     turned Protestant.  These nations would far sooner remain
     out of step with the Sun in accordance with the dictates of
     the pagan Caesar, than consent to be corrected by the
     Pope.  Therefore they kept the Julian year.
        The year 1600 introduced no crisis.  It was a century
     year but one that was divisible by 400.  Therefore, it was
     a leap year by both the Julian and Gregorian calendars.
     But 1700 was a different matter.  The Julian calendar had
     it as a leap year and the Gregorian di 'd not. By March 1,
     1700, the Julian calendar was going to be an additional
     day ahead of the Sun (eleven days altogether).  Denmark,
     the Netherlands, and Protestant Germany gave in and
     adopted the Gregorian calendar.
                                  23

        Great Britain and the American colonies held out until
     1752 before giving in.  Because of the additional day
     gained in 1700, they had to drop eleven days and changed
     September 2, 1752 to September 13, 1752.  There were
     riots all over England as a result, for many people came
     quickly to the conclusion that they had suddenly been
     made eleven days older by legislation.
        "Give us back our eleven days!" they cried in despair.
        (A more rational objection was the fact that although
     the third quarter of 1752 was short eleven days, landlords
     calmly charged a full quarter's rent.)
        As a result of this, it turns out that Washington was not
     born on "Washington's birthday." He was born on Febru-
     ary 22, 1732 on the Gregorian calendar, to be sure, but
     the date recorded in the family Bible had to be the Julian
     date, February 11, 1732.  When the changeover took place,
     Washington-a remarkably sensible man changed the
     date of his birthday and thus preserved the actual day.
        The Eastern Orthodox nations of Europe were more
     stubborn than the Protestant nations.  The years 1800 and
     1900 went by.  Both were leap years by the Julian calendar,
     but not by the Gregorian calendar.  By 1900, then, the
     Julian vernal equinox was on March 8 and the Julian
     calendar was 13 days ahead of the Sun.  It was not until
     after World War I that the Soviet Union, for instance,
     adopted the Gregorian calendar. (In doing so, the Soviets
     made a slight modification of the leap year pattern which
     made matters even more accurate.  The Soviet calendar will
     not gain a day on the Sun until fully 35,000 years pass.)
        The Orthodox churches themselves, however, still cling
     to the Julian year, which is why the Orthodox Christmas
     falls on January 6 on our calendar.  It is still December
     25 by their calendar.
        In fact, a horrible thought occurs to me-
        I was myself born at a time when the Julian calendar
     was still in force in the-ahem-old country.* Unlike
     George Washington, I never changed the birthdate and, as
     a result, each year I celebrate my birthday 13 days earlier
        * WEII, the Soviet Union, if you must know.  I came here at the
     age of 3.
                                  24

     than I should, making myseff 13 days older than I have to
     be.
       And this 13-day older me is in all the records and I
     can't ever change it back.
       Give me back my 13 days!  Give me back my 13 days!
     Give me back . . .

                               25

                2. BEGIN AT THE BEGINNING

     Each year, another New Year's Day falls upon us; and
     because my birthday follows hard upon New Year's Day,
     the beginning of the year is always a doubled occasion for
     great and somber soul-searching on my part.
        Perhaps I can make my consciousness of passing time
     less poignant by thinking more objectively.  For instance,
     who says the year starts on New Year's Day?  What is
     there about New Year's Day that is different from any
     other day?  What makes January I so special?
        In fact, when we chop up time into any kind of units,
     how do we decide with which unit to start?
        For instance, let's begin at the beginning (as I dearly
     love to do) and consider the day itself.

        The day is composed of two parts, the daytime* and
     the night.  Each, separately, has a natural astronomic
     beginning.  The daytime begins with sunrise; the night be-
     gins with sunset. (Dawn and twilight encroach upon the
     night but that is a mere detail.)
        In the latitudes in which most of humanity live'            how-
     ever, both daytime and night change in length during the
     year (one growing longer as the other grows shorter) and
     there is, therefore, a certain convenience in using daytime
     plus night as a single twenty-four-hour unit of time.  The
     combination of the two, the day, is of nearly constant
     duration.
         It is very annoying that "day" means both the sunlit portion
     of time and the twenty-four-hour period of daytime and night
     together.  This is a completely unnecessary shortcoming of the
     admirable English language.  I understand that the Greek language
     contains separate words for the two entities.  I shall use "daytime"
     for the sunlit period and "day" for the twenty-four-hour period.
                                     26

        Well, then, should the day start at sunrise or at sunset?
     You might argue for the first, since in a primitive society
     that is when the workday begins.  On the other hand, in
     that same society sunset is when the workday ends, and
     surely an ending means a new beginning.
        Some groups made one decision and some the other.
     The Egyptians, for instance, began the day at sunrise,
     while the Hebrews began it at sunset.
        The latter state of affairs is reflected in the very first
     chapter of Genesis in which the days of creation are de-
     scribed.  In Genesis 1:5 it is written- "And the evening
     and the morning were the first day." Evening (that is,
     night) comes ahead of morning (that is, daytime) be-
     cause the day starts at sunset.
        This arrangement is maintained in Judaism to this day,
     and Jewish holidays still begin "the evening before'        "
     Christianity began as an offshoot of Judaism and remnants
     of this sunset beginning cling even now to some non-
     Jewish holidays.
        The expression Christmas Eve, if taken literally, is   the
     evening of December 25, but as we all know it really
     means the evening of'Dccember 24-which it would natu-
     rally mean if Christmas began "the evening before" as a
     Jewish holiday would.  The same goes for New Year's
     Eve.
        Another familiar example is All Hallows' Eve, the eve-
     ning of the day before All Hallows' Day, which is given
     over to the commemoration of all the "hallows" (or
     "saints").  All Hallows' Day is on November 1, and All
     Hallows' Eve is therefore on the evening of October 31..
     Need I tell you that AU Hallows' Eve is better known by
     its familiar contracted form of "Halloween."
        As a matter of fact, though, neither.sunset nor sunrise is
     now the beginning of the day.  The period from sunrise to
     sunrise is slightly more than 24 hours for half the year as
     the daytime periods grow shorter, and slightly less than 24
     hours for the remaining half of the year as the daytime
     periods grow longer.  This is also true for the period from
     sunset to sunset.
        Sunrise and sunset change in opposite directions, either
                                  27

     approaching each other or receding from each other, so
     that the middle of daytime (midday) and the middle
     of night (midnight) remain fixed at 24-hour intervals
     throughout the year. (Actually, there are minor deviations
     but these can be ignored.)
        One can begin the day at midday and count on a steady
     24-hour cycle, but then the working period is split between
     two different dates.  Far better to start the day at midnight
     when all decent people are asleep; and that, in fact, is what
     we do.
        Astronomers, who are among the indecent minority not
     in bed asleep at midnight, long insisted on starting their
     day at n-fidday so as not to break up a night's observation
     into two separate-dates.  However, the spirit of conformity
     was not to be withstood, and in 1925, they accepted the in-
     convenience of a beginning at midnight in order to get into
     step with the rest of the world.

        All the units of time that are shorter than a day depend
     on the day and offer no problem.  You start counting the
     hours from the beginning of the day; you start counting
     the minutes from the beginning of the hour; and so on.
        Of course, when the start of the day changed its posi-
     tion, that affected the counting of the hours.  Originally, the
     daytime and the night were each divided into twelve hours,
     beginning at, respectively, sunrise and sunset.  The hours
     changed length with the change in length of daytime and
     night so that in June (in the northern hemisphere) the
     daytime was made up of twelve long hours and the night of
     twelve short hours, while in December the situation was
     reversed.
        This manner of counting the hours still survives in the
     Catholic Church as "canonical hours." Thus, "           prime"
     ("one") is the term for 6 A.M. "Tierce" ("three") is 9
     A.M., "sext" ("six") is 12 A.M., and "none" ("nine") is 3
     P.M. Notice that "none" is located in the middle of the
     afternoon when the day is warmest.  The warmest part of
     the day might well be felt to be the middle of the day,
     and the word'was somehow switched to the astronomic
     midday so that we call 12 A.M. "nOon.IY
                                   28

       This older method of counting the hours also plays a
    part in one of the parables of Jesus (Matt. 20:1-16), in
    which laborers are hired at various times of the day, up
    to and including "the eleventh hour." The eleventh hour
    referred to in the parable is one hour before sunset'when'
    the working day ends.  For that reason, "the eleventh hour"
    has come to mean the last moment in which something can
    be done.  'ne force of the expression is lost on us, how-
    ever, for we think of the eleventh hour as being either I 1
    A.M. or 1 1 P.m., and 1 1 A.M. is too early in the day to
    begin to feel panicky, while II P.m. is too late-we ought
    to be asleep by then.

       The week originated in the Babylonian calendar where
    one day out of seven was devoted to rest. (The rationale
    was that it was an unlucky day.)
       The Jews, captive in Babylon in the sixth century B.C.,
    picked up the notion and established it on a religious
    basis, making it a day of happiness rather than of ill
    fortune.  They explained its beginnings in Genesis 2:2
    where, after the work of the six days of creation-"on
    the seventh day God ended his work wbich'he had made;
    and he rested on the seventh day."
       To "those societies which accept   the Bible as a book
    of special significance, the Jewish   "sabbatb" (from the
    Hebrew word for "rest") is thus defined as the seventh,
    and last, day of the week.  This day is the one marked
    Saturday on our calendars., and Sunday, therefore, is the
    first day of a new week.  All our calendars arrange the
    days in seven colunins with Sunday first and Saturday
    seventh.
       The early Christians began to attach special significance
    to the first day of the week.  For one thing, it was the
    "Lord's day" since the Resurrection had taken place on
    a Sunday.  Then, too, as time went on and Christians
    began to think of themselves as something more than a
    Jewish sect, it became important to them to have distinct
    rituals of their own.  In Christian societies, therefore,
    Sunday, and not Saturday, became the day of rest. (Of
    course, in our modem effete times, Saturday and Sunday
                                 29

      are both days of rest, and are lumped together as the
      "weekend," a period celebrated by automobile accidents.)
        The fact that the work week begins on Monday causes
      a great many people to think of that as the first day of the
      week, and leads to the following children's puzzle (which
      I mention only because it trapped me neatly the first time
      I heard it).
        You ask your victim to pronounce t-o, t-o-o, and t-w-o,
      one at a time, thinking deeply between questions.  In each
      case he says (wondering what's up) "tooooo."
        Then you say, "Now pronounce the second day of the
      week" and his face clears up, for he thinks he sees the
      trap.  He is sure you are hoping he will say "toooosday"
      like a lowbrow.  With exaggerated precision, therefore, he
      says "tyoosday."
        At which you look gently puzzled and say, "Isn't that
      strange?  I always pronounce it Monday."

        The month, being tied to the Moon, began, in ancient
      times, at a fixed phase.  In theory, any phase will do.  The
      month can start at each full Moon, or each first quarter,
      and so on.  Actually, the most logical Way is to begin
      each month with the new Moon-that is, on that evening
      when the first sliver of the growing crescent makes itself
      visible immediately after sunset.  To any logical primitive,
      a new Moon is clearly being created at that time and the
      month. should start then.
        Nowadays, however, the month is freed of the Moon
      and is tied to the year, which is in turn based on the Sun.
      In our calendar, in ordinary years, the first month begins
      on the first day of the year, the second month on the 32nd
      day of the year, the third month on the 60th day of the
      year, the fourth month on the 91st day of the year, and
      so on-quite regardless of the phases of the Moon. (In
      a leap year, all the months from the third onward start
      a day late because of the existence of February 29.

        But that brings us to the year. When does that       begin
      and why?
        Primitive agricultural societies must have been first
                                  30

     aware of the year as a succession of seasons.  Spring,
     summer, autumn, and winter were the morning, midday,
     evening and night of the year and, as in the case of the day,
     there seemed two equally qualified candidates for the
     post of beginning.
       The beginning of the work year is the time of spring,
     when warmth returns to the earth and planting can begin.
     Should that not also be the beginning of the year in
     general?  On the other hand, autumn marks the end of the
     work year, with the harvest (it is to be devoutly hoped)
     safely in hand.  With the work year ended, ought-not the
     new year begin?
       With the development of astronomy, the beginning of
     the spring season was associated with the vernal equinox
     (see Chapter 4) which, on our calendar, falls on March
     20, while the beginning of autumn is associated with the
     autumnal equinox which falls, half a year later, on
     September 23.
       Some societies chose one equinox as the beginning
     and some the other.  Among the Hebrews, both equinoxes
     came to be associated with a New Year's Day.  One of
     these fell on the first day of the month of-Nisan (which
     comes at about the vernal equinox).  In the middle of
     that month comes the feast of Passover, which is thus
     tied to the vernal equinox.
       Since, according to the Gospels, Jesus' Crucifixion and
     Resurrection occurred during the Passover season (the
     Last Supper was a Passover seder), Good Friday and
     Easter are also tied to the vernal equinox (see Chap-
     ter I ).
       The Hebrews also celebrated a New Year's Day on
     the first two days of Tishri (which falls at about the
     autumnal equinox), and this became the more important
     of the two occasions.  It is celebrated by Jews today as
     "Rosh Hashonah" ("head of the year"), the familiarly
     known "Jewish New Year."
       A much later example of. a New Year's Day in con-
     nection with the autumnal equinox came in connection
     with the French Revolution.  On September 22, 1792,
     the French monarchy was abolished and a republic pro-
                                  31

     claimed The Revolutionary idealists felt that since a new
     epoch in human history had begun, a new calendar was
     needed.  They made September 22 the New Year's Day
     and established a new list of months.  The first month
     was Vend6miare, so that September 22 became Vend6-
     miare 1.
     . For thirteen years, Vend6miare I continued to be the
     official New Yeaes Day of the French Government, but
     the calendar never caught on outside France or,even
     among the people inside France.  In 1806 Napoleon gave
     up the struggle and officially reinstated the old calendar.
        There are two important solar events in addition to the
     equinoxes.  After the vernal equinox, the noonday Sun con-
     tinues to rise higher and higher until it reaches a maximum
     height on June 21, which is the summer solstice (see
     Chapter 4), and this day, in consequence, has the longest
     daytime period of the year.
        The height of the noonday Sun declines thereafter until
     it reaches the position of the autumnal equinox.  It then
     continues to decline farther and farther fill it reaches a
     minimum height on December 21, the winter solstice and
     the shortest daytime period of the year.
        The summer solstice is not of much significance.  "Mid-
     summer Day" falls at about the summer solstice (die tradi-
     tional English day is June 24).  This is a time for gaiety
     and carefree joy, even folly.  Shakespeare's A Midsummer
     Night's Dream is an example of a play devoted to the kind
     of not-to-be-taken-seriously fun of the season, and the
     phrase "midsummer madness" may have arisen similarly.
        The winter solstice is a much more serious affair.  The
     Sun is declining from day to day, and to a primitive so-
     ciety, not sure of the invariability of astronomical laws, it
     might well appear that this time, the Sun will continue its
     decline and disappear forever so that spring will never
     come again and all life will die.
        Therefore, as the Sun's decline slowed from day to day
     and came to a halt and began to turn on December 21,
     there must have been great relief and joy which, in the
     end, became ritualized into a great religious festival,
     marked by gaiety and licentiousness.
                                   32

        The best-known examples of this are the several days of
      holiday among the Romans at this season of the year.  The
      holiday was in honor of Saturn (an ancient Italian god of
      agriculture) and was therefore called the "Satumalia." It
      was a time of feasting and of giving of presents; of good
      will to men, even to the point where slaves were given
      temporary freedom while their masters waited upon them.
      There was also a lot of drinking at Satumalia parties.
        In fact, the word "saturnalian" has come to mean dis-
      solute, or characterized by unrestrained merriinent.
        There is logic, then, in beginning the year at the winter
      solstice which marks, so to speak, the birth of a new Sun,
      as the first appearance of a crescent after sunset marks the
      birth of a new Moon.  Something like this may have been
      in Julius Caesar's mind when he reorganized the Roman
      calendar and made it solar rather than lunar (see Chap-
      ter I ).
        The Romans had, traditionally, begun their year on
      March 15 (the "Ides of March"), which was intended to
      fall upon the vernal equinox originally but which, thanks
      to the sloppy way in which the Romans maintained their
      calendar, eventually moved far out of synchronization with
      the equinox.  Caesar adjusted matters and moved the beg-
      ning of the year to January 1 instead, placing it nearly at
      the winter solstice.
        This habit of beginning the year on or about the winter
      solstice did not become universal, however.  In England
      (and the American colonies) March 25, intended to repre-
      sent the vernal equinox, remainedthe official beginning of
      the year until 1752.  It was only then that the January I
      beginning was adopted.
        The beginning of a    new Sun reflects itself in modem
      times in another way, too.  In the days of the Roman Em-
      pire, the rising power of Christianity found its most dan-
      gerous competitor in Nfithraism, a cult that was Persian
      in origin and was devoted to sun worship.  The ritual cen-
      tered about the mythological character of NEthras, who
      represented the Sun, and whose birth was celebrated on
      December 25-about the time of the winter solstice.  This
      was a good time for a holiday, anyway, for the Romans
                                   33

    were used to celebrating the SatumaEa at that time of
    year.
       Eventually, though, Christianity stole Mithraic thunder
    by establishing the birth of Jesus on December 25 (there
    is no biblical authority for this), so that the period of the
    winter solstice has come to mark the birth of both the Son
    and the Sun.  There are some present-day moralists (of
    whom I am one) who find something unpleasantly remi-
    niscent of the Roman Satumalia in the modem secular
    celebration of Christmas.

       But where do the years begin?  It is certainly convenient
    to number the years, but where do we start the numbers?
    In ancient times, when the sense of history was not highly
    developed, it was sufficient to begin numbering the years
    with the accession of the local king or ruler.  The number-
    ing would begin over again with each new kin . Where a
                                                      9
    city has an annually chosen magistrate, the year might not
    be numbered at all, but merely identified by the name of
    the magistrate for that year.  Athens named its years by
    its archons.
       When the Bible dates things at all, it does it in this
    manner.  For instance, in II Kings 16:1, it is written: "In
    the seventeenth year of Pekah the son of Remallah, Ahaz
    the son of Jotham king of Judah began to reign." (Pekah
    was the contemporary king of Israel.)
       And in Luke 2:2, the time of the taxing, during which
    Jesus was born, is dated only as follows: "And this taxing
    was first made when Cyrenius was governor of Syria."
       Unless you have accurate lists of kings and magistrates
    and know just how many years each was in power and
    how to relate the list of one region with that of another,
    you are in trouble, and it is for that reason that so many
    ancient dates are uncertain even (as I shall soon explain)
    a date as important as that of the birth of Jesus.
       A much better system would be to pick some important
    date in the past (preferably one far enough in the past
    so that you don't have to deal with negative-numbered
    years before that time) and number the years in progres-
    sion thereafter, without ever starting over.
                                  34

        The Greeks made use of the Olympian Games for that
     purpose.  This was celebrated every four years so that a
     four-year cycle was an "Olympiad." The Olympiads were
     numbered progressively, and the year itself was the Ist,
     2nd, 3rd or 4th year of a particular Olympiad.
        This is needlessly complicated, however, and in the time
     following Alexander the Great something better was in-
     troduced into the Greek world.  The ancient East was being
     fought over by Alexander's generals, and one of them,
     Seleucus, defeated another at Gaza.  By this victory Seleu-
     cus was confirmed in his rule over a vast section of Asia.
     He determined to number the years from that battle, which
     took place in the Ist year of the 117th Olympiad.  That
     year became Year 1 of the "Seleucid Era," and later years
     continued in succession as 2, 3, 4, 5, and so on.  Nothing
     more elaborate than that.
        The Seleucid Era was of unusual importance because Se-
     leucus and his descendants ruled over Judea, which there-
     fore adopted the system.  Even after the Jews broke free
     o If the Seleucids under the leadership of the Maccabees,
     they continued to use the Seleucid Era in dating their com-
     mercial transactions over the length and breadth of the
     ancient world.  Those commercial records can be tied in
     with various local year-dating systems, so that many of
     them could be accurately synchronized as a result.
        The most important year-dating system of the ancient
     world, however, was that of the "Roman Era." This began
     with the year in which Rome was founded.  According to
     tradition, this was the 4th Year of the 6th Olympiad,
     which came to be considered as I A.U.C. (The abbrevia-
     tion "A.U.C." stands for "Anno Urbis Conditae"; that is,
     "The Year of the Founding of the City.")
        Using the Roman Era, the Battle of Zama, in which
     Hannibal was defeated, was fought in 553 A.U.C.,
     while Julius Caesar was assassinated in 710 A.U.C., and
     so on.  This system gradually spread over the ancient
     world, as Rome waxed supreme, and lasted well into early
     medieval times.
        The early Christians, anxious to show that biblical
     records antedated those of Greece and Rome, strove to
                                  35

    begin counting at a date earlier than that of either the
    founding of Rome or the beginning of the Olympian
    Games.  A Church historian, Eusebius of Caesarea, who
    lived about 1050 A.U.C., calculated that the Patriarch,
    Abraham, bad been born 1263 years before the founding
    of Rome.  Therefore he adopted that year as his Year 1, so
    that 1050 A.u.c. became 2313, Era of Abraham.
       Once the Bible was thoroughly established as the book
    of the western world, it was possible to carry matters to
    their logical extreme and date the years from the creation
    of the world.  The medieval Jews calculated that the crea-
    tion of the world had taken place 3007 years before the
    founding of Rome, while various Christian calculators
    chose years varying from 3251 to 4755 years before the
    founding of Rome.  These are the various "Mundane Eras"
    ("Eras of the World").  The Jewish Mundane Era is used
    today in the Jewish calendar, so that in September 1964,
    the Jewish year 5725 began.

       The Mundane Eras have      one important factor in their
    favor.  They start early enough so that there are very few,
    if any, dates in recorded history that have to be given
    negative numbers.  This is, not true of the Roman Era, for
    instance.  The founding of the Olympian Games, the
    Trojan War, the reign of David, the building of the
    Pyramids, all came before the foundin of Rome and have
                                           9
    to be given negative year numbers.
       The Romans wouldn't have cared, of course, for none
    of the ancients were very chronology conscious, but
    modem historians would.  In fact, modem historians are
    even worse off than they would have been if the Roman
    Era had been retained.
       About 1288 A.U.c.,    a Syrian monk named Dionysius
    Exiguus, working from    biblical data and  secular records,
    calculated that Jesus must have been born in 754 A.U.C.
    This seemed a good time to use as a beginning for counting
    the years, and in the time of Charlemagne (two and a
    half centuries after Dionysius) this notion won out.
       The year 754 A.U.c. became A.1). I (standing for Anno
    Domini, meaning "the year of the Lord").  By this new
                                 36

     "Christian Era," the founding of Rome took place in 753
     B.C. ("before Christ").  The first year of the first Olvmt)iad
     was in 776 B.C., the first year of the Seleucid Era was in
     312 Bc., and so on.
        This is the system used today, and means that all or
     ancient history from Sumer to Augustus must be dated in
     negative numbers, and we must forever remember that
     Caesar was assassinated in 44 B.C. and that the next year
     is number 43 and not 45.
        Worse still, Dionysius   was wrong in his calculations.
     Matthew 2: 1 clearly states that "Jesus was born in Bethle-
     hem of Judea in the days of Herod the king." This Herod
     is the so-called Herod the Great, who was born about 681
     A.u.c., and was made king of Judea by Mark Antony in
     714 A.u.c. He died (and this is known as certainly as any
     ancient date is known) in 750 A.U.c., and therefore Jesus
     could not have been born any later than 750 A.U.C.
        But 750 A.U.c., according to the system of Dio'nysius
     Exiguus, is 4 B.C., and therefore you constantly find in lists
     of dates that Jesus was born in 4 B.C.; that is, four years
     before the birth of Jesus.
        In fact, there is no reason to be sure that Jesus was
     born in the very year that Herod died.  In Matthew 2:16,
     it is written that Herod, in an attempt to kill Jesus, ordered
     all male children of two years and under to be slain.  This
     verse can be interpreted as indicating that Jesus may have
     been at least two years old while Herod was still alive, and
     might therefore have been born as early as 6 B.C. Indeed,
     some estimates have placed the birth of Jesus as early as
     17 B.C.
        Which forces me to admit sadly that although I lo
     begin at the beginning, I can't always be sure where
     beginning is.

                                   37

              3. GHOST LINES IN THE SKY

     My son is bearing, with strained patience, the quasi-hu-
     morous changes being rung upon his last name by his
     grade,school classmates.  My explanation to him that the
     name "Asimov," properly pronounced, has a noble reso-
     nance like the distant clash of sword on shield in the age
     of chivalry, leaves him unmoved.  The hostile look in his
     eyes tells me quite plainly that he considers it my duty as
     a father to change my name to "Smith" forthwith.
       Of course, I sympathize with him, for in my time, 1,
     too, have been victimized in this fashion.  The ordinary
     misspellings of the uninformed I lay to one side.  However,
     there was one time . . .
       It was when I was in the Army and working out my
     stint in basic training.  One of the courses to which we were
     exposed was map-reading, which had the great advantage
     of being better than drilling and hiking.  And then, like a
     bolt of lightning, the sergeant in charge pronounced the
     fatal word "azimuth" and all faces turned toward me.
       I stared back at those stalwart soldier-boys in horror,
     for I realized that behind every pair of beady little eyes,
     a small brain had suddenly discovered a source of infinite
     fun.
       You're right.  For what seemed months, I was Isaac
     Azimuth to every comic on the post, and every soldier on
     the post considered himself a comic.  But, as I told myself
     (paraphrasing a great American poet), "This is the army,
     Mr. Azimuth."
       Somehow, I survived.
       And, as fitting revenge, what better than to tell all you
     inoffensive Gentle Readers, in full and leisurely detail,
     exactly what azimuth is?
                                 38

         It all starts with direction.  The first, most primitive, and
      most useful way of indicating direction is to point.  "They
      went that-a-way." Or, you can make use of some land-
      mark known to one and all, "Let's head them off at the
      gulch.
         This is all right if you are concerned with a small sec-
      tion of the Earth's surface; one with which you and your
      friends are intimately familiar.  Once the horizons widen,
      however, there is a search for methods of giving directions
      that do not depend in any way on local terrain, but are the
      same everywhere on the Earth.
         An obvious method is to make use of the direction of
      the rising Sun and that of the setting Sun. (These direc-
      tions change from day to day, but you can take the average
      over the period of a year.) These are opposite directions,
      of course, which we call "east" and "west." Another pair
      of opposites can be set up perpendicular to these and be
      called "north" and "south."
         If, at any place, north, east, south, and west are deter-
      mined (and this could be done accurately enough, even in
      prehistoric times, by careful observations of the Sun) there
      is nothing, in principle, to prevent still finer directions
      from being established.  We can have northeast, north-
      northeast, northeast by north, and so on.
         With a compass you can accept directions of this sort,
      follow them for specified distances or via specified land-
      marks, and go wherever you are told to go.  Furthermore,
      if you want to map the Earth, you can start at some point,
      travel a known distance in a known direction to another
      point, and locate that point (to scale) on the map.  You
      can then do the same for a third point, and a fourth, and
      a fifth, and so on.  In principle the entire surface of the
      planet can be laid out in this manner, as accurately as
      you wish, upon a globe.
         However, the fact that a thing can be done "in prin-
      ciple" is cold comfort if it is unbearably tedious and would
      take a million men a million years.  Besides, the compass
      was unknown to western man until the thirteenth century,
      and the Greek geographers, in trying to map the world,
      had to use other dodges.
                                    39

       One method was to note the position of the Sun at mid-
    day; that is at the moment just halfway between sunrise
    and sunset.  On any particular day there will be some spots
    on Earth where the Sun will be directly overhead at mid-
    day.  The ancient Greeks knew this to be true of southern
    Egypt in late June, for instance.  In Europe, however, the
    sun at midday always fell short of the overhead point.
       This could easily be explained once it was realized that
    the Earth was a sphere.  It could furthermore be shown,
    without difficulty that all points on Earth at which the Sun,
    on some particular day, fell equally short of the overhead
    point at midday, were on a single east-west line.  Such a
    line could be drawn on the map and used as a reference
    for the location of other points.  The first to do so was a
    Greek geographer named Dicaearchus, who lived about
    300 B.c. and was one of Aristotle s pupils.
       Such a line is called a line of "latitude," from a Latin
    word meaning broad or wide, for when making use of the
    usual convention of putting north at the top of a map,
    the east-west lines run in the direction of its width.
       Naturally, a number of different lines of latitude can be
    determined.  All run east-west and all circle the sphere of
    the Earth at constant distances from each other, and so are
    parallel.  They are therefore referred to as "parallels of
    latitude."
       The nearer the parallels of latitude to either pole, the
    smaller the circles they make. (If you have a globe, look
    at it and see.) The longest parallel is equidistant from the
    poles and makes the largest circle, taking in the maximum
    girth of the Earth.  Since it divides the Earth into two equal
    halves, north and south, it is called the "equator" (from
    a Latin word meaning "equalizer").
       If the Earth were cut through at the equator, the section
    would pass through the center of the Earth.  That makes
    the equator a "great circle." Every sphere has an infinite
    number of great circles, but the equator is the only parallel
    of latitude that is one of them.
       It early became customary to measure off the parallels
    of latitude in degrees.  There are 360 degrees, by coilven-
                                 40

     tion, into which the full circumference of a sphere can be
     divided.  If you travel from the equator to the North Pole,
     you cover a quarter of the Earth's circumference and
     therefore pass over 90 degrees.  Consequently, the parallels
     range from O' at the equator to 90' at the North Pole
     (the small ' representing "degrees").
       .If you continue to move around the Earth past the
     North Pole so as to travel toward the equator again, you
     must pass the parallels of latitude (each of which encircles
     the Earth east-west) in reverse order, traveling from 90'
     back to O' at the equator (but at a point directly opposite
     that of the equatorial beginning).  Past the equator, you
     move across a second set of parallels circling the southern
     half of the globe, up to 90' at the South Pole and then
     back to O', finally at the starting point on the equator.
       To differentiate the O' to 90' stretch from equator to
     North Pole and the similar stretch from equator to South
     Pole, we speak of "north latitude" and "south latitude."
     Thus, Philadelphia, Pennsylvania is on the 400 north
     latitude parallel, while Valdivia, Chile is on the 40' south
     latitude parallel.

       Parallels of latitude, though excellent as references
     about which to build a map, cannot by themselves be used
     to locate points on the Earth's surface.  To say that Quito,
     Ecuador is on the equator merely tells you that it is some-
     where along a circle 25,000 miles in circumference.
       For accurate location one needs a gridwork of lines-a
     set of north-sbuth lines as well as east-west ones.  These
     north-south lines, running up and down the conventionally
     oriented map (longways) would naturally be called "longi-
     tude."
       Whenever it is midday upon some spot of the Earth it is
     midday at all spots on the same north-south line, as one
     can easily show if the Earth is considered to be a rotating
     sphere.  The north-south line is therefore a "meridian" (a
     corruption of a Latin word for "midday"), and we speak
     of "meridians of longitude."
       Each meridian extends due north and south, reaching
                                  41

      the North Pole at one extreme and the South Pole        at the
      other.  All the meridians therefore converge at both poles
      and are spaced most widely apart at the equator, for all
      the world like the boundary lines of the segments of a
      tangerine.  If one imagines the Earth sliced in two along
      any meridian, the slice always cuts through the Earth's
      center, so that all meridians are great circles, and each
      stretches around the world a distance of approximately
      25,000 miles.

         By 200 B.C. maps being prepared by Greeks were
      marked off with both longitude and latitude.  However,
      making the gridwork accurate was another thing.  Latitude
      was all right.  That merely required the determination of
      the average height of the midday sun or, better yet, the
      average height of the North Star.  Such determinations
      could not be made as accurately in ancient Greek times as
      in modem times, but they could be made precisely enough
      to produce reasonably accurate results.
         Longitude was another matter.  For that you needed the
      time of day.  You had to be able to compare the time at
      which the Sun, or better still, another star (the sun is a
      star) was directly above the local meridian, as compared
      with the time it was directly,above another meridian.  If
      a star passed over the meridian of Athens in Greece at a
      certain time, and over the meridian of Messina in Sicily
      32 minutes later, then Messina was 8 degrees of longitude
      west of Athens.  To determine such matters, accurate time-
      pieces were necessary; timepieces that could be relied on
      to maintain synchronization to within fractions of a minute
      over long periods while separated by long distance; and to
      remain in synchronization with the Earth's rotation, too.
        In ancient times, such timepieces simply did not exist
      and therefore even the best of the ancient geographers
      managed to get their meridians tangled up.  Eratosthenes of
      Cyrene, who flourished at Alexandria in 200 B.c., thought
      that the meridian that passed through Alexandria also
      passed through Byzantium (the modern city of Istanbul,
      Turkey).  That meridian actually passes about 70 miles
                                   42

     east of Istanbul.  Such discrepancies tended to increase in
     areas farther removed from home base.
       Of course, once the circumference of the earth is known
     (and Eratosthenes himself calculated it), it is possible to
     calculate the east-west distance between degrees of longi-
     tude.  For instance, at the equator, one degree of longitude
     is equal to about 69.5 miles, while at a latitude of 40'
     (either north or south of the equator), it is only about
     53.2 miles, and so on.  However, accurate measurements of
     distance over mountainous territory or, worse yet, over
     stretches -of open ocean, are quite difficult.
       In early modem times, when European nations first
     began to make long ocean voyages, this became a horrible
     problem.  Sea captains never knew certainly where they
     were, and making port was a matter of praying as well as
     sailing.  In 1598 Spain, then still a major seagoing nation,
     offered a reward for anyone who would devise a timepiece
     that could be used on board ship, but the reward went
     begging.
       In 1656 the I)rutch astronomer Christian Huygens in-
     vented the pendulum clock-the first accurate timepiece.
     It could be used only on land, however.  The pitching, roll-
     ing, and yawing of a ship put the pendulum off its feed at
     once.
       Great Britain was a   major maritime nation after 1600,
     and in 1675 Charles 11 founded the observatory in Green-
     wich (then a London suburb, now Part of Greater Lon-
     don) for the express purpose of carrying through the
     necessary astronomical observations that would make the
     accurate determination of longitude possible.
       But a good timepiece was still needed, and in 1714 the
     British Government offered a large fortune (in those days)
     of 20,000 pounds for anyone who could devise a good
     clock that would work on shipboard.
       The problem was tackled by John Harrison, a Yorkshire
     mechanics self-trained and gifted with mechanical genius.
     Beginning in 1728 he built a series of five clocks, each
     better than the one before.  Each was so mounted that it
     could take the sway of a ship without being affected.  Each
                                 43

      was more accurate at sea than other clocks of the time
      were on land.  One of them was off by less than a minute
      after five months at sea.  Harrison's first clocks were per-
      haps too large and heavy to be completely practical, but
      the fifth was no bigger than a large watch.
         The British Parliament put on an extraordinary display
      of meanness in this connection, for it wore Harrison out
      in its continual delays in paying him the money he had
      earned and in demanding more and ever more models and
      tests. (Possibly this was because Harrison was a provincial
      mechanic and not a gentleman scientist of the Royal So-
      ciety.) However, King George III himself took a personal
      interest in the case and backed Harrison, who finally re-
      ceived his money in 1765, by which time he was over 70
      years old.
         It is only -in the last two hundred years, then, that the
      latitude-longitude gridwork    on the earth became really
      accurate.

         Even after precise longitude determinations became pos-
      sible, a problem remained.  There is no natural reference
      base for longitude; nothing like the equator in the case of
      latitude.  Different nations therefore used different systems,
      usually basing "zero longitude" on the meridian passing
      through the local capital.  The use of different systems was
      confusing and the risk was run of rescue operations at sea
      being hampered, to say nothing of war maneuvers among
      allies being stymied.
         To settle matters, the important maritime nations of
      the world gathered in Washington, D.C. in 1884 and held
      the "Washington Meridian Conference." The logical de-
      cision was reached to let the Greenwich observatory serve
      as base since Great Britain was at the very height of its
      maritime power.  The meridian passing through Greenwich
      is, therefore, the "prime meridian" and has a longitude of
      00.

         The degrees of longitude are then marked off to the
      west and east as "west longitirde" and "east longitude."
      The two meet again at the opposite side of the world from
                                    44

    the prime meridian.  There we have the 180' meridian
    which runs down the middle of the Pacific Ocean.
       Every degree of latitude (or longitude) is broken up
    into 60 minutes ('), every minute into 60 seconds ("),
    while the seconds can be broken up into tenths, hun-
    dredtbs, and so on.  Every point on the earth can be located
    uniquely by means of latitude and longitude.  For instance,
    an agreed-upon reference point within New York City is
    at 40' 45' 06" north latitude and 73' 59' 39" west longi-
    tude; while Los Angeles is at 34' 03' 15" north latitude
    and 118' 14' 28" west longitude.
       The North Pole and the South Pole have no longitude,
    for all the meridians converge there.  The North Pole is
    defined by latitude alone, for 90' north latitude represents
    one single point-the North Pole.  Similarly, 90' south lati-
    tude represents the single point of the South Pole.
       It is possible to locate longitude in terms of time rather
    than in terms of degrees.  The complete day of 24 hours is
    spread around the 360'     of longitude. This means that if
    two places differ by 15'   in longitude, they also differ by
    1 hour in local time. If   it is exactly noon  on the prime
    meridian, it is 1 P.m. at 15' east longitude and 1 1 A.M.
    at 151 west longitude.
       If we decide to call prime meridian 0:00:00 we can
    assign west longitude positive time readings and east longi-
    tude negative time readings.  All points on 15' west longi-
    tude become +1:00:00 and all points on 15' east longi-
    tude become - 1: 00: 00.
       Since New York City is at 73' 59' 39" west longitude
    it is 4 hours 55 minutes 59 seconds earlier than London
    and can therefore be located at +4:55:59.  Similarly, Los
    Angeles, still farther west, is at +8:04:48.
       In short, every point on Earth, except for the poles, can
    be located by a latitude and a time.  The North and South
    Poles have latitude only and no local times, since they
    have no meridians.  This does not mean, of course, that
    there is no time at the poles; only that the system for
    measuring local times, which works elsewhere on Earth,
    breaks down at the poles.  Other systems can be used
                                  45

       there; one pole might be assigned Greenwich time, for
       instance, while the other is assigned the time of the 180'
       meridian.
         In the ordinary mapping of the globe, both latitude and
       longitude are given in ordinary degrees.  However, the
       time system for longitude is used to establish local time
       zones over the face of the Earth, and the 180' meridian
       becomes the "International Date Line" (slightly bent for
       geographical convenience).  AU sorts of interesting para-
       doxes become possible, but that is for another article
       another day.

         And what about mapping the sky?  This concerned
       astronomers even before the problem of the mapping of
       the Earth, really, for whereas only small portions of the
       Earth are visible to any one man at any one time, the
       entire expanse of half a sphere is visible overhead
         The "celestial sphere" is most easily mapped as an ex-
       tension of the earthly sphere.  If the axis of the Earth is
       imagined extended through space until it cuts the celestial
       sphere, the intersection would come at the "North Celestial
       Pole" and the "South Celestial Pole." ("Celestial," by the
       way, is from a Latin word for "sky.")
         The celestial sphere seems to rotate east to west about
       the Earth's axis as a reflection of the actual rotation of the
       Earth west to east about that axis.  Therefore, the North
       Celestial Pole and the South Celestial Pole are fixed points
       that do not partake in the celestial rotation, just as the
       North Pole and the South Pole do not partake in the
       earthly rotation.
         The near neighborhood of the North Celestial Pole is
       marked by a bright star, Polaris, also called the "pole
       star" and the "north star," which is only a degree or so
       from it and makes a small circle about it each day.  The
       circle is so small that the star seems fixed in position day
       after day, year after year, and can be used as a,reference
       point to determine north, and therefore all other directions.
       Its importance to travel in the days before the compass
       was incalculable.
         The imaginary reference lines on the     Earth  can all be
                                    46

    transferred by projection to the sky, so that the sky, like
    the Earth, can be covered with a gridwork of ghost nes.
    There would be the "celestial equator," making up a great
    circle equidistant from the celestial poles; and "celestial
    latitude" and "celestial longitude" also.
       The celestial latitude is called "declination," and is
    measured in degrees.  The northern half of the celestial
    sphere ("north celestial latitude") has its declination given
    as a positive value; the southern half ("south celestial
    latitude") as a negative value.  Thus, Polaris has a declina-
    tion of roughly +89'; Pollux one of about +30'; Sirius
    one of about -15'; and Acrux (the brightest star of the
    Southern Cross) a declination of about -60'.
       The celestial longitude is called "right ascension" and
    the sky has a prime meridian of its own that is less
    arbitrary than the one on Earth, one which could therefore
    be set and agreed upon quite early in the game.
     I The plane of the Earth's orbit about the Sun cuts the
    celestial sphere in a great circle called the "ecliptic" (see
    Chapter 4).  The Sun seems to move exactly along the line
    of the ecliptic, in other words.
       Because the Earth's axis is tipped to the plane of Earth's
    orbit by 23.5', the two great circles of the ecliptic and the
    celestial equator are angled to one another by that same
    23.50.
       The ecliptic crosses the celestial equator at two points.
    When   the Sun is at either point, the day and night are
    equal in length (twelve hours each) all over the Earth.
    Those points are therefore the "equinoxes," from Latin
    words  meaning "equal nights."
       At one of these points the Sun is moving from negative
    to positive declination, and that is the "vernal equinox"
    because it occurs on March 20 and marks the beginning of
    spring in the Northern Hemisphere, where most of man-
    kind lives.  At the other point the Sun is moving from
    positive to negative declination and that is the autumnal
    equinox, falling on September 23, the beginning of the
    northern autumn.
       The point of the vernal equinox falls on a celestial
    meridian which is assigned a value of O' right ascension.
                                  47

       The celestial longitude is then measured eastward only
       (either in degrees or in hours) all the way around, until it
       returns to itself as 360' right ascension.
         By locating a star through declination and right ascension
       one does precisely the same thing as locating a point on
       Earth through latitude and longitude.
         An odd difference is this, though.  The Earth's prime
       meridian is fixed through time, so that a point on the
       Earth's surface does not change its longitude from day
       to day.  However, the Earth's axis makes a slow revolution
       once in 25,800 years, and because of this the celestial
       equator slowly shifts, and the points at which it crosses
       the ecliptic move slowly westward.
         The vernal equinox moves westward, then, circling the
       sky every 25,800 years, so that each year the moment in
       time of the vernal equinox comes just a trifle sooner than
       it otherwise would, The moment precedes the theoretical
       time and the phenomenon is therefore called "the preces-
       sion of the equinoxes."
         As the vernal equinox moves westward, every point on
       the celestial sphere has its right ascension (measured from
       that vernal equinox) increase.  It moves up about 1/7 of
       a second of arc each day, if my calculations are correct.

         This system of locating points in the sky is'ealled the
       "Equatorial System" because it is based on the location of -
       the celestial equator and the celestial poles.
         A second system may be established         based on the
       observer himself.  Instead of a "North Celestial Pole"
       based on a rotating Earth, we can establish a point
       directly overhead, each person on Earth having his own
       overhead point-although for people over a restricted
       area, say that of New York City, the different overhead
       points are practically identical.
         The overhead point is the "zenith," which is a medieval
       misspelling of part of an Arabic phrase meaning "over-
       head." The point directly opposite in that part of the
       celestial sphere which lies under the Earth is the 'nadir,"
       a medieval misspelling of an Arabic word meaning "op-
       posite."
                                   48

          The great circle that runs around the celestial sphere,
       equidistant from the zenith and nadir, is the "horizon,"
       from a Greek word meaning "boundary," because to us
       it seems the boundary between sky and Earth (if the Earth
       were perfectly level, as it is at sea).  This system of locating
       points in the sky is therefore called the "Horizon System."
          The north-south great circle traveling from horizon to
       horizon through the zenith is the meridian.  The cast-west
       great circle traveling from horizon to horizon through the
       zenith, and making a right angle with the meridian, is the
       14 prime vertical."
          A point in the sky can then be said to be so          I many
       degrees (positive) above the horizon or so many degrees
       (negative) below the horizon, this being the "altitude."
       Once that is determined, the exact point in the sky can be
       located by measuring on that altitude the number of
       degrees westward from the southern half of the meridian.
       At least astronomers do that.  Navigators and surveyors
       measure the number of -degrees eastward from the north
       end of the meridian. (In both cases the direction of meas-
       ure is clockwise.)
          The number of degrees west of the southern edge of the
       meridian (or east of the northern edce, depending on
       the system used) is the azimuth.  The word is a less corrupt
       form of the Arabic expression from which "zenith" also
       comes.
          If you set north as having an azimuth of O', then east
       has an azimuth of 90', south an azimuth of 180', and
       west an azimuth of 270'.  Instead of boxing the compass
       with outlandish names you can plot direction by degrees.
          And as for myseff?
          Why, I have an azimuth of isaac.  Naturally.

                                     49

                  4. THE HEAVENLY ZOO

    On July 20, 1963 there was a total eclipse of the Sun,
    visible in parts of Maine, but not quite visible in its total
    aspect from my house.  In order to see the total eclipse I
    would have had to drive two hundred miles, take a chance
    on clouds, then drive back two hundred miles, braving the
    traffic congestion produced by thousands of other New
    Englanders with the same notion.
       I decided not to (as it happened, clouds interfered with
    seeing, so it was just as well) and caught fugitive glimpses
    of an eclipse that was only 95 per cent total, from my
    backyard.  However, the difference between a 95 per cent
    eclipse and a 100 per cent eclipse is the difference between
    a notion of water and an ocean of water, so I did not feel
    very overwhelmed by what I saw.
       V-/bat makes a total eclipse so remarkable is the sheer
    astronomical accident that the Moon fits so snugly over
    the Sun.  The Moon is just large enougb. to cover the Sun
    completely (at times) so that a temporary night falls and
    the stars spring out.  And it is just small enough so that
    during the Sun's obscuration, the corona, especially the
    brighter parts near the body of the Sun, is completely
    visible.
       The apparent size of the Sun and Moon depends upon
    both their actual size and their distance from us.  The
    diameter of the Moon is 2160 miles while that of, the
    Sun is 864,000 miles.  The ratio of the diameter of the
    Sun to that of the Moon is 864,000/2160 or 400.  In other
    words, if both were at the same distance from us, the
    Sun would appear to be 400 times as broad as the Moon.
       However,   the Sun is farther away from us than the
    Moon is, and therefore appears smaller for its size than
                                  50

       the Moon does.  At great distances, such as -those which
       characterize the Moon and the Sun, doubling the distance
       halves the apparent diameter.  Remembering that, consider
       that the average distance of the Moon from us is 238,000
       miles while that of the Sun is 93,000,000 miles.  The ratio
       of the distance of the Sun to that of the Moon is 93,000,-
       000/238,000 or 390.  The Sun's apparent diameter is cut
       down in proportion.
          In other words, the two effects just about cancel.  The
       Sun's greater distance makes up for its greater size and the
       result is that the Moon and the Sun appear to be equal-
       in size.  The apparent angular diameter of the Sun averages
       32 minutes of arc, while that of the Moon averages 31
       minutes of arc.*
          These are average values because both Moon and          Earth
       possess elliptical orbits.  The Moon is closer to the Earth
       (and therefore appears larger) at some times than at
       others, while the Earth is closer to the Sun (which therefore
       appears larger) at some times than at others.  This variation
       in apparent diameter is only 3 per cent for the Sun and
       about 5 per cent for the Moon, so that it goes unnoticed
       by the casual observer.
          There is no astronomical reason why Moon and Sun
       should fit so well.  It is the sheerest of coincidence, and
       only the Earth among all the planets is blessed in this
       fashion.  Indeed, if it is true, as astronomers suspect, that
       the Moon's distance from the Earth is gradually increasing
       as a result of tidal friction, then this excellent fit even here
       on Earth is only true of our own geologic era.  The Moon
       was too large for an ideal total eclipse in the far past and
       will be too small for any total eclipse at all in the far
       future.
          Of course, there is a price to pay for this excellent fit.
       The fact that the Moon and Sun are roughly equal in ap-
       parent diameter means that the conical shadow of the
       Moon comes to a vanishing point near the Earth's surface.
       If the two bodies were exactly equal in apparent size the
       shadow would come to a pointed end exactly at the

           One degree equals 60 minutes, so that both Sun and Moon
       are about half a degree in diameter.
                                      51

    Earth's surface, and the eclipse would be total for only
    an instant of time.  In other words, as the Moon covered
    the last sliver of Sun (and kept on moving, of course)
    the first sliver of Sun would begin to appear on the other
    side.
      Under the most favorable conditions, when the Moon
    is as close as possible (and therefore as apparently large
    as possible) while the Sun is as far as possible (and there-
    fore as apparently small as possible), the Moon's shadow
    comes to a point well below the Earth's surface and we
    pass through a measurable thickness of that shadow.  In
    other words, after the unusually large Moon covers the
    last sliver of the unusually small Sun, it continues to move
    for a short interval of time before it ceases to overlap the
    Sun and allows the first sliver of it to appear at the other
    side.  An eclipse, under the most favorable conditions, can
    be 71/2 minutes long.
      On the other hand, if the Moon is smaller than average
    in appearance, and the Sun larger, the Moon's shadow
    will fall short of the Earth's surface altogether.  The small
    Moon will not completely cover the larger Sun, even when
    both are centered in the sky.  Instead, a thin ring of Sun
    wilt appear all around the Moon.  This is an "annular
    eclipse" (from a Latin word for "ring").  Since the Moon's
    apparent diameter averages somewhat less than the Sun's,
    annular eclipses are a bit more likely than total eclipses.
      This situation scarcely allows astronomers (and ordinary
    beauty-loving mortals, too) to get a good look, since not
    only does a total eclipse of the Sun last for only a few
    ,minutes, but it can be seen only over that small portion of
    the Earth's surface which is intersected by the narrow
    shadow of the Moon.
      To make matters worse, we don't even get as many
    eclipses as we might.  An eclipse of the Sun occurs whenever
    the Moon gets between ourselves and the Sun.  But that
    happens at every new,Moon; in fact the Moon is "new"
    because it is between us and the Sun so that it is the op-
    posite side (the one we don't see) that is sunlit, and we
    only get, at best, the sight of a very thin crescent sliver of
    light at one edge of the Moon.  Well, since there are twelve
                                  52

      new Moons each year (sometimes thirteen) we ought to
      see twelve eclipses of the Sun each year, and sometimes
      thirteen.  No?
         No! At most we see five eclipses of the Sun each year
      (all at widely separated portions of the Earth's surface,
      of course) and sometimes as few as two.  What happens the
      rest of the time?  Let's see.

         The Earth's orbit about the Sun is all in one plane.
      That is, you can draw an absolutely flat sheet through the
      entire orbit.  The Sun itself will be located in this plane as
      well. (This is no coincidence.  The law of gravity makes it
      necessary.)
         If we imagine this plane of the Earth's orbit carried out
      infinitely to the stars, we, standing on the Earth's surface,
      will see that plane cutting the celestial sphere into two
      equal halves.  The line of intersection will form a "great
      circle" about the sky, and this line is called the "ecliptic."
         Of course, it is an imaginary line and not visible to the
      eye.  Nevertheless, it can be located if we use the Sun as
      a marker.  Since the plane of the Earth's orbit passes
      through the Sun, we are sighting along the,plane when we
      look at the Sun.  The Sun's position in the sky always falls
      upon the line of the ecliptic.  Therefore, in order to mark
      out the ecliptic against the starry background, we need
      only follow the apparent path of the Sun through the
      sky. (I am referring now not to the daily path from east
      to west, which is the reflection of Earth's rotation, but
      rather the path of the Sun from west to east against the
      starry background, which is the reflection of the Earth's
      revolution about the Sun.)
         Of course, when the Sun is in the sky the stars are not
      visible, being blanked out by the scattered sunlight that
      turns the sky blue.  How then can the position of the Sun
      among the stars be made out?
         Well, since the Sun travels among the stars, the half
      of the sky which is invisible by day and the half which is
      visible by night shifts a bit from day to day and from night
      to night.  By watching the night skies throughout the year
      the stars can be mapped throughout the entire circuit of the
                                    53

     ecliptic.  It then becomes possible to calculate the position
     of the Sun against the stars on each particular day, since
     there is always just one position that will account for the
     exact appearance of tile night sky on any particular night.
       If you prepare a celestial sphere-that is, a globe with
     the stars marked out upon it-you can draw an accurate
     great circle upon it representing the Sun's path.  The time
     it takes the Sun to make one complete trip about the
     ecliptic (in appearance) is about 3651/4 days, and it is
     this which defines the "year."
       The Moon travels about the Earth in an ellipse and there
     is a plane that can be drawn to include its entire orbit,
     this plane passing through the Earth itself.  Wien we look
     at the Moon we are sighting along this plane, and the
     Moon marks out the intersection of the plane with the
     starry background. The stars may be seen even when the
     Moon   is in the sky, so that marking out the Moon's path
     (also a great circle) is far easier than marking out the
     Sun's. The time it takes the Moon to make one complete
     trip about its path, about 271/3 days, defines the "sidereal
     month" (see Chapter 6).
       Now if the plane of the Moon's orbit about the Earth
     coincided with the plane of the Earth's orbit about the
     Sun, both Moon and Sun would mark out the same circu-
     lar line against the stars.  Imagine them starting from the
     same position in the sky.  The Moon would make a
     complete circuit of the ecliptic in 28 days, then spend an
     additional day and a half catching up to the Sun, which
     had also been moving (though much more slowly) in the
     interval.  Every 29'h days there would be a new Moon
     and an eclipse of the Sun.
       Furthermore, once every 291/2 days, there, would be a
     full Moon, when the Moon was precisely on the side op-
     posite to that of the Sun so that we would see its entire
     visible hemisphere lit by the Sun.  But at that time the
     Moon should pass into the Eartb's shadow and there
     would be a total eclipse of the Moon.
       AR this does not happen-every 291/2 days because the
     plane of the Moon's orbit about the Earth does not coincide
     with the plane of the Earth's orbit about the Sun.  The two
                                   54

      planes make an angle of 5'8' (or 308 minutes of arc)         '
      The two great circles, if marked out on a celestial sphere
      would be set off from each other at a slight slant.  They
      would cross at two points, diametrically opposed and
      would be separated by a maximum amount exactly half-
      way between the crossing point. (The crossin2 points are
      called "nodes," a Latin word meaning "knots.,,)
        If you have trouble visualizing this, the best thing is to
      get a basketball and two rubber bands and try a few ex-
      periments.  If you form a great circle of each rubber band
      (one that divides the globe into two equal halves) and
      make them non-coincident, you will see that they cross
      each other.in the manner I have described.
        At the points of maximum separation of the Moon's
      path from the ecliptic, the angular distance between them
      is 308 minutes of are.  This is a distance equal to roughly
      ten times the apparent diameter of either the Sun or the
      Moon.  This means that if the Moon happens to overtake
      the Sun at a point of maximum separation, there will be
      enough space between them to fit in nine circles in a row,
      each the apparent size of Moon or Sun.
        In most cases, then, the Moon, in overtaking the Sun,
      will pass above it or below it with plenty of room to spare,
      and there will be no eclipse.
        Of course, if the Moon happens to overtake the Sun
      at a point near one of the two nodes, then the Moon does
      get into the way of the Sun and an eclipse takes place.
      This happens only, as I said, from two to five times a year.
      If the motions of the Sun and Moon are adequately
      analyzed mathematically, then it becomes easy to predict
      when such meetings will take place in the future, and when
      they have taken place in the past, and exactly from what
      parts of the Eaith's surface the eclipse will be visible.
        Thus, Herodotus tells us that the Ionian philosopher,
      Thales, predicted an eclipse that came just in time to stop
      a battle between the Lydians and the Medians'    (With such
      a sign of divine displeasure, there was no use going on
      with the war.) The battle took place in Asia Minor some-
      time after 600 B.c., and astronomical calculations show
      that a total eclipse of the Sun was visible from Asia
                                   55

    Minor on May 28, 585 B.c. This star-crossed battle, there-
    fore, is the earliest event in history which can be dated
    to the'exact day.
       The ecliptic served early mankind another purpose
    besides acting as a site for eclipses.  It was an eternal
    calendar, inscribed in the sky.
       The earliest calendars were  based on the circuits of the
    Moon, for as the Moon moves about the sky, it goes
    through very pronounced phase changes that even the most
    casual observer can't help but notice.  The 291/2 days it
    takes to go from new Moon to new Moon is the "synodic
    month" (see Chapter 6).
       The trouble with this system is that in the countries
    civilized enough to have a calendar, there are important
    periodic phenomena (the flooding of the Nile, for in-
    stance, or the coming of seasonal rains, or seasonal cold)
    that do not fit in well with the synodic month, There
    weren't a whole number of months from Nile flood to
    Nile flood.  The average interval was somewhere between
    twelve and thirteen months.
       In Egypt it came to be noticed that the average intervals
    between the floods coincided with one complete Sun-circuit
    (the year).  The result was that calendars came to consist
    of years subdivided into months.  In Babylonia and, by
    dint of copying, among the Greeks and Jews, the months
    were tied firnay to the Moon, so that the year was made
    up sometimes   'of 12 months and sometimes of 13 months
    in a complicated pattern that repeated itself every 19
    years.  This served to keep the years in line with the
    seasons and the months in line with the phases of the
    Moon.  However, it meant that individual years were of
    different lengths (see Chapter 1).
       The Egyptians and, by dint of copying, the Romans and
    ourselves abandoned the Moon and made each year
    equal in length, and each with 12 slightly long months'
    The "calendar month" averaged 301/2 days long in place
    of the 291/2. days of the synodic month.  This meant the
    months fell out of line with the phases of the Moon, but
    mankind survived that.
       The progress of the Sun along the ecliptic marked off
                                 56

     the calendar, and since the year (one complete circuit) was
     divided into 12 months it seemed natural to divide the
     ecliptic into 12 sections.  The Sun would travel through one
     section in one month, through the section to the east of
     that the next month, through still another section the third
     month, and so on.  After 12 months it would come back
     to the first section.
       Each section of the ecliptic has its own pattern of stars,
     and to identify one section from another it is the most
     natural thing in the world to use those patterns.  If one
     section has four stars in a roughly square configuration it
     might be called "the square"; another section might be the
     "V-shape," another the "large triangle," and so on.
       Unfortunately, most people don't have my neat, geo-
     metrical way of thinking and they tend to see complex
     figures rather than simple, clean shapes.  A group of stars
     arranged in a V might suggest the head and homs of a bull,
     for instance.  The Babylonians worked up such imaginative
     patterns for each section of the ecliptic and the Greeks
     borrowed these giving each a Greek name.  The Romans
     borrowed the iist next, giving them Latin names, and
     passing them on to us.
       The following is the list, with each name in Latin and
     in English: 'I) Aries, the Ram; 2) Taurus'      the Bull; 3)
     Gemini, the Twins; 4) Cancer, the Crab; 5) Leo, the
     Lion; 6) Virgo, the Virgin; 7) Libra, the Scales; 8)
     Scorpio, the Scorpion; 9) Sagittarius, the Archer; 10)
     Capricomus, the Goat; 11) Aquarius, the Water-Carrier;
     12) Pisces, the Fishes.
       As you see, seven of the constellations represent ani-
     mals.  An eighth, Sagittarius, is usually drawn as a centaur,
     which may be considered an animal, I suppose.  Then, if
     we remember that human beings are part of the animal
     kingdom, the only strictly nonanimal constellation is Libra.
     The Greeks consequently called this band of constellations
     o zodiakos kyklos or "the circle of little animals," and
     this has come down to us as the Zodiac.
       In fact, in the sky as a whole, modem astronomers
     recognize 88 constellations.  Of these 30 (most of them
     constellations of the southern skies' invented by modems)
                                  57

      represent inaniinate objects.  Of the remaining 58, mostly
      ancient, 36 represent mammals (including 14 human
      beings), 9 represent birds,, 6 represent reptiles, 4 represent
      fish, and 3 represent arthropods.  Quite a heavenly zoo!
        Odd, though, considering that most of the constellations
      were invented by an agricultural society, that not one
      represents a member of the plant kingdom.  Or can,that be
      used to argue that the early star-gazers were herdsmen and
      not farmers?

        The line of the ecliptic is set at an angle of 231/2 ' to the
      celestial equator (see Chapter 3) since, as is usually
      stated, the Earth's axis is tipped 23V2'.
        At two points, then, the ecliptic crosses the celestial
      equator and those two crossing points are the "equinoxes"
      ("equal nights").  When the Sun is at those crossing points,
      it shines directly over the equator and days and nights are
      equal (twelve hours each) the world over.  Hence, the
      name.
        One of the equinoxes is reached when the Sun, in its
      path along the ecliptic, moves from the southern celestial
      hemisphere into the northern.  It is rising higher in the
      sky (to us in the Northern Hemisphere) and spring is
      on its way.  That, therefore, is the "vernal equinox," and it
      is on March 20.
        On that day (at least in ancient Greek times) the Sun
      entered the constellation of Aries.  Since the vernal equinox
      is a good time to begin the year for any agricultural society,
      it is customary to begin the list of the constellations of the
      Zodiac, as I did, with Aries.
        The Sun stays about one month 'm each constellation,
      so it is in Aries from March 20 to April 19, in Taurus
      from April 20 to May 20, and so on (at least that was the
      lineup in Greek times).
        As the Sun continues to move along the ecliptic after
      the vernal equinox, it moves farther and farther north
      of the celestial equator, rising higher and higher in our
      northern skies.  Finally, halfway between the two equinoxes,
      on June 21, it reaches the point of maximum separation
      between ecliptic and celestial equator.  Momentarily it
                                    58

     "stands stiff" in its north-soufh rdotion, then "turns" and
     begins (it appears to us) to travel south again.  This is
     the time of the "summer solstice," where "solstice" is
     from the Latin meaning "sun stand-still."
        At that time the position of the Sun is a full 231/2'
     north of the celestial equator and it is entering the con-
     stellation of Cancer.  Consequently the line of 231/2'
     north latitude on Earth, the line over which the Sun is
     shining on June 20, is the "Tropic of Cancer." ("Tropic"
     is from a Greek word meaning "to turn.")
        On September 23, the Sun has reached the "autumnal
     equinox" as it enters the constellation of Libra.  It then
     moves south of the celestial equator, reaching the point of
     maximum southerliness on December 21, when it enters
     the constellation of Capricorn.  This is the "winter solstice,"
     and the line of 231/2 ' south latitude on the Earth is (you
     guessed it) the "Tropic of Capricorn."

        Here is a complication!  The Earth's axis "wobbles."
     If the line of the axis were extended to the celestial sphere,
     each pole would draw a slow circle, 47' in diameter, as it
     moved.  The position of the celestial equator depends on the
     tilt of the axis and so the celestial equator moves bodily
     against the background of the stars from east to west in a
     direction parallel to the ecliptic.  The position of the equi-
     noxes (the intersection of the moving celestial equator
     with the unmoving ecliptic) travels westward to meet the
     Sun.
        The equinox completes a circuit about the ecliptic in
     25,760 years, which means that in 1 year the vernal
     equinox moves 360/25,760 or 0.014 degrees.  The, Sun,
     in making its west-to-east circuit, comes to the vernal
     equinox which is 0.014 degrees west of its position at the
     last crossing.  The Sun must travel that additional 0.014
     degrees to make a truly complete circuit with respect to
     the stars.  It takes 20 minutes of motion to cover that
     additional 0.014 degrees.  Because the equinox precedes
     itself and is reached 20 minutes ahead of schedule each
     year, this motion of the Earth's axis is called "the pre-
     cession of the equinoxes."
                                   59

        Because of the precession of the equinoxes, the vernal
     equinox moves one full constellation of the Zodiac every
     2150 years.  In the time of the Pyramid builders, the Sun
     entered Taurus at the time of the vernal equinox.  In the
     time of the Greeks, it entered Aries.  In modem times, it
     enters Pisces.  In A.D. 4000 it will enter Aquarius.
        The complete circle made by the Sun with respect to the
     stars takes 365 days, 6 hours, 9 minutes, 10 seconds.  This
     is the "sidereal year." The complete circle from equinox
     to equinox takes 20 minutes less; 365 days, 5 hours, 48
     minutes, 45 seconds.  This is the "tropical year," because it
     also measures the time required for the Sun to move from
     tropic to tropic and back again.
        It is the tropical year and not the sidereal year that
     governs our seasons, so it is the tropical year we mean
     when we speak of the year.

        The scholars of -ancient times noted that the position of
     the Sun in the Zodiac had a profound effect on the Earth.
     Whenever it was in Leo, for instance, the Sun shone with
     a lion's strength and it was invariably hot; when it was in
     Aquarius, the water-carrier usually tipped his um so that
     there was much snow.  Furthermore, eclipses were clearly
     meant to indicate catastrophe, since catastrophe always
     followed eclipses. (Catastrophes also always followed lack
     of eclipses but no one paid attention to that.)
        Naturally, scholars sought for other effects and found
     them in the movement of the five bright star-like objects,
     Mercury, Venus, Mars, Jupiter, and Saturn.  These, like
     the Sun and Moon, moved against the starry background
     and all were therefore called "planctes" ("wanderers")
     by the Greeks.  We call them "planets."
        The five star-like planets circle the Sun as the Earth
     does and the planes of their orbits are tipped only slightly
     to that of the Earth.  Thir% means they seem to move in the
     ecliptic, as the Sun and Moon do, progressing through the
     constellations of the Zodiac.
        Their motions, unlike those of the Sun and the Moon,
     are quite complicated.  Because of the motion of the Earth,
     the tracks made by the star-like planets form loops now
                                  60

    and then.  This made it possible for the Greeks to have
    five centuries of fun working out wrong theories to ac-
    count for those motions.
       Still, though the theories might be wrong, they sufficed
    to work out what the planetary positions were in the past
    and what they would be in the future.  All one had to do
    was to decide what particular influence was exerted by
    a particular planet in a particular constellation of the
    Zodiac; note the positions of all the planets at the time of
    a person's birth; and everything was set.  The decision as
    to the particular influences presents no problem.  You make
    any decision you care to.  The pseudo-science of astrology
    invents such influences without any visible difficulty.  Every
    astrologer has his own set.
       To astrologers, moreover, nothing has happened since
    the time of the Greeks.  The period from March 20 to
    April 19 is still governed by the "sign of Aries," even
    though the Sun is in Pisces at that time nowadays, thanks
    to the precession of the equinoxes.  For that reason it is now
    necessary to distinguish between the "signs of the Zodiac"
    and the "constellations of the Zodiac." The signs now
    are what the constellations were two thousand years ago.
    I've never heard that this bothered any astrologer in the
    world.

       AU this and more occurred to me some time ago when
    I was invited to be on a well-known television conversa-
    tion show that was scheduled to deal with the subject of
    astrology.  I was to represent science against the other
    three members of the panel, all of whom were professional
    astrologers.
       For a moment I felt that I must accept, for surely it
    was my duty as a rationalist to strike a blow against folly
    and superstition.  Then other thoughts occurred to me.
       The three practitioners would undoubtedly be experts
    at their own particular line of gobbledygook and could
    easily speak a gallon of nonsense while I was struggling
    with a half pint of reason.
       Furthermore, astrologers are adept at that line of argu-
    ment that all pseudo-scientists consider "evidence." The
                                 61

      line would be something like this, "People       born under
      Leo are leaders of men, because the lion is      the king of
      ,beasts, and the proof is that Napoleon was      born under
      the sign of Leo."
         Suppose, then, I were to say, "But one-twelfth of living
      human beings, amounting to 250,000,000 individuals, were
      born in Taurus.  Have you, or has anybody, ever tried to
      determine whether the proportion of leaders among them
      is significantly greater than among non-Leos?  And how
      would you test for leadership, objectively, anyway'.?"
         Even if I managed to say all this, I would merely be
      stared at as a lunatic and, very likely, as, a dangerous sub-
      versive.  And the general public, which, in this year of
      1968, ardently believes in astrology and supports more
      astrologers in affluence (I strongly suspect) than existed in
      all previous centuries combined, would arrange lynching
      parties.
         So as I wavered between the desire to fight for the right,
      and the suspicion that the right would be massacred and
      sunk without a trace, I decided to turn to astrology for
      help.  Surely, a bit of astrologic analysis would tell me what
      was in store for me in any such confrontation.
         Since I was born on January 2, that placed me under the,
      sign of Capricornus-the goat.
         That did it! Politel   but very firmly, I refused to be
         on the program!

                                    62

                        5. ROLL CALL

    When all the world was young (and I was a teen-ager),
    one way to give a science fiction story a good title was to
    make use of the name of some heavenly body.  Among
    my own first few science fiction stories, for instance, were
    such items as "Marooned off Vesta," "Christmas on
    Ganymede," and "The Callistan Menace." (Real swino,,inc,
    titles, man!)
      This has gone out of fashion, alas, but the fact remains
    that in the 1930's, a whole generation of science fiction
    fans grew up with the names of the bodies of the Solar
    System as familiar to them as the names of the American
    states.  Ten to one they didn't know why the names were
    what they were, or how they came to be applied to the
    bodies of the Solar System or even, in some cases, bow
    they were pronounced-but who cared?  When a tentacled
    monster came from Umbriel or lo, how much more im-
    pressive that was than if it had merely come from Pbila-
    delphia.
      But ignorance must be battled.  Let us, therefore, take
    up the matter of the names, call the roll of the Solar
    System in the order (more or less) in which the names
    were applied, and see what sense can be made of them.

      'ne Earth itself should come first, I suppose.  Earth is
    an old Teutonic word, but it is one of the glories of the
    English language that we always turn to the classic
    tongues as well.  The Greek word for Earth was Gaia
    or, in Latin spelling, Gaea.  This gives us "geography"
    ("earth-writing"), "geology" ("earth-discourse"), "geom-
    etry" ("earth-measure"), and so on.
      The Latin word is Terra.  In science fiction stories a
                                 63

      human being from Earth may be an "Earthl;ng" or an
      "Earthman," but he is frequently a "Terrestrial," while a
      creature from another world is almost invariably an "extra-
      Terrestrial."
         The Romans also referred to the Earth as Tellus Mater
      ("Mother Earth" is what it means).  The genitive form of
      tellus is telluris, so Earthmen are occasionally referred
      to in s.f. stories as "TeHurians." There is also a chemical
      element "tellurium," named in honor of this version of the
      name of our planet.

         But putting Earth to one side, the first two heavenly
      bodies to have been noticed were, undoubtedly and obvi-
      ously, the Sun and the Moon, which, like Earth, are old
      Teutonic words.
         To the Greeks the Sun was Helios, and to the Romans
      it was Sol.  For ourselves, Helios is almost gone, although
      we have "helium" as the name of an element originally
      found in the Sun, "heliotrope" ("sun-turn") for the sun-
      flower, and so on.
         Sol persists better.  The common adjective derived from
      41
       sun" may be "sunny," but the scholarly one is "solar."
      We may speak of a sunny day and a sunny disposition, but
      never of the "Sunny System." It is always the "Solar
      System." In science fiction, the Sun is often spoken of as
      Sol, and the Earth may even be referred to as "Sol Ill."
         The Greek word for the Moon is Selene, and the Latin
      word is Luna.  The first lingers on in the name of the
      chemical element "selenium," which was named for the
      Moon.  And the study of the Moon's surface features may
      be called "selenography." The Latin name appears -m the
      common adjective, however, so that one speaks of a
      "lunar crescent" or a "lunar eclipse." Also, because of
      the theory that exposure to the li ht of the full Moon
      drove men crazy ("moon-struck"), we obtained the word
      "lunatic."

         I have a theory that the notion of naming the heavenly
      bodies after mythological characters did not originate with
                                  64

     the Greeks, but that it was a deliberate piece of copy
     cattishness.
      . To be sure, one speaks of Helios as the god of the Sun
     and Gaea as the goddess of the Earth, but it seems obvi-
     ous to me that the words came first, to express the physical
     objects, and that these were personified into gods and
     goddesses later on.
       The later Greeks did, in fact, feel this lack of mytho-
     logical character and tried to make Apollo the god of the
     Sun and Artemis (Diana to the Romans) the goddess of
     the Moon.  This may have taken hold of the Greek
     scholars but not of the ordinary folk, for whom Sun and
     Moon remained Helios and Selene. (Nevertheless, the in-
     fluence of this Greek attempt on later scholars was such
     that no other impo   rtant heavenly body was named for
     Apollo and Artemis.)
       I would like to clinch this theory of mine, now, by
     taking up another heavenly body.

       After the Sun and Moon, the next bodies to be recog-
     nized as important individual entities must surely have
     been the five bright "stars" whose positions with respect
     to the real stars were not fixed and which therefore, along
     with the Sun and the Moon, were called planets (see
     Chapter 4).
       The brightest of these "stars" is the one we call Venus,
     and it must have been the first one noticed-but not
     necessarily as an individual.  Venus sometimes appears in
     the evening after sunset, and sometimes in the morning
     before sunrise, depending on which part of its orbit it
     happens to occupy.  It is therefore the "Evening Star" some-
     times and the "Morning Star" at other times.  To the early
     Greeks, these seemed two separate objects and each was
     given a name.
       The Evening Star, which always appeared in the west
     near the setting Sun, was named Hesperos ("evening" or
     44 west"). The equivalent Latin name was Vesper. The
     Morning Star was named Phosphoros ("light-bringee'),
     for when the Morning Star appeared the Sun and its light
                                  65

    were not far behind. (The chemical element "phosphorus"
    -Latin spelling-was so named because it glowed in the
    dark as the result of slow combination with oxygen.) The
    Latin name for the Morning Star was Lucifer. which also
    means "light-bringer."
      Now notice that the Greeks made no use of mythology
    here.  Their words for the Evening Star and Morning Star
    were logical, descriptive words.  But then (during the sixth
    century B.c.) the Greek scholar, Pythagoras of Samos,
    arrived back in the Greek world after his travels in
    Babylonia.  He brought with him a skullfull of Babylonian
    notions.
      At the time, Babylonian astronomy was well developed
    and far in advance of the Greek bare beginnings.  The
    Babylonian interest in astronomy was chiefly astrological
    in nature and so it seemed natural for them to equate the
    powerful planets with the powerful gods. (Since both had
    power over human beings, why not?) The Babylonians
    knew that the Evening Star and the Morning Star were
    a single planet-after all, they never appeared on the
    same day; if one was present, the other was absent, and
    it was clear from their movements that the Morning Star
    passed the Sun and became the Evening Star and vice
    versa.  Since the planet representing both was so bright
    and beautiful, the Babylonians very logically felt it ap-
    propriate to equate it with Ishtar, their goddess of beauty
    and love.
      Pythagoras brought back to Greece this Babylonian
    knowledge of the oneness of the Evening and Morning Star,
    and Hesperos and Phosphoros vanished from the heavens.
    Instead, the Babylonian system was copied and the planet
    was named for the Greek goddess of beauty and love,
    Aphrodite.  To the Romans this was their corresponding
    goddess Yenus, and so it is to us.
      Thus, the habit of naming heavenly bodies for gods
    and goddesses was, it seems to me, deliberately copied
    from the Babylonians (and their predecessors) by the
    Greeks.
      The name "Venus," by the way, represents a problem.
                                66

     Adjectives from these classical words have to be taken
     from the genitive case and the genitive form of "Venus"
     is Veneris. (Hence, "venerable" for anything worth the
     respect paid by the Romans to the goddess; and because
     the Romans respected old age, "venerable" came to be
     applied to old men rather than young women.)
       So we cannot speak of "Venusian atmosphere" or
     "Venutian atmosphere" as science fiction writers some-
     times do.  We must say "Venerian atmosphere." Un-
     fortunately, this has uncomfortable associations and it is
     not used.  We might turn back to the Greek name but the
     genitive form there is .4phrodisiakos, and if we speak of
     the "Aphrodisiac atmosphere" I think we will give a false
     impression.
       But something must be done.  We are actually exploring
     the atmosphere of Venus with space probes and some
     adjective is needed.  Fortunately, there is a way out.  The
     Venus cult was very prominent in early days in a small
     island south of Greece.  It was called Kythera (Cythera
     in Latin spelling) so that Aphrodite was referred to,
     poetically, as the "Cytherean go'ddess." Our poetic astron-
     omers have therefore taken to speaking of the "Cytherean
     atmosphere."

       The other four planets present no problem.  The second
     brightest planet is truly the king planet.  Venus may be
     brighter but it is confined to the near neighborhood of the
     Sun and is never seen at midnight.  The second brightest,
     however, can shine through all the hours of night and so
     it should fittingly be named for the chief god.  The Babi
     lonians accordingly named it "Marduk." The Greeks
     followed suit and called it "Zeus," and the Romans named
     it Jupiter.  The genitive form of Jupiter is fovis, so that
     we speak of the "Jovian satellites." A person bom under
     the astrological influence of Jupiter is "jovial."
       Then there -is a reddish planet and red is obviously the
     color of blood; that is, of war and conflict.  The Baby-
     lonians named this planet "Nergal" after their god of war,
     and the Greeks again followed suit by naming it "Ares"
                                 67

    after theirs.  Astronomers who study the surface features
    of the planet are therefore studying "areography." The
    Latins used their god of war, Mars, for the planet.  The
    genitive form is Martis, so we can speak of the "Martian
    canals."
      The planet nearest the Sun, appears, like Venus, as both
    an evening star and morning star.  Being smaller and less
    reflective than Venus, as well as closer to the Sun, it is
    much harder to see.  By the time the Greeks got around to
    naming it, the mythological notion had taken hold.  The
    evening star manifestation was named "Hermes," and the
    morning star one "Apollo."
      The latter name is obvious enough, since the later
    Greeks associated Apollo with the Sun, and by the time
    the planet Apollo was in the sky the Sun was due very
    shortly.  Because the planet was closer to the Sun than
    any other planet (though, of course, the Greeks did not
    know this was the reason), it moved more quickly against
    the stars than any object but the Moon.  This made it
    resemble the wing-footed messenger of the gods, Hermes.
    But giving the planet two names was a matter of conserv-
    atism.  With the Venus matter straightened out, Hermes/
    Apollo was quickly reduced to a single planet and Apollo
    was dropped.  The Romans named it "Mercurius," which
    was their equivalent of Hermes, and we call it Mercury.
    The quick journey of Mercury across the stars is like the
    lively behavior of droplets of quicksilver, which came to
    be called "mercury," too, and we know the type of
    personality that is described as "mercurial."
      There is one planet left.  This is the most slowly moving
    of all the planets known to the ancient Greeks (being the
    farthest from the Sun) and so they gave it the name of
    an ancient god, one who would be "pected to move in
    grave, and solemn steps.  They called it "Cronos," the
    father of Zeus and ruler of the universe before the suc-
    cessful revolt of the Olympians under Zeus's leadership.
    The Romans gave it the name of a god they considered the
    equivalent of Cronos and called it "Saturnus," which to
    us is Saturn.  People born under Saturn are supposed to
    reflect its gravity and are "satumine."
                                68

        For two thousand years the Earth, Sun, Moon, Mercury,
     Venus, Mars, Jupiter, and Saturn remained the only known
     bodies of the Solar System.  Then came 1610 and the
     Italian astronomer Galileo Galilei, who built himself a
     telescope and turned it on the heavens.  In no time at all
     he found four subsidiary objects circling the planet Jupiter.
     (The German astronomer Johann Kepler promptly named
     such subsidiary bodies "satellites," from a Latin word for
     the hangers-on of some powerful man.)
        There was a question as to what to name the new bodies.
     The mythological names of the planets had hung on into
     the Christian era, but I imagine there must have been some
     natural hesitation about using heathen gods for new bodies.
     Galileo himself felt it wise to honor Cosimo Medici H,
     Grand Duke of Tuscany from whom he expected (and
     later received) a position, and called them Sidera MetUcea
     (the Medicean stars).  Fortunately this didn't stick.  Nowa-
     days we call the four satellites the "Galilean satellites" as
     a group, but individually we use mythological names after
     all.  A German astronomer, Simon Marius, gave them
     these names after having discovered the satellites one day
     later than Galileo.
        The names are all in honor of Jupiter's (Zeus's) loves,
     of which there were many.  Working outward from Jupiter,
     the first is lo (two syllables please, eye'oh), a maiden
     whom Zeus turned into a heifer to hide her from his wife's
     jealousy.  The second is Europa, whom Zeus in the form
     of a bull abducted from the coast of Phoenicia in Asia and
     carried to Crete (which is how Europe received its name).
     The third is Ganymede, a young Trojan lad (well, the
     Greeks were liberal about such things) whom Zeus ab-
     ducted by assuming the guise of an eagle.  And the fourth
     is Callisto, a nymph whom Zeus's wife caught and turned
     into a bear.
        As it happens, naming the third satellite for a male
     rather than for a female turned out to be appropriate, for
     Ganymede is the largest of the Galilean satellites and,
     indeed, is the largest of any satellite in the Solar System.
     (It is even larger than Mercury, the smallest planet.)
        The naming of the Galilean satellites established once
                                  69

    and for all the convention that bodies of the Solar System
    were to be named mythologically, and except in highly
    unusual instances this custom has been followed since.

       In 1655 the Dutch astronomer Christian Huygens dis-
    covered a satellite of Saturn (now known to be the sixth
    from the planet).  He named it Titan.  In a way this was
    appropriate, for Saturn (Cronos) and his brothers and
    sisters, who ruled the Universe before Zeus took over,
    were referred to collectively as "Titans." However, since
    the name refcrs to a group of beings and not to an indi-
    vidual being, its use is unfortunate.  The name was ap-
    propriate in a second fashion, too.  "Titan" has come to
    mean "giant" because the Titans and their allies were
    pictured by the Greeks as- being of superhuman size
    (whence the word "titanic"), and it turned out that Titan
    was one of the largest satellites in the Solar System.
       The Italian-French astronomer Gian Domenico Cassini
    was a little more precise than Huygens had been.  Between
    1671 and 1684 he discovered four more satellites of Saturn,
    and these he named after individual Titans and Titanesses.
    The satellites now known to be 3rd, 4th, and 5th from
    Saturn he named Tethys, Dione, and Rhea, after three
    sisters of Saturn.  Rhea was Saturn's wife as well.  The 8th
    satellite from Saturn he named Iapetus after one of
    Satum's brothers. (Iapetus is frequently mispronounced.
    In English it is "eye-ap'ih-tus.") Here finally the Greek
    names were used, chiefly because there were no Latin
    equivalents, except for Rhea.  There the Latin equivalent
    is Ops.  Cassini tried to lump the four satellites he had
    discovered under the name of "Ludovici" after his patron,
    Louis XIV-Ludovicus, in Latin-but that second at-
    tempt to honor royalty also failed.

       And so within 75 years after the discovery of the tele-
    scope, nine new bodies of the Solar System were discovered,
    four satellites of Jupiter and five of Saturn.  Then some-
    thing more exciting turned up.
       On March 13, 1781, a German-English astronomer,
    William Herschel, surveying the heavens, found what he
                                 70

      thought was a comet.  This, however, proved quickly to
      be no comet at all, but a new planet with an orbit outside
      that of Saturn.
        There arose a serious problem as to what to name the
      new planet, the first to be discovered in historic times.
      Herschel himself called it "Georgium Sidus" ("George's
      star") after his patron, George III of England, but this
      third attempt to honor royalty failed.  Many astronomers
      felt it should be named for the discoverer and called it
      "Herschel." Mythology, however, won out.
        The German astronomer Johann Bode came up with a
      truly classical suggestion.  He felt the planets ought to make
      a heavenly family.  The three innermost planets (exclud-
      ing the Earth) were Mercury, Venus, and Mars, who were
      siblings, and children of Jupiter, whose orbit lay outside
      theirs.  Jupiter in turn was the son of Saturn, whose orbit
      lay outside his.  Since the new planet had an orbit outside
      Satum's, why not name it for Uranus, god of the sky and
      father of Saturn?  The suggestion was accepted and Uranus*
      it was.  What's more, in 1798 a German chemist, Martin
      Heinrich Klaproth, discovered a new element he named
      in its honor as "uranium."
        In 1787 Herschel went on to discover Uranus's two
      largest satellites (the 4th and 5th from the planet, we
      now know).  He named them from mythology, but not
      from Graeco-Roman mythology.  Perhaps, as a naturalized
      Englishman, he felt 200 per cent English (it's that way,
      sometimes) so he turned to English folktales and named
      the satellites Titania and Oberon, after the queen and
      king of the fairies (who make an appearance, notably, in
      Shakespeare's A Midsummer Night's Dream).
        In 1789 be went on to discover two more satellites of
      Saturn (the two closest to the planet) and here too he
      disrupted mythological logic.  The planet and the five
      satellites then known were all named for various Titans
      and Titanesses (plus the collective name, Titan).  Herschel
      named his two Mimas and Enceladus (en-seYa-dus) after

        * Uranus is pronounced "yooruh-nus." I spent almost all my
      life accenting the second syllable and no one ever corrected me.  I
      just happened to be reading Webster's Unabridged one day . . .
                                   71

   two of the giants who rose in rebellion against Zeus long
   after the defeat of the Titans.

     After the discovery of Uranus, astronomers climbed
   hungrily upon the discover-a-planet bandwagon and
   searched particularly in the unusually large gap between
   Mars and Jupiter.  The first to find a body there was the
   Italian astronomer Giuseppe Piaz2i.  From his observatory
   at Palermo, Sicily he made his first sighting on January
   1, 1801.
     Although a priest, he adhered to the mythological con-
   vention and named the new body Ceres, after the tutelary
   goddess of his native Sicily.  She was a sister of Jupiter
   and the goddess of grain (hence "cereal") and agriculture.
   This was the second planet to receive a feminine name
   (Venus was the first, of course) and it set a fashion.  Ceres
   turned out to be a small body (485 miles in diameter),
   and many more were found in the -gap between Mars and
   Jupiter.  For a hundred years, all the bodies so discovered
   were given feminine names.
     Three "planetoids" were discovered in addition to Ceres
   over the next six years.  Two were named Juno and Vesta
   after Ceres' two sisters.  They were also the sisters of
   Jupiter, of course, and Juno was his wife as well.  The
   remaining planetoid was named Pallas, one of the alternate
   names for Athena, daughter of Zeus (Jupiter) and there-
   fore a niece of Ceres. (Two chemical elements discovered
   in that decade were named "ceriunf' and "paradiunf' after
   Ceres and Pallas.)
     Later planetoids were named after a variety of minor
   goddesses, such. as Hebe, the cupbearer of the gods,
   Iris, their messenger, the various Muses, Graces, Horae,
   nymphs, and so on.  Eventually the list was pretty well
   exhausted and planetoids began to receive trivial and
   foolish names.  We won't bother with those.

     New excitement came in 1846.  The motions of Uranus
   were slightly erratic, and from them the Frenchman Urbain
   J. J. Leverrier and the Englishman John Couch Adams
   calculated the position of a planet beyond Uranus, the grav-
                                72

     itational attraction of which would account for Uranus's
     anomalous motion.  The planet was discovered in that
     position.
        Once again there was difficulty in the naniing.  Bode's
     mythological family concept could not be carried on, for
     Uranus was the first god to come out of chaos and had no
     father.  Some suggested the planet be named for Leverrier.
     Wiser council prevailed.  The new planet, rather greenish in
     its appearance, was named Neptune after the god of the
     sea.
        (Leverrier also calculated the possible existence of a'
     planet inside the orbit of Mercury and named it Vulcan,
     after the god of fire and the forge, a natural reference to
     the planet's closeness to the central fire of the Solar
     System.  However, such a planet was never discovered and
     undoubtedly does not exist.)
        As soon as Neptune was- discovered, the English astron-
     omer William Lassell turned his telescope upon it and dis-
     covered a large satellite which he named Triton, ap-
     propriately enough, since Triton was a demigod of the sea
     and a son of Neptune (Poseidon).
        In 1851 Lassell discovered two more satellites of
     Uranus, closer to the planet than Herschel's Oberon and
     Titania.  Lassell, also English, decided to continue Her-
     schel's English folklore bit.  He turned to Alexander Pope's
     The Rape of the Lock, wherein were two elfish characters,
     Ariel and Umbriel, and these names were given to the
     satellites.

        More satellites were turning up.  Saturn was already
     known to have seven satellites, and in 1848 the American
     astronomer George P. Bond discovered an eighth; in 1898
     the American astronomer William H. Pickering discovered
     a ninth and completed the list.  These were named Hy-
     perion and Phoebe after a Titan and Titaness.  Pickering
     also thought he had discovered a tenth in 1905, and
     named it Themis, after another Titaness, but this proved
     to be mistaken.
        In 1877 the American astronomer Asaph Hall, waiting
     for an unusually close approach of Mars, studied its sur-
                                  73

   roundings carefully and discovered two tiny satellites,
   which he named Phobos ("fear") and Deimos ("teffor"),
   two sons of Mars (Ares) in Greek legend, though obvi-
   ously mere personifications of the inevitable consequences
   of Mars's pastime of war.
      In 1892 another American astronomer, Edward E.
   Barnard, discovered a fifth satellite of Jupiter, closer than
   the Galilean satellites.  For a long time it received no
   name, being called "Jupiter V" (the fifth to be discovered)
   or "Barnard's satellite." Mythologically, however, it was
   given the name Amalthea by the French astronomer
   Camille Flammarion, and this is coming into more com-
   mon use.  I am glad of this.  Amalthea was the nurse of
   Jupiter (Zeus) in his infancy, and it is pleasant to have
   the nurse of his childhood closer to him than the various
   girl and boy friends of his maturer years.
      In the twentieth dentury,no less than seven more Jovian
   satellites were discovered, all far out, all quite small, all
   probably captured planetoids, all nameless.  Unofficial
   names have been proposed.  Of these, the three planetoids
   nearest Jupiter bear the names Hestia, Hera, and Demeter,
   after the Greek names of the three sisters of Jupiter (Zeus).
   Hera, of course, is his wife as well.  Undeithe Roman
   versions of the names (Vesta, Juno, and Ceres, respec-
   tively) all three are planetoids.  The two farthest are Posei-
   don and Hades, the two brothers of Jupiter (Zeus).  The
   Roman version of Poseidon's name (Neptune) is applied
   to a planet.  Of the remaining satellites, one is Pan, a
   grandson of Jupiter (Zeus), and the other is Adrastea,
   another of the nurses of his infancy.
      The name of Jupitees (Zeus's) wife, Hera, is thus
   applied to a satellite much farther and smaller than those
   commemorating four of his extracurricular affairs.  I'm not
   sure that this is right, but I imagine astronomers under-
   stand these things better than I do.

      In 1898 the German astronomer G. Witt discovered an
   unusual planetoid, one with an orbit that lay closer to the
   Sun than did any other of the then-known planetoids.  It
   inched past Mars and came rather close to Earth's orbit.

                                 74

     Not counting the Earth, this planetoid might be viewed as
     passing between Mars and Venus and therefore Witt gave
     it the name of Eros, the god of love, and the son of Mars
     (Ares) and Venus (Aphrodite).
       This started a new convention, that of giving planetoids
     with odd orbits masculine names.  For instance, the planet-
     oids that circle in Jupiter's orbit all received the names of
     masculine participants in the Trojan war: Achilles, Hector,
     Patroclus, Ajax, Diomedes, Agamemnon, Priamus, Nestor,
     Odysseus, Antilochus, Aeneas, Anchises, and Troilus.
       A particularly interesting case arose in 1948, when the
     German-American astronomer Walter Baade discovered a
     planetoid that penetrated more closely to the Sun than
     even Mercury did.  He named it Icarus, after the mythical
     character who flew too close to the Sun, so that the wax
     holding the feathers of his artificial wings melted, with the
     result that be fell to his death.
       Two last satellites were discovered.  In 1948 a Dutch-
     American astronomer, Gerard P. Kuiper, discovered an
     innermost satellite of Uranus.  Since Axiel (the next inner-
     most) is a character in William Shakespeare's The Tem-
     pest as well as in Pope's The Rape of the Lock, free asso-
     ciation led Kuiper to the heroine of The Tempest and he
     named the new satellite Miranda.
       In 1950 be discovered a second satellite of Neptune.
     The first satellite, Triton, represents not only the name of
     a particular demigod, but of a whole class of merman-like
     demigods of the sea.  Kuiper named the second, then, after
     a whole class of mermaid-like nymphs of the sea, Nereid.

       Meanwhile, during the first decades of the twentieth
     century, the American astronomer Percival Lowell was
     searching for a ninth planet beyond Neptune.  He died in
     1916 without having succeeded but in 1930, from his ob-
     servatory and in his spirit, Clyde W. Tombaugh made the
     discovery.
       The new planet was named Pluto, after the god of the
     Underworld, as was appropriate since it was the planet
     farthest removed from the light of the Sun. (And in 1940,
     when two elements were found beyond uranium, they were
                                  75

    named "neptunium!' and "plutonium" after Neptune and
    Pluto, the two planets beyond Uranus.)
      Notice, though, that the first two letters of "Pluto,' are
    the initials of Percival Lowell.  And so, ft0y, an astron-
    omer got his name attached to a planet.  Where Herschel
    and Leverrier had failed, Percival Lowell had succeeded,
    at least by initial, and under cover of the mythological
    conventions.

                                 76

           6. ROUND AND ROUND AND ...

    Any-one who writes a book on astronomy for the general
    public eventually comes up against the problem of trying
    to explain that the Moon always presents one face to the
    earth, but is nevertheless rotating.
      To the average reader who has not come up against this
    problem before and who is inpatient with involved
    subtleties, this is a clear contradiction in terms.  It is easy
    to accept the fact that the Moon always presents one face
    to the Earth because even to the naked eye, the shadowy
    blotches on the MooWs surface are always found in the
    same position.  But in that case it seems clear that the
    Moon is not rotating, for if it were rotating we would, bit
    by bit, see every portion of its surface.
      Now it is no use sm.Uing gently at the lack of sophistica-
    tion of the average reader, because he happens to be right.
    The Moon is not rotating with respect to the observer on
    the Earth's surface.  When the astronomer says that the
    Moon is rotating, he means with respect to other observers
    altogether.
      For instance, if one watches the Moon over a period of
    time, one can see that the line marking off the sunlight
    from the shadow progresses steadily around the Moon; the
    Sun shines on every portion of the Moon in steady pro-
    gression.  This means that to an observer on the surface of
    the Sun (and there are very few of those), the Moon
    would seem to be rotating, for the observer would, little
    by little'see every portion of the Moon's surface as it
    turned to be exposed to the suiidight.
      But our average reader may reason to himself as fol-
    lows: "I see only one face of the Moon and I say it is
    not rotating.  An observer on the Sun sees all parts of the
                                  77

     Moon and he says it is rotating.  Clearly, I am more im-
     portant than the Sun observer since, firstly, I exist and be
     doesn't, and, secondly, even if he existed, I am me and he
     isn't.  Therefore, I insist on having it my way.  The Moon
     does not rotate!"
       There has to be a way out of this confusion, so let's
     think things through a little more systematically.  And to
     do so, let's start with the rotation of the Earth itself, since
     that is a point nearer to all our hearts.

       One thing we can admit to begin with: To an observer
     on the Earth,,the Earth is not rotating.  If you stay in one
     place from now till doomsday, you will see but one portion
     of the Earth's surface and no other.  As far as you are
     concerned, the planet is standing still.  Indeed, through
     most of civilized human history, even the wisest of men
     insisted that "reality" (whatever that may be) exactly
     matched the appearance and that the Earth "really" did
     not rotate.  As late as 1633, Galileo found himself in a spot
     of trouble for maintaining otherwise.
       But suppose we had an observer on a star situated (for
     simplicity's sake) in the plane of the EartWs equator; or,
     to put it another way, on the celestial equator (see Chapter
     3). Let us further suppose that the observer was equipped
     with a device that made it possible for Mm to study the
     Earth's surface in detail.  To him, it would seem that the
     Earth rotated, for little by little he would see every part
     of its surface pass before his eyes.  By taking note of some
     particular small feature (for example, you and I standing
     on some point on the equator) and timing its return, he
     could even determine the exact period of the Earth's
     rotation-that is, as far as he is concerned.
       We can duplicate his feat, for when the observer on the
     star sees us exactly in the center of that part of Earth's
     surface visible to himself, we in turn see. the observer's star
     directly overhead.  And just as he would time the periodic
     return of ourselves to that centrally located position, so
     we could time the return of his star to the overhead point.
     The period determined wiU be the same in either case.
     (Let's measure this time in minutes, by the way.  A minute
                                   79

   can be defined as 60 seconds, where I second is equal to
   1/31,556,925.9747 of the tropical year.)
     The period of Earth's rotation with respect to the star
   is just about 1436 minutes.  It doesn't matter which star we
   use, for the apparent motion of the stars with respect to
   one another, ii viewed from the Earth, is so vanishingly
   small that the constellations can be considered as moving
   all in one piece.
     The period of 1436 minutes is called Earth's "sidereal
   day." The word "sidereal" comes from a Latin word for
   "star," and the phrase therefore means, roughly speaking,
   "the star-based day."
     Suppose, though, that we were considering an observer
   on the Sun.  If he were watching the Earth, he, too, would
   observe it rotating, but the period of rotation would not
   seem the same to him as to the observer on the star.  Our
   solar observer would be much closer to the Earth; close
   enough, in fact, for Earth's motion about the Sun to intro-
   duce a new factor.  In the course of a single rotation of
   the Earth (judging by the star's observer), the Earth
   would have moved an appreciable distance through space,
   and the solar observer would find himself viewing the
   planet from a different angle.  The Earth would have to
   turn for four more minutes before it adjusted itself to the
   new angle of view.
     We could interpret these results from the point of view
   of an observer on the Earth.  To duplicate the measure-
   ments of the solar observer, we on Earth would have to
   measure the period of time from one passage of the Sun
   overhead to the next (from noon to noon, in other words).
   Because of the revolution of the Earth about the Sun, the
   Sun seems to move from west to east against the back-
   ground of the stars.  After the passage of one sidereal day,
   a particular star would have returned to the overhead posi-
   tion, but the Sun would have drifted eastward to a point
   where four more minutes would be required to make it
   pass overhead.  The solar day is therefore 1440 minutes
   long, 4 ' ates longer than the sidereal day.
     Next, suppose we have an observer on the Moon.  He is
   even closer to the @h and the apparent motion of the
                               79

      Earth against the stars is some thirteen times greater for
      him than for an observer on the Sun.  Therefore, the dis-
      crepancy between what he sees and what the star observer
      sees is about thirteen times greater than is the Sun/star
      discrepancy.
        If we consi er this same si       tion from t. ie Earth, we
      would be measuring the time between successive passages
      of the Moon exactly overhead.  The Moon drifts eastward
      against the starry background at thirteen times the rate the
      Sun does.  After one sidereal day is completed, we have to
      wait a total of 54 additional minutes for the Moon to
      pass overhead again.  The Earth's "lunar day" is therefore
      1490 minutes long.
        We could also figure out the periods of Earth's rotation
      with respect to an ob    'server on Venus, on Jupiter, on
      Halley's Comet, on an artificial satellite, and so on, but I
      shall have mercy and refrain.  We can instead summarize
      the little we do have as follows:

                    sidereal day       1436 minutes
                    solar day          1440 minutes
                    lunar day          1490 minutes

        By now it may seem reasonable to ask: But which is
      the day?  The real day?
        The answer to that question is that the question is not a
      reasonable one at all, but quite unreasonable; and that
      there is no real day, no real period of rotation.  There are
      only different apparent periods, the lengths of which de-
      pend upon the position of the observer.  To use a prettier-
      sounding phrase, the length of the period of the Earth's
      rotation depends on the frame of reference, and all frames
      of reference are equally valid.
        But if all frames of reference are equally valid, are we
      left nowhere?
        Not at all!  Frames of reference may be equally valid,
      but they are usually not equally useful.  In one respect, a
      particular frame of reference may be most useful; in an-
      other respect, another frame of reference may be most
      useful.  We are free to pick and choose, using now one,
      now another, exactly as suits our dear little hearts.
                                     80

      For instance, I said that the solar day is 1440 minutes
    long but actually thafs a He.  Because the Earth's axis is
    tipped to the plane of its orbit and because the Earth is
    sometimes closer to the Sun and sometimes farther (so
    that it moves now faster, now slower in its orbit), the solar
    day is sometimes a little longer than 1440 minutes and
    sometimes a little shorter.  If you mark off "noons" that
    are exactly 1440 minutes apart all through the year, there
    will be times during the year when the Sun will pass over-
    head fully 16 minutes ahead of schedule, and other times
    when it will pass overhead fully 16 minutes behind
    schedule.  Fortunately, the Fffors cancel out and by the end
    of the year all is even agmn.
      For that reason it is not the solar day itself that is 1440
    minutes Ion& but the average length of all the solar days
    of the year; this average is the "mean solar day." And at
    noon of all but four days a year, it is not the real Sun that
    crosses the overhead point but a fictitious body called the
    "mean Sun." The mean Sun is located where the real Sun
    would be if the real Sun moved perfectly evenly.
      The lunar day is even more uneven than the solar day,
    but the sidereal day is a really steady affair.  A particular
    star passes overhead every 1436 minutes virtually on the
    dot.
      If we7re going to measure time, then, it seems obvious
    that the sidereal day is the most useful, since it is the most
    constant.  Where the sidereal day is used as the basis for
    checking the clocks of the world by the passage of a star
    across the hairline of a telescope eyepiece, then the Earth
    itself, as it rotates with respect to the stars, is serving as
    the reference clocl The second can then be defined as
    1/1436.09 of a sidereal day. (Actually, the length of the
    year is even more constant than that of the sidereal day,
    which is why the second is now officially defined as a frac-
    tion of the tropical year.)

      The solar day, uneven as it is, carries one important
    advantage.  It is based on the position of the Sun, and the
    position of the Sun determines whether a particular por-
    tion of the Earth is in light or in shadow.  In short, the
                                  81

      solar day is equal to one period of light (daytime) plus
      one period of darkness (night).  The average man through-
      out history has managed to remain unmoved by the posi-
      tion of the stars, and couldn't have cared less when one
      of them moved overhead; but he certainly couldn't help
      noticing, and even being deeply concerned, by the fact that
      it might be day or night at a particular moment; surmise
      or sunset; noon or twilight.
        It is the solar day, therefore, which is by far the most
      useful and important day of all.  It was the original basis
      of time measurement and it is divided into exactly 24
      hours, each of which is divided into 60 minutes (and 24
      times 60 is 1440, the number of minutes in a solar day).
      On this basis, the sidereal day is 23 hours 56 minutes long
      and the lunar day is 24 hours 50 minutes long.
        So useful is the solar day, in fact, that mankind has
      become accustomed to thinking of it as the day, and of
      thinking that the Earth "really" rotates in exactly 24 hours,
      where actually this is only its apparent rotation with re-
      spect to the Sun, no more "real" or "unreal" than its ap-
      parent rotation with respect to any other body.  It is no
      more "real" or "unreal," in fact, than the apparent rota-
      tion of the Earth with respect to an observer on the Earth
      -that is, to the apparent lack of rotation altogether.
        The lunar day has its uses, too.  If we adjusted our
      watches to lose 2 minutes 5 seconds every hour, it would
      then be running on a lunar day basis.  In that case, we
      would find that high tide (or low tide) came exactly twice
      a day and at the same times every day-indeed, at twelve-
      hour intervals (with minor variations).
        And extremely useful is the frame of reference of the
      Earth itself; to wit, the assumption that the Earth is not
      rotating at all.  In judging a billiard shot, in throwing a
      baseball, in planning a trip cross-country, we never take
      into account any rotation of the Earth.  We always assume
      the Earth is standing still.

        Now we can pass on to the Moon.  For the viewer from
      the Earth, as I said earlier, it does not rotate at all so
      that its "terrestrial day" is of infinite length.  Nevertheless,
                                    82

     we can maintain that the Moon rotates if we shift our
     frame of reference (-usually without warning or explana'-
     tion so that the reader has trouble following).  As a matter
     of fact, we can shift our plane of reference to either the
     Sun or the stars so that not only can the--Moon be con-
     sidered to rotate but to do so in either of two periods.
        With respect to the stars, the period of the Moon's rota-
     tion is 27 days, 7 hours, 43 minutes, 11.5 seconds, or
     27.3217 days (where the day referred to is the 24-hour
     mean solar day).  This is the Moon's sidereal day.  It is
     also the period (with respect to the stars) of its revolu-
     tion about the Earth, so it is almost invariably called the
     "sidereal month."
        In one sidereal month, the Moon moves about 1/1 .1 of
     the length of its orbit about the Sun, and to an observer
     on the Sun the change in angle of viewpoint is consider-
     able.  The Moon must rotate for over two more days to
     make up for it.  The period of rotation of the Moon with
     respect to the Sun is the same as its perio   ,d of revolution
     about the Earth with respect to the Sun, and this may be
     called the Moon's solar day or, better still, the solar
     month. (As a matter of fact, as I shall shortly point out,
     it is called neither.) The solar month is 29 days, 12 hours,
     44 minutes, 2.8 seconds long, or 29.5306 days long.
        Of these two months, the solar month is far more useful
     to mankind because the phases of the Moon depend on
     the relative positions of Moon and -Sun.  It is therefore
     29-5306 days, or one solar month, from new Moon to
     new Moon, or from full Moon to full Moon.  In ancient
     times, when the phases of the Moon were used to mark
     off the seasons, the solar month became the most iinpor-
     tant unit of time.
        Indeed, great pains were taken to detect the exact day
     on which successive new Moons appeared in order that the
     calendar be accurately kept (see Chapter 1).  It was the
     place of the priestly caste to take care of this, and the very
     word "calendar," for instance, comes from the Latin word
     meaning "to proclaim," because the beginning of each
     month was proclaimed with much ceremony.  An assembly
     of priestly officials, such as those that, in ancient times,
                                   83

    might have proclaimed the beginning of each month, is
    called a "synod." Consequently, what I have been calling
    the solar month (the logical name) is, actually, called the
      synodic month."
       The farther a planet is from the Sun and the faster it
    turns with respect to the stars, the smaller the discrepancy
    between its sidereal day and solar day.  For the planets
    beyond Earth, the discrepancy can be ignored.
       For the two planets closer to the Sun than the Earth the
    discrepancy is very great.  Both Mercury and Venus turn
    one face eternally to the Sun and have no solar day.  They
    turn with respect to the stars, however, and have a sidereal
    day which @ out to be as long as the period of their
    revolution about the Sun (again with respect to the stars).
       If the various true satellites of the Solar System (see
    Chapter 7) keep one face to their primaries at all times,
    as is very likely true, their sidereal day would be equal
    to their period of revolution about their primary.
       If this is so I can prepare a table (not quite like any I
    have ever seen) listing the sidereal period of rotation for
    each of the 32 major bodies of the Solar System: the Sun,
    the Earth, the eight other planets (even Pluto, which has
    a rotation figure, albeit an uncertain one), the Moon, and
    the 21 other true satellites.  For the sake of direct corn-
    parison I'll give the period in minutes and list them in
    the order of length.  After each satellite I shall put the
    name of the primary in parentheses and give a number to
    represent the position of that satellite, counting outward
    from the primary.

                                                 Sidereal Day
                        Body                       (minutes)

          Venus                                      324,000
          Mercury                                    129,000
          Iapetus (Satum-8)                          104,000
          Moon (Earth-1)                             39,300
          Sun                                        35,060
          Hyperion (Saturn-7)                        30,600
          Callisto (Jupiter-5)                       24,000
          Titan (Satum-6)                            23,000
                                   84

           Oberon (Uranus-5)                          19,400
           Titania (Uranus-4)                         12,550
           Ganymede (Jupiter-4)                       10,300
           Pluto                                       8650
           Triton (Neptune-1)
           Rhea (Saturn-5)                             6500
           Umbriel (Uranus-3)                          5950
           Europa (Jupiter-3)                          5100
           Dione (Satum-4)                             3950
           Ariel (Uranus-2)                            3630
           Tethys (Saturn-3)                           2720
           lo (Jupiter-2)                              2550
           Miranda (Uranus-1)                          2030
           Enceladus (Saturn-2)                        1975
           Deimos (Mars-2)                             1815
           Mars                                        1477
           Earth                                       1436
           Mimas (Satum-1)                             1350
           Neptune                                      948
           Amaltheia (Jupiter-1)                        720
           Uranus                                       645
           Saturn                                       614
           Jupiter                                      590
           Phobos                                       460

       These figures-represent the time it takes        for stars to
     make a complete circuit of the skies from the frame of
     reference of an observer on the surface of the body in
     question.  If you divide each figure by 720, you get the
     number of minutes it would take a star (in the region of
     the body's celestial equator) to travel the width of the Sun
     or Moon as seen from the Earth.
       On Earth itself, this takes about 2 minutes and no more,
     believe it or not.  On Phobos (Mars's inner satellite), it
     takes only a little over half a minute.  The stars will be
     whirling by at four times their customary rate, while a
     bloated Mars hangs motionless in the sky.  What a sight
     that would be to see.
        On the Moon, on the other hand, it would take 55
     minutes for a star to cover the apparent width of the Sun.
     Heavenly bodies could be studied over continuous sustained
     intervals nearly thirty times as long as is possible on the
                                    85

    Earth.  I have never seen this mentioned as an advantage
    for a Moon-based telescope, but, combined with the
    absence of clouds or other atmospheric, interference, it
    makes a lunar observatory something for which astron-
    omers ought to be willing to undergo rocket trips.
      On Venus, it would take 450 minutes or 7'h hours for
    a star to travel the apparent width of the Sun as we see
    it. What a fix astronomers could get on the heavens there
    -if only there were no clouds.

                               86

               7. JUST MOONING AROUND

    Almost every book on astronomy I have ever seen, large
    or small, contains a little table of the Solar System.  For
    each planet, there's given its diameter, its distance from
    the sun, its time of rotation, its albedo, its density, the
    number of its moons, and so on.
       Since I am morbidly fascinated by numbers, I jump on
    such tables with the perennial hope of finding new items
    of information.  Occasionally, I am rewarded with such
    things as surface temperature or orbital velocity, but I
    never really get enough.
       So every once in a while'   when the ingenuity-circuits in
    my brain are purring along with reasonable smoothness,
    I deduce new types of data for myself out of the material
    on band, and while away some idle hours. (At least I did
    this in the long-gone days when I had idle hours.)
       I can still do it, however, provided I put the results into
    formal essay-form; so come join me and we will just moon
    around together in this fashion, and see what turns up.

       Let's begin this way, for instance . . .
       According to Newton, every object in the universe
    attracts every other object in the universe with a force
    (i) that is proportional to the product of the masses (ml
    and M2) of the two objects divided by the square of the
    distance (d) between them, center to center.  We multiply
    by the gravitational constant (g) to convert the propor-
    tionality to an equality, and we have-.

                 f = 9MIM2              (Equation 1)
                       d2
                                  87

       This means, for instance, that there is an attraction be-
     tween the Earth and the Sun, and also between the Earth
     and the Moon, and between the Earth and each of the
     various planets and, for that matter, between the Earth
     and any meteorite or piece of cosmic dust in the heavens.
       Fortunately, the Sun is so overwhelmingly massive corn-
     'Pared with everything else in the Solar System that in
     calculating the orbit of the Earth, or of any other planet,
     an excellent first approximation is attained if only the
     planet and the Sun are considered, as though they were
     alone in the Universe.  The effect of other bodies can be
     calculated later for relatively minor refinements.
       In the same way, the orbit of a satellite can be worked
     out first by supposing that it is alone in the Universe with
     its primary.
       It is at this point that something interests me.  If the Sun
     is so much more massive than any planet, shouldwt it
     exert a considerable attraction on the satellite even though
     it is at a much greater distance from that satellite than the
     primary is?  If so, just how considerable is "considerable"?
       To put it another way, suppose we picture a tug of war
     going on for each satellite, with its planet on one side of
     the gravitational rope and the Sun on the other.  In this tug
     of war, how well is the Sun doing?
       I suppose astronomers have calculated such things, but
     I have never seen the results reported in any astronomy
     text, or the subject even discussed, so I'll de it for myself.
       Here's how we can go about it.  Let us call the mass of a
     satellite m, the mass of its primary (by which, by the way,
     I mean the planet it circles) m,, and the mass of the
     Sun m.. The distance from the satellite to its primary will
     be d, and the distance from the satellite to the Sun will be
     d.. The gravitational force between the satellite and its
     primary would be J, and that between the satellite and the
     Sun would be fg-and that's the whole business.  I promise
     to use no other symbols in this chapter.
       From Equation 1, we can say that the force of attraction
     between a satellite and its primary would be:
                                   88

                    fp = gmmp               (Equation 2)

       while that between the same satellite and the Sun would
       be:

                         gmm
                    f,, = ds2               (Equation 3)

          What we are interested in is how the gravitational force
       between satellite and primary compares with that between
       satellite and Sun.  In other words we want the ratio
       which we can call the "tug-of-war value." To get that we
       must divide equation 2 by equation 3. The result of such
       a division would be:

              fl,/f. = (M,/M.) (d./d,) 2        (Equation 4)

          In making the division, a number of simplications have
       taken place.  For one thing the gravitational constant has
       dropped out, which means we won't have to bother with
       an inconveniently small number and some inconvenient
       units.  For another, the mass of the satellite has dropped
       out. (In other words, in obtaining the tug-of-war value,
       it doesn't matter how big or little a particular satellite is.
       The result would be the same in any case.)
          What we need for the tug-of-war value                is the
       ratio of the mass of the planet to that of the sun (mlm,,)
       and the square of the ratio of the distance from satellite
       to Sun to the distance from satellite to primary (dld,)2.
          There are only six planets that have satellites and these,
       in order of decreasing distance from the Sun, -are: Nep-
       tune, Uranus, Saturn, Jupiter, Mars, and Earth. (I place
       Earth at the end, instead of at the beginning, as natural
       chauvinism would dictate, for my own reasons.  YouR find
       out.)
          For these, we will first calculate the mass-ratio and the
       results turn out as follows:
                                     89

                 Neptune                   0.000052
                 Uranus                    0.000044
                 Saturn                    0.00028
                 Jupiter                   0.00095
                 Mars                      0.00000033
                 Earth                     0.0000030

      As you see, the mass ratio is really heavily in favor of
   the Sun.  Even Jupiter, which is by far the most massive
   planet, is not quite one-thousandth as massive as the Sun.
   In fact, all the planets together (plus satellites, planetoids,
   comets, and meteoric matter) make up, no more than
   1/750 of the mass of the Sun.
      So far, then, the tug of war is all on the side of the Sun.
      However, we must next get the distance ratio, and that
   favors the planet heavily, for each satellite is, of course,
   far closer to its primary than it is to the Sun.  And what's
   more, this favorable (for the planet) ratio must be squared,
   making it even more favorable, so that in the end we can
   be reasonably sure that the Sun will lose out in the tug of
   war.  But we'll check, anyway.

      Let's take Neptune first.  It has two satellites, Triton and
   Nereid.  The average distance of each of these from the
   Sun is, of necessity, precisely the same as the average dis-
   tance of Neptune from the Sun, which is 2,797,000,000
   miles.  The average distance of Triton from Neptune is,
   however only 220,000 miles, while the average distance
   of Nerei@ from Neptune is 3,460,000 miles.
      If we divide the distance from the Sun by the distance
   frbm Neptune for each satellite and square the result we
   get 162,000,000 for Triton and 655,000 for Nereid.  We
   multiply each of these figures by the mass-ratio of Neptune
   to the Sun, and that gives us the tug-of-war value, which
   is:

                       Triton              8400
                       Nereid                34

      The conditions differ    markedly    for the two satellites.
   The gravitational influence of Neptune on its nearer satel-
   lite, Triton, is overwhelmingly greater than the influence
                                  90

       of the Sun on the same satellite.  Triton is @y in Nep-
       tune's grip.  The outer satellite, Nereid, however, is at-
       tracted by Neptune considerably, but not overwhelmingly,
       more strongly than by the Sun.  Furthermore, Nereid has
       a highly eccentric orbit, the most eccentric of any satellite
       in the system.  It approaches to within 800,000 miles of
       Neptune at one end of its orbit and recedes to as far as 6
       million miles at the other end.  When most distant from
       Neptune, Nereid experiences a tug-of-war value as low as

         For a variety of reasons (the eccentricity of Nereid's
       orbit, for one thing) astronomers generally suppose that
       Nereid is not a true satellite of Neptune, but a planetoid
       captured by Neptm on the occasion of a too-close ap,-
       proach.
         Neptune's weak hold on Nereid certainly seems to sup-
       port this.  In fact, from the long astronomic view, the asso-
       ciation between Neptune and Nereid may be a temporary
       one.  Perhaps the disturbing effect of the solar pull will
       eventually snatch it out of Neptune's grip.  Triton, on the
       other hand, will never leave Neptune's company short of
       some catastrophe on tL System-wide scale.

         There's no point in going through all the details of the
       calculations for all the satellites.  I'll do the work on my
       own and feed you the results.  Uranus, for instance, has
       five known satellites, all revolving in the plane of Uranus's
       equator and all considered true satellites by astronomers.
       Reading outward from the planet, they are: Miranda,
       Ariel, UmbrieL Titania, and Oberon.
         The tug-of-war values for these satellites are:

                       Miranda               24,600
                       Ariel                  9850
                       Umbriel                4750
                       Titania                1750
                       Oberon                 1050

       All are safely and overwhelming in Uranus's grip, and
       the high of-war values fit Vith their status as true
       satellites.
                                    91

                  I
      We pass on, then, to Saturn, which has nine satellites:
   Mimas, Enceladus, Tethys, Dione, Rhea, Titan, Hyperion,
   ,Iapetus, and Phoebe.  Of these, the eight innermost revolve
   in the plane of Satum's equator and are considered true
   satellites.  Phoebe, the ninth, has a highly inclined orbit and
   is considered a captured planetoid.
      The tug-of-war values for these satellites   are:

                    Mimas 1                 15,500
                    Enceladus                9800
                    Tethys                   6400
                    Dione                    4150
                    Rhea                     2000
                    Titan                     380
                    Hyperion                  260
                    Iapetus                     45
                    Phoebe                      31/2

   Note the low value for Phoebe.

      Jupiter has twelve satellites and I'll take them in two
   installments.  The first five: Amaltheia, lo, Europa, Gany-
   mede, and Callisto all revolve in the plane of Jupiter's
   equator and all are considered true satellites.  The tug-o&
   war values for   these are:

                    Amaltheia               18,200
                    lo                       3260
                    Europa                   1260
                    Ganymede                  490
                    Callisto                  160

   and all are clearly in Jupiter's grip.
      Jupiter, however, has seven more satellites which have
   no official names (see Chapter 5), and which are com-
   monly known by Roman numerals (from VI to XII) given
   in the order of their discovery.  In order of distance from
   Jupiter, they are VI  'X, VII, XII, XI, VIII, and IX. All
   are small and with orbits that are eccentric and highly
                                 92

       inclined to the plane of Jupitet's equator.  Astronomers
       consider them captured planetoids. (Jupiter is far more
       massive than the other planets and is nearer the planetoid
       belt, so it is not surprising that it would capture seven
       planetoids.)
         The tug-of-war results for these seven certainly bear
       out the captured planetoid notion, for the values are:

                             VI               4.4
                             x                4.3
                             vii              4.2
                             xii              1.3
                             xi               1.2
                             Vill             1.03
                             ix               1.03

       Jupitees grip on these outer satellites is feeble indeed.
         Mars has two satellites, Phobos and Deimos, each tiny
       and very close to Mars.  They rotate in the plane of Mars's
       equator, and are considered true satellites.  The tug-of-war
       values are:

                           Phobos              195
                           Deimos               32

         So far I have fisted 30 satellites,  of which 21 are con-
       sidered true satellites and 9 are usually tabbed as (prob-
       ably) captured planetoids.  I would like, for the moment,
       to leave out of consideration the 31st satellite, which hap-
       pens to be our own Moon (I'll get back to it, I promise)
       and summarize the 30 as follows:

                                     Number of Satellites
                   Planet             true        captured
                  Neptune               I             I
                  Uranus                5             0
                  Saturn                8             1
                  Jupiter               5             7
                  Mars                  2             0
                                      93

      It is unlikely that any additional true satellites will be
    discovered (though, to be sure, Miranda was discovered
    as recently as 1948).  However, any number of tiny bodies
    coming under the classification of captured planetoids may
    yet tum up, particularly once we go out there and actually
    look.
      But now let's analyze this list in terms of tug-of-war
    values.  Among the true satellites the lowest tug-of-war
    value is that of Deimos, 32.  On the other hand, among
    the nine satellites listed as captured, the highest tug-of-war
    value is that of Nereid with an average of 34.
      Let us accept this state of affairs and assume that the
    tug-of-war figure 30 is a reasonable mibimum for a true
    satellite and that any satellite with a lower figure is, in all
    likelihood, a captured and probably temporary member of
    the planet's family.
      Knowing the mass of a planet and its distance from the
    Sun, we can calculate the distance from the planet's center
    at which this tug-of-war value will be found.  We can use
    Equation 4 for the purpose, setting flf, equal to 30, put-
    ting in the known values for m,, m,, and d,, and then
    solving for d,.  That will be the maximum distance at
    which we can expect to find a true satellite.  The only
    planet that can't be handled in this way is Pluto, for which
    the value of m, is very uncertain, but I omit Pluto cheer-
    fully.
      We can also set a minimum distance at which we can
    expect a true satellite; or, at least, a true satellite in the
    usual form.  It has been calculated that if a true satellite is
    closer to its primary than a certain distance, tidal forces
    will break it up into fragments.  Conversely, if fragments
    already exist at such a distance, they will not coalesce into
    a single body.  This limit of distance is called the "Roche
    limit" and is named for the astronomer E. Roche, who
    worked it out in 1849.  The Roche limit is a distance from
    a planetary center equal to 2.44 times the planet's radius.

      So'  sparing you the actual calculations, here are the
    results for the four outer planets:
                                  94

                                    Distance of True Satellite
                            (miles from the center of the primary)
             Planet              maximum                  minimum
                            (tug-of-war = 30)         (Roche limit)
           Neptune               3,700,000                  38,000
           Uranus                2,200,000                  39,000
           Saturn                2,700,000                  87,000
           Jupiter               2,700,000                106,000

           As you see, each      of these   outer planets, with     huge
        masses and far distant from the competing Sun, has ample
        room for large and complicated satellite systems within
        these generous limits, and the 21 true satellites all fall
        within them.
           Saturn does possess something within Roche's limit-its
        ring system.  The outermost edge of the ring system
        stretches out to a distance of 85,000 miles from the
        planet's center.  Obviously the material in the rings could
        have been collected into a true satellite if it had not been
        so near Saturn.
           The ring system is unique as far as visible planets are
        concerned, but of course the only planets we can see are
        those of our own Solar System.  Even of these, the only
        ones we can reasonably consider in connection with satel-
        lites (I'll explain why in a moment) are the four large
        ones.
           Of these, Saturn has a ring system and Jupiter just
        barely misses one.  Its innermost satellite, Amaltheia, is
        about 110,000 miles from the planet's center, with the
        Roche limit at 106,000 miles.  A few thousand miles in-
        ward and Jupiter would have rings.  I would like to make
        the suggestion therefore that once we reach outward to
        explore other stellar systems we will discover (probably to
        our initial amazement) that about half the large planets
        we find will be equipped with rings after the fashion of
        Saturn.

           Next we can try to do the same thing for the inner
        planets.  Since the inner planets are, one and all, much less
                                        95

  massive than the outer ones and much closer to the com-
  peting Sun, we might guess that the range of distances
  open to true satellite formation would be more limited,
  and we would be right.  Here are the actual figures as I
  have calculated them.

                          Distance of True Satellite
                     (miles from the center of the primary)
       Planet           maximum                 minimum
                    (tug-of-war = 30)        (Roche limit)
      Mars                15,000                  5150
      Earth               29,000                  9600
      Venus               19,000                  9200
      Mercury                1300                 3800

     Thus, you see, where each    of the outer planets has a
  range of two million miles or more within which true satel-
  lites could form, the situation is far more restricted for
  the inner planets.  Mars and Venus have a permissible
  range of but 10,000 miles.  Earth does a little better, with
  20,000 miles.
     Mercury is the most interesting case.  The maximum dis-
  tance at which it can expect to form a natural satellite
  against the overwhelming competition of the nearby Sun
  is well within the Roche limit.  It follows from that, if my
  reasomng is correct, that Mercury cannot have a true satel-
  lite, and that anything more than a possible spattering of
  gravel is not to be expected.
     In actual truth, no satellite has been located for Mercury
  but, as far as I know, nobody has endeavored to present
  a reason for, this or treat it as anything other than an
  empirical fact.  If any Gentle Reader, with a greater knowl-
  edge of astronomic detail than myself, will write to tell me
  that I have been anticipated in this, and by whom, I Will
  try to take the news philosophically.  At the very least, I
  will confine my kicking and screaming to the privacy of
  my study.
     Venus, Earth, 'and Mars are better off than Mercury
  and do have a little room for true satellites beyond the
  Roche limit.  It is not much room, however, and the
                               96

       chances of gathering enough material over so small a
       volume of space to make anything but a very tiny satellite
       is minute.
         And, as it happens, neither Venus nor Earth has any
       satellite at all (barring possible minute chunks of gravel)
       within the indicated limits, and Mars has two small satel-
       .Iites, one perhaps 12 miles across and the other 6, which
       scarcely deserve the name.
         It is amazing, and very gratifying to me, to note how all
       this makes such delightful sense, and how well I can reason
       out the details of the satellite systems of the various
       planets.  It is such a shame that one small thing remains
       unaccounted for; one trifling thing I have ignored so far,
       but-
         WHAT IN BLAZES IS OUR OWN MOON DOING
       WAY OUT THERE?
         It's too far out to be a true satellite of the Earth, if we
       go by my beautiful chain of reasoning-which is too beau-
       tiful for me to abandon.  It's too big to have been cap-
       tured by the Earth.  The chances of such a capture having
       been effected and the Moon then having taken up a nearly
       circular orbit about the Earth are too small to make such
       an eventuality credible.
         There are theories, of course, to the effect that the
       Moon was once much closer to the Earth (within my per-
       mitted limits for a true satellite) and then gradually moved
       away as a result of tidal action.  Well, I have an objection
       to that.  If the Moon were a true satellite that originally
       had circled Earth at a distance of, say, 20,000 miles, it
       would almost certainly be orbiting in the plane of Earth's
       equator and it isn't.
         But, then, if the Moon is neither a true satellite of the
       Earth nor a captured one, what is it?  This may surprise
       you, but I have an answer; and to explain what that an-
       swer is, let's get back to my tug-of-war determinations.
       There is, after all, one satellite for which I have not cal-
       culated it, and that is our Moon.  We'll do that now.

         The average distance of the Moon from the Earth is
       237,000 miles, and the average distance of the Moon from
                                     97

   the Sun is 93,000,000 miles.  The ratio of the Moon-Sun
   distance to the Moon-Earth distance is 392.  Squaring that
   gives us 154,000.  The ratio of the mass of the Earth to
   that of the Sun was given earlier in the chapter and is
   0.0000030. Multiplying this figure by 154,000 gives us
   the tug-of-war value, which comes out to:

                       Moon              0.46

      The Moon, in other words, is unique among the satel-
   lites of the Solar System in that its primary (us) loses the
   tug of war with the Sun.  The Sun attracts the Moon twice
   as strongly as the Earth does.
      We might look upon the Moon, then, as neither a true
   satellite of the Earth nor a captured one, but as a planet
   in its own right, moving about the Sun in careful step with
   the Earth.  To be sure, from within the Earth-Moon sys-
   tem, the simplest way of picturing the situation is to have
   the Moon revolve about the Earth; but if you were to
   draw a picture of the orbits of the Earth and Moon about
   the Sun exactly to scale, you would see that the Moon's
   orbit is everywhere concave toward the Sun.  It is always
   "falling" toward the Sun.  All the other satellites, without
   exception, "fall" away from the Sun through part of their
   orbits, caught as they are by the superior puR of their
   pri.rnary-but not the Moon.
      And consider this-the Moon does not revolve about
   the Earth in the plane of Earth's equator, as would be ex-
   pected of a true satellite.  Rather it revolves about the Earth
   in a plane quite close to that of the ecliptic; that is, to
   the plane in which the planets, generally, rotate about the
   Sun.  This is just what would be expected of a planet!
      Is it possible then, that there is an intermediate point
   between the situation of a massive planet far distant from
   the Sun, which, develops about a single core, with numer-
   ous satellites formed, and that of a small planet near the
   Sun which develops about a single core with no satellites?
   Can there be a boundary condition, so to speak, in which
   there is condensation about two major cores so that a
   double planet is formed?
                                 98

        Maybe Earth just hit the edge of the permissible mass
     and distance; a little too small, a little too close.  Perhaps
     if it were better situated the two halves of the double
     planct would have been more of a size.  Perhaps both might
     have bad atmospheres and oceans and-life.  Perhaps in
     other stellar systems with a double planet, a greater equal-
     ity is more usual.
        What a shame if we have missed that
        Or, maybe (who knows), what luck!

                                  99

                   8. FIRST AND REARMOST

     When I was in junior high school I used to amuse myself
     by swinging on the rings in gym. (I was lighter then, and
     more foolhardy.) On one occasion I grew weary of the
     exercise, so at the end of one swing I let go.
        It was my feeling at the time, as I distinctly remember,
     that I would continue my semicircular path and go swoop-
     ing upward until gravity took hold; and that I would then
     come down light as gossamer, landing on my toes after a
     perfect entrechat.
        That is not the way it happened.  My path followed
     nearly a straight line, tangent to the semicircle of swing
     at the point at which I let go.  I landed good and hard on
     one side..
        After my head cleared, I stood up* and to this day that
     is the hardest fall I have ever taken.
        I might have drawn a great deal of intellectual good out
     of this incident.  I might have pondered on the effects of
     inertia; puzzled out methods of sumn-ting vectors; or de-
     duced some facts about differential calculus.
        However, I will be frank with you.  What really im-
     pressed itself upon me was the fact that the force of gravity
     was both mighty and dangerous and that if you weren't
     watching every minute, it would clobber you.
        Presumably, I had learned that, somewhat less dras-
     tically, early in life; and presumably, every human being
     who ever got onto his hind legs at the age of a year or less
     and promptly toppled, learned the same fact.
        In fact, I have been told that infants have an instinctive
         People react oddly.  After I stood up, I completely ignored my
     badly sprained (and possibly broken, though it later turned out
     not to be) right wrist imd lifted my untouched left wrist to my ear.
     What worried me was whether my wristwatch were still running.
                                    100

      fear of falling, and that this arose out of the survival value
      of having such an instinctive fear during the tree-living
      aeons of our simian ancestry.
         We can say, then, that gravitational force is the first
      force with which each individual human being comes in
      contact.  Nor can we ever manage to forget its existenc6,
      since it must be battled at every step, breath, and heart-
      beat.  Never for one moment must we cease exerting a
      counterforce.
         It is also comforting that this mighty and overwhelming
      force protects us at all times.  It holds us to our planet and
      doesn't allow us to shoot off into space.  It holds our air
      and water to the planet too, for our perpetual use.  And it
      holds the Earth itself in its orbit about the Sun, so
      that we always get the light and warmth we need.

         What with all this, it generally comes as a rather sur-
      prising shock to many people to learn that gravitation is
      not the strongest force in the universe.  Suppose, for in-
      stance, we compare it with the electromagnetic force that
      allows a magnet to attract iron or a proton to attract an
      electron. (The electromagnetic force also exhibits repul-
      sion, which gravitational force does not, but that is a detail
      that need not distress us at this moment.)
         How can we go about comparing the relative strengths
      of the electromagnetic force and the gravitational force?
       . Let's begin by considering two objects alone in the uni-
      verse.  The gravitational force between them, as was dis-
      covered by Newton, can be expressed by the following
      equation (see also Chapter 7):

                       Gmr&
                  Fg =                    (Equation 1)
                         d2

      where F, is the gravitational force between the objects; m
      is the mass of one object; the mass of the other; d the
      distance between them; and G a universal "gravitational
      constant."
         We must be careful about our units of measurement.  If
      we measure mass in grams, distance in centimeters, and
                                   101

     G in somewhat more complicated units, we will end up
     by determining the gravitational force in something called
     "dynes." (Before I'm through this chapter, the dynes will
     cancel out, so we need not, for present purposes, consider
     the dyne anything more than a one-syllable noise.  It will
     be explained, however, in Chapter 13.)
       Now let's get to work.  The value of G is fixed (as far
     ,as we know) everywhere in the universe.  Its value in the
     units I am using is 6.67 x 10-8.  If you prefer long zero-
     riddled decimals to exponential figures, you can express
     G as 0.0000000667.
       Let's suppose, next, that we are considering two objects
     of identical mass.  This means that m = m'. so that mm'
     becomes mm, or M2. Furthermore, let's suppose the parti-
     cles to be exactly I centimeter apart, center to center.  In
     that case d = 1, and d2 = 1 also.  Therefore, Equation 1
     simplifies to the following:

             F, = 0.0000000667 m2           (Equation 2)

       We can now proceed to the electromagnetic force,
     which we can symbolize as F,.
       Exactly one hundred years after Newton worked out the
     equation for gravitational forces, the French physicist
     Charles Augustin de Coulomb (1736-1806) was able'to
     show that a very similar equation could be used to deter-
     mine the electromagnetic force between two electrically
     charged objects.
     - Let us suppose, then, that the two objects for which we
     have been trying to calculate gravitational forces also carry
     electric charges, so that they also experience an electro-
     magnetic force.  In order to make sure that the electromag-
     netic force is an attracting one and is therefore directly
     comparable to the gravitational force, let us suppose that
     one object carries a positive electric charge and the other
     a negative one. (The principle would remain even if we
     used like electric charges and measured the force of clec-
     tromagnetic repulsion, but why introduce distractions?)
       According to Coulomb, the electromagnetic force be-
                                 102

     tween the two objects would be expressed by the foflo '
                                                                   wmg
     equation:

                   F.                     (Equation 3)
                         d2

     where q is the charge on one object, q' on the other, and
     d is the distance between them.
       If we let distance be measured in centimeters and elec-
     tric charge in units called "electrostatic units" (usually

     abbreviated "esu7'), it is not necessary to insert a term
     analogous to the gravitational constant, provided the ob-
     jects are separated by a vacuum.  And, of course, since I
     started by assuming the objects were alone in the universe,
     there is necessarily a vacuunf between them.
       Furthermore, if we use the units just mentioned, the
     value of the electromagnetic force will come out in dynes.
       But lefs simplify matters by supposing that the positive
     electric charge on one object is exactly equal to the nega-
     tive electric charge on the other, so that q = q,* which
     means that                                            the objects
                . qq = qq = q2. Again, we can allow
     to be separated by just one centimeter, center to center, so
     that d2 = 1. Consequently, Equation 3 becomes:

                   Fe = q2                (Equation 4)

       Let's summarize.  We have two objects separated by one
     centimeter, center to center, each object possessing identi-
     cal charge (positive in one case and negative in the other)
     and identical mass (no qualifications).  There is both a
     gravitational and an electromagnetic attraction, between
     them.

       The next problem is to determine how much stronger
     the electromagnetic force is than the gravitational force
     (or how much weaker, if that is how it turns out).  To do

       * We could make one of them negative to allow for the fact
     that one object carries a negative electric charge.  Then we could
     say that a negative value for- the electromagnetic force implies an
     attraction and a positive value a repulsion.  However, for our pur-
     poses, none of this folderol is needed.  Since electromagnetic at-
     traction and repulsion are but opposite manifestations of the same
     phenomenon, we shall ignore signs.

                                    103

      this we must determine the ratio of the forces by dividing
      (let us say) Equation 4 by Equation 2. The result is:

              F,            q2                (Equation 5)
              F,    0.0000000667 M2

         A decimal is an inconvenient thing to have in a denomi-
      nator, but we can move it up into the numerator by taking
      its reciprocal (that is, by dividing it into 1 ). Since 1 di-
      vided by 0.0000000667 is equal to 1.5 x 101, or 15,000,-
      000, we can rewrite Equation 5 as:

               F, _ 15,000,000 q2           (Equation 6)
               Fg         m2

      or, still more simply, as:

              F,. = 15,000,000 (VM)2          (Equat;on 7)
              F.

         Since both F, and F, are measured in dynes, then in
      taking the ratio we find we are dividing dynes by dynes.
      The units, therefore, cancel out, and we are left with a
      "pure number." We are going to find, in other words, that
      one force is stronger than the other by a fixed amount;
      an amount that will be the same whatever units we use or
      whatever units an intelligent entity on the fifth planet of
      the star Fomalhaut wants to use.  We will have, therefore,
      a universal constant.

         In order to determine the ratio 0 the two          es, we
      see from Equation 7 that we must first determine the
      value of qlm; that is, the charge of an object divided by
      its mass.  Let's consider charge first.
         AJI objects are made up of subatomic particles of a
      number of varieties.  These particles fall into exactly three
      classes, however, with respect to electric charge:
         1) Class A are those particles which, like the neutron
      and the neutrino, have no charge at all.  Their charge is 0.
         2) Class B are those particles which, like the proton
                                   104

   and the positron, carry a positive electric charge.  But all
   particles which carry a positive electric charge invariably
   carry the same quantity of positive electric charge what-
   ever their differences in other respects (at least as far as
   we know).  Their charge can therefore be specified as +I.
      3) Class C are those particles which, like the electron
   and the anti-proton, carry a negative electric charge.
   Again, this charge is always the same in quantity.  Their
   charge is - 1.
      You see, then, that an object of any size can have a
   net electric charge of zero, provided it happens to be made
   up of neutral particles and/or equal numbers of positive
   and negative particles.
      For such an object q   = 0, and no matter how large its
   mass, the value of qlm is also zero.  For such bodies,
   Equation 7 tells us, FIF, is zero.  The gravitational force
   is never zero (as long as the objects have any mass at all)
   and it is, therefore, under these conditions, infinitely
   stronger than the electromagnetic force and need be the
   only one considered.
      This is just about the case for actual bodies.  The over-
   all net charge of the Earth and the Sun is virtually zero,
   and in plotting the EartWs orbit it is only necessary to con-
   sider the gravitational attraction between the two bodies.
      Still, the case where F. = 0 and, therefore, FIF,, = 0
   is clearly only one extreme of the situation and not a par-
   ticularly interesting one.  What about the other extreme?
   Instead of an object with no charge, what about an object
   with maximum charge?
      If we are going to make charge maximum, let's first
   eliminate neutral particles which add mass without charge.
   Let's suppose, instead, that we have a piece of matter com-
   posed exclusively of charged particles.  Naturally it is of
   no use to include charged particles of both varieties, since
   then one " of charge would cancel the other and total
   charge would be less than maximum.
      We will want one object then, composed exclusively of
   positively charged particles- and another exclusively of
   negatively charged particles.  We can't possibly do better
   than that as a general thing.
                                 105

         And yet while all the charged particles have identical
       charges of either + 1 or - 1, as the case may be, they pos-
       sess different masses.  What we want are charged particles
       of, the smallest possible mass.  In that case the largest pos-
       sible individual charge is hung upon the smallest possible
       mass, and the ratio qlm is at a maximum.
         It so happens that the negatively charged particle of
       smallest mass is the electron and the positively charged
       particle of smallest mass is the positron.  For those bodies,
       the ratio qltn is greater than for any other known object
       (nor have we any reason, as yet, for suspecting that any
       object of higher qlm remains to be discovered).

         Suppose, then, we start with two bodies, one of which
       contains a certain number of electrons and the other the
       same number of positrons.  There will be a certain electro-
       magnetic force between them and also a certain gravi-
       tational force.
         If you triple the number of electrons in the first body
       and triple the number of positrons in the other, the total
       charge triples for each body and the total electromagnetic
       force, therefore, becomes 3 times 3, or 9 times greater.
       However, the total mass also triples for each bod and the
                                                          y
       total gravitational force also becomes 3 times 3, or 9 times
       greater.  While each force increases, they do so to an equal
       extent, and the ratio of the two remains the same.
         In fact the ratio of the two forces remains the same,
       even if the charge and/or mass on one body is not equal
       to the charge and/or mass on the other; or if the charge
       and/or mass of one body is changed by an amount different
       from the charge in the other.
         Since we are concerned only with the ratio of the two
       forces, the electromagnetic and the gravitational, and
       since this remains the same, however much the number of
       electrons in one body and the number of positrons in the
       other are changed, why bother with any but the simplest
       possible number-one?
         In other words, let's consider a Single electron and a
       simple positron separated by exactly I centimeter.  This
                                   106

      system will give us the maximum value'for the ratio of
      electromagnetic force to gravitational force.
        It so happens that the electron and the positron have
      equal masses. That mass, in grams (which        are the mass-
      units we are using in this calculation) is 9.1 X 10-28 or,
      if you prefer, 0.00000000000000000000000000091.
        The electric charge of the electron is equal to that of the
      positron (though different in sign).  In electrostatic units
      (the charge-units being used in this calculation), the value
      is 4.8 x 10-111, or 0.00000000048.
        To get the value qlm for the electron (or the positron)
      we must divide the charge by the mass.  If we divide
      4.8 x 10-10 by 9.1 X 10-28, we get the answer 5.3 x 1017
      or 530,000,000,000,000,000.
        But, as Equation 7 tells us, we must square the ratio
      qlm.  We multiply 5.3 x 1017 by itself and obtain for
      (qlm)2 the value of 2.8 x 101,1, or 280,000,000,000,000,-
      000,000,000,000,000,000,000.
        Again, consulting Equation 7, we find we must multiply
      this number by 15,000,000, and then we finally have the
      ratio we are looking for.  Carrying through this multiplica-
      tion gives us 4.2 x   1042, or 4,200,000,000,000,000,000,-
      000,000,000,000,000,000,000,000.
        We can come to the conclusion, then, that the electro-
      magnetic force is, under the most favorable conditions,
      over four million trillion trillion trillion times as strong as
      the gravitational force.
        To be sure, under normal conditions there are no elec-
      tron/positron systems in our surroundings, for positron
      virtually do not exist.  Instead our universe (as far as we
      know) is held together electromagnetically by electron/
      proton attractions.  The proton is 1836 times as massive as
      the electron, so that the gravitational attraction is increased
      without a concomitant increase in electromagnetic attrac-
      tion.  In this case the ratio F,IF, is only 2.3 x 10il".
        There are two other major forces in the physical world.
      There is the nuclear strong interaction force which is over
      a hundred times as strong as even the electromagnetic
      force; and the nuclear weak interaction force, which is
                                    107

     considerably weaker than the electromagnetic force.  All
     three, however, are far, far strcinger than the gravitational
     force.
       In fact, the force of gravity-though it is the first force
     with which we are acquainted, and though it is always
     with us, and though it is the one with a strength we most
     thoroughly appreciate-is by far the weakest known force
     in nature. It is first and rearmostl

       What makes the gravitational force seem so strong?
       First, the two nuclear forces ;ire short-range forces
     which make themselves felt only over distances about the
     width of an atomic nucleus.  The electromagnetic force and
     the gravitational force are the only two long-range forces.
     Of these, the electromagnetic force cancels itself out (with
     slight and temporary local exceptions) because both an
     attraction and a repulsion exist.
       This leaves gravitational force alone in the field.
       What's more, the most conspicuous bodies in the uni-
     verse happen to be conglomerations of vast mass, and we
     live on the surface of one of these conglomerations.
       Even so, there are hints that give away the real weak-
     ness of gravitational force.  Your weak muscle can lift a
     fifty-pound weight with the whole mass of the earth pull-
     ing, gravitationally, in the other direction.  A to magnet
                                                     I Y
     will lift a pin against the entire counterpufl of the earth.
       Oh, gravity is weak all right.  But let's see if we can
     dramatize that weakness further.
       Suppose that the Earth were an assemblage of nothing
     but its mass in positrons, while the Sun were an assem-
     blage of nothing but its mass in electrons.  The force of at-
     traction between them would be vastly greater than the
     feeble gravitational force that holds them together now.
     In fact, in order to reduce the electromagnetic attraction to
     no more than the present gravitational one, the Earth and
     Sun would have to be separated by some 33,000,000,000,-
     000,000 light-years, or about five million times the diame-
     ter of the known universe.
       Or suppose you imagined in the place of the Sun a mil-
                                 108

     lion tons of electrons (equal to the mass of a very small
     asteroid).  And in the place of the Earth, imagine 31/3 tons
     of positrons.
        The electromagnetic attraction between these two in-
     significant masses, separated by the distance from the
     Earth to the Sun, would be equal to the gravitational at-
     traction between the colossal masses of those two bodies
     right now.
        In fact, if one could scatter a million tons of electrons
     on the Sun, and 31/3 tons of positrons on the Earth, you
     would double the Sun's attraction for the Earth and alter
     the nature of Earth's orbit considerably.  And if you made
     it electrons, both on Sun and Earth, so as to introduce a
     repulsion, you would cancel the gravitational attraction al-
     together and send old Earth on its way out of the Solar
     System.
        Of course, all this is just paper calculation.  The mere
     fact that electromagnetic forces are as strong as they are
     means that you cannot collect a significant number of like-
     charged particles in one place.  They would repel each other
     too strongly.
        Suppose you divided the Sun into marble-sized fragments
     and strewed them through the Solar System at mutual rest.
     Could you, by some manmade device, keep those fragments
     from falling together under the pull of gravity?  Well, this
     is no greater a task than that of getting bold of a million
     tons of electrons and squeezing them together into a ball.
        The same would hold true if you tried to separate a
     sizable quantity of positive charge from a sizable quantity
     of negative charge.
        If the universe were composed of electrons and posi-
     trons as the chief charged particles, the electromagnetic
     force would make it necessary for them to come together.
     Since they are anti-particles, one being the precise reverse
     of the other, they would melt together, cancel each other,
     and go up in one cosmic flare of gamma rays.
        Fortunately, the universe is composed of electrons and
     protons as the chief charged particles.  Tbough their charges
     are exact opposites (-I for the former and +1 for the
                                  109

      latter), this is not so of other properties-such as mass,
      for instance.  Electrons and protons are not antiparticles,
      in other words, and cannot cancel each other.
         Their opposite charges, however, set up a strong mutual
      attraction that cannot, within limits, be gainsaid.  An elec-
      tron and ia proton therefore approach closely and then
      maintain themselves at a wary distance, forming the hy-
      drogen atom.
         Individual protons can cling together despite electro-
      magnetic repulsion because of the existence of a very
      short-range nuclear strong interaction force that sets up
      an attraction between neighboring protons that far over-
      balances the electromagnetic repulsion.  This makes atoms
      other than hydrogen possible.
         In short: nuclear forces dominate the atomic nucleus;
      electromagnetic forces dominate the atom itself; and grav-
      itational forces dominate the large astronomic bodies.

         The weakness of the gravitational force is a source of
      frustration to physicists.
         The different forces, you see, make themselves felt by
      transfers of particles.  The nuclear strong interaction force,
      the strongest of all, makes itself evident by transfers of
      pions (pi-mesons), while the electromagnetic force (next
      strongest) does it by the transfer of photons.  An analogous
      particle involved in weak interactions (third strongest) has
      recently been reported.  It is called the "W particle" and
      as yet the report is a tentative one.
         So far, so good.  It seems, then, that if gravitation is a
      force in the same sense that the others are, it should make
      itself evident by transfers of particles.
         Physicists have given this particle a name, the "graviton."
      They have even decided on its properties, or lack of prop-
      erties.  It is electrically neutral and without mass. (Because
      it is without mass, it must travel at an unvarying velocity,
      that of light.) It is stable, too; that is, left to itself, it Will
      not break down to form other particles.
         So far, it is rather like the neutrino,* which is also stable,

         * See Chapter 13 of my book View from a Height, Doubleday,
      1963.
                                     110

    electrically neutral, and massless (hence traveling at the
    velocity of light).
       The graviton and the neutrino differ in some respects,
    however.  The neutrino comes in two varieties, an electron
    neutrino and a muon (mu-meson) neutrino, each with its
    anti-particle; so there are, all told, four distinct kinds of
    neutrinos.  The graviton comes in but one variety and is
    its own anti-particle.  There is but one kind of graviton.
       Then, too, the graviton has a spin of a type that is as-
    signed the number 2, while the neutrino along with most
    other subatomic particles have spins of 1/2. (There are also
    some mesons with a spin of 0 and the photon with a spin
    of 1. )
       The graviton has not yet been detected.  It is even more
    elusive than the neutrino.  The neutrino, while massless
    and chargeless, nevertheless has a measurable energy con-
    tent. Its existence was first suspected,   indeed, because it
    carried off enough energy to make a sizable gap in the
    bookkeeping.
       But gravitons?
       Well, remember that factor of 10421
       An individual graviton must be trillions of trillions of
    trillions of times less energetic than a neutrino.  Considering
    how difficult it was to detect the neutrino, the detection of
    the graviton is a problem that will really test the nuclear
    physicist.

                   9. THE BLACK- OF NIGHT

      I suppose many of you are familiar with the comic strip
      "Peanuts." My daughter Robyn (now in the fourth grade)
      is very fond of it, as I am myself.
         She came to me one day, delighted with a particular
      sequence in which one of the little characters in "Peanuts"
      asks his bad-tempered older sister, "Why is the sky blue,?"
      and she snaps back, "Because it isn't green!"
         When Robyn was all through laughing, I thought I would
      seize the occasion to maneuver the conversation in the
      direction of a deep and subtle scientific discussion (entirely
      for Robyn's own good, you understand).  So I said, "Wen,
      tell me, Robyn, why is the night sky black?"
         And she answered at once (I suppose I ought to have
      foreseen it), "Because it isn't purple!"
         Fortunately, nothing like this can ever seriously frustrate
      me. If Robyn won't cooperate, I can always turn, with a
      snarl, on the Helpless Reader.  I will discuss the blackness
      of the night sky with youl

         Ile story of the black of night begins with a German
      physician and astronomer, Heinrich Wilhelm Matthias
      Olbers, bom in 1758.  He practiced astronomy as a hobby,
      and in midlife suffered a peculiar disappointment.  It came
      about in this fashion . . .
         Toward the end of the eighteenth century, astronomers
      began to suspect, quite strongly, that some sort of planet
      must exist between the orbits of Mars and Jupiter.  A team
      of German astronomers, of whom Olbers was one of the
      most important, set themselves up with the intention of
      dividing the ecliptic among themselves and each searching
      his own portion, meticulously, for the planet.
         Olbers and his friends were so systematic and thorough
                                   112

      that by rights they should have discovered the planet and
      received the credit of it.  But life is funny (to coin a phrase).
      While they were still arranging the details, Giuseppe Piazzi,
      an Italian astronomer who wasn't looking for planets at
      all, discovered, on the night of January 1, 1801, a point of
      light which had shifted its position against the background
      of stars.  He followed it for a period of time and found it
      was continuing to move steadily.  It moved less rapidly than
      Mars and more rapidly than Jupiter, so it was very likely
      a planet in an intermediate orbit.  He reported it as such so
      :hat it was the casual Piazzi and not the thorough Olbers
      who got the nod in the history books.
        Olbers didn't lose out altogether, however.  It seems that
      after a period of time, Piazzi fell sick and was unable to
      continue his observations.  By the time he got back to the
      telescope the planet was too close to the Sun to be observ-
      able.
        Piazzi didn't have enough observations to calculate an
      orbit and this was bad.  It would take months for the
      slow-moving planet to get to the other side of the Sun and
      into observable position, and without a calculated orbit it
      might easily take years to rediscover it.
        Fortunately, a young German mathematician, Karl
      Friedrich Gauss, was just blazing his way upward into the
      mathematical firmament.  He had worked out something
      called the "method of least squares," which made it possible
      to calculate a reasonably good orbit from no more than
      three good observations of a planetary position.
        Gauss calculated the orbit of Piazzi's new planet, and
      when it was in observable range once more there was Olbers
      and his telescope watching the place where Gauss's calcula-
      tions said it would be.  Gauss was right and, on January 1,
      1802, Olbers found it.
        To be sure, the new planet (named "Ceres") was a
      peculiar one, for it turned out to be less than 500 miles in
      diameter.  It was far smaller than any other known planet
      and smaller than at least six of the satellites known at that
      time.
        Could Ceres be all that existed between Mars and
      Jupiter?  The German astronomers continued looking (it
                                    113

      would be a shame to waste all that preparation) and sure
      enough, three more planets between Mars and Jupiter were
      soon discovered.  Two of them, Pallas and Vesta, were dis-
      covered by Olbers. (In later years many more were
      discovered.)
         But, of course, the big payoff isn't for second place.  All
      Olbers got out of it was the name of a planetoid.  The thou-
      sandth planetoid between Mars and Jupiter was named
      "Piazzia," the thousand and first "Gaussia," and the thou-
      sand and second (hold your breath, now) "Olberia."
         Nor was Olbers much luckier in his other observations.
      He specialized in comets and discovered five of them, but
      practically anyone can do that.  There is a comet called
      "Olbers' Comet" in consequence, but that is a minor dis-
      tinction.
         Shall we now dismiss Olbers?  By no means.
         It is hard to tell just what will win you a place in the
      annals of science.  Sometimes it is a piece of interesting
      reverie that does it.  In 1826 Olbers indulged himself in an
      idle speculation concerning the black of night and dredged
      out of it an'apparently ridiculous conclusion.
         Yet that speculation became "Olbers' paradox," which
      has come to have profound significance a century after-
      ward.  In fact, we can begin with Olbers' paradox and end
      with the conclusion that the only reason life exists any-
      where in the universe is that the distant galaxies are reced-
      ing from us.
         What possible effect can the distant galaxies have on us?
      Be patient now and we'll work it out.

         In ancient times, if any astronomer had been asked why
      the night sky was black, he would have answered-quite
      reasonably-that it was because the light of the Sun was
      absent.  If one had then gone on to question him why the
      stars did not take the place of the Sun, he would have
      answered-again reasonably-that the stars were limited
      in number and individually dim.  In fact, all the stars we
      can see would, if lumped together, be only a half-birionth
      as bright as the Sun.  Their influence on the blackness of
      the night sky is therefore insignificant.
                                   114

         By the nineteenth century, however, this last argument
      had lost its force.  The number of stars was tremendous.
      Large telescopes revealed them by the countless millions.
         Of course, one might argue that those countless millions
      of stars were of no importance for they were not visible to
      the naked eye and therefore did not contribute to the light
      in the night sky.  This, too, is a useless argument.  The stars
      of the Milky Way are, individually, too faint to be made
      out, but en masse they make a dimly luminous belt about
      the sky.  The Andromeda galaxy is much farther away than
      the stars of the Milky Way and the individual stars that
      make it up are not individually visible except (just barely)
      in a very large telescope.  Yet, en masse, the Andromeda
      galaxy is faintly visible to the naked eye. (It'is, in fact, the
      farthest object visible to the unaided eye; so if anyone ever
      asks you how far you can see; tell him 2,000,000 light-
      years.)
         In short distant stars-no matter how distant and no
      matter how dim, individually-must contribute to the light
      of the night sky, and this contribution can even become
      detectable without the aid of instruments if these dim
      distant stars exist in sufficient density.
         Olbers, who didn't know about the Andromeda galaxy,
      but did know about the Milky Way, therefore set about
      asking himself how much light ought to be expected from
      the distant stars altogether.  He began by making several
      assumptions:
         1. That the universe is infinite in extent.
         2. That the stars are infinite in number and evenly
      spread throughout the universe.
         3. That the stars are of uniform average brightness
      through all of space.
         Now let's imagine space divided up into shells (like
      those of an onion) centering about us, comparatively thin.
      shells compared with the vastness of space, but large
      enough to contain stars within them.
         Remember that the amount of light that reaches us from
      individual stars of equal luminosity varies inversely as the
      square of the distance from us.  In other words, if Star A
      and Star B are equally bright but Star A is three times as
                                     115

      far as Star B, Star A delivers only % the light.  If Star A
      were five times as far as Star B, Star A would deliver
      1/2r, the light, and so on.
        This holds for our shells.  The average star in a shell
      2000 light-years from us would be only 1/4 as bright in
      appearance as the average star in a shell only 1000 light-
      years from us. (Assumption 3 tells us, of course, that the
      intrinsic brightness of the average star in both shells is the
      same, so that distance is the only factor we need consider.)
      Again, the average star in a shell 3000 light-years from us
      would be only % as bright in appearance as the average
      star in the 10004ight-year shell, and so on.
        But as you work your way outward, each succeeding
      shell is more voluminous than the one before.  Since each
      shell is thin enough to be considered, without appreciable
      error, to be the surface of the sphere made up of all the
      shells within, we can see that the volume of the shells in-
      creases as the surface of the spheres would-that is, as
      the square of the radius.  The 2000-light-year shell would
      have four times the volume of the 1000-light-year shell.
      The 3000-light-year shell would have nine times the
      volume of the 1000-light-year shell, and so on.
        If we consider the stars to be evenly distributed through
      space (Assumption 2), then the number of stars in any
      given shell is proportional to the volume of the shell.  If
      the 2000-light-year shell is four times as voluminous as the
      1000-light-year shell, it contains four times as many stars.
      If the 3000-light-year shell is nine times as voluminous as
      the 1000-light-year shell, it contains nine times as many
      stars, and so on.
        Well, then, if the 2000-light-year shell contains four
    ,times as many stars as the IOOG-light-year shell, and if
      each star in the former is % as bright (on the average)
      as each star of the latter, then the total light delivered by
      the 20GO-light-year shell is 4 times Y4 that of the 1000-
      fight-year shell.  In other words, the 2000-light-year shell
      delivers just as much total light as the 1000-light-year
      shell.  The total brightness of the 3000-light-year shell is
      9 times % that of the 1000-light-year shell, and the bright-
      ness of the two shells is equal again.
                                  116

         In summary, if we divide the universe into successive
       shells, each shell delivers as much light, in toto, as do any
       of the others.  And if the universe is infinite in extent (As-
       sumption 1) and therefore consists of an finate number
       of shells, the stars of the universe, however dim they may
       be individually, ought to deliver an infinite amount of light
       to the Earth.
         The one catch, of course, is that the nearer stars may
       block the light of the more distant stars.
         To take this into account, let's look at the problem in
       another way.  In no matter which direction one looks, the
       eye will eventually encounter a star, if it is true they are
       infinite in number and evenly distributed in space (As-
       sumption 2).  The star may be individually invisible, but
       it will contribute its bit of light and will be immediately
       adjoined in all directions by other bits of light.
         The night sky would then not be black at all but would
       be I an absolutely solid smear of starlight.  So would the
       day sky be an absolutely solid smear of starlight, with the
       Sun itself invisible against the luminous background.
         Such a sky would be roughly as bright as 150,000 suns
       like ours, and do you question that under those conditions
       life on Earth would be impossible?
         However, the sky is not as bright as 150,000 suns.  The
       night sky is black.  Somewhere in the Olbers' paradox there
       is some mitigating circumstance or some logical error.       .

         Olbers himself thought he found it.  He suggested that
       space was not truly transparent; that it contained clouds of
       dust and gas which absorbed most of the starlight, allowing
       only an insignificant fraction to reach the Earth.
         That sounds good, but it is no good at all.  There are
       indeed dust clouds in space but if they absorbed all the
       starlight that fell upon them (by the reasoning of Olbers'
       paradox) then their temperature would go up until they
       grew hot enough to be luminous.  They would, eventually,
       emit as much light as they absorb and the Earth sky would
       still be star-bright over all its extent.
         But if the logic of an argument is faultless and the con-
       clusion is still wrong, we must investigate the assumptions.
                                    117

     What about Assumption 2, for instance?  Are the stars in-
     deed infinite in number and evenly spread throughout the
     universe?
       Even in Olbers' time there seemed reason to believe this
     assumption to be false.  The German-English astronomer
     William Herschel made counts of stars of different bright-
     ness.  He assumed that, on the average, the dimmer stars
     were more distant than the bright ones (which follows from
     Assumption 3) and found that the density of the stars in
     space fell off with distance.
       From the rate of decrease in density in different direc-
     tions, Herschel decided that the stars made up a lens-
     shaped figure.  The long diameter, he decided, was 150
     times the distance from the Sun to Arcturus (or 6000
     light-years, we would now say), and the whole conglomer-
     ation would consist of 100,000,000 stars.
       This seemed to dispose of Olbers' paradox.  If the lens-
     shaped conglomerate (now called the Galaxy) truly con-
     tained all the stars in existence, then Assumption 2 breaks
     down.  Even if we imagined space to be infinite in extent
     outside the Galaxy (Assumption 1), it would contain no
     stars and would contribute no illumination.  Consequently,
     there would be only a finite number of star-containing
     shells and only a finite (and not very large) amount of
     illumination would be received on Earth.  That would be
     why the night sky is black.
       The estimated size of the Galaxy has been increased
     since Herschel's day.  It is now believed to be 100,000
     light-years in diameter, not 6000; and to contain 150,000,-
     000,000 stars, not 100,000,000.  This change, however,
     is not crucial; it still leaves the night sky black.

       In the twentieth century Olbers' paradox came back to
     life, for it came to be appreciated that there were indeed
     stars outside the Galaxy.
       The foggy patch in Andromeda had been felt through-
     out the nineteenth century to be a luminous mist that
     formed part of our own Galaxy.  However, other such
     patches of mist (the Orion Nebula, for instance) contained
     stars that lit up the mist.  The Andromeda patch, on the
                                118

     other hand, seemed to contain no stars but to glow of
     itself.
        Some astronomers began to suspect the truth, but it
     wasn't definitely established until 1924, when the Amer-
     ican astronomer Edwin Powell Hubble turt'ied the 100-
     inch telescope on the glowing mist and was able to make
     out separate stars in its outskirts.  These stars were in-
     dividually so dim that it became clear at once that the
     patch must be hundreds of thousands of light-years away
     from us and far outside the Galaxy.  Furthermore, to be
     seen, as it was, at that distance, it must rival in size our
     entire Galaxy and be another galaxy in its own right.
        And so it is.  It is now believed to be over 2,000,000
     light-years from us and to contain at least 200,000,000,-
     000 stars.  Still other galaxies were discovered at vastly
     greater distances.  Indeed, we now suspect that within the
     observable universe there are at least 100,000,000,000
     galaxies, and the distance of some of them has been esti-
     mated as high as 6,000,000,000 light-years.
        Let us take Olbers' three assumptions then and substi-
     tute the word "galaxies" for "stars" and see how they
     sound.
        Assumption 1, that the universe is infinite, sounds good.
     At least there is no sign of an end even out to distances
     of billions of light-years.
        Assumption 2, that galaxies (not stars) are infinite in
     number and evenly spread throughout the universe,
     sounds good, too.  At least they are evenly distributed for
     as far out as we can see, and we can see pretty far.
        Assumption 3, that galaxies (not stars) are of uniform
     average brightness throughout space, is harder to handle.
     However, we have no reason to suspect,--6at distant
     galaxies are consistently larger or smaller than nearby
     ones, and if the galaxies come to some uniform average
     size and star-content, then it certainly seems reasonable
     to suppose they are uniformly bright as well.
        Well, then, why is the night sky black?  We're back to
     that.

        Let's try another tack.  Astronomers can determine
                                 119

       whether a distant luminous object is approaching us- or
       receding from us by studying its spectrum (that is, its lijzht
       as spread out in a rainbow of wavelengths from short-
       wavelength violet to long-wavelength red).
         The spectrum is crossed by dark lines which are in         a
       fixed position if the object is motionless with respect to
       us. If the object is approaching us, the lines shift toward
       the violet.  If the object is receding from us, the lines shift
       toward the red.  From the size of the shift astronomers can
       determine the velocity of approach or recession.
         In the 1910s and 1920s the spectra of some galaxies
       (or bodies later understood to be galaxies) were studied,
       and except for one or two of the very nearest, all are re-
       ceding from us.  In fact, it soon became apparent that the
       farther galaxies are receding more rapidly than the nearer
       ones.  Hubble was able to formulate what is now called
       "Hubble's Law" in 1929.  This states that the velocity of
       recession of a galaxy is proportional to its distance from
       us. If Galaxy A is twice as far as Ga  laxy D, it is receding
       at twice the velocity.  The farthest observed galaxy, 6,000,-
       000,000 light-years from us, is receding at a velocity half
       that of light.
         The reason for Hubble's Law is taken to lie in the ex-
       pansion of the universe itseff-an expansion which can be
       made to follow from the equations set up by Einstein's
       General Theory of Relativity (which, I hereby state firmly,
       I will not go into).
         Given the expansion of the universe, now, how are
       Olbers' assumptions affected?
         If, at a distance of 6,000,000,000 light-years a galaxy
       recedes at half the speed of light, then at a distance of
       12,000,000,000 light-years a galaxy ought to be receding
       at the speed of light (if Hubble's Law holds).  Surely,
       further distances are meaningless, for we cannot halve
       velocities greater than that of light.  Even if that were pos-
       sible, no light, or any other "message" could reach us from
       such a more-distant galaxy and it would not, in effect, be
       in our universe.  Consequently, we can imagine the universe
       to be finite after all, with a "Hubble radius" of some
       12,000,000,000 light-years.
                                    120

        But that doesn't wipe out Olbers' paradox.  Under the
     requirements of Einstein's theories, as galaxies move faster
     and faster relative to an observer, they become shorter
     and shorter in the line of travel and take up less and less
     space, so that there is room for larger and larger numbers
     of galaxies.  In fact, even in a finite universe, with a radius
     of 12,000,000,000 light-years, there might still be an in-
     finite number of galaxies; almost all of them (paper-thin)
     existing in the outermost few miles of the Universe-sphere.
        So Assumption 2 stands even if Assumption I does not;
     and Assumption 2, by itself, can be enough to insure a
     star-bright sky.
        But what about the red shift?
        Astronomers measure the red shift by the change in
     position of the spectral lines, but those lines move only
     because the entire spectrum moves.  A shift to the red is a
     shift in the direction of lesser energy.  A receding galaxy
     delivers less radiant energy to the Earth than the same
     galaxy would deliver if it were standing still relative to us
     -just because of the red shift.  The faster a galaxy recedes
     the less radiant energy it delivers.  A galaxy receding at the
     speed of light delivers no radiant energy at all no matter
     how bright it might be.
        Thus, Assumption 3 falls!  It would hold true if the uni-
     verse were static, but not if it is expanding.  Each succeed-
     ing shell in an expanding universe delivers less light than
     the one within because its content of galaxies is succes-
     sively farther from us; is subjected to a successively greater
     red shift; and falls short, more and more, of the expected
     radiant energy it might deliver.
        And because Assumption 3 fails, we receive only a finite
     amount of energy from the universe and the night sky is
     black.

        According to the most popular models of the universe,
     this expansion will always continue.  It may continue with-
     out the production of new galaxies so that, eventually,
     billions of years hence, our Galaxy (plus a few of its
     neighbors, which together make up the "local cluster" of
     galaxies) will seem alone in the universe.  AU the other
                                   121

      galaxies will have receded too far to detect.  Or new galaxies
      may continuously form so that, the universe will always
      seem full of galaxies, despite its expansion.  Either way,
      however, expansion will continue and the night sky will
      remain black.
         There is another suggestion, however, that the universe
      oscillates; that -the expansion will gradually slow down
      until the universe comes to a moment of static pause, then
      begins to contract again, faster and faster, till it tightens at
      last into a small sphere that explodes and brings about a
      new expansion.
         If so, then as the expansion slows the diinming effect of
      the red shift will diminish and the night sky will slowly
      brighten.  By the time the universe is static the sky will be
      uniformly star-brigbt as Olbers' paradox required.  Then,
      once the universe starts contracting, there will be a "violet-
      shift" and the energy delivered will increase so that the sky
      will become far brighter and still brighter.
         This will be true not only for the Earth (if it still existed
      in the far future of a contracting universe) but for any
      body of any sort in the universe.  In a static or, worse still,
      a contracting universe there could, by Olbers' paradox, be
      no cold bodies, no solid bodies.  There would be uniform
      high temperatures everywhere-in the millions of degrees,
      I suspect-and life simply could not exist.
         So I get back to my earlier statement.  The reason there
      is life on Earth, or anywhere in the universe, is simply
      that the'distant galaxies are moving away from us.
         In fact, now that we know the ins and outs of Olbers'
      paradox, might we, do you suppose, be able to work out
      the recession of the distant galaxies as a necessary conse-
      quence of the blackness of the night sky?  Maybe we could
      amend the famous statement of the French philosopher
      Ren6 Descartes.
         He said, "I think, therefore I am!"
         And we could add: "I am, therefore the universe ex-
      pandsl"

                                     122

                   10. A GALAXY AT A TIME

       Four or five'vears a2o there was a small fire at a school
       two blocks from my house.  It wasn't much of a fire, really,
       producing smoke and damaging some rooms in the base-
       ment, but nothing more.  What's more, it was outside
       school hours so that no lives were in danger.
         Nevertheless, as soon as the first piece of fire apparatus
       was on the scene the audience had begun to gather.  Every
       idiot in town and half the idiots from the various con-
       tiguous towns came racing down to see the fire.  They came
       by auto and by oxcart, on bicycle and on foot.  They came
       with girl friends on their arms, with aged parents on their
       shoulders, and with infants at the breast.
         They parked all the streets solid for miles around and
       after the first fire engine had come on the scene nothing
       more could have been added to it except by helicopter.
         Apparently this happens every time.  At every disaster,
       big or small, the two-legged ghouls gather and line up
       shoulder to shoulder and chest to back.  They do this, it
       seems, for two purposes: a) to stare goggle-eyed and
       slack-jawed at destruction and misery, and b) to prevent
       the approach of the proper authorities who are attempting
       to safeguard life and property.
         Naturally, I wasn't one of those who rushed to see the
       fire and I felt very self-righteously noble about it.  How-
       ever (since we are all friends), I will confess that this is
       not necessarily because I am free of the destructive in-
       stinct.  It's just that a messy little fire in a basement isn't
       my idea of destruction; or a good, roaring blaze at the
       munitions dump, either.
         If a star were to blow up, then we might have some-
       thing.
                                    123

       Come to think of it, my instinct for destruction must be
     well developed after all, or I wouldn't find myself so
     fascinated by the subject of supernovas, those colossal
     stellar explosions.
       Yet in thinking of them, I have, it turns out, been a
     piker.  Here I've been assuming for years that a supernova
     was the grandest spectacle the universe had to offer (pro-
     vided you were standing several dozen light-years away)
     but, thanks to certain 1963 findings, it turns out that a
     supemova taken by itself is not much more than a two-
     inch firecracker.
       This realization arose out of radio astronomy.  Since
     World War 11, astronomers have been picking up micro-
     wave (very short radio-wave) radiation from various parts
     of the sky, and have found that some of it comes from our
     own neighborhood.  The Sun itself is a radio source and so
     are Jupiter and Venus.
       The radio sources of the Solar System, however, are
     virtually insignificant.  We would never spot them if we
     weren't right here with them.  To pick up radio waves
     across the vastness of stellar distances we need something
     better.  For instance, one radio source from beyond the
     Solar System is the Crab Nebula.  Even after its radio
     waves have been diluted by spreading out for five thousand
     light-years before reaching us, we can still pick up what
     remams and impinges upon our instruments.  But then the
     Crab Nebula represents the remains of a supernova that
     blew itself to kingdom come-the first light of the explo-
     sion reaching the Earth about 900 years ago.
       But a great number of radio sources lie outside our
     Galaxy altogether and are millions and even billions of
     light-years distant.  Still their radio-wave emanations can be
     detected and so they must represent energy sources that
     shrink mere supemovas to virtually nothing.
       For instance, one particularly strong source turned out,
     on investigation, to arise from a galaxy 200,000,000 light-
     years away.  Once the large telescopes zeroed in on that
     galaxy it turned out to be distorted in shape.  After closer
     study it became quite clear that it was not a galaxy at all,
     but two galaxies in the process of collision.
                                 124

        When two galaxies collide like that, there is little likeli-
      hood of actual collisions between stars (which are too
      small and too widely spaced).  However, if the galaxies
      possess clouds of dust (and many galaxies, including our
      own, do), these clouds will collide and the turbulence of
      the collision will set up radio-wave emission, as does the
      turbulence (in order of decreasing intensity) of the gases
      of the Crab Nebula, of our Sun, of the atmosphere of
      Jupiter, and of the atmosphere of Venus.
        But as more and more radio sources were detected and
      pinpointed, the number found among the far-distant',ga-
      laxies seemed impossibly high.  There might be occasional
      collisions among galaxies but it seemed most unlikely that
      there could be enough collisions to account for all those
      radio sources.
        Was there any other possible explanation?  What was
      needed was some cataclysm just as vast and intense as
      that represented by a pair of colliding galaxies, but one
      that involved a single gallaxy.  Once freed from the neces-
      sity of supposing collisions we can explain any number of
      radio sources.
        But what can a single galaxy do alone, without the help
      of a sister galaxy?
        Well, it can explode.
        But how?  A galaxy isn't really a single object.  It is
      simply a loose aggregate of up to a couple of hundred
      billion stars.  These stars can explode individually, but how
      can we have an explosion of a whole galaxy at a time?

        To answer that, let's begin by understanding that a
      galaxy isn't really as loose an aggregation as we might tend
      to think.  A galaxy like our own may stretch out 100,000
      light-years in its longest diameter, but most of that consists
      of nothing more than a thin powdering of stars-thin
      enough to be ignored.  We happen to live in this thinly
      starred outskirt of our own Galaxy so we accept that as
      the norm, but it isn't.
        The nub of a galaxy is its nucleus, a dense packet of
      stars roughly spherical in shape and with a diameter of,
      say, 10,000 light-years.  Its volume is then 525,000,000,000
                                   125

      cubic light-years, and if it contains 100,000,000,000 stars,
      that means there is I star per 5.25 cubic light-years.
         With stars massed together like that, the average dis-
      tance between stars in the galactic nucleus is 1.7 light-years
      -but that's the average over the entire volume.  The den-
      sity of star numbers in such a nucleus increases as one
      moves toward the center, and I think it is entirely fair to
      expect that toward the center of the nucleus, stars are not
      separated by more than half a light-year.
         Even half a light-year is something like 3,000,000,000,-
      000 miles or 400 times the extreme width of Pluto's orbit,
      so that the stars aren't actually crowded, they're not likely
      to be colliding with each other, and yet . . .

         Now suppose that, somewhere in a galaxy, a supernova
      lets go.
         What happens?
         In most cases, nothing (except that one star is smashed
      to flinders).  If the supernova were in a galactic suburb-
      in our own neighborhood, for instance-the stars would
      be so thinly spread out that none of them would be near
      enough to pick up much in the way of radiation.  The in-
      credible quantities of energy poured out into space by such
      a supemova would simply spread and thin out and come
      to nothing.
         In the center of a galactic nucleus, the supernova is not
      quite as easy to dismiss.  A good supernova at its height is
      releasing energy at nearly 10,000,000,000 times the rate
      of our Sun.  An object five light-years away would pick up
      a tenth as much energy per second as the Earth picks up
      from the Sun.  At half a light-year from the supernova it
      would pick up ten times as much energy per second as
      Earth picks up from the Sun.
         This isn't good.  If a supernova let go five light-years
      from us we would have a year of bad heat problems.  If it
      were half a light-year away I suspect there would be little
      left of earthly life.  However, don't worry.  There is only
      one star-system within five light-years of us and it is not the
      kind that can go supemova.
                                    126

         But what about the effects on the stars themselves?  If
      our Sun were in the neighborhood of a supernova it would
      be subjected to a batb of energy and its own temperature
      would have to go up.  After the supernova is done, the Sun
      would seek its own equilibrium again and be as good as
      before (though life on its planets may not be).  However,
      in the process, it would have increased its fuel consump-
      tion in proportion to the fourth power of its absolute tem-
      perature.  Even a small rise in temperature might lead to a
      surprisingly large consumption of fuel.
         It is by fuel consumption that one measures a star's age.
      When the fuel supply shrinks low enough, the star expands
      into a red giant or explodes into a supernova.  A distant
      supenova by war@ng the Sun slightly for a year might
      cause it to move a century, or ten centuries closer to such
      a crisis.  Fortunately, our Sun has a long lifetime ahead of
      it (several billion years), and a few centuries or even a
      million years would mean little.
         Some stars, however, cannot afford to age even slightly.
      They are already close to that state of fuel consumption
      which will lead to drastic changes, perhaps even supernova-
      -hood.  Let's call such stars, which are on the brink, pre-
      supernovas.  How many of them would there be per
      galaxy?
         It has been estimated that there are an average of 3
      supemovas per century in the average galaxy.  That means
      that in 33,000,000 years there are about a million super-
      novas in the average galaxy.  Considering that a galactic
      life span may easily be a hundred billion years, any star
      that's only a few million years removed from supemova-
      hood may reasonably well be said to be on the brink.
         if, out of the hundred billion stars in an average galac-
      tic nucleus, a million stars are on the brink, then 1 star
      out of 100,000 is a pre-supern6va.  This means that pre-
      supemovas within galactic nuclei are separated by average
      distances of 80 light-years.  Toward the center of the nu-
      cleus, the average distance of separation might be as low
      as 25 light-years.
         But iven-at 25 light-years, the light from a supemova
                                   127

     would be only 1/2:-,o that which the Earth receives from the
     Sun, and its effect would be trifling.  And, as a matter of
     fact, we frequently see supemovas light up one galaxy or
     another and nothing happens.  At least, the supemova
     slowly dies out and the galaxy is then as it was before.
       However, if the average galaxy has I pre-supemova in
     every 100,000 stars, particular galaxies may be poorer
     than that in supernovas richer.  An occasional galaxy
     may be particularly rich and I star out of every 1000 may
     be a pre-supernova.
       In such a galaxy, the nucleus would contain 100,000,-
     000 pre-supemovas, separated by an average distance of
     17 light-years.  Toward the center, the average separation
     might be no more than 5 light-years.  If a supemova lights
     up a pre-supernova only 5 light-years away it will shorten
     its life significantly, and if that supernova had been a
     thousand years from explosion before, it might be only
     two months from explosion afterward.
       Then, when it lets go, a more distant pre-supemova
     which has had its lifetime shortened, but not so drastically,
     by the first, may have its lifetime shortened again by the
     second and closer supernova, and after a few months it
     blasts.
       On and on like a bunch of tumbling dominoes this
     would go, until we end up with a galaty in which not a
     single supernova lets bang, but several million,perhaps,
     one after the other.
       There is the galactic explosion.  Surely such a tumbling
     of dominoes would be sufficient to give birth to a corusca-
     tion of radio waves that would still be easily detectable
     even after it had spread out for a billion light-years.

       Is this just speculation?  To begin with, it was, but in
     late 1963 some observational data made it appear to be
     more than that.
       It involves a galaxy in Ursa Major which is called M82
     because it is number 82 on a list of objects in the heavens
     prepared by the French astronomer Charles Messier about
     two hundred years ago.
                                 128

          Messier was a comet-hunter and was always looking
       through his telescope and thinking he had found a comet
       and turning handsprings and then finding out that he had
       been fooled by some foggy object which was always there
       and was not a comet.
          Finally, he decided to map each of 101 annoying ob-
       jects that were foggy but were not comets so that others
       would not be fooled as he was.  It was that list of annoy-
       ances that made his name immortal.
          The first on his list, Ml, is the Crab Nebula.. Over two
       dozen are globular clusters (spherical conglomerations of
       densely strewn stars), Ml 3 being the Great Hercules Clus-
       ter, which is the largest known.  Over thirty members of
       his list are galaxies, including the Andromeda Galaxy
       (M31) and the Whirlpool Galaxy (M51).  Other famous
       objects on the list are the Orion Nebula (M42), the Ring
       Nebula (M57), and the Owl Nebula (M97).
          Anyway, M82 is a galaxy about 10,000,000 light-years
       from Earth which aroused interest when it proved to be a
       strong radio source.  Astronomerp. turned the 200-inch
       telescope upon it and took pictures, through filters that
       blocked all light except that coming from hydrogen ions.
       There was reason to suppose that any disturbances that
       might exist would show up most clearly among the hydro-
       gen ions.
          They did!  A three-hour exposure revealed jets of bydro-
       gen up to a thousand light-years long, bursting out of the
       galactic nucleus.  The total mass of hydrogen being shot
       out was the equivalent of at least 5,000,000 average stars.
       From the rate at which the jets were traveling and the
       distance they had covered, the explosion must have taken
       place about 1,500,000 years before. (Of course, it takes
       light ten million years to reach us from M82, so that the
       explosion took place 11,500,000 years ago, Earth-time-
       just at the beginning of the Pleistocene Epoch.)
          M82, then, is the case of an exploding galaxy.  The
       energy expended is equivalent to that of five million super-
       novas formed in rapid succession, like uranium atoms
       undergoing fission in an atomic bomb-though on a vastly
                                    129

    greater scale, to be sure.  I feel quite certain that if there
    had been any life anywhere in that galactic nucleus, there
    isn't any now.
       In fact, I suspect that even the outskirts of the galaxy
    may no longer be examples of prime real estate.

       Which brings up a horrible thought . . . Yes, you
    guessed it!
       What if the nucleus of our own dear Galaxy explodes?
    It very likely won't, of course (I don't want to cause fear
    and despondency among the Gentle Readers), for explod-
    ing galaxies are probably as uncommon among galaxies as
    exploding stars are among stars.  Still, if it's not going to
    happen, it is all the more comfortable then, as an intellec-
    tual exercise, to wonder about the consequences of such an
    explosion.
       To begin with, we are not in the nucleus of our Galaxy
    but far in the outskirts and in distance there is a modicum
    of safety.  This is especially so since between ourselves and
    the nucleus are vast clouds of dust that will effectively
    screen off any visible fireworks.
       Of course, the radio waves would come spewing out
    through dust and all, and this would probably ruin radio
    astronomy for millions of years by blanking out everything
    else.  Worse still would be the cosmic radiation that might
    rise high enough to become fatal to life.  In other words,
    we might be caught in the fallout of that galactic explo-
    sion.
       Suppose, though, we put cosmic radiation to one side,
    since the extent of its formation is uncertain and since
    consideration of its presence would be depressing to the
    spirits.  Let's also abolish the dust clouds with a wave of
    the speculative hand.
       Now we can see the nucleus.  What does it look like
    without an explosion?
       Considering the nucleus to be 10,000 light-years in
    diameter and 30,000 light-years away from us, it would
    be visible as a roughly spherical area about 20' in dia-
    meter.  When entirely above the horizon it would make up
    a patch about %5 of the visible sky.
                                 130

          Its total light would be about 30 times that given off by
       Venus at its brightest, but spread out over so large an
       area it would look comparatively dim.  An area of the
       nucleus equal in size to the full Moon would have an
       average brightness only 1/200,000 of the full Moon.
          It would be visible then as a patch of luminosity broad-
       ening out of the Milky Way in the constellation of Sagit-
       tarius, distinctly brighter than the Milky Way itself; bright-
       est at the center, in fact, and fading off with distance from
       the center.
          But what if the nucleus of our Galaxy exploded?  The
       explosion would take place, I feel certain, in the center
       of the nucleus, where the stars were thickest and the effect
       of one pre-supemova on its neighbors would be most
       marked.  Let us suppose that 5,000,000 supernovas are
       formed, as in M82.
          If the nucleus has pre-supemovas separated by 5 light-
       years in its central regions (as estimated earlier in the
       chapter, for galaxies capable of explosion), then 5,000,000
       pre-supernovas would fit into a sphere about 850 light-
       years in diameter.  At a distance of 30,000 light-years,
       such a sphere would appear to have a diameter of 1.6',
       which is a little more than three times the apparent di-
       ameter of the full Moon.  We would therefore have an ex-
       cellent view.
          Once the explosion started, supernova ought to follow
       supemova at an accelerating rate.  It would be a chain
       reaction.
          If we were to look back on that vast explosion millions
       of years later, we could say (and be roughly correct) that
       the center of the nucleus had all exploded at once.  But
       this is only roughly correct.  If we actually watch the ex-
       plosion in process, we will find it will take considerable
       time, thanks entirely to the fact that light takes considerable
       time to travel from one star to another.
          When a supernova explodes, it can't affect a neighbor-
       ing presupemova (5 light-years away, remember) until
       the radiation of the first star reaches the second-and that
       would take 5 years.  If the second star was on the far side
       of the first (with respect to ourselves), an additional 5
                                     131

     years would be lost while the light traveled back to the
     vicinity of the first.  We would therefore see the second
     supernova 10 years later than the first.
       Since a supemova will not remain visible to the naked
     eye for more than a year or so even under the best condi-
     tions (at the distance of the Galactic nucleus), the second
     supemova would not be visible until long after the first had
     faded off to invisibility.
       In short, the 5,000,000 supemovas, forming in a sphere
     850 light-years in diameter, would be seen by us to appear
     over a stretch of time equal to roughly a thousand years.
     If the explosions started at the near edge of that sphere so
     that radiation had to travel away from us and return to set
     off other supernovas, the spread might easily be 1500 years.
     If it started at the far end and additional explosions took
     place as the light of the original explosion passed the pre-
     supernovas en route to ourselves, the time-spread might be
     considerably less.
       On the whole, the chances are that the Galactic nucleus
     would begin to show individual twinkles.  At first there
     might be only three or four twinkles a decade, but then, as
     the decades and centuries passed, there would be more and
     more until finally there.might be several hundred visible
     at one time.  And finally, they would all go out and leave
     behind dimly glowing gaseous turbulence.

       How bright will the individual twinkles be?  A single
     supemova can reach a maximum absolute magnitude of
     -17.  That means if it were at a distance of 10 parsecs
     (32.5 light-years) from ourselves, it would have an appar-
     ent magnitude of -17, which is 1/10,000 the brightness of
     the Sun.
       At a distance of 30,000 light-years, the apparent magni-
     tude of such a supemova would decline by l@ magnitudes.
     The apparent magnitude would now be -2, which is about
     the brightness of Jupiter at its brightest.
       This is quite a static statistic. At   the distance of the
     nucleus, no ordinary star can be individually seen with the
     naked eye.  The hundred billion stars of the nucleus just
     make up a luminous but featureless haze under ordinary
                                 132

       conditions.  For a single star, at that distance, to fire up to
       the apparent brightness of Jupiter is simply colossal.  Such
       a supemova, in fact, burns with a tenth the light intensity
       of an entire non-exploding galaxy such as ours.
          Yet it is unlikely that every supemova forming will be
       a supemova of maximum brilliance.  Let's be conservative
       and suppose that the supemovas will be, on the average,
       two magnitudes below the maximum.  Each will then have
       a magnitude of 0, about that of the star Arcturus.
          Even so, the "twinkles" would be prominent indeed.  If
       humanity were exposed to such a sight in the early stages
       of civilization, they would never make the mistake of think-
       ing that the heavens were eternally fixed and unchangeable.
       Perhaps the absence of that particular misconception
       (which, in actual fact, mankind labored under until early
       modern times) might have accelerated the development of
       astronomy.
          However, we can't see the Galactic nucleus and that's
       that.  Is there anything even faintly approaching such a
       multi-explosion that we can see?

          There's one conceivable possibility.  Here and there, in
       our Galaxy, are to be found globular clusters.  It is estimated
       there are about 200 of these per galaxy. (About a hundred
       of our own clusters have been observed, and the other
       hundred are probably obscured by the dust clouds.)
          These globular clusters are like detached bits of galactic
       nuclei, 100 light-years or so in diameter and containing
       from 100,000 to 10,000,000 stars-symmctricary scat-
       tered about the galactic center.
          The largest known globular cluster is the Great Hercules
       Cluster, M13, but it is not the closest.  The nearest globular
       cluster is Omega Centauri, which is 22,000 light-years from
       us and is clearly visible to the naked eye as an object of the
       fifth magnitude.  It is only a point of light to the naked eye,
       however, for at that distance even a diameter of 100 light-
       years covers an area of only about 1.5 minutes of arc in
       diameter.
          Now let us say that Omega Centauri contained 10,000
       pre-supemovas and that every one of these exploded at
                                    133

     their earliest opportunity.  There would be fewer twinkles
     altogether, but they would appear over a shorter time in-
     terval and would be, individually, twice as bright.
       It would be a perfectly ideal explosion, for it would be
     unobscured by dust clouds; it would be small enough to
     be quite safe; and large enough to be sufficiently spectacular
     for anyone.
       And yet, now that I've worked up my sense of excite-
     ment over the spectacle, I must admit that the chances of
     viewing an explosion in Omega Centauri are just about nil.
     And even if it happened, Omega Centauri is not visible in
     New England and I would have to travel quite a bit south-
     ward if I expected to see it high in the sky in full glory
     and I don't like to travel.
       Hmm . . . Oh well, anyone for a neighborhood fire?

                                 134

                   Part 11
             OF OTHER THINGS

                                      , - i

                        11. FORGET IT!

    The other day I was looking through a new textbook on
    biology (Biological Science: An Inquiry into Life, written
    by a number of contributing authors and published by Har-
    court, Brace & World, Inc. in 1963). 1 found it fascinating.
       Unfortunately, though, I read the Foreword first (yes,
    I'm one of that kind) and was instantly plunged into the
    deepest gloom.  Let me quote from;the first two paragraphs:
       "With each new generation our fund of scientific knowl-
    edge increases fivefold. . . . At the current rate of s.cien-
    tific advance, there is about four times as much'significant
    biological knowledge today as in 1930, and about sixteen
    times as much as in 1900.  By the year 2000, at this rate of
    increase, there will be a hundred times as much biology to
    dcover' in the introductory course as at the beginning of the
    century."
       Imagine how this affects me.  I am a professional "keeper-
    upper" with science and in my more manic, ebullient, and
    carefree moments, I even think I succeed fairly well.
       Then I read something like the above-quoted passage
    and the world falls about my ears.  I don't keep up with
    science.  Worse, I can't keep tip with it.  Still worse, I'm
    falling farther behind every day.
       And finally, when I'm all through sorrowing for myself,
    I devote a few moments to worrying about the world
    generally.  What is going to become of Homo sapiens?
    We're going to smarten ourselves to death.  After a while,
    we will all die of pernicious education, with our brain cells
    crammed to indigestion with facts and concepts, and with
    blasts of information exploding out of our ears.
       But then, as luck would have it, the very day after I
    read the Foreword to Biological Science I came across an
    old, old book entitled Pike's Arithmetic.  At least that is the
                                  137

      name on the spine.    On the title page it spreads itself a bit
      better, for in those days titles were titles. It goes "A New
      and Complete System of Arithmetic Composed for the Use
      of the Citizens of the United States," by Nicolas Pike, A.M.
      It was first published in 1785, but the copy I have is only
      the "Second Edition, Enlarged," published in 1797.
         It is a large book of over 500 pages, crammed full of
      small print and with no relief whatever in the way of
      illustrations or diagrams.  It is a solid slab of arithmetic
      except for small sections at the very end that introduce
      algebra and geometry.
         I was amazed.  I have two children in grade school (and
      once I was in grade school myself), and I know what arith-
      metic books are like these days.  They are nowhere near as
      large.  They can't possibly have even one-fifth the wordage
      of Pike.
         Can it be that we are leaving anything out?
         So I went through Pike and, you know, we are leaving
      something out.  And there's nothing wrong with that.  The
      trouble is we're not leaving enough out.

         On page 19, for instance, Pike devotes half a page to a
      listing of numbers as expressed in Roman numerals, ex-
      tending the list to numbers as high as five hundred thou-
      sand.
         Now Arabic numerals reached Europe in the High
      Middle Ages, and once they came on the scene the Roman
      numerals were completely outmoded.  They lost all pos-
      sible use, so infinitely superior was the new Arabic nota-
      tion.  Until then who knows how many reams of paper
      were required to explain methods for calculating with
      Roman numerals.  Afterward the same calculations could
      be performed with a hundredth of the explanation.  No
      knowledge was lost only inefficient rules.
         And yet five hundred years after the deserved death of
      the Roman numerals, Pike still included them and ex-
      pected his readers to be able to translate them into Arabic
      numerals and vice versa even though he gave no instruc-
      tions for how to manipulate them.  In fact, nearly two hun-
                                   138

    dred years after Pike, the Roman numerals are still being
    taught.  My little daughter is learning them now.
       But why?  Where's the need?  To be sure, you will find
    Roman numerals on cornerstones and gravestones, on
    clockfaces and on some public buildings and documents,
    but it isn't used for any need at all.  It is used for show,
    for status, for antique flavor, for a craving for some kind
    of phony classicism.
       I dare say there are some sentimental fellows who feel
    that knowledge of the Roman numerals is a kind of gate-
    way to history and culture; that scrapping them would be
    like knocking over what is left of the Parthenon, but I
    have no patience with such mawkishness.  We might as
    well suggest that everyone who learns to drive a car be
    required to spend some time at the wheel of a Model-T
    Ford so he could get the flavor of early cardom.
       Roman numerals?  Forget iti-And make room instead
    for new and valuable material.
       But do we dare forget things?  Why not?  We've forgot-
    ten much; more than you imagine.  Our troubles stem not
    from the fact that we've forgotten, but that we remember
    too well; we don't forget enough.
       A great deal of Pike's book consists of material we have
    imperfectly forgotten.  That is why the modern arithmetic
    book is shorter than Pike.  And if we could but perfectly
    forget, the modern arithmetic book could grow still
    shorter.
       For instance, Pike devotes many pages to tables-pre-
    sumably important tables that he thought the reader ought
    to be familiar with.  His fifth table is labeled "cloth meas-
    ure.29
       Did you know that 2% inches make a "nail"?  Well,
    they do.  And 16 nails make a yard; while 12 nails make
    an ell.
       No, wait a while.  Those 12 nails (27 inches) make a
    Flemish ell.  It takes 20 nails (45 inches) to make an
    English ell, and 24 nails (54 inches) to make a French
    ell.  Then, 16 nails plus 1% inches (371/5 inches) make a
    Scotch ell.
                                 139

         Now if you're going to be in the business world and
      import and export cloth, you're going to have to know all
      those ells-unless you can figure some way of getting the
      ell out of business.
         Furthermore, almost every piece of goods is measured
      in its own units.  You speak of a firkin of butter, a punch
      of prunes, a fother of lead, a stone of butcher's meat, and
      so on.  Each of these quantities weighs a certain number of
      pounds (avoirdupois pounds, but there are also troy pounds
      and apothecary pounds and so on), and Pike carefully
      gives all the equivalents.
         Do you want to measure distances?  Well, how about
      this: 7 92/100 inches make I link; 25 links make I pole;
      4 poles make I chain; 10 chains make I furlong; and 8
      furlongs make I mile.
         Or do you want to measure ale or beer-a very com-
      mon line of work in Colonial tim6s.  You have to know the
      language, of course.  Here it is: 2 pints make a quart and
      4 quarts make a gallon.  Well, we still know that much
      anyway.
         In Colonial times, however, a mere gallon of beer or ale
      was but a starter.  That was for infants.  You had to know
      how to speak of man-sized quantities.  Well, 8 gallons
      make a firkin-that is, it makes "a firkin,of ale in Lon-
      don." It takes, however, 9 gallons to make "a firkin of beer
      in London." The intermediate quantity, 81/2 gallons, is
      marked down as "a firkin of ale or beer"-presumably
      outside of the environs of London where the provincial
      citizens were less finicky in distinguishing between the two.
         But we go on: 2 firkins (I suppose the intermediate
      kind, but I'm not sure) make a kilderkin and 2 kilderkins
      make a barrel.  Then ll/z barrels make I hogshead; 2 bar-
      rels make a puncheon; and 3 barrels make a butt.
         Have you got all that straight?
         But let's try dry measure in case your appetite has been
      sharpened for something still better.
         Here, 2 pints make a quart and 2 quarts make a pottle.
      (No, not bottle, pottle.  Don't tell me you've never heard
      of a pottle!) But let's proceed.
         Next, 2 pottles make a gallon, 2 gallons make a peck,
                                  140

     and 4 pecks make a bushel. (Long breath now.) Then 2
     bushels make a strike, 2 strikes make a coom, 2 cooms
     make a quarter, 4 quarters make a chaldron (though in
     the demanding city of London, it takes 41/2 quarters to
     make a chaldron).  Finally, 5 quarters make a wey and 2
     weys make a last.
       I'm not making this up.  I'm copying it right out of Pike,
     page 48.
       Were people who were studying arithmetic in 1797 ex-
     pected to memorize all this?  Apparently, yes, because Pike
     spends a lot of time on compound addition.  That's right,
     compound addition.
       . You see, the addition you consider addition is just
     44 simple addition." Compound addition is something
     stronger and I will now explain it to you.

       Suppose you have 15 apples, your friend has 17 apples,
     and a passing stranger has 19 apples and you decide to
     make a pile of them.  Having done so, you wonder bow
     many  you have altogether. Preferring not to count, you
     draw  upon your college education and prepare to add
     15 +  17 + 19. You begin with the units column and find
     that 5 + 7 + 9 = 21.;You therefore divide 21 by 10 and
     find the quotient is 2 plus a remainder of I,. so you put
     down the remainder, 1, and carry the quotient 2 into the
     tens col---
       I seem to hear loud yells from the audience.  "What is
     all this? comes the fevered demand.  "Where does this
     'divide by 10' jazz come from?"
       Ah, Gentle Readers, but this is exactly what you do
     whenever you add.  It is only that the kindly souls who
     devised our Arabic system of numeration based it on the
     number 10 in such a way that when any two-digit num-
     ber is divided by 10, the first digit represents the quotient
     and the second the remainder.
       For that reason, having the quotient and remainder in
     our hands without dividing, we can add automatically.  If
     the units column adds up to 21, we put down I and carry
     2; if it bad added up to 57, we would have put down 7
     and carried 5, and so on.
                                 141

        The only reason this works, mind you, is that in adding
      a set of figures, each column of dicits (starting from the
      right and working leftward) represents a value ten times
      as great as the column before.  The rightmost column is
      units, the one to its left is tens, the one to its left is hun-
      dreds, and so on.
        It is this combination of a number system based on ten
      and a value ratio from column to column of ten that
      makes addition very simple.  It is for this reason that it is,
      as Pike calls it, "simple addition."
        Now suppose you have I dozen and 8 apples, your
      friend has 1 dozen and 10 apples, and a passing stranger
      has I dozen and    9 apples. Make a pile of those and add
      them as follows:

                         I dozen           8 units
                         1 dozen          10 units
                         1 dozen           9 units

        Since 8 + 10 + 9 = 27, do we put down 7 and carry
      2? Not at all!  The ratio of the "dozens" column to the
      (tunits" column is not 10 but 12, since there are 12 units
      to a dozen.  And since the number system we are using is
      based on I 0 and not on 12, we can no longer let the dicits
      do our thinking for us.  We have to go long way round.
        If 8 + 10 + 9 -- 27, we must divide that sum by the
      ratio of the value of the columns; in this case, 12.  We find
      that 27 divided by 12 gives a quotient of 2 plus a remain-
      der of 3, so we put down 3 and carry 2. In the dozens
      column we get I + I + 1 + 2 = 5. Our total therefore is
      5 dozen and 3 apples.
        Whenever a ratio of other than 10 is used so that you
      have to make actual divisions in adding, you have "com-
      pound addition." You must indulge in compound addition
      if you try to add 5 pounds 12 ounces and 6 pounds 8
      ounces, for there are 16 ounces to a pound.  You are stuck
      again if you add 3 yards 2 feet 6 inches to I yard 2 feet
      8 inches, for there are 12 inches to a foot, and 3 feet to a
      yard.
        You do the former if you care to; I'll do the latter.
                                   142

     First, 6 inches and 8 inches are 14 inches.  Divide 14 by
     12, getting 1 and a remainder of 2, so you put down 2
     and carry 1. As for the feet, 2 + 2 + I = 5. Divide 5 by
     3 and get I and a remainder of 2, put down 2 and carry
     1. In the yards, you have 3 + 1 + 1 = 5. Your answer,
     then, is 5 yards 2 feet 2 inches.

        Now why on Earth should our unitratios vary         all over
     the lot, when our number system is so firmly based on 10?
     There are many reasons (valid in their time) for       the use
     of odd ratios like 2, 3, 4, 8, 12, 16, and 20, but surely we
     are now advanced and sophisticated enough to use 10 as
     the exclusive (or n arly exclusive) ratio.  If we could do
     so, we could with such pleasure forget about compound
     addition-and compound subtraction, compound multipli-
     cation, compound division, too. (They also exist, of
     course.)
        To be sure, there are times when nature makes the uni-
     versal ten impossible.  In measuring time, the day and the
     year have their lengths fixed for us by astronomical condi-
     tions and neither unit of time can be abandoned.  Com-
     pound addition and the rest will have to be retained for
     suchspecial cases, alas.
        But who in blazes says we must measure things in
     firkins and pottles and Flemish ells?  These are purely man-
     made measurements, and we must remember that measures
     were made for man and not man for measures.
        It so happens that there is a system of measurement
     based exclusively on ten in this world.  It is called the
     metric system and it is used all over the civilized world
     except for certain English-speaking nations such as the
     United States and Great Britain.
        By not adopting the metric system, we waste our time
     for we gain. nothing, not one thing, by learning- our own
     measurements.  The loss in time (which is expensive in-
     deed) is balanced by not one thing I can imagine. (To be
     sure, it would be expensive to convert existing instruments
     and tools but it would have been nowhere nearly as ex-
     pensive if we had done it a century ago, as we should
     have.)
                                   143

       There are those, of course, who object to violating our
     long-used cherished measures.  They have given up cooms
     and ehaldrons but imagine there is something about inches
     and feet and pints and quarts and pecks and bushels that
     is "simpler" or "more natural" than meters and liters.
       There may even be people who find something danger-
     ously foreign and radical (oh, for that vanished word of
     opprobrium, "Jacobin") in the metric system-yet it was
     the United Stettes that led the way.
       In 1786, thirteen years before the wicked French revo-
     lutionaries designed the metric system, Thomas Jefferson
     (a notorious "Jacobin," according to the Federalists, at
     least) saw a suggestion of his adopted by the infant, United
     States.  The nation established a decimal currency.
       What we had been using was British currency, and that
     is a fearsome and wonderful thing.  Just to point out bow
     preposterous it is, let me say that the British people who,
     over the centuries, have, with monumental patience, taught
     themselves to endure anything at all provided it was "tra-
     ditional"-are now sick and tired of their durrency and
     are debating converting it to the decimal system. (Tley
     can't agree on the exact details of the change.)
       But consider the British currency as it has been.  To
     begin with, 4 farthings make 1- penny; 12 pennies make I
     shilling, and 20 shillings make I pound.  In addition, there
     is a virtual farrago of terms, if not always actual coins,
     such as ha'pennies and thruppences and sixpences and
     crowns and balf-crowns and florins and guineas and
     heaven knows what other devices with which to cripple the
     mental development of the British schoolchild and line the
     pockets of British tradesmen whenever tourists come to
     call and attempt to cope with the currency.
       Needless to say, Pike gives careful instruction on how
     to manipulate pounds, shillings, and pence-and very
     special instructions they are.  Try dividing 5 pounds, 13
     shillings, 7 pence by 3. Quick now!
       In the United States, the money system, as originally
     established, is as follows: 10 mills make I cent; 10 cents
     make I dime; 10 dimes make 1 dollar; 10 dollars make I
                                 144

     eagle.  Actually, modern Americans, in their calculations,
     stick to dollars and cents only.
        The result?  American money can be expressed in deci-
     mal form and can be treated as can any other decimals.  An
     American child who has learned decimals need only be
     taught to recognize the dollar sign and he is all set.  In the
     time that he does, a British child has barely mastered the
     fact that thruppence ba'penny equals 14 farthings.
        What a pity that when, thirteen years later, in 1799, the
     metric system came into being, our original anti-British,
     pro-French feelings had not lasted just long enough to
     allow us to adopt it.  Had we done so, we would have been
     as happy to forget our foolish pecks and ounces, as we are
     now happy to have forgotten our pence and shillings.
     (After all, would you like to go back to British currency
     in preference to our own?)
        What I would like to see is one form of money do for
     all the world.  Everywhere.  Why not?
        I appreciate the fact that I may be accused because of
     this of wanting to pour humanity into a mold, and of being
     a conformist.  Of course, I am not a conformist (heavens!).
     I have no objection to local customs and local dialects
     and local dietaries.  In fact, I insist on them for I constitute
     a locality all by myself.  I just don't want to keep provin-
     cialisms that were w    'ell enough in their time but that
     interfere with human well-being in a world which is now
     90 minutes in circumference.
        If you think provincialism is cute and gives humanity
     color and charm, let me quote to you once more from Pike.
        "Federal Money" (dollars and cents) had been intro-
     duced eleven years before Pike's second edition, and he
     gives the exact wording of the law that established it and
     discusses it in detail-under the decimal system and not
     under compound addition.
        Naturally, since other systems than the Federal were
     still in use, rules had to be formulated and given for con-
     verting (or "reducing") one system to another.  Here is
     the list.  I won't give you the actual rules, just the list of
     reductions that were necessary, exactly as he lists them:
                                   145

       1. To reduce New Hampshire, Massachusetts,, Rnode
     Island, Connecticut, and Virginia currency:
          1. To Federal Money
          2. To New York and North Carolina currency
          3. To Pennsylvania, New Jersey, Delaware, and
          Maryland currency
          4. To South Carolina and Georgia currency
          5. To English money
          6. To Irish money
          7. To Canada and Nova Scotia currency
          8. To Livres Toumois (French money)
          9. To Spanish m;lled dollars
       II. To reduce Federal Money to New England and
     Virginia currency.
       III.  To reduce New Jersey, Pennsylvania, Delaware,
     and Maryland currency:
          1. To New Hampshire, Massachusetts, Rhode Island,
          Connecticut, and Virginia currency
          2. To New York and . . .
       Oh, the heck with it.  You get the idea.
       Can anyone possibly be sorry that all   that cute provin-
     cial flavor has vanished?  Are you sorry that every time
     you travel out of state you don't have to throw yourself
     into fits of arithmetical discomfort whenever you want to
     make a purchase?  Or into similar fits every time someone
     from another state invades yours and tries to dicker with
     you?  What a pleasure to have forgotten all that.
       Then tell me what's so wonderful about having fifty sets
     of marriage and divorce laws?

       In 1752, Great Britain and her colonies (some two
     centuries later than Catholic Europe) abandoned the
     Julian calendar and adopted the astronomically more cor-
     rect Gregorian calendar (see Chapter 1).  Nearly half a
     century later, Pike was still giving rules for solving com-
     plex calendar-based problems for the Julian calendar as
     well as for the Gregorian.  Isn't it nice to have forgotten
     the Julian calendar?
       Wouldn't it be nice if we could forget most of calendri-
     cal complications by adopting a rational calendar that
                                 146

     would tie the day of the month firmly to the day of the
     week and have a single three-month calendar serve as a
     perpetual one, repeating itself over and over every three
     months?  There is a world calendar proposed which would
     do just this.
        It would enable us to do a lot of useful forgetting.

        I would like to see the English language come into
     worldwide use.  Not necessarily as the only language or
     even as the major language.  It would just be nice if every-
     one-whatever his own language was-could also speak
     English fluently.  It would help in communications and per-
     haps, eventually, everyone would just choose to speak English.
        That would save a lot of room for other things.
        Why English?  Well, for one thing more people speak
     English as either first or second language than any other
     language on Earth, so we have a head start.  Secondly, far
     more science is reported in English than in any other lan-
     guage and it is communication in science that is critical
     today and will be even more critical tomorrow.
        To be sure, we ought to make it as easy as possible for
     people to speak English, which means we should rational-
     ize its spelling and grammar.
        English, as it is spelled today, is almost a set of Chinese
     ideograms.  No one can be sure how a word is pronounced
     by looking at the letters that make it up.  How do you
     pronounce: rough, through, though, cough, hiccough, and
     lough; and why is it so terribly necessary to spell all those
     sounds with the mad letter combination "ough"?
        It looks funny, perhaps, to spell the words ruff, throo,
     thoh, cawf, hiccup, and lokh; but we already write hiccup
     and it doesn't look funny.  We spell colour, color, and
     centre, center, and shew, show and grey, gray.  The result
     looks funny to a Britisher but we are us     'ed to it. We can
     get used to the rest, too, and save a lot of wear and tear
     on the brain.  We would all become more intelligent, if
     intelligence is measured by proficiency at spelling, and we'll
     not have lost one thing.
        And grammar?  Who needs the eternal hair-splitting
                                   147

     arguments about "shall" and "will" or "which" and "that"?
     The uselessness of it can be demonstrated by the fact
     that virtually no one gets it straight anyway.  Aside from
     losing valuable time, blunting a child's reasoning faculties,
     and instilling him or her with a ravening dislike for the
     English language, what do you gain?
       If there be some who think that such blurring of fine
     distinctions will ruin the language, I would like to point
     out that English, before the grammarians got hold of it,
     had managed to lose its gender and its declensions almost
     everywhere except among the pronouns.  The fact that we
     have only one definite article (the) for all genders and
     cases and times instead of three, as in French (le, la, les)
     or six, as in German (der, die, das, dem, den, des) in no
     way blunts the English language, which remains an ad-
     mirably flexible instrument.  We cherish our follies only
     because we are used to them and not because they are not
     really follies.

       We must make room for expanding knowledge, or at
     least make as much room as possible.  Surely it is as im-
     portant to forget the old and useless as it is to learn the
     new and important.
       Forget it, I say, forget it more and more.  Forget it!
       But why am I getting so excited?  No one is listening to
     a word I say.

                                 148

                   12.  NOTHING COUNTS

     In the previous chapter, I spoke of a variety of things;
     among them, Roman numerals.  These seem, even after five
     centuries of obsolescence, to exert a peculiar fascination
     over the inquiring mind.
       It is my theory that the reason for this is that Roman
     numerals appeal to the ego.  When one passes a corner-
     stone which says: "Erected MCMXVIII," it gives one a
     sensation of power to say, "Ah, yes, nineteen eighteen" to
     one's self.  Whatever the reason, they are worth further
     discussion.

       The notion of number and of counting, as well as the
     names of the smaller and more-often-used numbers, date
     back to prehistoric times and I don't believe that there is a
     tribe of human beings on Earth today, however primitive,
     that does not have some notion of number.
       With the invention of writing (a step which marks the
     boundary line between "prehistoric" and "historic"), the
     next step had to be taken-numbers had to be written.
     One can, of course, easily devise written symbols for the
     words that represent particular numbers, as easily as for
     any other word.  In English we can write the number of
     fingers on one hand as "five" and the number of digits on
     all four limbs as "twenty."
       Early in the game, however, the kings' tax-collectors,
     chroniclers, and scribes saw that numbers bad t-he pe-
     culiarity of being ordered.  There was one set way of count-
     ing numbers and any number could be defined by counting
     up to it.  Therefore why not make marks which need be
     counted up to the proper number.
       Thus, if we let "one" be represented as ' and "two" as
                                 149

        and "three" as "', we can then work out the number
      indicated by a given symbol without trouble.  You can see,
      for instance, that the symbol                    stands for
      "twenty-three." What's more, such a symbol is universal.
      Whatever language you count in, the symbol stands for
      the number "twenty-three" in whatever sound your par-
      ticular language uses to represent it.
        It gets hard to read too many marks in an unbroken row,
      so it is only natural to break it up into smaller groups.  If
      we are used to counting on the fingers of one hand, it
      seems natural to break up the marks into groups of five.
      "Twenty-three" then becomes ""' @"" 'if" fl@lf "f.  If we are
      more sophisticated and use both hands in counting, we
      would write it fl"pttflf     '//. If we go barefoot and use
      our toes, too, we might break numbers into twenties.
        All three methods of breaking up number symbols into
      more easily handled groups have left their mark on the
      various number systems of mankind, but the favorite was
      division into ten.  Twenty symbols in one group are, on the
      whole, too many for easy grasping, while five symbols in
      one group produce too many groups as numbers grow
      larger.  Division into ten is the happy compromise.
        It seems a natural thought to go on to indicate groups of
      ten by a separate mark.  There is no reason to insist on
      writing out a group of ten as Ifillittif every time, when a
      separate mark, let us say -, can be used for the purpose.
      In that case "twenty-three" could be written as -- "'.
        Once you've started this way, the next steps are clear.
      By the time you have ten groups of ten (a hundred), you
      can introduce another symbol, for instance +. Ten hun-
      dreds, or a thousand, can become = and so on.  In that
      case, the number "four thousand six hundred seventy-five"
      can be written ==== ++++++
        To make such a set of symbols more easily graspable,
      we can take advantage of the ability of the eye to form a
      pattern. (You know how you can tell the numbers displayed
      by a pack of cards or a pair of dice by the pattern itself.)
      We could therefore write "four thousand six hundred sev-
      enty-five" as
                                  150

       And, as a matter of fact, the ancient Babylonians used
     just this system of writing numbers, but they used cunei-
     form wedges to express it.

       The Greeks, in the earlier stages of their development,
     used a system similar to that of the Babylonians, but in
     later times an alternate method grew popular.  They made
     use of another ordered system-that of the letters of the
     alphabet.
       It is natural to correlate the alphabet and the number
     system.  We are taught both about the same time in child-
     hood, and the two ordered systems of objects naturally tend
     to match up.  The series "ay, bee, see, dee . . ." comes as
     glibly as "one, two, three, four . . ." and there is no dif-
     ficulty in substituting one for the other.
       If we use undifferentiated symbols such as '" for
     ggseven," all the components of the symbol are identical. and
     all must be included without exception if. the symbol is to
     mean "seven" and nothing else.  On the other hand, if
     "A,BCDEFG" stands for "seven" (count the letters and
     see) then, since each symbol is different, only the last need
     be written.  You can't confuse the fact that G is the seventh
     letter of the alphabet and therefore stands for "seven." In
     this way, a one-component symbol does the work of a
     seven-component symbol.  Furthermore, "" (six) looks
     very much like """' (seven); whereas F (six) looks n6th-
     ing at all like G (seven).
       The Greeks used their own alphabet, of course, but let's
     use our own alphabet here for the complete demonstration:
     A = one, B = two, C = three, D = four, E          Five, F
     six, G = seven, H = eight, I = nine, and J = ten.
       We could let the letter K go on to equal "eleven," but
     at that rate our alphabet will only help us up through
     "twenty-six." The Greeks had a better system.  The Baby-
     lonian notion of groups of ten had left its mark. If J    ten,
                                  151

     then J equals not only ten objects but also one group of
     tens.  Why not, then, continue the next letters as numbering
     groups of tens?
        In other words J = ten, K       twenty, L = thirty, M =
     forty, N = fifty, 0 = sixty, P     seventy, Q = eighty, R =
     ninety.  Then we can go on to number groups of hundreds:
     S    one hundred, T = two hundred, U = three hundred,
     V     four hundred, W = five hundred, X = six hundred,
     Y     seven hundred, Z = eight hundred. It would be con-
     venient to go on to nine hundred, but we have run out of
     letters.  However, in old-fashioned alphabets the amper-
     sand (&) was sometimes placed at the end of the alphabet,
     so we can say that & = nine hundred.
        The first nine letters, in other words, represent the units
     from one to nine, the second nine letters represent the tens
     groups from one to nine, the third nine letters represent
     the hundreds groups from one to nine. (The Greek alpha-
     bet, in classic times, had only twenty-four letters where
     twenty-seven are needed, so the Greeks made use of three
     archaic letters to fill out the list.)
        This system possesses its advantages and disadvantages
     over the Babylonian system.  One advantage is that any
     number under a thousand can be given in three symbols.
     For instance, by the system I have just set up with our
     alphabet, six hundred seventy-five is XPE, while eight hun-
     dred sixteen is ZJF.
        One disadvantage of the Greek system, however, is that
     the significance of twenty-seven different symbols must be
     carefully memorized for the use of numbers to a thousand,
     whereas in the Babylonian system only three different sym-
     bols must be memorized.
        Furthermore, the Greek system cofnes to a natural end
     when the letters of the alphabet are used up.  Nine hun-
     dred ninety-nine (&RI) is the largest number that can be
     written without introducing special markings to indicate
     that a particular symbol indicates groups of thousands,
     tens of thousands, and so on.  I will get back to this later.

        A rather subtle disadvantage of the Greek system was
     that the same symbols were used for numbers and words
                                  152

     so that the mind could be easily distracted.  For instance,
     the Jews of Graeco-Roman times adopted the Greek sys-
     tem of representing numbers but, of course, used the He-
     brew alphabet-and promptly ran into a difficulty.  The
     number "fifteen" would naturally be written as "ten-five."
     In the Hebrew alphabet, however, "ten-five" represents a
     short version of the ineffable name of the Lord, and the
     Jews, uneasy at the sacrilege, allowed "fifteen" to be repre-
     sented as "nine-six" instead.
        Worse yet, words in the Greek-Hebrew system look like
     numbers.  For instance, to use our own alphabet, WRA is
     "five hundred ninety-one." In the alphabet system it doesn't
     usually matter in which order we place the symbols though,
     as we shall see, this came to be untrue for the Roman
     numerals, which are alphabetic, and WAR also means "five
     hundred ninety-one." (After all, we can say "five hundred
     one-and-ninty" if we wish.) Consequently, it is easy to be-
     lieve that there is something warlike, martial, and of omi-
     nous import in the number "five hundred ninety-one."
        The Jews, poring over every syllable of the Bible in
     their effort to copy the word of the Lord with the exactness
     that reverence required, saw numbers in all the words, and
     in New Testament times a whole system of mysticism rose
     over the numerical interrelationships within the Bible.  This
     was the nearest the Jews came to mathematics, and they
     called this numbering of words gematria, which is a distor-'
     tion of the Greek geometria.  We now call it "numerology."
        Some poor souls, even today, assign numbers to the dif-
     ferent letters and decide which names are lucky and which
     unlucky, and which boy should marry which girl and so
     on. It is on'e of the more laughable pseudo-sciences.
        In one case, a piece of gematria had repercussions in
     later history.  This bit of gematria is to be found in "The
     Revelation of St. John the Divine," the last book of the
     New Testament-a book which is written in a mystical
     fashion that defies literal understanding.  The reason for
     the lack of clarity seems quite clear to me.  The author of
     Revelation was denouncing the Roman government and
     was laying himself open to a charge of treason and to sub-
     sequent crucifixion if he made his words too clear.  Conse-
                                  153

     quently, he made an effort to write in such a way as to be
     perfectly clear to his "in-group" audience, while remaining
     completely meaningless to the Roman authorities.
        In the thirteenth chapter he speaks of beasts of diaboli-
     cal powers, and in the eighteenth verse he says, "Here is
     wisdom.  Let him that hath understandino, count the number
     of the beast: for it is the number of a man; and his number
     is Six hundred three-score and six."
        Clearly, this is designed not to give the pseudo-science
     of gematria holy sanction, but merely to serve as a guide
     to the actual person meant by the obscure imagery of the
     chapter.  Revelation, as nearly as is known, was written
     only a few decades after the first great persecution of Chris-
     tians under Nero.  If Nero's name ("Neron Caesar") is
     written in Hebrew characters the sum of the numbers rep-
     resented by the individual letters does indeed come out to
     be six hundred sixty-six, "the number of the beast."
        Of course, other interpretations are possible.  In fact, if
     Revelation is taken as having significance for all time as
     well as for the particular time in which it was written, it
     may also refer to some anti-Christ of the future.  For this
     reason, generation after generation, people have made at-
     tempts to show that, by the appropriate ju-glings of the
     spelling of a name in an appropriate language, and by the
     appropriate assignment of numbers to letters, some par-
     ticular personal enemy could be made to possess the num-
     ber of the beast.
        If the Christians could apply it to Nero, the Jews them-
     selves might easily have applied it in the next century to
     Hadrian, if they had wished.  Five centuries later it could be
     (and was) applied to Mohammed.  At the time of the Ref-
     ormation, Catholics calculated Martin Luther's name and
     found it to be the number of the beast, and Protestants re-
     turned the compliment by making the same discovery in
     the case of several popes.
        Later still, when religious rivalries were replaced by na-
     tionalistic ones, Napoleon Bonaparte and William 11 were
     appropriately worked out.  What's more, a few minutes'
     work with my own system of alphabet-numbers shows me
                                   154

      that "Herr Adolif Hitler" has the number of the beast. (I
      need that extra "I" to make it work.)

         The Roman system of number symbols had similarities
      to both the Greek and Babylonian systems.  Like the
      Greeks, the Romans used letters of the alphabet.  However,
      they did not use them in order, but use just a few letters
      which they repeated as often as necessary-as in the Baby-
      lonian system.  Unlike the Babylonians, the Romans did
      not invent a new symbol for every tenfold increase of
      number, but (more primitively) used new symbols for
      fivefold increases as well.
         'Thus, to begin with, the symbol for "one" is 1, and
      "two," "three," and "four," can be written II, III, and
      iiii.
         The symbol for five, then, is not 11111, but V. People
      have amused themselves no end trying to work out the
      reasons for the particular letters chosen as symbols, but
      there are no explanations that are universally accepted.
      However, it is pleasant to think that I represents the up-
      held fin-er and that V might symbolize the hand itself
      with all five fingers-one branch of the V would be the out-
      held thumb, the other, the remaining fingers.  For "six,"
      11 seven," "eight," and "nine," we would then have VI, VII,
      'VIII, and VIIII.
         For "ten" we would then have X, which (some peo-
      ple think) represents both hands held wrist to wrist.
      "Twenty-three" would be XXIII, "forty-eight" would be
      XXXXVIII, and so on.
         The symbol for "fifty" is L, for "one hundred" is C, for
      "five hundred" is D, and for "one thousand" is M. The C
      and M are easy to understand, for C is the first letter of
      centum (meaning "one hundred") and M is the first letter
      of rnille (one thousand).
         For that very reason, however, those symbols are sus-
      picious.  As initials they may have come to oust the original
      less-meaningful symbols for those numbers.  For instance,
      an alternative symbol for "thousand" looks something like
      this (1).  Half of a thousand or "five hundred" is the right
                                   155

    half of the symbol, or (1), and this may have been con-
    verted into D. As for the L which stands for "fifty," I don't
    know why it is used.
      Now, then, we can write nineteen sixty-four, in Roman
    numerals, as follows: MDCCCCLXIIII.
      One advantage of writing numbers according to this sys-
    tem is that it doesn't matter in which order the numbers
    are written.  If I decided to write nineteen sixty-four as
    CDCLIIMXCICT, it would still represent nineteen sixty-
    four if I add up the number values of each letter.  However,
    it is not likely that anyone would ever scramble the letters
    in this fashion.  If the letters were written in strict order of
    decreasing value, as I.did the first time, it would then be
    much simpler to add the values of the letters.  And, in fact,
    this order of decreasing value is (except for special cases)
    always used.
      Once the order of writing the letters in Roman numerals
    is made an established convention, one can make use of
    deviations from that set order if it will help simplify mat-
    ters.  For instance, suppose we decide that when a symbol
    of smaller value follows one of larger value, the two are
    added; while if the symbol of smaller value precedes one of
    larger value, the first is subtracted from the second.  Thus
    VI is "five" plus "one" or "six,"' while IV is "five" minus
    "one" or "four." (One might even say that IIV is "three,"
    but it is conventional to subtract no more than one sym-
    bol.) In the same way LX is "sixty" while XL is "forty";
    CX is "one hundred ten," while XC is "ninety"; MC is
    44 one thousand one hundred," while CM is "nine hundred."
      The value of this "subtractive principle" is that two sym-
    bols can do the work of five.  Why write VIIII il you can
    write IX; or DCCCC if you can write CM?  The year nine-
    teen sixty-four, instead of being written MDCCCCLXIIII
    (twelve symbols), can be written MC@XIV (seven sym-
    bols).  On the other hand, once you make the order of
    writing letters significant, you can no longer scramble
    them even if you wanted to.  For instance, if MCMLXIV is
    scrambled to MMCLXVI it becomes "two thousand one
    hundred sixty-six."
      The subtractive principle was used on and off in ancient
                                 156

      times but was not regularly adopted until the Middle Ages.
      One interesting theory for the delay involves the simplest
      use of the principle-that of IV ("four").  These are the
      first letters of IVPITER, the chief of the Roman gods, and
      the Romans may have had a delicacy about writing even
      the beginning of the name.  Even today, on clockfaces bear-
      ing Roman numerals, "four" is represented as 1111 and
      never as IV.  This is not because the clockf ace does not ac-
      cept the subtractive principle, for "nine" is represented as
      IX and never as VIIII.
         With the symbols already,given, we can go up to the
      number "four thousand nine hundred ninety-nine" in Ro-
      man numerals.  This would be MMMMDCCCCLXXXX-
      VIIII or, if the subtractive principle is used   '  MMMM-
      CMXCIX.  You might suppose that "five thousand" (the
      next number) could be written MMMMM, but this is not
      quite right.  Strictly speaking, the Roman system never re-
      quires a symbol to be repeated more than four times.  A new
      symbol is always invented to prevent that: 11111 = V;
      XXXXX = L; and CCCCC = D. Well, then, what is
      MMMMM?
         No letter was decided upon for "five thousand." In an-
      cient times there was little need in ordinary life for num-
      bers that high.  And if scholars and tax collectors had oc-
      casion for larger numbers, their systems did not percolate
      down to the common man.
         One method of penetrating to "five thousand" and be-
      yond is to use a bar to represent thousands.  Thus, V would
      represent not "five" but "five thousand." And sixty-seven
      thousand four hundred eighty-two would be LX-VIICD-
      LXXXII.
         But another method of writing large numbers harks back
      to the primitive symbol (1) for "thousand." By adding to
      the curved lines we can increase the number by ratios of
      ten. Thus "ten thousand" would be          (1) ), and "one
      hundred thousand" would be           (1)       Then just as
      "five hundi7ed" was 1) or D, "five thousand" would be
      1) ) and "fifty thousand" would be I) ) ).
         Just as the Romans made special marks to indicate tbou-
      sands, so did the Greeks.  What's more, the Greeks made
                                   157

   special marks for ten thousands and for millions (or at
   least some of the Greek writers did).  That the Romans
   didn't carry this to the logical extreme is no surprise.  The
   Romans prided themselves on being non-intellectual.  That
   the Greeks missed it also, however, will never cease to
   astonish me.
      Suppose that instead of making special marks for large
   numbers only, one were to make special marks for every
   type of group from the units on.  If we stick to the system I
   introduced at the start of the chapter-that is, the one in
   which ' stands for units, - for tens, + for hundreds, and =
   for thousands-then we could get by with but one set of
   nine syrrbols.  We could write every number with a little
   heading, marking off the type of groups -+-'.  Then for
   "two thousand five hundred eighty-one" we could get by

   with only the letters from A to I and write it GEHA.  What's
   more, for "five thousand five hundred fifty-five" we could

   write EEEE.  There would be no confusion with all the E's,
   since the symbol above each E would indicate that one was
   a "five," another a "fifty," another a "five hundred," and
   another a "five thousand." By using additional symbols for
   ten thousands, hundred thousands, millions, and so on,
   any number, however large, could be written in this same
   fashion.
      Yet it is not surprising that this would not be popular.
   Even if a Greek had thought of it he would have been re-
   peucd by the necessity of writing those tiny symbols.  In an
   age of band-copying, additional symbols meant additional
   labor and scribes would resent that furiously.
      Of course, one might easily decide that the symbols
   weren't necessary.  The Groups, one could agree, could al-
   ways be written right to left in increasing values.  The units
   would be at the right end, the tens next on the left, the hun-
   dreds next, and so on.  In that case, BEHA would be "two
   thousand five hundred eighty-one" and EEEE would be
   "five thousand five hundred fifty-five" even without the little
   symbols on top.
                                 158

         Here, though, a difficulty would creep in.  What if there
      were no groups of ten, or perhaps no units, in a particular
      number?  Consider the number "ten" or the number "one
      hundred and one." The former is made up of one group of
      ten and no units, while the latter is made up of one group
      of hundreds, no groups of tens, and ont unit.  Using sym-

      bols over the columns, the numbers could be written A and

      A A, but now you would not dare leave out the little sym-
      bols.  If you did, how could you differentiate A meaning
      "ten" from A meaning "one" or AA meaning "one hun-
      dred and one" from AA meaning "eleven" or AA meaning
      "one hundred and ten"?
         You might try to leave a gap so as to indicate "one hun-
      dred and one" by A A. But then, in an age of hand-copy-
      ing, how quickly would that become AA, or, for that mat-
      ter, how quickly might AA become A A? Then, too, how
      would you indicate a gap at the end of a symbol?  No, even
      if the Greeks thought of this system, they must obviously
      have come to the conclusion that the existence of gaps in
      numbers made this attempted simplification impractical.
      They decided it was safer to let J stand for "ten" and SA
      for "one hundred and one" and to Hades with little sym-
      bols.
         What no Greek ever thought of-not even Archimedes
      himself-was that it wasn't absolutely necessary to work
      with gaps.  One could fill the gap with a symbol by letting
      one stand for nothing-for "no groups." Suppose we use $
      as such a symbol.  Then, if "one hundred and one",is made
      up of one group of hundreds, no groups of tens, an one
                              + - I
      unit, it can be written A$A.  If we do that sort of thing, all
      gaps are eliminated and we don't need the little symbols
      on top.  "One" becomes A, "ten" becomes A$, "one hun-
      dred" becomes A$$, "one hundred and one" becomes
      A$A, "one hundred and ten" becomes AA$, and so on.
      Any number, however large, can be written with the use of
      exactly nine letters plus a symbol for nothinc,
                                   159

      Surely this is the simplest thing in the world-after you
    think of it.
      Yet it took men about five thousand years, counting
    from the beginning of number symbols, to think of a sym-
    bol for nothing.  The man who succeeded (one of the most
    creative and original thinkers in history) is unknown.  We
    know only that he was some Hindu who lived no later
    than the ninth century.
      The Hindus called the symbol sunyo, meaning "empty."
    This symbol for nothing was picked up by the Arabs, who
    termed it sifr, which in their language meant "empty." This
    has been distorted into our own words "cipher" and, by
    way of zefirum, into "zero."
      Very slowly, the new svstem of numerals (called "Ara-
    bic numerals" because the Europeans learned of them from
    the Arabs) reached the West and replaced the Roman sys-
    tem.
      Because the Arabic numerals came from lands which
    did not use the Roman alphabet, the shape of the numerals
    was nothing like the letters of the Roman alphabet and
    this was good, too.  It rerroved word-number confusion
    and reduced gematria from the everyday occupation of
    anyone who could read, to a burdensome folly that only a
    few would wish to bother with.
      The Arabic numerals as now used by us are, of course,
    1, 2, 3, 4, 5, 6, 7, 8, 9, and the all-important 0. Such is
    our reliance on these numerals (which are internationally
    accepted) that we are not even aware of the extent to which
    we rely on them.  For instance, if this chapter has seemed
    vaauely queer to you, perhaps it was because I had delib-
    eratclv refrained from using Arz.bic numerals all through.
      We ail know the great simplicity Arabic numerals have
    lent 'Lo arithmetical computation.  The unnecessary load
    they took off the human mind, all because of the presence
    of t' e zero, is simply incalculable.  Nor has this fact gone
    unnot.ccd in the Engl'sh language.  Tle importance of the
    zero is reflected in the fact that when we work out an
    arithmetical computation we are (to use a term now slightly
                                160

    old-fashioned) "ciphering." And when we work out some
    code, we are "deciphering" it.
       So if you look once more at the title of this chapter, you
    will see that I am not being cynical.  I mean it literally.
    Nothing counts!  The symbol for nothing makes all the dif-
    ference in the world.

                               161

                       13. C FOR CELERITAS

      If ever an equation has come into its own it is Ein         stein's
      e = mc  2. Everyone can rattle it off now, from the highest
      to the lowest; from the rarefied intellectual height of the
      science-fiction reader, through nuclear physicists, college
      students, newspapers reporters, housewives, busboys, all
      the way down to congressmen.
         Rattling it off is not, of course, the same as understand-
      ing it; any more than a quick paternoster (from which, in-
      cidentally, the word "patter" is derived) is necessarily evi-
      dence of deep religious devotion.
         So let's take a look at the equation.  Each letter is the
      initial of a word representing the concept it stands for.
      Thus, e is the initial letter of "energy" and m of "mass."
      As for c, that is the speed of light in a vacuum, and if you
      ask why c, the answer is that it is the initial letter of celeri-
      tas, the Latin word meaning "speed."
         This is not all, however.  For any equation to have mean-
      ing in physics, there must be an understanding as to the
      units being used.  It is meaningless to speak of a mass of
      2.3, for instance.  It is necessary to say 2.3 grams or 2.3
      pounds or 2.3 tons; 2.3 alone is worthless.
         Theoretically, one can choose whatever units are most
      convenient, but as a matter of convention, one system used
      in physics is to start with "grams" for mass, "centimeters"
      for distance, and "seconds" for time; and to build up, as
      far as possible, other units out of appropriate combinations
      of these three fundamental ones.
         Therefore, the m in Einstein's equation is expressed in
      grams, abbreviated gm.  The c represents a speed-that is,
      a distance traveled in a certain time.  Using the fundamental
                                     162

     units, this means the number of centimeters traveled in a
     certain number of seconds.  The units of c are therefore
     centimeters per second, or cm/sec.
        (Notice that the word "per" is represented by a fraction
     line.  The reason for this is that to get a speed represented
     in lowest terms, that is, the number of centimeters traveled
     in one second, you must divide the number of centimeters
     traveled by the number of seconds of traveling. _If you
     travel 24 centimeters in 8 seconds, your speed is 24 centi-
     meters -- 8 seconds, or 3 cm/sec.)
        But, to get back to our subject, c occurs as its square in
     the equation.  If you multiply c by c, you get C2.  It is, how-
     ever, insufficient to multiply the numerical value of c by it-
     self.  You must also multiply the unit of c by itself.
        A common example of this is in connection with meas-
     urements of area.  If you have a tract of land that is 60 feet
     by 60 feet, the area is not 60 x 60, or 3600 feet.  It is 60
     feet x 60 feet, or 3600 square feet.
        Similarly, in dealing with  C2, you  must multiply cm/sec
     'by cm/sec and end with the units     CM2 /seC2 (which can be
     read as centimeters squared per seconds squared).
        The next question is: What is the unit to be used for e?
     Einstein's equation itself will tell us, if we remember to
     treat units as we treat any other algebraic symbols.  Since
     e = mc  2, that means the unit of e can be obtained by mul-
     tiplying the unit of m by the unit  Of C2. Since the unit of m
     is gm and that of c2 is    CM2  /seC2, the unit of e is gm x
     CM2/seC2.  In algebra we represent a x b as ab; conse-
     quently, we can run the multiplication sign out of the unit
     of e and make it simply gm    CM2/SCC2   (which is read "gram
     centimeter squared per second squared).

        As it happens, this is fine, because long before Einstein
     worked out his equation it had been decided that the unit
     of energy on the gram-centimeter-second basis had to be
     gm CM2  /seC2. I'll explain why this should be.
        The unit of speed is, as I have said, cm/sec, but what
     happens when an object changes speed?  Suppose that at a
     given instant, an object is traveling at 1 cm/sec, while a
     second later it is travelling at 2 cm/sec; and another second
                                   163

      later it is traveling at 3 cm/sec.  It is, in other words, "ac-
      celeratin " (also from the Latin word celeritas).
               9
         In the case I've just cited, the acceleration is 1 centi-
      meter per secondevery second, since each successive sec-
      ond it is going I centimeter per second faster.  You might
      say that the acceleration is I emlsec per second.  Since we
      are letting the word "per" be represented by a fraction
      mark, this may be represented as 1 cm/sec/sec.
         As I said before, we can treat the units by the same
      manipulations used for algebraic symbols.  An expression
      like alblb is equivalent to alb     b, which is in turn equiva-
      lent to alb x Ilb, which is in turn equivalent to alb2.  By
      the same reasoning, I cm/sec/sec is equivalent to 1 cm/
      seC2 and it is CM/SCC2 that is therefore the unit of accelera-
      tion.
         A "force" is defined, in Newtonian physics, as some-
      thing that will bring about an acceleration.  By Newton's
      First Law of Motion any object in motion, left to itself,
      will travel at constant speed in a constant direction forever.
      A speed in a particular direction is referred to as a t'veloc-
      ity," so we might, more simply, say that an object in mo-
      tion, left to itself, will travel at constant velocity forever.
      This velocity may well be zero, so that Newton's First'Law
      also says that an object at rest, left to itself, will remain at
      rest forever.
         As soon as a force, which may be gravitational, electro-
      magnetic, mechanical, or anything, is applied, however,
      the velocity is changed.  This means that its speed of travel
      or its direction of travel or both is changed.
         The quantity of force applied to an object is measured
      by the amount of acceleration induced, and also by the
      mass of the object, since the force applied to a massive ob-
      ject produces less acceleration than the same force applied
      to a light object. (If you want to check this for yourself,
      kick a beach ball with all your might and watch it accel-
      erate from rest to a good speed in a very short time.  Next
      kick a cannon ball with all your might and observe-while
      hopping in agony-what an unimpressive acceleration you
      have imparted to it.)
                                    164

     to assure yourself, first, of a supply of nine hundred quin-
     tiflion ergs.
         This sounds impressive.  Nine hundred quintillion ergs,
     wow!
         But then, if you are cautious, you might stop and think:
     An erg is an unfamiliar unit.  How large is it anyway?
         After all, in Al Capp's Lower Slobbovia, the sum of a
     billion slobniks sounds like a lot-until you find that the rate
     of exchange is ten billion slobniks to the dollar.

         So-How large is an erg?
         Well, it isn't large.  As a matter of fact, it is quite a small
     unit.  It is forced on physicists by the lo 'c of the gram-cen-
                                                91
     timeter-second system of units, but it ends in being so small
     a unit as to be scarcely useful.  For instance, consider the
     task of lifting a pound weight one foot against gravity.
     That's not difficult and not much energy is expended.  You
     could probably lift a hundred pounds one foot without
     completely incapacitating yourself.  A professional strong
     man could do the same for a thousand pounds.
         Nevertheless, the energy expended in lifting one pound
     one foot is equal to 13,558,200 ergs.  Obviously, if any
     trifling bit of work is going to involve ergs in the tens of
     millions, we need other and larger units to keep the nu-
     merical values conveniently low.
         For instance, there is an energy unit called a joule, which
     is equal to 10,000,000 ergs.
         This unit is derived from the name of the British physi-
     cist James Prescott Joule, who inherited wealth and a brew-
     ery but spent his time in research.  From 1840 to 18 9 e
     ran a series of meticulous experiments which demonstrated
     conclusively the quantitative interconversion of heat and
     work and brought physics an understanding of the law of
     conservation of energy.  However, it was the erman sci-
     entist Hermann Ludwig Ferdinand von Helmholtz who first
     put the law into actual words in a paper presented in 1847,
     so that he consequently gets formal credit for -,the discov-
     ery.
         (The word "joule," by the way, is most commonly pro-
     nounced "jowl," although Joule himself probably pro-
                                     167

      nounced his name "jool." In any case, I have heard over-
      precise people pronounce the word "zhool" under the im-
      pression that it is a French word, which it isn't.  These are
      the same people who pronounce "centigrade" and "centri-
      fuge" with a strong nasal twang as "sontigrade" and "son-
      trifugp,," under the impression that these, too, are French
      words.  Actually, they are from the Latin and no pseudo-
      French pronunciation is required.  There is some justifica-
      tion for pronouncing "centimeter" as "sontimeter," since
      that'is a French word to begin with, but in that case one
      should either stick to English or go French all the way and
      pronounce it "sontimettre," with a light accent on the third
      syllable.)
        Anyway, notice the usefulness of the joule in everyday
      affairs.  Lifting a pound mass a distance of one foot against
      gravity requires energy to the amount, roughly, of 1.36
      joules-a nice, convenient figure.

        Meanwhile, physicists who were studying heat had in-
      vented a unit that would be convenient for their purposes.
      This was the "calorie" (from the Latin word color meaning
      "heat").  It can be abbreviated as cal.  A calorie is the
      amount of heat required to raise the temperature of I gram
      of water from 14.5' C. to 15.5' C. (The amount of heat
      necessary to raise a gram of water one Celsius degree varies
      slightly for different temperatures, which is why one must
      carefully specify the 14.5 to 15.5 business.)
        Once it was demonstrated that all other forms of energy
      and all forms of work can be quantitatively converted to
      heat, it could be seen that any unit that was suitable for
      heat would be suitable for any other kind of energy or
      work.
        By actual measurement it was found (by Joule) that
      4.185 joules of energy or work could be converted into pre-
      cisely I calorie of heat.  Therefore, we can say that I cal
      equals 4.185 joules equals 41,850,000 ergs.
        Althouo the calorie, as defined above, is suitable for
      physicists, it is a little too small for chemists.  Chemical re-
      actions usually release or absorb heat in quantities that,
                                   168

     under the conventions used for chemical calculations, re-
     sult in numbers that are too large..For instance, I gram of
     ,carbohydrate burned to carbon dioxide and water (either
     in a furnace or the human body, it doesn't matter) liberates
     roughly 4000 calories.  A gram of fat would, on burning,
     liberate roughly 9000 calories.  Then again, a human being,
     doing the kind of work I do, would use up about 2,500,000
     calories per day.
        The figures would be more convenient if a larger unit
     were used, and for that purpose a larger calorie was in-
     vented, one that would represent the amount of heat         re-
     quired to raise the temperature of 1000 grams (1 kilo-
     gram) of water from 14.50 C. to 15.5' C. You see, I sup-
     pose, that this larger calorie is a thousand times as great as
     the smaller one.  However, because both units'are called
      calorie," no end of confusion has resulted.
        Sometimes the two have been distinguished as "small
     calorie" and "large calorie"; or "gram-calorie" and "kilo-
     gram-calorie"; or even "calorie" and "Calorie." (The last
     alternative is a particularly stupid one, since' in speech-
     and scientists must occasionally speak-there is no way of
     distinguishing a C and a c by pronunciation alone.)
        My idea of the most sensible way of handling the matter
     is this: In the metric system, a kilogram equals 1000
     grams; a kilometer equals 1000 meters, and so on.  Let's
     call the large calorie a kilocalorie (abbreviated kcal) and
     set it equal to 1000 calories.
        In summary, then, we can say that 1 kcal equals 1000
     cal or 4185 joules or 41,850,000,000 ergs.

        Another type of energy unit arose in a roundabout way,
     via the concept of "power." Power is the rate at which
     work is done.  A machine might lift a ton of mass one foot
     against gravity in one minute or in one hour.  In each case
     the energy consumed in the process is the same, but it takes
     a more powerful heave to lift that ton in one minute than
     in one hour.
        To raise one pound of mass one foot against gravity
     takes one foot-pound (abbreviated I ft-lb) of energy.  To
                                   169

     expand that energy in one second is to deliver 1 foot-
     pound per second (1 ft-lb/sec) and the ft-lb/sec is there-
     fore a permissible unit of power.
        The first man to make a serious effort to measure power
     accuratel was James Watt (1736-1819).  He compared
              y
     the power   of the steam engine he had devised with the
     power delivered by a horse, thus measuring his machine's
     rate of delivering energy in horsepower (or hp).  In doing
     so, he first measured the power of a horse in ft-lb/sec and
     decided that I hp equals 550 ft-lb/sec, a conversion figure
     which is now standard and official.
        The use of foot-pounds per second and horsepower is
     perfectly legitimate and, in fact, automobile and airplane
     engines have their power rated in horsepower.  The trouble
     with these units, however, is that they don't tie in easily
     with the gram-centimeter-second system.  A foot-pound is
     1.355282 joules and a horsepower is 10.688 kilocalories
     per minute.  These are inconvenient numbers to deal with.
        The ideal am centimeter-second unit of power would
     be ergs per     on@ (erg/sec). However, since the erg is
     such a small unit, it is more convenient to deal with joules
     per second (joule/sec).  And since I joule is equal to 10,-
     000,000 ergs, 1 joule/sec equals 10,000,000 erg/sec, or
     10,000,000 gM CM2/sec3.
        Now we need a monosyllable to express the unit joule/
     see, and what better monosyllable than the monosyllabic
     name of the gentleman who first tried to measure power.
     So 1 joule/sec was set equal to 1 watt.  The watt may be
     defined as representing the delivery of I joule of energy per
     second.
        Now if power is multiplied by time, you are back to
     energy.  For instance, if 1 watt is multipled by 1 second, you
     have I watt-sec.  Since 1 watt equals 1 joule/sec, 1 watt-sec
     equals I joule/sec x see, or I joule sec/sec.  The sees can-
     cel as you would expect in the ordinary algebraic manipu-
     lation tG which units can be subjected, and you end with
     the statement that I watt-sec is equal to 1 joule and is,
     therefore, a unit of energy.
        A larger unit of energy of this sort is the kilowatt-,hour
                                  170

      (or kw-hr).  A kilowatt is equal to 1000 watts and an hour
      -is equal to 3600 seconds.  Therefore a kw-hr is equal to
      1000 x 3600 watt-sec, or to 3,600,000 joules, or to 36,-
      000,000,000,OGO ergs.
        Furthermore, since there are 4185 joules in a kilocalorie
      (kcal), 1 kw-hr is equal to 860 kcal or to 860,000 cal.
        A human being who is living on 2500 kcal/day is de-
      livering (in the form of heat, eventually) about 104 kcal/
      hr, which is equal to 0.120 kw hr/hr or 120 watts.  Next
      tirhe you're at a crowded cocktail party (or a crowded sub-
      way train or a crowded theater audience) on a hot evening
      in August, think of that as each additional person walks in.
      Each entrance is equivalent to turning on another one hun-
      dred twenty-watt electric bulb.  It will make you feel a lot
      hotter and help you appreciate the new light of understand-
      ing that science brings.

        But back to the subject.  Now, you see, we have a variety
      of units into which we can translate the amount of energy
      ,resulting from the complete conversion of I gram of mass.
      That gram of mass will liberate:

             900,000,000,000,000,000,000 ergs,
             or        90,000,000,000,000 joules,
             or        21,500,000,000,000 calories,
             or            21,500,000 000 kilocalories,
                                       '600 kilowatt-hours.
             or                 25,000,

        Which brings us to the conclusion that although the erg
      is indeed a tiny unit, nine hundred quintillion of them still
      mount up most impressively.  Convert a mere one gram of
      mass into energy and use it with perfect efficiency and you
      can keep  a thousand-watt electric light bulb running for
      25,000,000 hours, which is equivalent to 2850 years, or
      the time from the days of Homer to, the present.
        How's that for solving the fuel problem?
        We could work it the other way around, too.  We might
      ask: How much mass need we convert to produce I kilo-
      watt-hour oi energy?
                                    171

        Well, if I gram of mass produces 25,000,000 kilowatt-
     hours of energy, then 1 kilowatt-hour of energy is produced
     by 1/25,000,000 gram.
        You can see that this sort of calculation is going to take
     us into small mass units indeed.  Suppose we choose a unit
     smaller than the gram, say the microgram.  This is equal to
     a millionth of a gram, i.e., 10-11 gram.  We can then say
     that I kilowatt-hour of energy is produced by the conver-
     sion of 0.04 micrograms of mass.
        Even the microgram is an inconveniently large unit of
     mass if we become interested in units of energy smaller
     than the kilowatt-hour.  We could therefore speak of a
     micromicrogram (or, as it is now called, a picogram).  This
     is a millionth of a millionth of a gram (10-12     gram) or a
     trillionth of a gram.  Using that as a unit, we can say that:

     1 kilowatt-hour is equivalent to 40,000               picograms
     I kilocalorie         fl,           46.5
     1 calorie                             0.0465
     1 joule                               0.0195
     I erg                                 0.00000000195

        To give you some idea    of what this means, the mass of
     a typical human cell is about 1000 picograms.  If, under
     conditions of dire emergency, the body possessed the abil-
     ity to convert mass to energy, the conversion of the con-
     tents of 125 selected cells (which the body, with 50,000,-
     000,000 000 cells or so, could well afford) would supply
     the boY; with 2500 kilocalories and keep it going for a full
     day.

        The amount of mass which, upon conversion, yields 1
     erg of energy (and the erg, after all, is the proper unit of
     energy in the gram-centimeter-second system) is an incon-
     veniently small fraction even in terms of picograms.
        We need units smaller still, so suppose we turn to the
     picopicogram   (10-24 gram), which is a trillionth of a tril-
     lion of a gram, or a septillionth of a gram.  Using the pico-
     picogram, we find that it takes the conversion of 1950
     picopicograms of mass to produce an erg of energy.
                                   172

        And the significance?  Well, a single hydrogen atom has
     a mass of about 1.66 picopicograms.  A uranium-235 atom
     has a mass of about 400 picopicograms.  Consequently, an
     erg of energy is produced by the total conversion of 1200
     hydrogen atoms or by 5 uranium-235 atoms.
        In ordinary fission, only 1/1000 of the mass is converted
     to energy so it takes 5000 fissioning uranium atoms to
     produce I erg of energy.  In hydrogen fusion, 1/100 of the
     mass is converted to energy, so it takes 120,000 fusing
     hydrogen atoms to produce 1 erg of energy.
        And with that, we can let e    mc,2 rest for the nonce.

                                 173

               14. A PIECE OF THE ACTION

     When my book 1, Robot was reissued by the estimable
     gentlemen of Doubleday & Company, it was with a great
     deal of satisfaction that I noted- certain reviewers (posses-
     sing obvious intelligence and good taste) beginning to refer
     to it as a "classic."
        "Classic" is derived in exactly the same way, and has
     precisely the same meaning, as our own "first-class" and
     our colloquial "classy"; and any of these words represents
     my own opinion of 1, Robot, too; except that (owing to
     my modesty) I would rather die than admit it.  I mention
     it here only because I am speaking confidentially.
        However, "classic" has a secondary meaning that dis-
     pleases me.  The word came into its own when the literary
     men of the Renaissance used it to refer to those works of
     the ancient Greeks and Romans on which they were model-
     ing their own efforts.  Consequently, "classic" has come to
     mean not only good, but also old.
        Now 1, Robot first appeared a number of years    -ago and
     some of the material in it was written . . . Well, never
     mind.  The point is that I have decided to feel a little hurt
     at being considered old enough to have written a classic,
     and therefore I will devote this chapter to the one field
     where "classic" is rather a term of insult.
        Naturally, that field must be one where to be old is,
     almost automatically, to be wrong and incomplete.  One
     may talk about Modem Art or Modern Literature or
     Modem Furniture and sneer as one speaks, comparing
     each, to their disadvantage, with the greater work of earlier
     ages.  When one speaks of Modem Science, however, one
     removes one's hat and places it reverently upon the breast.
        In physics, particularly, this is the case.  There is Modern
                                  174

     Physics and there is (with an offhand, patronizing half-
     smile) Classical Physics.  To put it into Modern Terrninol-
     ogy, Modern Physics is in, man, in, and Classical Physics
     is like squaresvhle.
       What's more, the division in physics is sharp.  Everything
     after 1900 is Modern; everything before 1900 is Classical.
       That looks arbitrary, I admit; a strictly parochial
     twentieth-century outlook.  Oddly enough, though, it is per-
     fectly legitimate.  The year 1900 saw a major physical
     theory entered into the books and nothing has been quite
     the same since.
       By now you have guessed that I am going to tell you
     about it.

       The problem began with German physicist Gustav
     Robert Kirchhoff who, with Robert Wilhelm Bunsen
     (popularizer of the Bunsen burner), pioneered in the de-
     velopment of spectroscopy in 1859.  Kirchhoff discovered
     that each element, when brought to incandescence, gave
     off certain characteristic frequencies of light; and that the
     vapor of that element, exposed to radiation from a source
     hotter than itself, absorbed just those frequencies it itself
     emitted when radiating. In short, a material will        absorb
     those frequencies which, under other conditions, it will
     radiate; and will radiate those frequencies which, under
     other conditions, it will absorb.'
       But su Ippose that we consider a body which will absorb
     all frequencies of radiation that fall upon it-absorb them
     completely.  It will then reflect none and will therefore ap-
     pear absolutely black.  It is a "black body." Kirchhoff
     pointed out that such a body, if heated to incandescence,
     would then necessarily have to radiate all frequencies of
     radiation' Radiation over a complete range in this manner
     would be "black-body radiation."
       Of course, no body was absolutely black.  In the 1890s,
     however, a German physicist named Wilhelm Wien
     thought of a rather interesting dodge to get around tiat.
     Suppose you had a furnace with a small opening.  Any
     radiation that passes through the opening is either ab-
     sorbed by the rough wall opposite or reflected.  The re-
                                   175

     flected radiation strikes another wall and is again partially
     absorbed.  What is reflected strikes another wall, and so
     on. Virtually none of the radiation survives to find its way
     out the small opening again.  That small opening, then,
     absorbs the radiation and, in a manner of speaking, reflects
     none.  It is a black body.  If the furnace is heated, the radia-
     tion that streams out of that small opening should be
     black-body radiation and should, by Kircbhoff's reasoning,
     contain all frequencies.
        Wien proceeded to study the characteristics of this
     black-body radiation.  He found that at any temperature, a
     wide spread of frequencies was indeed included, but the
     spread was not an even one.  There was a peak in the mid-
     dle.  Some intermediate frequency was radiated to a greater
     extent than other frequencies either higher or lower than
     that peak frequency.  Moreover, as the temperature was
     increased, this peak was found to move toward the higher
     frequencies.  If the absolute temperature were doubled, the
     frequency at the peak would also double.
        But now the question arose: Why did black-body radia-
     tion distribute itself like this?
        To see why the question was puzzling, let's consider
     infrared light, visible light, and ultraviolet light.  The fre-
     quency range of infrared light, to begin with, is from one
     hundred billion (100,000,000,000) waves per second to
     four hundred trillion (400,000,000,000,000) waves per
     second.  In order to make the numbers easier to handle,
     let's divide by a hundred billion and number the frequency
     not in individual waves per second but in hundred-billion-
     wave packets per second.  In that case the range of infrared
     would be from 1 to 4000.
        Continuing to use this system, the range of visible licht
     would be from 4000 to 8000; and the range of ultraviolet
     light would be from 8000 to 300,000.
        Now it might be supposed that if a black body absorbed
     all radiation with equal ease, it ought to give off all radia-
     tion with equal case.  Whatever its temperature, the energy
     it had to radiate might be radiated at any frequency, the
     particular choice of frequency being purely random.
        But suppose you were choosing numbers, any numbers
                                  176

      with honest radomness, from I to 300,000.  If you did this
      repeatedly, trillions of times, 1.3 per cent of your numbers
      would be less than 4000; another 1.3 per cent would be
      between 4000 and 8000      ' and 97.4 per cent would be
      between 8000 and 300,000.
        This is like saying that a black body ought to radiate
      1.3 per cent of its energy in the infrared, 1.3 per cent in
      visible light, and 97.4 per cent in the ultraviolet.  If the
      temperature went up and it had more energy to radiate,
      it ought to radiate more at every frequency but the relative
      amounts in each range ought to be unchanged.
        And this is only if we confine ourselves to nothing of
      still higher frequency than ultraviolet.  If we include the
      x-ray frequencies, it would turn out that just about nothing
      should come off in the visible light at any temperature.
      Everything would be in ultraviolet and x-rays.
        An English physicist, Lord Rayleigh (1842-1919),
      worked out an equation which showed exactly this.  The
      radiation emitted by a black body increased steadily as one
      went up the frequencies.  However, in actual practice, a
      frequency peak was reached after which, at higher fre-
      quencies still, the quantity of radiation decreased again.
      Rayleigh's equation was interesting but did not reflect
      reality.
        Physicists referred to this prediction of the Rayleigh
      equation as the "Violet Catastrophe"-the fact that every
      body that bad energy to radiate ought to radiate practically
      all of it in the ultraviolet and beyond.
        Yet the whole point is that the Violet Catastrophe does
      not take place.  A radiating body concentrated its radiation
      in the low frequencies.  It radiated chiefly in the infrared at
      temperatures below, say, 1000' C., and radiated mainly
      in the visible region even at a temperature as high as
      6000' C., the temperature of the solar surface.
        Yet Rayleigh's equation was worked out according to
      the very best principles available anywhere in physical
      theory-at the time.  His work was an ornament of what
      we now call Classical Physics.
        Wien himself worked out an equation which described
      the frequency distribution of black-body radiation in the
                                   177

    bigh-frequency range, but he had no explanation for why
    it worked there, and besides it only worked for the high-
    frequency range, not for the low-frequency.
       Black, black, black was the color of the physics mood
    all through the later 1890s.

       Bt4t then arose in 1899 a champion, a German physicist,
    Max Karl Ernst Ludwig Planck.  He reasoned as fol-
   -lows . . .
       If beautiful equations worked out by impeccable reason-
    ing from highly respected physical foundations do not de-
    scribe the truth as we observe it, then either the reason-
    ing or the physical foundations or both are wrong.
       And if there is nothing wrong about the reasoning (and
    nothing wrong could be found in it), then the physical
    foundations had to be altered.
       The physics of the day required that all frequencies of
    light be radiated with equal probability by a black body,
    and Planck therefore proposed that, on the contrary, they
    were not radiated with equal probability.  Since the equal-
    probability assumption required that more and more light
    of higher and higher frequency be radiated, whereas the
    reverse was observed, Planck further proposed that the
    probability of radiation ought to decrease as frequency
    increased.
       In that case, we would now have two effects.  The first
    effect would be a tendency toward randomness which
    would favor high frequencies and increase radiation as
    frequency was increased.  Second, there was the new Planck
    effect of decreasing probability of radiation as frequency
    went up.  This would favor low frequencies and decrease
    radiation as frequency was increased.
       In the low-frequency range the first effect is dominant,
    but in the high-frequency range the second effect increas-
    ingly overpowers the first.  Therefore, in black-body tadia-
    tion, as one goes up the frequencies, the amount of radia-
    tion first increases, reaches a peak, then decreases again-
    exactly as is observed.
       Next, suppose the temperature is raised.  'ne first effect
    can't be changed, for randomness is randomness.  But sup-
                                178

      pose that as the temperature is raised, the probability of
      emitting high-frequency radiation increases.  The second
      effect, then, is steadily weakened as the temperature goes
      up. In that case, the radiation continues to increase with
      increasing frequency for a longer and longer time before it
      is overtaken and repressed by the gradually weakening
      second effect.  The peak radiation, consequently, moves
      into higher and higher frequencies as the temperature goes
      up-precisely as Wien had discovered.
        On this basis, Planck was able to work out an equation
      that described black-body radiation very nicely both in the
      low-frequency and high-frequency range.
        However, it is all very well to say that the higher the
      frequency the lower the probability of radiation, but why?
      There was nothing in the physics of the time to explain
      that, and Planck had to make up something new.
        Suppose that energy did not flow continuously, as
      physicists had, always assumed, but was given off in pieces.
      Suppose there were "energy atoms" and these increased in
      size as frequency went up.  Suppose, still further, that light
      of a particular frequency could not be emitted unless
      enough energy had been accumulated to make up an
      66energy atom" of the size required by that frequency.
        The higher the frequency the larger the "energy atom"
      and the smaller the probability of its accumulation at any
      given instant of time.  Most of the energy would be lost
      as radiation of lower frequency, where the "energy atoms"
      were smaller and more easily accumulated.  For that rea-
      son, an object at a temperature of 400' C. would radiate
      its heat in the infrared entirely.  So few "energy atoms"
      of visible light size would be accumulated that no visible
      glow would be produced.
        As temperature went up, more energy would be gen-
      erally available and the probabilities of accumulating a
      high-frequency "energy atom" would increase.  At 6000' C.
      most of the radiation would be in "energy atoms" of visible
      light, but the still larger "energy atoms" of ultraviolet
      would continue to be formed only to a minor extent.

        But how big is an "energy atom"?  How much energy
                                  179

    does it contain?  Since this "how much" is a key question,
    Planck, with admirable directness, named the "energy
    atom" a quantum, which is Latin for "how much?" the
    plural is quanta.
       For Planck's equation for the distribution of black-body
    radiation to work, the size of the quantum had to be
    directly proportional to the frequency of the radiation.  To
    express this mathematically, let us represent the size of the
    quantum, or the amount of energy it contains, by e (for
    energy).  The frequency of radiation is invariably repre-
    sented by physicists by means of the Greek letter nu (v).
       If energy (e) is proportional to frequency (v), then e
    must be equal to v multiplied by some constant.  This con-
    stant, called Planck's constant, is invariably represented as
    h. The equation, giving the size of a quantum for a par-
    ticular frequency of radiation, becomes:

                  e = hv              (Equation 1)

       It is this equation, presented to the world in 1900,
    which is the Continental Divide that separates Classical
    Physics from Modern Physics.  In Classical Physics, energy
    was considered continuous; in Modern Physics it is con-
    sidered to be composed of quanta.  To put it another way,
    in Classical Physics the value of h is considered to be 0; in
    Modern Physics it is considered to be greater than 0.
       It is as though there were a sudden change from con-
    sidering motion as taking place in a smooth glide, to mo-
    tion as taking place in a series of steps.
       There would be no confusion if steps were long ga-
    lumphing strides.  It would be easy, in that case, to dis-
    tinguish steps from a glide.  But suppose one minced along
    in microscopic little tippy-steps, each taking a tiny frac-
    tion of a second.  A careless glance could not distinguish
    that from a glide.  Only a painstaking study would show
    that your head was bobbing slightly with each step.  The
    smaller the steps, the harder to detect the difference from
    a glide.
       In the same way, everything would depend on just how
    big individual- quanta were; on how "grainy" energy was.
                                 180

      'ne size of the quanta depends on     'the size of Planck's
      constant, so let's consider that for a while.

        If we solve Equation I for h, we get:

                   h = elv              (Equation 2)

      Energy is very frequently measured in ergs (see Chapter
      13).  Frequency is measured as "so many per second" and
      its units are therefore "reciprocal seconds" or "I/second."
        We must treat the units of h as we treat h itself.  We
      get h by dividing e by v; so we must get the units of h
      by dividing the units of e by the units of v. When we
      divide ergs by I/second we are multiplying ergs by sec-
      onds, and we find the units of h to be "erg-seconds." A
      unit which is the result of multiplying energy by time is
      said, by physicists, to be one of "action." Therefore,
      Planck's constant is expressed in units of action.
        Since the nature of the universe depends on the size of
      Planck's constant, we are all dependent on the size of the
      piece of action it represents.  Planck, in other words, had
      sought and found the piece of the action. (I understand
      that others have been searching for a piece of the action
      ever since, but where's the point since Planck has found
      it?)
        And what is the exact size of h? Planck found it had
      to be very small indeed.  The best value, currently ac-
      cepted, is: 0.0000000000000000000000000066256 erg-
      seconds,or 6.6256 x 10-2" erg-seconds.
        Now let's see if I can find a way of expressing just how
      small this is.  The human body, on an average day, con-
      sumes and expends about 2500 kilocalories in maintaining
      itself and performing its tasks.  One kilocalorie is equal to
      1000 calories, so the daily supply is 2,500,000 calories.
        One calorie, then, is a small quantity of energy from
      the human standpoint.  It is 1/2,500,000 of your daily
      store.  It is the amount of energy contained in 1/113,000
      of an ounce of sugar, and so on.
        Now imagine you are faced with a book weighing one
      pound and wish to lift it from the floor to the top of a
      bookcase three feet from the ground.  The energy expended
                                  181

    in lifting one pound through a distance of three feet against
    gravity is just about 1 calorie,.
       Suppose that Planck's constant were of the order of a
    calorie-second in size.  The universe would be a very
    strange place indeed.  If you tried to lift the book, you
    would have to wait until enough energy had been accumu-
    lated to make up the tremendously sized quanta made
    necessary by so large a piece of action.  Then, once it was
    accumulated, the book would suddenly be three feet in the
    air.
       But a calorie-second is equal to 41,850,000 erg-seconds,
    and since Planck's constant is 'Such a minute fraction of
    one erg-secoiid, a single calorie-second equals 6,385,400,-
    000,000,000,000,000,000,000,000,000 Planck's constants,
    or 6.3854 x 10:1@' Planck's constants, or about six and a
    third decillion Planck's constants.  However you slice it, a
    calorie-second is equal to a tremendous number of Planck's
    constants.
       Consequently, in any action such as the lifting of a one-
    pound book, matters are carried through in so many tril-
    lions of trillions of steps, each one so tiny, that motion
    seems a continuous glide.

       When Planck first introduced his "quantum theory      91  in
    1900, it caused remarkably little stir, for the quanta
    seemed to be pulled out of midair.  Even Planck himself
    was dubious-not over      his equation describing the dis-
    tribution of black-body radiation, to be sure, for that
    worked well; but about    the quanta he had introduced to
    explain the equation.
       Then came 1905, and in that year a 26-year-old theo-
    retical physicist, Albert Einstein, published fivo separate
    scientific papers on three subjects, any one of which would
    have been enough to establish him as a first-magnitude star
    in the scientific heavens.
       In two, he worked out the theoretical basis for "Brown-
    ian motion" and, incidentally, produced the machinery by
    which the actual size of atoms could be established for
    the first time.  It was one of these papers that earned him
    his Ph.D.
                                 182

        In the third paper, he dealt with the "photoelectric
      effect" and showed that although Classical Physics could
      not explain it, Planck's quantum theory could.
        This really startled physicists.  Planck had invented
      quanta merely to account for black-body radiation, and
      here it turned out to explain the photoelectric effect, too,
      something entirely different.  For quanta to strike in two
      different places like this, it seemed suddenly very reason-
      able to suppose that they (or something very like them)
      actually existed.
        (Einstein's fourth and fifth papers set up a new view of
      the universe which we call "The Special Theory of Rela-
      tivity." It is in these papers that he introduced his famous
      equation e =  MC2; see Chapter 13.
        These papers on relativity, expanded into a "General
      Theory" in 1915, are the achievements for which Einstein
      is known to people outside the world of physics.  Just the
      same, in 1921, when he was awarded the Nobel Prize for
      Physics, it was for his work on the photoelectric effect and
      not for his theory of relativity.)

        The value of h is so incredibly small that in the ordinary
      world we can ignore it.  The ordinary gross events of
      everyday life can be considered as though energy were a
      continuum.  This is a good "first approximation."
        However, as we deal with smaller and smaller energy
      changes, the quantum steps by which those changes'must
      take place become larger and larger in comparison.  Thus,
      a flight of stairs consisting of treads 1 millimeter high and
      3 millimeters deep would seem merely a slightly roughened
      ramp to a six-foot man.  To a man the size of an ant, how-
      ever, the steps would seem respectable individual obstacles
      to be clambered over with difficulty.  And to a man the
      size of a bacterium, they would be mountainous precipices
        lin the same way, by the time we descend into the world
      within the atom the quantum step has become a gigantic
      thing.  Atomic physics cannot, therefore, be described in
      Classical terms, not even as an approximation.
        The first to realize this clearly was the Danish physicist
      Niels Bohr.  In 1913 Bohr pointed out that if an electron
                                  183

    absorbed energy, it had to absorb it a whole quantum at
    a time and that to an electron a quantum was a large piece
    of en 'ergy that forced it to change its relationship to the
    rest of the atom drastically and all at once.
       Bohr pictured the electron as circling the atomic nucleus
    in a fixed orbit.  When it absorbed a quantum of energy, it
    suddenly found itself in an orbit farther from the nucleus
    -there was no in-between, it was a one-step proposition.
       Since only certain orbits were possible, according to
    Bohr's treatment of the subject, only quanta of certain size
    could be absorbed by the atom-only quanta large enoug
    to raise an electron from one permissible orbit to another.
    When the electrons dropped back down the line of per-
    missible orbits, they emitted radiations in quanta.  They
    emitted just those frequencies which went along with the
    size of quanta they could emit in going from one orbit to
    another.
       In this way, the science of spectroscopy was rational-
    ized.  Men understood a little more deeply why each ele-
    ment (consisting of one type of atom with one type of
    energy relationships among the electrons making up that
    type of atom) should radiate certain frequencies, and cer-
    tain frequencies only, when incandescent.  They also under-
    stood why a substance that could,absorb certain frequen-
    cies should also emit those same frequencies under other
    circumstances.
       In other words, Yirchhoff had started the whole problem
    and now it had come around fuil-circle to place his em-
    pirical discoveries on a rational basis.
       Bohr's initial picture was oversimple; but he and other
    men gradually made it more complicated, and capable of
    explaining finer and finer points of observation.  Finally,
    in 1926, the Austrian physicist Erwin Schri3dinger worked
    out a mathematical treatment that was adequate to an-
    alyze the workings of the particles making up the interior
    of the atom according to the principles of the quantum
    theory.  This was called "quantum mechanics," as opposed
    to the "classical mechanics" based on Newton's three laws
    of motion and it is quantum mechanics that is the founda--
    tion of Modern Physics.
                                184

                  15. WELCOME, STRANGER!

      There are fashions in science as in everything else.  Con-
      duct an experiment that brings about an unusual success
      and before you can say, "There are a dozen imitations!"
      there are a dozen imitations!
        Consider the element xenon (pronounced zee'non), dis-
      covered in 1898 by William Ramsay and Morris William
      Travers.  Like other elements of the same type it was iso-
      lated from liquid air.  The existence of these elements in air
      had remained unsuspected through over a century of
      ardent chemical analysis of the air, so when they finally
      dawned upon the chemical consciousness they were greeted
      as strange and unexpected newcomers.  Indeed, the name,
      xenon, is the neutral form of the Greek word for "strange,"
      so that xenon is "the strange one" in all literalness.
        Xenon belongs to a group of elements commonly known
      as the "inert gases" (because they are chemically inert)
      or the "rare gases" (because they are rare), or "noble
      gases" because the standoffishness that results from chemi-
      cal inertness seems to indicate a haughty sense of seff-
      importance.
        Xenon is the rarest of the stable inert gas and, as a
      matter of fact, is the rarest of all the stable elements on
      Earth.  Xenon occurs only in the atmosphere, and there it
      makes up about 5.3 parts per million by weight.  Since the
      atmosphere weighs about 5,500,000,000,000,000 (five
      and a half quadrillion) tons, this means that the planetary
      supply of xenon comes to just about 30,000,000,000
      (thirty billion) tons.  This seems ample, taken in full, but
      picking xenon atoms out of the overpoweringly more corn-
      ,mon constituents of the atmosphere is an arduous task and
                                   185

    so xenon isn't a common substance and never will be.
       What with one thing and another, then, xenon was not
    a popular substance in the chemical laboratories.  Its chem-
    ical, physical, and nuclear properties were worked out, but
    beyond that there seemed little worth doing with it.  It
    remained the little strange one and received cold shoulders
    and frosty smiles.
       Then, in 1962, an unusual experiment involving xenon
    was announced whereupon from all over the world broad
    smiles broke out across chemical countenances, and little
    xenon was led into the test tube with friendly solicitude.
    "Welcome, stranger!" was the cry everywhere, and now
    you can't open a chemical journal anywhere without find-
    ing several papers on xenon.
       What happened?
       If you expect a quick answer, you little know me.  Let
    me take my customary route around Robin Hood's barn
    and begin by stating, first of all, that xenon is a gas.

       Being a gas is a matter of accident.  No substance is a
    gas intrinsically, but only insofar as temperature dictates.
    On Venus, water and ammonia are both gases.  On Earth,
    ammonia is a gas, but water is not.  On Titan, neither am-
    monia nor water are gases.
       So I'll have to set up an arbitrary criterion to suit my
    present purpose.  Let's say that any substance that remains
    a gas at -1000 C. (-148' F.) is a Gas with a capital
    letter, and concentrate on those.  This is a temperature
    that is never reached on Earth, even in an Antarctic winter
    of extraordinary severity, so that no Gas is ever anything
    but gaseous on Earth (except occasionally in chemical lab-
    oratories).
       Now why is a Gas a Gas?
       I can start by saying that every substance is made up of
    atoms, or of closely knit groups of atoms, said groups
    being called molecules.  There are attractive forces between
    atoms or molecules which make them "sticky" and tend
    to hold them together.  Heat, however, lends these atoms
    or molecules a certain kinetic energy (energy of motion)
                                 186

      which tends to drive them apart,.since each atom or mole-
      cule has its own idea of where it wants to go.*
        The attractive forces among a given set of atoms or
      molecules are relatively constant, but the kinetic energy
      varies with the temperature.  Therefore, if the temperature
      is raised high enough, any group of atoms or molecules
      will fly apart and the material becomes a gas.  At tempera-
      tures over 60000 C. all known substances are gases.
        Of course, there are only a, few exceptional substances
      with interatomic or intermolecular forces so strong that it
      takes 6000' C. to overcome them.  Some substances, on
      the other hand, have such weak intermolecular attractive
      forces that the warmth of a summer day supplies enough
      kinetic energy to convert them to gas (the common anes-
      thetic, ether, is an example).
        Still others have intermolecular attractive forces so
      much weaker still that there is enough heat at a tempera-
      ture of -I 00' C. to keep them gases, and it is these that
      are the Gases I am talking about.
        The intermolecular or interatomic forces arise out of
      the distribution of electrons within the atoms or molecules.
      The electrons are distributed among various "electron
      shells," according to a system we can,accept without de-
      tailed explanation.  For instance, the aluminum atom con-
      tains 13 electrons, which are distributed as follows: 2 in
      the innermost shell, 8 in the next shell, and 3 in the next
      shell.  We can therefore signify the electron distribution in
      the aluminum atom as 2,8,3.
        The most stable and symmetrical distribution of the
      electrons among the electron shells is that distribution in
      which the outermost shell holds either all the electrons it
      can hold, or 8 electrons-whichever is less.  The innermost
      electron shell can hold only 2, the next can hold 8, and
      each of the rest can hold more than 8. Except for the situ-
      ation where only the innermost shell contains electrons,

        * No, I am not implying that atoms know what they are doing
      and have consciousness.  This is just my teleological way of talk-
      ing.  Teleology is forbidden in scientific'articies, 1-ut it s'o happens
      I enjoy sin.
                                  187

     then, the stable situation consists of 8 electrons in the
     outermost shell.
        There are exactly six elements known in which this situ-
     ation of maximum stability exists:

                                         Electron             Electron
     Element          Symbol           Distribution            Total
     helium              He           2                            2
     neon                Ne           2,8                        10
     argon               Ar           2,8,8                      is
     krypton             Kr           2,8,18,8                   36
     xenon               Xe           2,8,18,18,8                54
     radon               Rn           2,8,18,32,18,8             86

        Other atoms without this      fortunate electronic distribu-
     tion are forced to attempt to achieve it by grabbing addi-
     tional electrons, or getting rid of some they already pos-
     sess, or sharing electrons.  In so doing, they undergo chem-
     ical reactions.  The atoms of the six elements listed above,
     however, need do nothing of this sort and are sufficient
     unto themselves.  They have no need to shift electrons in
     any way and that means they take part in no chemical
     reactions and are inert. (At least, this is what I would have
     said prior to 1962.)
        The atoms of the inert gas family listed above are so
     self-sufficient, in fact, that the atoms even ignore one
     another.  There is little interatomic attraction, so that all
     are gases at room temperature and all but radon are
     Gases.
        To be sure, there is some interatomic attraction (for no
     atoms or molecules exist among which there is no attrac-
     tion at all).  If one lowers the temperature sufficiently, a
     point is reached where the attractive forces become dom-
     inant over the disruptive effect of kinetic energy, and every
     single one of the inert gases will, eventually, become an
     inert liquid.

        What about other elements?  As I said, these have atoms
     with electron distributions of less than maximum stability
                                    188

      and each has a tendency to alter that distribution in the
      direction of stability.  For instance, the sodium atom (Na)
      has a distribution of 2,8, I. If it could get rid of the outer-
      most electron, what would be left would have the stable
      2 8 configuration of neon.  Again, the chlorine atom (CI)
      b@s a distribution of 2,8,7.  If it could gain an electron,
      it would have the 2,8,8 distribution of argon.
         Consequently, if a sodium atom encounters a chlorine
      atom, the transfer of an electron from the sodium atom to
      the chlorine atom satisfies both.  However, the loss of a
      negatively charged electron leaves the sodium atom with
      a deficiency of negative charge or, which is the same thing,
      an excess of positive charge.  It becomes a positively
      charged sodium ion (Na+).  The chlorine atom, on the
      other band, gaining an electron, gains an excess of nega-
      tive charge and becomes a negatively charged chloride
      ion* (CI-).
         Opposite charges attract, so the sodium ion attracts all
      the chloride ions within reach and vice versa.  These strong
      attractions cannot be overcome by the kinetic energy in-
      duced at ordinary temperatures, and so the ions hold to-
      gether firmly enough for "sodium chloride" (common
      salt) to be a solid.  It does not become a gas, in fact, until
      a temperature of 1413' C. is reached.
        .Next, consider the carbon atom (C).  Its electron dis-
      tribution is 2,4.  If it lost 4 electrons, it would gain the 2
      helium configuration; if it gained 4 electrons, it would
      gain the 2,8 neon configuration.  Losing or gaining that
      many electrons is not easy,_so the carbon atom shares
      electrons instead.  It can, for instance, contribute one of
      its electrons to a "shared pool" of two electrons, a pool to
      which a neighboring carbon atom also contributes an elec-
      tron.  With its second electron it can form another shared
      pool with a second neighbor, and with its third and fourth,
      two more pools with two more neighbors.  Each neighbor

        * The charged chlorine atom is called "chloride ion" and not
      "chlorine ion" as a convention of chemi&al nomenclature we might
      just as well accept with a weary sigh.  Anyway, the "d" is not a
      typographical error.
                                    189

     ran set up additional pools with other neighbors.  In this
     way, each carbon atom is surrounded by four other carbon
     atoms.
       These shared electrons fit into the outermost electron
     shells of each carbon atom that contributes.  Each carbon
     atom has 4 electrons of its own in that outermost shell and
     4 electrons contributed (one apiece) by four neighbors.
     Now, each carbon atom has the 2,8 configuration of neon,
     but only at the price of remaining close to its neighbors.
     The result is a strong interatomic attraction, even though
     electrical charge is not involved.  Carbon is a solid'and
     is not a gas until a temperature of 42000 C. is reached.
       The atoms of metallic elements also stick together
     ,strongly, for similar reasons, so that tungsten, for instance,
     is not a gas until a temperature of 59000 C. is reached.
       We cannot, then, expect to have a Gas when atoms
     achieve stable electron distribution by transferring elec-
     trons in such a manner as to gain an electric charge; or
     by sharing electrons in so complicated a fashion that vast
     numbers of atoms stick together in one piece.
       What we need is something intermediate.  We need a
     situation where atoms achieve stability by sharing electrons
     (so that no electric charge arises) but where the total
     number of atoms involved in the sharing is very small so
     that only small molecules result.  Within the molecules,
     attractive forces may be large, and the molecules may not
     be shaken apart without extreme temperature.  The attrac-
     tive forces between one molecule and its neighbor, how-
     ever, may be smafl-and that will do.

       Let's consider the hydrogen atom, for instance.  It has
     but a single electron.  Two hydrogen atoms can each con-
     tribute its single electron to form a shared pool.  As long
     as they stay together, each can count both electrons in
     its outermost shell and each will have the stable helium
     configuration.  Furthermore, neither hydrogen atom will
     have any electrons left to form pools with other neighbors,
     hence the molecule will end there.  Hydrogen gas will con-
     sist of two-atom molecules (H2)-
       The attractive force between the atoms in the molecule
                                  190

      is large, and it takes temperatures of more than 20001 C.
      to shake even a small fraction of the hydrogen molecules
      into single atoms.  There will, however, be only weak at-
      tractions among separate hydrogen molecules, each of
      which, under the new arrangement, will have reached a
      satisfactory pitch of self-sufficiency. Hydrogen, therefore,
      will be a Gas not made up of          separate atoms as is
      the case with the inert gases, but of two-atom molecules.
        Something similar will be true in      the case of fluorine
      (electronic distribution 2,7), oxygen (2,6) and nitrogen
      (2,5).  The fluorine atom can contribute an electron and
      form a shared pool of two electrons with a,neighboring
      fluorine atom which also contributes an electron.  Two
      oxygen atoms can contribute two electrons apiece to form
      a shared pool of four electrons, and two nitrogen atoms
      can contribute three electrons each and form a shared pool
      of six electrons.
       I In each case, the atoms will achieve the 2,8 distribution
      of neon at the    cost of forining paired molecules. As a
      result, enough stability is achieved so that fluorine (F2).
      oxygen (02), and nitrogen (N2) are all Gases.
        The oxygen atom can also form a shared pool of two
      electrons with each of two neighbors, and those two neigh-
      bors can form another shared pool of two electrons among
      themselves.  The result is a combination of three oxygen
      atoms (O:j), each with a neon configuration.  This com-
      bination, 03, is called ozone, and it is a Gas too.
        Oxygen, nitrogen, and fluorine can form mixed mole-
      cules, too.  For instance, a nitrogen and an oxygen atom
      can combine to achieve the necessary stability for each.
      Nitrogen may also form shared pools of two electrons with
      each of three fluorine atoms, while oxygen may do so
      with each of two.  The resulting compounds: nitrogen
      oxide (NO), nitroen trifluoride (NF3), and oxygen di-
      fluoride (OF2) are all Gases.
        Atoms which, by themselves, will not form Gases may
      do so if combined with either hydrogen, oxygen, nitrogen,
      or fluorine.  For instance, two chlorine atoms (2,8,7, re-
      member) will form a shared pool of two electrons so that
      ,both achieve the 2,8,8 argon configuration.  Chlorine (CI2)
                                   191

     is therefore a gas at room temperature-with intermolecu-
     lar attractions, however, large enough to keep it from be-
     ing a Gas, Yet if a chlorine atom forms a shared pool of
     two electrons with a fluorine atom, the result, chlorine
     fluoride (CIF), is a.Gas.
        The boron atom (2,3) can form a shared pool of two
     electrons with each of three fluorine atoms, and the carbon
     atom a shared pool of two electrons with each of four
     fluorine atoms.  The resulting compounds, boron trifluoride
     (BF3) and carbon tetrafluoride (CF4), are Gases.
        A carbon atom can form a shared pool of two elec-
     trons with each of four hydrogen atoms, or a shared pool
     of four electrons with an oxygen atom, and the resulting
     compounds, methane (CH-4) and carbon monoxide (CO),
     are gases.  A two-carbon combination may set up a shared
     pool of two electrons with each of four hydrogen atoms
     (and a shared pool of four electrons with one another);
     a silicon atom may setup a shared pool of two electrons
     with each of four hydrogen atoms.  The compounds,
     ethylene (C2H4) and silane (SiH4), are Gases.

        Altogether, then, I can list twenty Gases which fall into
     the following categories:
        (1) Five elements made up of single atoms: helium,
     neon, argon, krypton, and xenon.
        (2) Four elements made up of two-atom molecules:
     hydrogen, nitrogen, oxygen, and fluorine.
        (3) One element form made up of three-atom mole-
     cules: ozone (of oxygen).
        (4) Ten compounds, with molecules built up of two
     different elements, at least one of which falls into category
     (2).
        The twenty Gases are listed in order of increasing boil-
     ing point in the accompanying table, and that boiling point
     is given in both the Celsius scale (' C.) and the Absolute
     scale (' K.).

        The five inert gases on the list are scattered among the
     fifteen other Gases.  To be sure, two of the three lowest-
                                  192

     boiling Gases are helium and neon, but argon is seventh,
     krypton is tenth, and xenon is seventeenth.  It would not be
     surprising if all the Gases, then, were as inert as the inert
     gases.

                            The Twenty Gases
          Substance            Fori  ula   B.P.  (C.-)     B.P. (K.-)
     Helium                     He           -268.9              4.2
     Hydrogen                   H,           -252.8            20.3
     Neon                       Ne           -245.9            27.2
     Nitrogen                   N,           -195.8            77.3        f
     Carbon monoxide            '-O          -192              81
     Fluorine                   F2           -188              85
     Argon                      Ar           -185.7            87.4
     Oxygen                     0,           -183.0            90.1
     Methane                    CH4          -161.5           111.6
     Krypton                    Kr           -152.9           120.2
     Nitrogen  oxide            NO           -151.8           121.3
     Oxygen difluoride          OF,          -144.8           128.3
     Carbon tetrafluoride       CF,          -128             145
     Nitrogen trifluoride       NF3          -120             153
     Ozone                      0,           -111.9           161.2
     Silane                     SiH,         -111.8           161.3
     Xenon                      Xe           -107.1           166.0
     Ethylene                   C,H,         -103.9           169.2
     Boron trifluoride          BF,          -101             172
     Chlorine fluoride          CIF          -100.8           172.3

        Perhaps they might be at that, if the smug, self-sufficient
     molecules that made them up were permanent, unbreak-
     able affairs, but they are not.  All the molecules can be
     broken down under certain conditions, and the free atoms
     (those of fluorine and oxygen particularly) are active in-
     deed.
        This does not show up in the Gases themselves.  Sup-
     pose a fluorine molecule breaks up,into two fluorine atoms,
     and these find themselves surrounded only by fluorine
     molecules?  The only possible result is the re-formation of
     a fluorine molecule, and nothing much has happened.  If,
     however, there are molecules other than fluorine present,
                                     193

     a new molecular combination of greater stability than F2
     is possible (indeed, almost certain in the case of fluorine),
     and a chemical reaction results.
       The fluorine molecule does have a tendency to break
     apart (to a very small extent)   even  at ordinary tempera-
     tures, and this is enough.  The free fluorine atom will
     attack virtually anything n.on-fluorine in sight, and the
     heat of reaction will raise the temperature, which will
     bring about a more extensive split in fluorine molecules,
     and so on.  The result is that molecular fluorine is the most
     chemically active of all the Gases (with chlorine fluoride
     almost on a par with it and ozone making a pretty good
     third).
       The   oxygen molecule is torn apart with greater diffi-
     culty and therefore remains intact (and inert) under con-
     ditions where fluorine will not.  You may think that oxygen
     is an active element, but for the most part this is only true
     under elevated temperatures, where more energy is avail-
     able to tear it apart.  After all, we live in a sea of free
     oxygen without damage.  Inanimate substances such as pa-
     per, wood, coal, and gasoline, all considered flammable,
     can be bathed by oxygen for indefinite periods without
     perceptible chemical reaction-until heated.
       Of course, once heated, oxygen does become active and
     combines easily with other Gases such as hydrogen, carbon
     monoxide, and methane which, by that token, can't be
     considered particularly inert either.
       The nitrogen molecule is torn apart with still more diffi-
     culty and, before the discovery of the inert gases, nitrogen
     was the inert gas par excellence.  It and carbon tetrafluoride
     are the only Gases on the list, other than the inert gases
     themselves, that are respectably inert, but even they can be
     torn apart.
       Life depends on the fact that-certain bacteria can split
     the nitrogen molecule; and important industrial processes
     arise out of the fact that man has learned to do the same
     thing on a large scale.  Once the nitrogen molecule is torn
     apart, the individual nitrogen atom is quite active, bounces
     around in all sorts of reactions and- in fact, is the fourth
                                  194

      most common atom in living tissue and is essential to all
      its workings.

        In the case of the inert gases, all is different.  There are
      no molecules to pull apart.  We are dealing with the self-
      sufficient atom itself, and there seemed little likelihood that
      combination with any other atom would produce a situa-
      tion of greater stability.  Attempts to get inert gases to form
      compounds, at the time they were discovered, failed, and
      chemists were quickly satisfied that this made sense.
        To be sure, chemists continued to try, now and again,
      but they also continued to fail.  Until 1962, then, the only
      successes chemists had had in tying the inert.gas atoms
      to other atoms was in the formation of "clathrates." In a
      clathrate, the atoms making up a molecule form a cage-
      like structure and, sometimes, an extraneous atom-even
      an inert gas atom-is trapped within the cage as it forms.
      The inert gas is then tied to the substance and cannot be
      liberated without breaking down the molecule.  However,
      the inert gas atom is only physically confined; it has not
      formed a chemical bond.
        And yet, let's reason things out a bit.   The boiling point
      of helium is 4.2' K.; that of neon is       27.20 K., that of
      argon 87.4' K., that of krypton 120.2'      K., that of xenon
      166.0' K. The boiling point of radon,       the sixth and last
      inert gas and the one with the most         massive atom, is
      211.3- K. (-61.8- C.) Radon is not even a Gas, but
      merely a gas.
        Furthermore, as the mass of the inert gas atoms in-
      creases, the ionization potential (a quantity which meas-
      ures the ease with which an electron can be removed alto-
      gether from a particular atom) decreases.  The increasing
      boiling point and decreasing ionization potential both indi-
      cate that the inert gases become less inert as the mass of
      the individual atoms rises.
        By this reasoning, radon would be the least inert of the
      inert gases and efforts to form compounds should concen-
      trate upon it as offering the best chance.  However, radon
      is a radioactive element with a half-life of less than four
                                   195

    days, and is so excessively rare that it can be worked with
    only under extremely specialized conditions.  The next best
    bet, then, is xenon.  This is very rare, but it is available and
    it is, at least, stable.
       Then, if xenon is to form a chemical bond, with what
    other atom might it be expected to react?  Naturally, the
    most logical bet would be to choose the most reactive sub-
    stance of all-fluorine or some fluorine-containing com-
    pound.  If xenon wouldn't react with that, it wouldn't react
    with anything.
       (This may sound as though I am being terribly wise
    after the event, and I am.  However, there are some who
    were legitimately wise.  I am told that Linus Pauling rea-
    soned thus in 1932, well before the event, and that a
    gentleman named A. von Antropoff did so in 1924.)
       In 1962, Neil Bartlett and others at the University of
    British Columbia were working with a very unusual com-
    pound, platinum hexafluoride (PtF6).  To their surprise,
    they discovered that it was a particularly active compound.
    Naturally, they wanted to see what it'could be made to do,
    and one of the thoughts that arose was that here might be
    something that could (just possibly) finally pin down an
    inert gas atom.
       So Bartlett mixed the vapors of PtF6 with xenon and, to
    his astonishment, obtained a compound which seemed to
    be XePtFc,, xenon platinum hexafluoride.  The announce-
    ment of this result left a certain area of doubt, however.
    Platinum hexafluoride was a sufficiently complex compound
    to make it just barely possible that it had formed a clath-
    rate and trapped the xenon.
       A group of chemists at Argonne National Laboratory in
    Chicago therefore tried the straight xenon-plus-fluorine
    experiment, heating one part of xenon with five parts of
    fluorine under pressure at 400' C. in a nickel container.
    They obtained xenon tetrafluoride (XeF4), a straightfor-
    ward compound of an inert gas, with no possibility of a
    clathrate. (To be sure, this experiment could have been
    tried years before, but it is no disgrace that it wasn't.  Pure
    xenon is very hard to get and pure fluorine is very danger-
    ous to handle, and no chemist could reasonably have been
                                  196

     expected to undergo the expense and the risk for so
     slim-chanced a catch as an inert gas compound until after
     Bartlett's experiment had increased that "slim chance"
     tremendously.)
        And once the Argonne results were announced, all
     Hades broke loose.  It.looked as though every inorganic
     chemist in the world went gibbering into the inert gas
     field.  A whole raft of xenon compounds, including not
     only XeF4, but also XeF., XeF6, XeOF2, XeOF3, XeOF4,
     XeO3, H4XeO4, and H,XeO,, have been reported.
        Enough radon was scraped together to form radon tetra-
     fluoride (RnF4).  Even krypton, which is more inert than
     xenon, has been tamed, and krypton difluoride (KrF2)
     and krypton tetrafluoride (KrF4) have been formed.
        The remaining three inert gases, argon, neon, and helium
     (in order of increasing inertness), as yet remain untouched.
     They are the last of the bachelors, but the world of chemis-
     try has the sound of wedding bells ringing in its ears, and
     it is a bad time for bachelors.
        As an old (and cautious) married man, I can only say
     to this-no comment.,

                                  197

                   16. THE HASTE-MAKERS

     When I first began writing about science for the general
     public-far back in medieval times-I coined a neat phrase
     about the activity of a "light-fingered magical catalyst."
       My editor stiffened as he came across that phrase, but
     not with admiration (as had been my modestly confident
     expectation).  He turned on me severely and said, "Nothing
     in science is magical.  It may be puzzling, mysterious, in-
     expbeable-but it is never magical."
       It pained me, as you can well imagine, to have to learn
     a lesson from an editor, of all people, but the lesson seemed
     too good to miss and, with many a wry grimace, I learned

       That left me, however, with the problem of describing
     the workings of a catalyst, without calling upon magical
     power for an explanation.
       Thus, one of the first experiments conducted by any
     beginner in a high school   chemistry laboratory is to pre-
     pare oxygen by heating potassium chlorate.  If it were only
     potassium chlorate he were heating, oxygen would be
     evolved but slowly and only at comparatively high temper-
     atures.  So he is instructed to add some manganese dioxide
     first.  When he heats the mixture, oxygen comes off rapidly
     at comparatively low temperatures.
       What does the manganese dioxide do?  It contributes no
     oxygen. At the conclusion of the reaction it 'is all still there,
     unchanged.  Its mere presence seems sufficient to hasten the
     evolution of oxygen.  It is a haste-maker or, more properly,
     a catalyst.
       And how can one explain influence by mere presence?
     Is it a kind of molecular action at a distance, an extra-
     sensory perception on the part of potassium chlorate that
     the influential aura of manganese dioxide is present?  Is it
                                 198

     telekinesis, a para-natural action at a distance on the part
     of the manganese dioxide?  Is it, in short, magic?
        Well, let's see . . .

        To begin at the beginning, as I almost invariably do,
     the first and most famous catalyst in scientific history
     never existed.
        The alchemists of old sought methods for turning base
     metals into gold.  They failed, and so it seemed to them that
     some essential ingredient was missing in their recipes.  The
     more imaginative among them conceived of a substance
     which, if added to the mixture they were heating (or what-
     ever) would bring about the production of gold.  A small
     quantity would suffice to produce a great deal of gold and
     it could be recovered and used again, no doubt.
        No one had ever seen this substance but it was de-
     scribed, for some reason, as a drv, earthy material.  The
     ancient alchemists therefore called it xenon, from a Greek
     word meaning "dry."
        In the eighth century the Arabs took over alchemy and
     called this gold-making catalyst "the xerion" or, in Arabic,
     at-iksir.  When West Europeans finally learned Arabic
     alchemy in the thirteenth century, at-iksir became "elixir."
        As a further tribute to its supposed dry, earthy prop-
     erties, it was commonly called, in Europe, "the philos-
     opber's stone." (Remember that as late as 1800, a "natural
     philosopher" was what we would now call a "scientist.")
        The amazing elixir was bound to have other marvelous
     properties as well, and the notion arose that it was a cure
     for all diseases and might very well confer immortality.
     Hence, alchemists began to speak of "the elixir of life."
        For centuries, the philosopher's stone and/or the elixir
     of life was searched for but not found.  Then, when finally
     a catalyst was found, it brought about the formation not of
     lovely, shiny gold, but messy, dangerous sulfuric acid.*
     Wouldn't you know?
        Before 1740, sulfuric acid was hard to prepare.  In the-

        * That's all right, though.  Sulfuric acid may not be as costly as
     gold, but it is conservatively speaking-a trillion times as in-
     trinsically useful.
                                  199

     ory, it was easy.  You bum sulfur, combining it with oxygen
     to form sulfur dioxide (SO2)- You burn sulfur dioxide
     further to make sulfur trioxide (SO3)- You dissolve sulfur
     trioxide in water to make sulfuric acid, (H2SO4) - The trick,
     though, was to make sulfur dioxide combine with oxygen.
     That could only be done slowly and with difficulty.
       In the 1740s, however, an English sulfuric acid man-
     ufacturer named Joshua Ward must have reasoned that
     saltpeter (potassium nitrate), though nonflammable itself,
     caused carbon and sulfur to burn with great avidity. (In
     fact, carbon plus sulfur plus saltpeter is gunpower.) Con-
     sequently, he added saltpeter to his burning sulfur and
     found that he now obtained sulfur tri'oxide without much
     trouble and could make sulfuric acid easily and cheaply.
       The most wonderful thing about the process was that, at
     the end, the saltpeter was still present, unchanged.  It could
     be used over and over again.  Ward patented the process
     and the price of sulfuric acid dropped to 5 per cent of what
     it was before.
       Magic?-Well, no.
       In 1806, two French chemists, Charles Bernard
     Ddsormes and Nicholas C16ment, advanced an explanation
     that contained a principle which is accepted to this day.
       It seems, you see, that when sulfur and saltpeter bum
     together, sulfur dioxide combines with a portion of the
     saltpeter molecule to form a complex.  The oxygen of the
     saltpeter portion of the complex transfers to the sulfur
     dioxide portion, which now breaks away as sulfur tri-
     oxide.
       What's left (the saltpeter fragment minus oxygen) pro-
     ceeds to pick up that missing oxygen, very readily, from
     the atmosphere.  The saltpeter fragment, restored again,
     is ready to combine with an additional molecule of sulfur
     dioxide and pass along oxygen.  It is the saltpeter's task
     simply to pass oxygen from air to sulfur dioxide as fast as
     it can.  It is a middleman, and of course it remains un-
     changed at the end of the reaction.
       In fact, the wonder is not that a catalyst hastens a re-
     action while remaining apparently unchanged, but that
     anyone should suspect even for a moment that anything
                                 200

      "magical" is involved.  If we were to come across the same
      phenomenon in the more ordinary affairs of life, we would
      certainly not make that mistake of assuming magic.
        For instance, consider a half-finished brick wall and, five
      feet from it, a heap of bricks and some mortar.  If that
      were all, then you would expect no change in the situation
      between 9 A.m. and 5 P.m. except that the mortar would
      dry out.
        Suppose, however, that at 9 A.M. you observed one fac-
      tor in addition-a man, in overalls, standing quietly be-
      tween the wall and the heap of bricks with his hands
      empty.  You observed matters again at 5 P.m. and the same
      man is standing there, his hands still empty.  He has not
      changed.  However, the brick wall is now completed and'
      the heap of bricks is gone.
        The man clearly fulfills the role of catalyst.  A reaction
      has taken place as a result, apparently, of his mere pres-
      ence and without any visible change of diminution in him.
        Yet would we dream for a moment of saying "Magic!"?
      We would, instead, take it for granted that had we ob-
      served the man in detail all day, we would have caught
      him transferring the bricks from the heap to the wall one
      at a time.  And what's not magic for the bricklayer is not
      magic for the saltpeter, either.

        With the birth and progress of the nineteenth century,
      more examples of this sort of    thing were discovered. In
      1812, for instance, the Russian chemist Gottlieb Sigis-
      mund Kirchhoff . . .
        And here I break off and begin a longish digression for
      no other reason than that I want to; relying, as I always
      do, on the infinite patience and good humor of the Gentle
      Readers.
        It may strike you that in saying "the Russian chemist,
      Gottlieb Sig7ismund Kirchhoff" I have made a humorous
      error.  Surely no one with a name like Gottlieb Sigismund
      Kirchhoff can be a Russian!  It depends, however, on
      whether you mean a Russian in an ethnic or in a geographic
      sense.
        To explain what I mean, let's go back to the beginning
                                   201

     of the thirteenth century.  At that time, the regions of our-
     land and Livonia, along the southeastern shores of the
     Baltic Sea (the modem Latvia and Estonia) were in-
     habited by virtually the last group of pagans in Europe.  It
     was the time of the Crusades, and the Germans to the
     southeast felt it a pious duty to slaughter the poorly armed
     and disorganized pagans for the sake of their souls.
       The crusading Germans were of the "Order of the
     Knights of the Sword" (better known by the shorter and
     more popular name of "Livonian Knights").  They were
     joined in 1237 by the Teutonic Knights, who had first
     established themselves in the Holy Land.  By the end of the
     thirteenth century the Baltic shores had been conquered,
     with the German expeditionary forces in control.
       The Teutonic Knights, as a political organization, did
     not maintain control for more than a couple of centuries.
     They were defeated by the Poles in the 1460s.  The Swedes,
     under Gustavus Adolphus, took over in the 1620s, and in
     the 1720s the Russians, under Peter the Great, replaced the
     Swedes.
       Nevertheless, however the political tides might shift and
     whatever flag flew and to whatever monarch the loyal in-
     habitants might drink toasts, the land itself continued to
     belong to the "Baltic barons" (or "Balts") who were the
     German-speaking descendants of the Teutonic Knights.
       Peter the Great was an aggressive Westernizer who
     built a new capital, St. Petersburg* at the very edge of the
     Livonian area, and the Balts were a valued group of sub-
     jects indeed.
       This remained true all through the eighteenth and nine-
     teenth centuries when the Balts possessed an influence
     within the Russian Empire out of all proportion to their
     numbers.  Their influence in Russian science was even
     more lopsided.
       The trouble was that public education within Russia
     lagged far behind its status in western Europe.  The Tsars
     saw no reason to encourage public education and make
     trouble for themselves.  No doubt they felt instinctively that

        The city was named for his name-saint and not for himself.
     Whatever Tsar Peter was, a saint he was not.
                                 202

      a corrupt and stupid government is only really safe with
      an uneducated populace.
        This meant that even elite Russians who wanted a
      secular education had to go abroad, especially if they-
      wanted a graduate education in science.  Going abroad was
      not easy, either, for it meant leaming a new language and
      new ways.  What's more, the Russian Orthodox Church
      viewed all Westerners as heretics and little better than
      heathens.  Contact with heathen ways (such as science) was
      at best dangerous and at worst damnation.  Consequently,
      for a Russian to travel West for an education meant the
      overcoming of religious scruples as well.
        The Balts, however, were German in culture and Lu-
      theran in religion and had none of these inhibitions.  They
      shared, with the Germans of Germany itself, in the,height-
      ening level of education-in particular, of scientific educa-
      tion-through the eighteenth and nineteenth centuries.
        So it follows that among the great Russian scientists of
      the nineteenth century we not only have a man with a name
      like Gottlieb Sigismund Kirchhoff, but also others with
      names like Friedrich Konrad Beilstein, Karl Ernst von
      Baer, and Wilhelm Ostwald.
        This is not to say that there weren't Russian scientists in
      this period with Russian names.  Examples are Mikhail
      Vasilievich Lomonosov, Aleksandr Onufrievich Kovalev-
      ski, and Dmitri Ivanovich Mendel6ev.
        However, Russian officialdom actually preferred the
      Balts (who supported the Tsarist government under which
      they flourished) to the Russian intelligentsia itself (which
      frequently made trouble and had vague notions of reform).
        In addition, the Germans were the nineteenth-century
      scientists par excellence, and to speak Russian with a
      German accent probably leiit distinction to a scientist.
      (And before you sneer at this point of view, just think of
      the American stereotype of a rocket scientist.  He has a
      thick German accent, nicht wahr?-And this despite the
      fact that the first rocketman, and the one whose experi-
      ments started the Germans on the proper track [Robert
      Goddard], spoke with a New England twang.)
        So it happened that the Imperial Academy of Sciences
                                   203

    of the Russian Empire (the most prestigious scientific
    organization in the land) was divided into a "German
    party" and a "Russian party," with the former dominant.
       In 1880 there was a vacancy in the chair of chemical
    technology at the Academy, and two names were proposed.
    The German party proposed Beilstein, and the Russian
    party proposed Mende]6ev.  There was no comparison
    really.  Beilstein spent years of his life preparing an encyclo-
    pedia of the properties and methods of preparation of
    many thousands of organic compounds which, with nu-
    merous supplements and additions, is still a chemical bible.
    This is a colossal monument to his thorough, hard-work-
    ing competence-but' it is no more.  Mendel6ev, who
    worked out the periodic table of the elements, was, on the
    other hand, a chemist of the first magnitude-an un-
    doubted genius in the field.
       Nevertheless, government officials threw,their weight be-
    bind Beilstein, who was elected by a vote of ten to nine.
       It is no wonder, then, that in recent years, when the
    Russians have finally won a respected place in the scientific
    sun, they tend to overdo things a bit.  They've got a great
    deal of humiliation to make up for.

       That ends the digression, so I'll start over-
       As the nineteenth century wore on, more examples of
    baste-making were discovered.  In 1812, for instance, the
    Russian chemist Gottlieb Sigismund Kirchhoff found that
    if he boiled starch in water to which a small amount of
    sulfuric acid had been added, the starch broke down to a
    simple form of sugar, one that is now called glucose.  This
    would not happen in the absence of acid.  When it did
    happen in the presence of acid, that acid was not consumed
    but was still present at the end.
       Then, in 1816, the English chemist Humphry Davy
    found that certain organic vapors, such as those of alcohol,
    combined with oxygen more easily in the presence of metals
    such as platinum.  Hydrogen combined more easily with
    oxygen in the presence of platinum also.
       Fun and games with platinum started at once.  In 1823
    a German chemist, Johann Wolfgang D6bereiner, set up a
                                 204

    hydrogen generator which, on turning an appropriate stop-
    cock, would allow a jet of hydrogen to shoot out against a
    strip of platinum foil.  The hydrogen promptly burst into
    flame and "Dbbereiner's lamp" was therefore the first
    cigarette lighter.  Unfortunately, impurities in the hydrogen
    gas quickly "poisoned" the expensive bit of platinum and
    rendered it useless.
       In 1831 an English chemist, Peregrine Phillips, reasoned
    that if platinum could bring about the combination of
    hydrogen and of alcohol with oxygen, why should it not do
    the same for sulfur dioxide?  Phillips found it would and
    patented the process.  It was not for years afterward, how-
    ever, that methods were discovered for delaying the
    poisoning of the metal, and it was only after that that a
    platinum catalyst could be profitably used in sulfuric acid
    manufacture to replace Ward's saltpeter.
       In 1836 such phenomena were brought to the attention
    of the Swedish chemist J6ns Jakob Berzelius who, during
    the first half of the nineteenth century, was the uncrowned
    king of chemistry.  It was he who suggested the words
    "catalyst" and "catalysis" from Greek words meaning "to
    break down" or "to decompose." Berzelius had in mind
    such examples of catalytic action as the decomposition of
    the large starch molecule into smaller sugar molecules by
    the action of acid.
       But platinum introduced a new glamor to the concept
    of catalysis.  For one thing, it was a rare and precious
    metal.  For another, it enabled people to begin suspecting
    magic again.
       Can platinum be expected to behave as a middleman as
    saltpeter does?
       At first blush, the answer to that would seem to be in
    the negative.  Of all substances, platinum is one of the most
    inert.  It doesn't combine with oxygen or hydrogen under
    any normal circumstances.  How, then, can it cause the two
    to combine?
       If our metaphorical catalyst is a bricklayer, then plati-
    num can only be a bricklayer tightly bound in a strait-
    jacket.
                                 205

        Well, then, are we reduced to magic?  To molecular
     action at a distance?
        Chemists searched for something more prosaic.  The
     suspicion grew during the nineteenth century that the inert-
     ness of platinum is, in one sense at least, an illusion.  In the
     body of the metal, platinum atoms are attached to each
     other in all directions and are satisfied to remain so.  In
     bulk, then, platinum will not react with oxygen or hydro-
     gen (or most other chemicals, either).
        On the surface of the platinum, however, atoms on the
     metal boundary and immediately adjacent to the air have
     no other platinum atoms, in the air-direction at least, to
     attach themselves to.  Instead, then, they attach themselves
     to whatever atoms or molecules they find handy oxygen
     atoms, for instance.  This forms a thin film over the surface,
     a film one molecule thick.  It is completely invisible, of
     course, and all we see is a smooth, shiny, platinum sur-
     face, which seems completely nonreactive and inert.
        As parts of a surface film, cixygen and hydrogen react
     more readily than they do when making up bulk gas.
     Suppose, then, that when a water molecule is formed by
     the combination of hydrogen and oxygen on the platinum
     surface, it is held more weakly than an oxygen molecule
     would be.  The moment an oxygen molecule struck that
     portion of the surface it would replace the water molecule
     in the film.  Now there would be the chance for the forma-
     tion of another water molecule, and so on.
        The platinum does act as a middleman after all, through
     its formation of the monomolecular gaseous film.
        Furthermore, it is also easy to see how a platinum
     catalyst can be poisoned.  Suppose there are molecules to
     which the platinum atoms will cling even more tightly than
     to oxygen.  Such molecules will replace oxygen wherever it
     is found on the film and will not themselves be replaced by
     any gas in the atmosphere.  They are on the, platinum sur-
     face to stay, and any catalytic action involving hydrogen
     or oxygen is killed.
        Since it takes very little substance to form a layer
     merely one molecule thick over any reasonable stretch of
     surface, a catalyst can be quickly poisoned by impurities
                                   206

      that are present in the working mixture of gases, even when
      those impurities are present only in trace amounts.
      . If this is all so, then anything which increases the amount
      of surface in a given weight of metal will also increase the
      catalytic efficiency.  Thus, powdered platinum, with a great
      deal of surface, is a much more effective catalytic agent
      than the same weight of bulk platinum.  It is perfectly fair,
      therefore, to speak of "surface catalysis."

        But what is there about a surface film that hastens the
      process of, let us say, hydrogen-oxygen combination?  We
      still want to remove the suspicion of magic.
        To do so, it helps to recognize what catalysts can't do.
        For instance, in the 187Ws, the American physicist
      Josiah Willard Gibbs painstakingly worked out the applica-
      tion of the laws of thermodynamics to chemical reactions.
      He showed that there is a quantity called "free energy"
      which always decreases in any chemical reaction that is
      spontaneous-that is, that proceeds without any input of
      energy.
        Thus, once hydrogen and oxygen start reacting, they
      keep on reacting for as long as neither gas is completely
      used up, and as a result of the reaction water is formed.  We
      explain this by saying that the free energy of the water is
      less than the free energy of the hydrogen-oxygen mixture.
      The reaction of hydrogen and oxygen to form water is
      analogous to sliding down an "energy slope."
        But if that is so, why don't hydrogen and oxygen mole-
      cules combine with'each other as soon as they are mixe(..
      Why do they linger for indefinite periods at the top of the
      energy slope after being mixed, and react and slide down-
      ward only after being heated?
        Apparently, before hydrogen and oxygen molecules
      (each composed of a pair of atoms) can react, one or the
      other must be pulled apart into individual atoms.  That
      requires an energy input.  It represents an upward energy
      slope, before the downward slope can be entered.  It is an
      "energy hump," so to speak.  The amount of energy that
      must be put into a reacting system to get it over that energy
      hump is called the "energy of activation," and the con-
                                  207

     cept was first advanced in 1889 by the Swedish chemist
     Svante August Arrhenius.
       When hydrogen and oxygen molecules are colliding at
     ordinary temperature, only the tiniest fraction happen to
     possess enough energy of motion to break up on collision.
     That tiniest fraction, which does break up and does react,
     then liberates enough energy, as it slides down the energy
     slope, to break up additional molecules.  However, so little
     energy is produced at any one-time that it is radiated away
     before it can do any good.  'ne net result is that hydrogen
     and oxygen mixed at room temperature do not react.
       ff the temperature is raised, molecules move more
     rapidly and a larger proportion of them possess the nec-
     essary energy to break up on collision. (More, in other
     words, can slide over the energy hump.) More and more
     energy is released, and there comes a particular tempera-
     ture when more energy is released than can be radiated
     away.  The temperature is therefore further raised, which
     produces more energy, which raises the temperature still
     further-and hydrogen and oxygen proceed to react with
     an explosion.
       In 1894 the Russian chemist Wilhelm Ostwald pointed
     out that a catalyst could not alter the free energy relation-
     ships.  It cannot really make a reaction go, that would not
     go without it-though it can make a reaction go rapidly
     that in its absence would prciceed with only imperceptible
     speed.
       In other words, hydrogen and oxygen combine in the
     absence of platinum but at an imperceptible rate, and the
     platinum baste-maker accelerates that combination.  For
     water to decompose to hydrogen and oxygen at room tem-
     perature (without the input of energy in the form of an
     electric current, for instance) is impossible, for that would
     mean spontaneously moving up an energy slope.  Neither
     platinum nor any other catalyst could make a chemical
     reaction move up an energy slope.  If we found one that did
     so, then that would be magic.*

        Or else we would have to modify the laws of thermodynamics.
                                  208

         But how does platinum hasten the reaction it does
      hasten?  What does it do to the molecules in the film?
         Ostwald's suggestion (accepted ever since) is that cata-
      lysts hasten reactions by lowering the energy of activation
      of the reaction-flattening out the hump.  At any given tem-
      perature, then, more molecules can cross over the hump
      and slide downward, and the rate of the reaction increases,
      sometimes enormously.
         For instance, the two oxygen atoms m an oxygen mole-
      cule hold together with a certain, rather strong, attachment,
      and it is not easy to split them apart.  Yet such splitting is
      necessary if a water molecule is to be formed.
         When an oxygen atom is attached to a platinum atom
      and forms part of a surface film, however, the situation
      changes.  Some of the bond-forming capabilities of the
      oxygen molecule are used up in forming the attachment to
      the platinum, and less is available for holding the two
      oxygen atoms together.  The oxygen atom might be said to
      be "strained."
         If a hydrogen atom happens to strike such an oxygen
      atom, strained in the film, it is more likely to knock it
      apart into individual oxygen atoms (and react with one of
      them) than would be the case if it collided with an oxygen
      atom free in the body of a gas.  The fact that the oxygen
      molecule is strained means thaf it is easier to break apart,
      and that the energy of activation for the hyqrogen-oxygen
      combination has been lowered.
         Or we can try a metaphor again.  Imagine a brick resting
      on the upper reaches of a cement incline.  The brick should,
      ideally, slide down the incline.  To do so, however, it must
      overcome frictional forces which hold it in place against the
      pull of gravity.  The frictional forces are here analogous to
      the forces holding the oxygen molecule together.
         To overcome the frictional force one must give the
      brick an initial push (the energy of activation), and then it
      slides down.
         Now, however, we will try a little "surface catalysis." We
      will coat the slide with wax.  If we place the brick on top
      of such an incline, the merest touch will start it moving
                                  209

    downward.  It may move downward without any help from
    us at all.
       In waxing the cement incline we haven't increased the
    force of gravity, or added energy to the system.  We have
    merely decreased the frictional forces (that is, the energy,
    hump), and bricks can be delivered down such a waxed
    incline much more easily and much more rapidly than down
    an unwaxed incline.
       So you see that on inspection, the magical clouds of
    glory fade into the light of common day, and the wonderful
    word "catalyst" loses all its glamor.  In fact, notlfing is left
    to it but to serve as the foundation for virtually all of
    chemical industry and, in the form of enzymes, the founda-
    tion of all of life, too.
       And, come to think of it, that ought to be glory enough
    for any reasonable catalyst.

                                 210

             17.  THE SLOWLY MOVING FINGER

      Alas, the evidences of mortality      are all about us; the
      other day our little parakeet died.   As nearly as we could
      make out, it was a trifle over five   years old, and we had
      always taken the best of care of it.  We had fed it, watered
      it, kept its cage clean, allowed it   to leave the cage and
      fly about the house, taught it a      small but disreputable
      vocabulary, perrffltted it to ride about on our shoulders and
      eat at will from dishes at the table.  In short, we encouraged
      it to think of itself as one of us humans.
         But alas, its aging process remained that of a parakeet.
      During its last year, it slowly grew morose and sullen; men-
      tioned its improper words but rarely; took to walking
      rather than flying.  And finally it died.  And, of course, a
      similar process is taking place within me.
         This thought makes me petulant.  Each year I break my
      own previous record and enter new high ground as far as
      age is concerned, and it is remarkably cold comfort to
      think that everyone else is doing exactly the same thing.
         The fact of the matter is that I resent growing old.  In
      my time I was a kind of mild infant prodigy-you know,
      the kind that teaches himself to read before he is five and
      enters college at fifteen and is writing for publication at
      eighteen and all like that there.  As you might expect, I
      came in for frequent curious inspection as a sort of
      ludicrous freak, and I invariably interpreted this inspection
      as admiration and loved it.
         But such behavior carries its own punishment, for the
      moving finger writes, as Edward Fitzgerald said Omar
      Khayyam said, and having writ, moves on.  And what that
      means is that the bright, young, bouncy, effervescent infant
      prodigy becomes a flabby, paunchy, bleary, middle-aged
      non-prodigy, and age sits twice as heavily on such as these.
                                   211

      It happens quite often that some huge, hulking, raw-
   boned fellow, checks bristling with black stubble, comes to
   me and says in his bass voice, "I've been reading you
   ever since I learned to read; and I've collected all the stuff
   you wrote before I learned to read and I've read that, too.",
   My impulse then is to hit him a stiff right cross to the side
   of the jaw, and I might do so if only I were quite sure he
   would respect my age and not hit back.
      So I see nothing for it but to find a way of looking at
   the bright side, if any exists . . .

      How long do organisms live anyway?  We can only guess.
   Statistics on the subject have been carefully kept only in
   the last century or so, and then only for Homo sapiens, and
   then only in the more "advanced" parts of the world.
      So most of what is said about longevity consists of quite
   rough estimates.  But then, if everyone is guessing, I can
   guess, too; and as lightheartedly as the next person, you
   can bet.
      In the first place, what do we mean. by length of life?
   There are several ways of looking at this, and one is to
   consider the actual length of time (on the average) that
   actual organisms live under actual conditions.  This is the
   "life expectancy- )I

      One thing we can be certain of is that life expectancy is
   quite trifling for all kinds of creatures.  If a codfish or an
   oyster produces millions or billions of eggs and only one
   or two happen to produce young thal are still alive at the
   end of the first year, then the average life expectancy of all
   the coddish or oysterish youngsters can be measured in
   weeks, or possibly even days.  I imagine that thousands
   upon thousands of them live no more than minutes.
      Matters are not so extreme among birds and mammals
   where there is a certain amount of infant care, but I'll bet
   relatively few of the smaller ones live out a single year.
      From the cold-blooded view of species survival, this is
   quite enough, however.  Once a creature has reached sexual
   maturity, and contributed to the birth of a litter of young
   which it sees through to puberty or near-puberty, it has
   done its bit for species survival and can go its way.  If it
                                212

      survives and produces additional litters, well and good, but
      it doesn't have to.
         There is, obviously, considerable survival value in reach-
      ing sexual maturity as early as possible, so that there is time
      to produce the next generation before the first is gone.
      Meadow mice reach puberty in three weeks and can bear
      their first litter six weeks after birth.  Even an animal as
      large as a horse or cow reaches the age of puberty after
      one year, and the largest whales reach puberty at two.
      Some large land animals can afford to be slower about it.
      Bears are adolescent only at six and elephants only at ten.
         The large carnivores can expect to live a number of
      years, if only because they have relatively few enemies (al-
      ways excepting man) and need not expect to be anyone's
      dinner.  The largest herbivores, such as elephants and hip-
      popotami, are also safe; while smaller ones such as baboons
      and water buffaloes achieve a certain safety by traveling
      in herds.
         Early man falls into this category.  He lived in small
      herds and he cared for his young.  He had, at the very least,
      primitive clubs and eventually gained the use of fire.  The
      average man, therefore, could look forward to a number
      of years of life.  Even so, with undernourishment, disease,
      the hazards of the chase, and the cruelty of man to man,
      life was short by modern standards.  Naturally, there was
      a limit to how short life could be.  If men didn't live long
      enough, on the average, to replace themselves, the race
      would die out.  However, I should guess that in a primitive
      society a life expectancy of 18 would be ample for species
      survival.  And I rather suspect that the actual life ex-
      pectancy of man in the Stone Age was not much greater.
         As mankind developed agriculture and as he domesti-
      cated animals, he gained a more dependable food supply.
      As he learned to dwell within walled cities and to live
      under a rule of law, he gained oTeater security against hu-
      man enemies from without and within.  Naturally, life ex-
      pectancy rose somewhat.  In fact, it doubled.
         However, throughout ancient and medieval times, I
      doubt that life expectancy ever reached 40.  In medieval
      England, the life expectancy is estimated to have been 35,
                                    213

    so that if you did reach the age of 40 you were a revered
    sage.  What with early marriage and early childbirth, you
    were undoubtedly a grandfather, too.
       This situation still existed into the twentieth century in
    some parts of the world.  In India, for instance, as of 1950,
    the life expectancy was about 32; in Egypt, as of 1938, it
    was 36; in Mexico, as of 1940, it was 38.
       The next great step was medical advance, which brought
    infection and disease under control.  Consider the United
    States.  In 1850, life expectancy for American white males
    was 38.3 (not too much different from the situation in
    medieval England or ancient Rome).  By 1900, however,
    after Pasteur and Koch had done their work, it was up to
    48.2; then 56.3 in 1920; 60.6 in 1930; 62.8 in 1940; 66.3
    in 1950; 67.3 in 1959; and 67.8 in 1961.
       All through, females had a bit the better of it (being
    the tougher sex).  In 1850, they averaged two years longer
    life than males; and by 1961, the edge had risen to nearly
    seven years.  Non-whites in the United States don't do quite
    as well-not for any inborn reason, I'm sure, but because
    they generally occupy a position lower on the economic
    scale.  They run some seven years behind whites in life ex-
    pectancy. (And if anyone wonders why Negroes are rest-
    less these days, there's seven years of life apiece that they
    have coming to them.  That might do as a starter.)
       Even if we restrict ourselves to whites, the United States
    does not hold the record in life expectancy.  I rather think
    Norway and Sweden do.  The latest figures I can find (the
    middle 1950s) give Scandinavian males a life expectancy
    of 71, and females one of 74.
       This change in life expectancy has introduced certain
    changes in social custom.  In past centuries, the old man
    was a rare phenomenon-an unusual repository of long
    memories and a sure guide to ancient traditions.  Old age
    was revered, and in some societies where life expectancy is
    still low and old men still exceptional, old age is still
    revered.
       It might also be feared.  Until the nineteenth century
    there were particular hazards to childbirth, and, few women
    survived the process very often (puerperal fever and all
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      that).  Old women were therefore even rarer than old men,
      and with their wrinkled cheeks and toothless gums were
      strange and frightening phenomena.  The witch mania of
      early modern times may have been a last expression of that.
        Nowadays, old men and women are very common and
      the extremes of both good and evil are spared them.  Per-
      haps that's just as well.

        One might suppose, what with the steady rise in life
      expectancy in the more advanced portions of the globe,
      that we need merely hold on another century to find men
      routinely living a century and a half.  Unfortunately, this is
      not so.  Unless there is a remarkable biological break-
      through in geriatrics, we have gone just about as far as
      we can go in raising, the life expectancy.
        I once read an allegory that has haunted me all my adult
      life.  I can't repeat it word for word; I wish I could.  But
      it goes something like this.  Death is an archer and life is a
      bridge.  Children begin to cross the bridge gaily, skipping
      along and growing older, while Death shoots at them.  Ms
      aim is miserable at first, and only an occasional child is
      transfixed and falls off the bridge into the cloud-enshrouded
      mists below.  But as the crowd moves farther along, Death's
      aim improves and the numbers thin.  Finally, when Death
      aiins at the aged who totter nearly to the end of the bridge,
      his aim is perfect and he never misses.  And not one man
      ever gets across the bridge to see what lies on the other
      side.
        This remains true despite all the advances in social struc-
      ture and medical science throughout history.  Death's aim
      has worsened through early and middle life, but those last
      perfectly aimed arrows are the arrows of old age, and even
      now they never miss.  All we have done to wipe out war,
      famine, and disease has been to allow more people the
      chance of experiencing old age.  When life expectancy was
      35, perhaps one in a hundred reached old age; nowadays
      nearly half the population reaches it-but it is the same
      old old age.  Death gets us all, and with every scrap of his
      ancient efficiency.
        In short, putting life expectancy to one side, there is a
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     "specific age" which is our most common time of death
     from inside, without any outside push at all; the age at
     which we would die even if we avoided accident, escaped
     disease, and took every care of ourselves.
        Three thousand years ago, the psalmist testified as to
     the specific age of man (Ps. 90:10), saying: "The days
     of our years are threescore years and ten; and if by reason
     of strength they be fourscore years, yet is their strength
     labor and sorrow; for it is soon cut -off, and we fly away."
     I And so it is today; three millennia of civilization and
     three centuries of science have not changed it.  The com-
     monest time of death by old age lies between 70 and 80.
        But that is just the commonest time.  We don't all die
     on our 75th birthday; some of us do better, and it is un-
     doubtedly the hope of each one of us that we ourselves,
     personally, will be one of those who will do better.  So
     what we have our eye on is not the specific age but the
     maximum age we can reach.
        Every species of multicellular creature has a specific age
     and a maximum age; and of the species that have been
     studied to any degree at all, the maximum age would
     seem to be between 50 and 100 per cent longer than the
     specific age.  Thus, the maximum age for man is considered
     to be about II S.
        There have been reports of older men, to be sure.  The
     most famous is the case of Thomas Parr ("Old Parr"),
     who was supposed to have been born in 1481 in England
     and to have died in 1635 at the age of 154.  The claim is
     not believed to be authentic (some think it was a put-up
     job involving three generations of the Parr family), nor are
     any other claims of the sort.  The Soviet Union reports
     numerous centenarians in the Caucasus, but all were born
     in a region and at a time when records were not kept.  The
     old man's age rests only upon his own word, therefore, and
     ancients are notorious for a tendency to lengthen their
     years.  Indeed, we can make it a rule, almost, that the
     poorer the recording of vital statistics in a particular region,
     the older the centenarians claim to be.
        In 1948, an English woman named Isabella Shepheard
                                   216

       died at the reported age of 115. She was the last survivo      'r,
       within the British Isles, from the period before the com-
       pulsory registration of births, so one couldn't be certain
       to the year.  Still, she could not have been younger by more
       than a couple of years.  In 1814, a French Canadian
       named Pieffe Joubert died and he, apparently, had reliable
       records to show that he was bom in 1701, so that he died at
       113.
          Let's accept 115 as man's maximum age, then, and ask
       whether we have a good reason to complain about this.
       How does the figure stack up against maximum ages for
       other types of living organisms?

          if we compare plants with animals, there is no question
       that plants bear off the palm of victory.  Not all plants
       generally, to be sure.  To quote the Bible again (Ps. 103:
       15-16), "As for man his days are as grass: as a flower
       of the field, so he flourisheth.  For the wind passeth over it,
       and it is gone; and the place thereof shall know it no
       more."
          This is a spine-tingling simile representing the evanes-
       cence of human life, but what if the psalmist had said that
       as for man. his days are as the oak tree; or better still, as
       the giant sequoia?  Specimens of the latter are believed to
       be over three thousand years old, and no maximum age is
       known for them.
          However, I don't suppose any of us wants long life at
       the cost of being a tree.  Trees live long, but they live
       slowly, passively, and in terribly, terribly dull fashion.  Let's
       see what we can do with animals.
          Very simple animals do surprisingly well and there are
       reports of sea-anemones, corals, and such-like creatures
       passing the half-century mark, and even some tales (not
       very reliable) of centenarians among them.  Among more
       elaborate 'invertebrates, lobsters may reach an age of 50
       and clams one of 30.  But I think we can pass invertebrates,
       too.  There is no reliable tale of a complex invertebrate liv-
       ing to be 100 and even if giant squids, let us say, did so,
       we don't want to be giant squids.
                                     217

      What about vertebrates?  Here we have legends, par-
   ticularly about fish.  Some tell us that fish never grow old
   but live and grow forever, not dying till they are killed.  In-
   dividual fish are reported with ages of several centuries.
   Unfortunately, none of this can be confirmed.  The oldest
   age reported for a fish by a reputable observer is that of a
   lake sturgeon which is supposed to be well over a century
   old, going by a count of the rings on the spiny ray of its
   pectoral fin.
      Among amphibia the record holder is the giant sala-
   mander, which may reach an age of 50.  Reptiles are better.
   Snakes ma reach an aoe of 30 and crocodiles may attain
              y             t,
   60, but it is the turtles that hold the record for the animal
   kingdom.  Even small turtles may reach the century mark,
   and at least one larger turtle is known, with reasonable
   certainty, to have lived 152 years.  It may be that the
   large Galapagos turtles can attain an age of 200.
      But then turtles live slowly and dully, too.  Not as slowly
   as plants, but too slowly for us.  In fact, there are only two
   classes of living creatures that live intensely and at peak
   level at all times, thanks to their warm blood, and these are
   the birds and the mammals. (Some mammals cheat a
   little and hibernate through the winter and probably ex-
   tend their life span in that nianner.) We might envv a
   tiger or an eagle if they. lived a long, long time and even
   -as the shades of old age closed in-wish we could trade
   places with them.  But do they live a long, long time?
      Of the two classes, birds on the whole do rather better
   than mammals as far as maximum age is concerned.  A
   pigeon can live as long as a lion and a herring gull as long
   as a hippopotamus.  In fact, we have long-life legends about
   some birds, such as parrots and swans, which are supposed
   to pass the century mark with ease.
      Any devotee of the Dr. Dolittle stories (weren't you?)
   must remember Polynesia, the parrot, who was in her third
   century.  Then there is Tennyson's poem Tithonus, about
   that mythical character who was granted immortality but,
   through an oversight, not freed from the incubus of old
   age so that he grew older and older and was finally, out of
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       pity, turned into a grasshopper.  Tennyson has him lament
       that death comes to all but him.  He begins by pointing out
       that men and the plants of the field die, and his fourth line
       is an early climax, going, "And after many a summer dies
       the swan." In 1939, Aldous Huxley used the line as a title
       for a book that dealt with the striving for physical im-
       mortalit
               y
          However, as usual, these stories remain stories.          The
       oldest confirmed age reached by a parrot is 73, and I
       imagine that swans do not do much better.  An age of 115
       has been reported for carrion crows and for some vultures,
       but this is with a pronounced question mark.
          Mammals interest us most, naturally, since we are mam-
       mals, so let me list the maximum ages for some mammalian
       types. (I realize, of course, that the word "rat" or "deer"
       covers dozens of species, each with its own aging pattern,
       but I can't help that.  Let's say the typical rat or the typical
       deer.)

           Elephant             77             Cat              20
           Whale                60             pig              20
           Hippopotamus         49             Dog              1 8
           Donkey               46             Goat             17
           Gorilla              45             Sheep            16
           Horse                40             Kangaroo         16
           Chimpanzee           39             Bat              15
           Zebra                38             Rabbit           15
           Lion                 35             Squirrel         15
           Bear                 34             Fox              14
           Cow                  30             Guinea Pig        7
           Monkey               29             Rat               4
           Deer                 25             Mouse             i
           Seal                 25             Shrew             2

          The maximum age,      be  it remembered,    is reached only
       by exceptional individuals.  While an occasional rabbit may
       make 15, for instance, the average rabbit would die of old
       age before it was 10 and might have an actual life ex-
       pectancy of only 2 or 3 years.
          In general, among all groups of organisms sharing a
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   common plan of structure, the large ones live longer than
   the small.  Among plants, the giant sequoia tree lives longer
   than the daisy.  Among animals, the giant sturgeon lives
   longer than the herring, the giant salamander lives longer.
   than the frog, the giant alligator lives longer than the
   lizard, the vulture lives longer than the sparrow, and the
   elephant lives longer than the shrew.
      Indeed, in mammals particularly, there seems to be a
   strong correlation between longevity and size.  There are
   exceptions, to be sure-some startling ones.  For instance,
   whales are extraordinarily short-lived for their size.  The
   age of 60 1 have given is quite exceptional.  Most cetaceans
   are doing very well indeed if they reach 30.  This may be
   because life in the water, with the continuous loss of beat
   and the never-ending necessity of swimming, shortens life.
      But much more astonishing is the fact that man has a
   longer life than any other mammal-much longer than the
   elephant or even than the closely allied gorilla.  When a
   human centenarian dies, of all the animals in the world
   alive on the day that he was born, the only ones that re-
   main alive on the day of his death (as far as we know)
   are a few sluggish turtles, an occasional ancient vulture or
   sturgeon, and a number of other human centenarians.  Not
   one non-human mammal that came into this world with him
   has remained.  All, without exception (as far as we know),
   are dead.
      If you think this is remarkable, wait!  It is more re-
   markable than you suspect.

      The smaller the mammal, the faster the rate of its
   metabolism; the more rapidly, so to speak, it lives.  We
   might well suppose that while a small mammal doesn't
   live as long as a large one, it lives more rapidly and more
   intensely.  In some subjective manner, the small mammal
   might be viewed as living just as long in terms of sensation
   as does the more sluggish large mammal.  As concrete
   evidence of this difference in metabolism among mammals,
   consider the heartbeat rate.  The following table lists some
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      rough figures for the average number of heartbeats         per
      minute in different types of mammal.

          Shrew       1000                   Sheep          75
          Mouse          550                 Man            72
          Rat            430                 Cow            60
          Rabbit         150                 Lion           45
          Cat            130                 Horse          38
          Dog            95                  Elephant       30
          Pig            75                  Whale          17

        For the fourteen    types of animals listed   we have the
      heartbeat rate (approximate) and the maximum age (ap-
      proximate), and by appropriate multiplications, we can
      determine the maximum age of each type of creature, not in
      years but in total heartbeats.  The result follows:

                  Shrew                  1,050,000,000
                  Mouse                    950,000,000
                  Rat                      900,000,000
                  Rabbit                 1,150,000,000
                  Cat                    1,350,000,000
                  Dog                      900,000,000
                  Pig                      800,000,000
                  Sheep                    600,000,000
                  Lion                     830,000,000
                  Horse                    800,000,000
                  Cow                      950,000,000
                  Elephant               1,200,000,000
                  Whale                    630,000,000

        Allowing for the approximate nature of all my figures,
      I look at this final table through squinting eyes from a dis-
      tance and come to the following conclusion: A mammal
      can, at best, live for about a billion heartbeats and when
      those are done, it is done.
        But you'll notice that I have left man out of the table.
      That's because I want to treat him separately.  He lives at
      the proper speed for his size.  His heartbeat rate is about
      that of other animals, of similar weight.  It is faster than
      the heartbeat of larger animals, slower than the heartbeat
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    of smaller animals.  Yet his maximum age is 115 years,
    and that means his maximum number of heartbeats is
    about 4,350,000,000.
       An occasional man can live for over 4 billion heartbeats!
    In fact, the life expectancy of the American male these
    days is 2.5 billion heartbeats.  Any man- who passes the
    quarter-century mark has gone beyond the billionth heart-
    beat mark and is still young, with the prime of life ahead.
       Why?  It is not just that we live longer than other mam-
    mals.  Measured in heartbeats, we live four times as long!
    Why??
       Upon what meat doth this, our species, feed, that we
    are grown so great?  Not even our closest non-buman rela-
    tives match us in this.  If we assume the chimpanzee to
    have our heartbeat rate and the gorilla to have a slightly
    slower one, each lives for a maximum of about 1.5 billion
    heartbeats, which isn't very much out of line for mammals
    generally.  How then do we make it to 4 billion?
       What secret in our hearts makes those organs work so
    much better and last so much longer than any other mam-
    malian heart in existence?  Why does the moving finger
    write so slowly for us, and for us only?
       Frankly, I don't know, but whatever the answer, I am
    comforted.  If I were a member of any other mamxnalian
    species my heart would be stilled long years since, for it
    has gone well past its billionth beat. (Well, a little past.)
       But since I am Homo sapiens, my wonderful heart beats
    even yet with all its old fire; and speeds up in proper
    fashion at all times when it should speed up, with a verve
    and efficiency that I find completely satisfying.
       Why, when I stop to think of it, I am a young fellow, a
    child, an infant prodigy.  I am a, member of the most un-
    usual species on earth, in longevity as well as brain power,
    and I laugh at birthdays.
       (Let's see now.  How many years to 115?)

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