done no better. The riddle of time continues to baffle, perplex, fascinate, and challenge. Pragmatic physicists cannot help becoming philosophical-even metaphysical-when they start pursuing the elusive concepts of time.

Much has been written of a scholarly and philosophical nature. But time plays a vital and practical role in the everyday lives of us all, and it is this practical role which we shall explore in this book.

THE NATURE OF TIME

Time is a necessary component of many mathematical formu-
las and physical functions. It is one of several basic quantities
from which most physical measurement systems are derived.
Others are length, temperature, and mass. Yet time is unlike
length or mass or temperature in several ways. For instance—
• We can see distance and we feel weight
and temperature, but time cannot be ap-
prehended by any of the physical senses.
We cannot see, hear, feel, smell, or taste
time. We know it only through conscious-
ness, or through observing its effects.
• Time "passes," and it moves in only one
direction. We can travel from New York
to San Francisco or from San Francisco to
New York, moving "forward" in either
case. We can weigh the grain produced on
an acre of land, beginning at any point,
and progressing with any measure "next."
But when we think of time, in even the
crudest terms, we must always think of it
as now, before now, and after now. We
cannot do anything in either the past or
the future-only "now."

• "Now" is constantly changing. We can buy
a good one-foot ruler or meter-stick, or a
one-gram weight, or even a thermometer,
put it away in a drawer or cabinet, and
use it whenever we wish. We can forget it
between uses-for a day or a week or ten
years and find it as useful when we bring
it out as when we put it away. But a
"clock"-the "measuring stick" for time—
is useful only if it is kept "running." If we
put it away in a drawer and forget it, and
it "stops," it becomes useless until it is
"started" again, and "reset" from informa-
tion available only from another clock.
• We can write a postcard to a friend and
ask him how long his golf clubs are or
how much his bowling ball weighs, and
the answer he sends on another postcard

gives us useful information. But if we write
and ask him what time it is-and he goes
to great pains to get an accurate answer,
which he writes on another postcard—well,
obviously before he writes it down, his in-
formation is no longer valid or useful.

This fleeting and unstable nature of time makes its measurement a much more complex operation than the measurement of length or mass or temperature.

WHAT IS TIME?

Time is a physical quantity that can be observed and measured with a clock of mechanical, electrical, or other physical nature. Dictionary definitions bring out some interesting points:

time-A nonspatial continuum in which
events occur in apparently irreversible suc-
cession from past through present to the
future. An interval separating two points on
this continuum, measured essentially by
selecting a regularly recurring event, such
as the sunrise, and counting the number of
its recurrences during the interval of
duration.

American Heritage Dictionary
⚫ time-1. The period during which an
action, process, etc. continues; measured
or measurable duration . . . . 7. A definite
moment, hour, day, or year, as indicated
or fixed by the clock or calendar.

Webster's New Collegiate Dictionary

At least part of the trouble in agreeing on what time is lies in the use of the single word time to denote two distinct concepts. The first is date or when an event happens. The other is time interval, or the "length" of time between two events. This distinction is important, and is basic to the problems involved in measuring time. We shall have a great deal to say about it.

DATE, TIME INTERVAL, AND SYNCHRONIZATION

We obtain the date of an event by counting the number of cycles, and fractions of cycles, of periodic events, such as the sun as it appears in the sky and the earth's movement around the sun, beginning at some agreed-upon starting point. The date of an event might be 13 February 1976, 14h, 35m, 37.27s; h, m, and s denote hours, minutes, and seconds; the 14th hour, on a 24-hour clock, would be two o'clock in the afternoon.

In the United States literature on navigation, satellite tracking, and geodesy, the word "epoch" is sometimes used in a similiar sense to the word "date." But there is considerable ambiguity in the word "epoch," and we prefer the term "date," the precise

WHEN? HOW LONG? TOGETHER!

more popular uses.

Time interval may or may not be associated with a specific date. A person timing the movement of a horse around a racetrack, for example, is concerned with the minutes, seconds, and fractions of a second between the moment the horse leaves the gate and the moment it crosses the finish line. The date is of interest only if he must have the horse at a particular track at a certain hour on a certain day.

Time interval is of vital importance to synchronization, which means literally "timing together." Two military units that expect to be separated by several kilometers may wish to surprise the enemy by attacking at the same moment from opposite sides. So before parting, men from the two units synchronize their watches. Two persons who wish to communicate with each other may not be critically interested in the date of their communication, or even in how long their communication lasts. But unless their equipment is precisely synchronized, their messages will be garbled. Many sophisticated electronic communications systems, navigation systems, and proposed aircraft collision-avoidance systems have little concern with accurate dates; but they depend for their very existence on extremely accurate synchronization.

The problem of synchronizing two or more time-measuring devices-getting them to measure time interval accurately and together, very precisely, to the thousandth or millionth of a second -presents a continuing challenge to electronic technology.

Among the most fascinating remains of many ancient civilizations are their elaborate time-watching devices. Great stone structures like Stonehenge, in Southern England, and the 4,000-year-old passage grave of Newgrange, near Dublin, Ireland, that have challenged anthropologists and archaeologists for centuries, have proved to be observatories for watching the movement of heavenly bodies. Antedating writing within the culture, often by centuries,

these crude clocks and calendars were developed by primitive peoples on all parts of our globe. Maya and Aztec cultures developed elaborate calendars in Central and North America. And even today scientists are finding new evidence that stones laid out in formation on our own western plains, such as the Medicine Wheel in northern Wyoming, formerly thought to have only a religious purpose, are actually large clocks. Of course they had religious significance, also, for the cycles of life-the rise and fall of the tides, and the coming and going of the seasons-powers that literally controlled the lives of primitive peoples as they do our own, naturally evoked a sense of mystery and inspired awe and worship.

Astronomy and time so obviously beyond the influence or control of man, so obviously much older than anything the oldest man in the tribe could remember and as nearly "eternal" as anything the human mind can comprehend-were of great concern to ancient peoples everywhere.

CLOCKS IN NATURE

The movements of the sun, moon, and stars are easy to observe, and one can hardly escape being conscious of them. But of course there are countless other cycles and rhythms going on around us-and inside of us-all the time. Biologists, botanists, and other life scientists study but do not yet fully understand many "built in" clocks that regulate basic life processes-from periods of animal gestation and ripening of grain to migrations of birds and fish; from the rhythms of heartbeats and breathing to those of the fertile periods of female animals. These scientists talk about "biological time," and have written whole books about it.

Geologists also are aware of great cycles, each one covering thousands or millions of years; they speak and write in terms of "geologic time." Other scientists have identified quite accurately the rate of decay of atoms of various elements-such as carbon 14, for example. So they are able to tell with considerable dependability the age of anything that contains carbon 14. This includes everything that was once alive, such as a piece of wood that could have been a piece of Noah's Ark or the mummified body of a king or a pre-Columbian farmer.

KEEPING TRACK OF THE SUN AND MOON

Some of the stone structures of the earliest clock watchers were apparently planned for celebrating a single date-Midsummer Day, the day of the Summer solstice, when the time from sunrise to sunset is the longest. It occurs on June 21-22, depending on how near the year is to leap year. For thousands of years, the "clock" that consists of the earth and the sun was sufficient to regulate daily activities. Primitive peoples got up and began their work at sunrise and ceased work at sunset. They rested and ate their main meal about noon. They didn't need to know time any more accurately than this.

But there were other dates and anniversaries of interest; and in many cultures calendars were developed on the basis of the revolutions of the sun, the moon, and the seasons.

If we think of time in terms of cycles of regularly recurring events, then we see that timekeeping is basically a system of counting these cycles. The simplest and most obvious to start with is days-sunrise to sunrise, or more usefully, noon to noon, since the "time" from noon to noon is, for most practical purposes, always the same, whereas the hour of sunrise varies much more with the season.

One can count noon to noon with very simple equipment-a stick in the sand or an already existing post or tree, or even one's own shadow. When the shadow points due North-if one is in the northern hemisphere or when it is the shortest, the sun is at its zenith, and it is noon. By making marks of a permanent or semipermanent nature, or by laying out stones or other objects in a preplanned way, one can keep track of and count days. With slightly more sophisticated equipment, one can count full moonsor months-and the revolutions of the earth around the sun, or years.

It would have been convenient if these cycles had been neatly divisible into one another, but they are not. It takes the earth about 36514 days to complete its cycle around the sun, and the moon circles the earth about 13 times in 364 days. This gave