Isaac Asimov - Of Time and Space and Other Things

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

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

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

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!

Part I

OF TIME AND SPACE

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 80 years, a man would

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

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.

Isaac Asimov - Of Time and Space and Other Things

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