PART ONE

ORIENTAL AND GREEK ORIGINS

I

THE DAWN OF SCIENCE

When did science begin? Where did it begin? It began whenever and wherever men tried to solve the innumerable problems of life. The first solutions were mere expedients, but that must do for a beginning. Gradually the expedients would be compared, generalized, rationalized, simplified, interrelated, integrated; the texture of science would be slowly woven. The first solutions were petty and awkward but what of it? A Sequoia gigantea two inches high may not be very conspicuous, but it is a Sequoia all the same. It might be claimed that one cannot speak of science at all as long as a certain degree of abstraction has not been reached, but who will measure that degree? When the first mathematician reognized that there was something in common between three palm trees and three donkeys, how abstract was his thought? Or when primitive theologians conceived the invisible presence of a supreme being and thus seemed to reach an incredible degree of abstraction, was their idea really abstract, or was it concrete? Did they postulate God or did they see Him? Were the earliest expedients nothing but expedients or did they include reasonings, religious or artistic cravings? Were they rational or irrational? Was early science wholly practical and mercenary? Was it pure science, such as it was, or a mixture of science with art, religion, or magic?

Such queries are futile, because they lack determination and the answers cannot be verified. It is better to leave out for the nonce the consideration of science as science, and to consider only definite problems and their solutions. The problems can be imagined, because we know the needs of man; he must be able to feed himself and his family, to find a shelter against the inclemencies of the weather, the attacks of wild beast or fellow men, and so on. Our imaginations are not arbitrary, for they are guided by a large number of observed facts. To begin with, archaeologic investigations reveal monuments which help us to realize the kind of objects and tools that our forefathers created and even to understand their methods of using them, and to guess their intentions. The study of languages brings to light ancient words which are like fossil witnesses of early objects or early ideas. Anthropologists have made us familiar with the manners and customs of primitive men who were living under their own eyes. Finally, psychologists have analyzed the reactions of children or of undeveloped minds in the face of the very problems that primitive men had to solve. The amount of information thus obtained from several directions is so large that a scholar’s life is too short to encompass it. There is no place here for a review of it, however brief, but only for a few hints.

In order to simplify our task a little, let us assume that the primitive men we are dealing with have already solved some of the most urgent problems, for otherwise their very existence would have remained precarious, not to speak of their progress, material or spiritual. Let us assume that they have discovered how to make a fire and have learned the rudiments of husbandry. They are already — that is, some of them are — learned people and technicians, and they may already be speaking of the good old days when life was more dangerous but simpler and a man did not have to remember so many things. I say “speaking,” for by this time they have certainly developed a language, though they are still unable to write it; indeed, they are still unconscious of the possibility of doing so. At this stage, and for a long time to come, writing is neither essential nor necessary. Our own culture is so closely dependent on writing that it requires some effort to imagine one independent of it. Man can go very far without writing, but not without language. Language is the bedrock upon which any culture is built. In the course of time it becomes the richest treasure house of that culture.

One of the greatest mysteries of life is that the languages of even the most primitive peoples, languages that have never been reduced to writing (except by anthropologists), are extremely complex. How did those languages develop as they did? The development was very largely unconscious and casual.

Our reference to investigations made today by field anthropologists is sufficient warning that when we speak of the dawn of science or of any prehistoric period we are not thinking in terms of a chronologic scale of universal application. There is no such scale. The dawn of science occurred ten thousand years ago or more in certain parts of the world; it can still be witnessed in other parts today; and irrespective of place we can observe it to some extent in the mind of any child.

EARLY TECHNICAL PROBLEMS

Let us consider rapidly the multitude of technical problems that early men had to solve if they wished to survive, and, later, to improve their condition and to lighten the burden of life. They had to invent the making of fire and experiment with it in various ways. Not only the husbandman but also the nomad needed many tools, for cutting and carving, flaying, abrading, smoothing, crushing, for the making of holes, for grasping and joining. Each tool was a separate invention, or rather the opening up of a new series of inventions, for each was susceptible of improvements which would be introduced one by one. In early times there was already room for key inventions, which might be applied to an endless group of separate problems and which ushered in unlimited possibilities. For example, there was the general problem of how to devise a handle and how to attach it firmly to a given tool. Many different solutions were found for that problem, one of the most ingenious being that of the Eskimos and Northern Indians, namely, the use of babiche (strings or thongs of rawhide) by means of which the tool and handle are bound together; as the hide dries it shrinks almost to half its length and the two objects are inseparable. A tighter fit could hardly be obtained otherwise.

The husbandman had to discover the useful plants one by one — plants to use as food, or as drugs, or for other domestic purposes — and this implied innumerable experiments. It was not enough for him to discover a plant; he had to select among infinite variations the best modalities of its use. He had to capture animals and to domesticate the very few that were domesticable, to build houses and granaries, to make receptacles of various kinds. There must have been somewhere a first potter, but the potter’s art involved the conscious or unconscious cooperation of thousands of people. Heavy loads had to be lifted and transported, sometimes to great distances. How could that be done? Well, it had to be done and it was done. Ingenious people invented the lever, the simple pulley, the use of rollers, and later, much later, that of wheels. A potter of genius applied the wheel to his own art. How could a man cover his body to protect it from the cold or the rain or the burning sun? The use of hides was one solution, the use of leaves or bark another, but nothing equaled the materials obtained by the weaving of certain fibres. When this idea occurred to a great inventor, the textile industry was born. The earliest tools were made of stone or bones; when the practical value of metals was finally realized it became worth while to dig for their ores and to smelt them, to combine them in various ways; this was the beginning of mining and metallurgy. Each of the sentences of this paragraph could easily be expanded into a treatise.

In order to illustrate the almost uncanny ingenuity of “primitive” people, it may suffice to display the three following examples, taken in three parts of the world very distant from each other. The Australian boomerang is so well known that it hardly requires discussion; it is a missile weapon the curved shape of which is so cunningly devised that the weapon when thrown describes extraordinary curves and may even return to the sender. The South American tipiti is an elastic plaited cylinder of jacitara-palm bark which is used to express the juice of the cassava (or manioc); as the cylinder is lengthened, by the weight of a stone or otherwise, the internal pressure increases and the juice flows out. This invention is admirable in its simplicity and effectiveness, but what is more astonishing is that the Indians were able to discover the great nutritive value of cassava. The juice contains a deadly substance (hydrocyanic acid) which must be removed by cooking; otherwise, the consumer would be killed instead of nourished. How did the Indians find the treasure which could be enjoyed only after the poison spoiling it had been removed? My third example is the li , a tripod used in China in prehistoric times. It is a three-legged cooking pot, the legs of which are shaped like cows’ udders; various foods may be cooked in each leg with a single fire burning in the middle.

These examples might easily be multiplied. Selected as they have been in three corners of the world as remote from one another as could be, they illustrate the wide distribution of genius. We well know that whatever amount of civilization we enjoy today is the gift of many nations; we do not know so well that the same was already true thousands of years ago. Prehistorians have proved beyond doubt the existence of sophisticated cultures at very early times in many places. This does not disprove the monogenesis of mankind. It is highly probable that the new species Homo sapiens originated in a single place, but so long ago that by the time at which the earliest observable cultures flourished man had already invaded a good part of the world.

PREHISTORIC TRAVEL AND TRADE

Travel was much slower and more difficult in the past than it is now, and one might be tempted to conclude that primitive man moved very little and did not rove far away from his hiding place. That conclusion would be wrong. To begin with, we may observe that the speed of communication did not increase materially until the steam age, a century ago. Primitive people could move as fast as Napoleon’s soldiers; sometimes they moved much faster. It is now generally agreed that there was considerable travel, individual and tribal (migrations), in the earliest days that scientific research can reach. For example, the Americas were discovered and colonized thousands of years ago by people coming over from Siberia and crossing the Bering Strait region; every American Indian is ultimately of Asiatic origin. The migrations were probably more frequent and more abundant in the oldest prehistoric periods before the invention of the agricultural arts, for as soon as people mastered those arts they became naturally more sedentary and more timid.

The passage from nomadic to settled life was perhaps the most pregnant step up in the whole history of mankind. That passage was far more important than the ones from stone to bronze or from bronze to iron; it might be called the passage from food gathering to food producing. Man could not settle down for life in any one place until he was secure from enemies, and this implied association with other men and some kind of government, nor until he was secure from want, and this implied the possibility of obtaining in the neighborhood enough food for himself, his family, and his beasts; it implied the arts and the folklore of agriculture. It has been remarked above that the development of mankind does not synchronize everywhere. Some people are more advanced than others, nor do they all pass through the same stages. The passage from nomadic to settled life occurred many millennia ago in some places, yet it has not been completed today by the Arab Bedouins. Man always was the child of circumstances, and since his environment varied enormously from place to place, he was bound to develop differently in different regions.

Men who had learned to cultivate the land were gradually blessed (and cursed) with the ownership of more and more things and bound to the soil by more and more ties. As to their nomadic brethren, roving in search of better hunting or fishing, they might come back periodically to the same grounds, but there was nothing save habit and incipient domestication to oblige them to do so. The real nomads kept moving on without retracing their steps and were likely to cover immense distances.

The distinction between settled people, seminomads, and nomads is generally made with regard to people moving on land, but it applies equally well to those moving on water. No savages have ever been found near water who were not able to navigate it, but some of them were more settled than others, and some were regular sea rovers. The canoe is probably one of the oldest inventions of man, older than the bow; in favored places, where canoes were especially needed and materials for making them were handy, they were invented perhaps as early as thirty thousand years ago. Seaworthy ships came later, yet so early that deep-sea navigation reached a climax many millennia ago. According to the Norwegian archaeologist Anton Wilhelm Brøgger,¹⁰ there was a golden age of oceanic navigation during the period roughly defined as 3000 to 1500 B.C., that is, before the days of Phoenician navigation. This is an archaeological interpolation, but its plausibility is confirmed from many sides. Sailing appealed to early men as it does to the young and strong of every time, and there are few fields wherein their inventiveness appeared more brilliantly. In this field, as in every other, it was not a matter of one invention but of a thousand, and the complete story would be endless. Among the masterpieces of primitive technology we may mention the wooden outrigger canoe of the South Seas, the Irish curragh (or coracle), the Eskimo dory-shaped umiak and their watertight kayak.

The early inhabitants of the northwestern European shores were not afraid of exploring the foggy and tempestuous Atlantic, and the South Sea islanders navigated the Pacific in every direction. For example, Polynesians did not hesitate to sail their canoes from Tahiti to Hawaii, a distance of 2400 nautical miles.

As to primitive commerce, there are many witnesses to it, one of the clearest being the relics of the amber trade. The best-known kind of amber (succinite) is a natural product of the Baltic shores, but pieces of it have been found in prehistoric tombs scattered in so many places that it has been possible to draw maps of the prehistoric amber routes.¹¹ As amber was very valuable and easy to transport, Scandinavians were able to obtain in exchange for it many goods of the southern regions, which had been favored by nature and were more advanced. Trade, then as now, was one of the main occasions of intercourse, one of the vehicles of civilization.

In the Stone Age the special value of flints for tools was soon realized, and good flints, breaking with sharp edges, were not found everywhere. The existence of flint quarries and of an international flint trade has been proved repeatedly. Alluvial gold must have been observed and collected very early and used for ornaments. The first ores to be exploited were probably sulfides of copper and antimony, both of which are very easily reducible, and thus copper and antimony were discovered. When grains of cassiterite were reduced, tin was obtained, and one of the first metallurgic geniuses had the idea of alloying a little tin with copper and thus obtaining a new metal, bronze, much harder and more serviceable than copper. Wherever that discovery was made or introduced, the Stone Age was followed by a Bronze Age. Later, other inventors found means of reducing the most fusible of the iron ores and the Iron Age began.¹²

It is not necessary to insist upon these momentous facts, with which the reader is presumably acquainted, but it is well to repeat a double warning. First, the Stone Age (or Ages), the Bronze Age, the Iron Age did not synchronize in every country; they might begin earlier and last longer in one region than in another. In the Americas, the Stone Age lasted until the European conquest. Second, they were never sharply separated from one another. Stone tools continued to be used in the Bronze Age and bronze tools in the Iron Age. Sometimes the use of old-fashioned materials was continued for religious or ceremonial purposes, for example, stone knives for circumcision in Egypt and Palestine,¹³ and jade implements in China. Social inertia often sufficed to perpetuate old usages and prevent the substitution of new tools for old ones. Thus one of Mariette’s¹⁴ foremen was still shaving his head with a flint razor. Indeed, prehistoric tools are still in use today. Women may still be seen in various parts of Europe (Scottish Highlands, Pyrenees, etc.) spinning with a hand spindle loaded with a stone whorl:¹⁵

The decorative arts, not only ancient and medieval, but even the present ones, ring the changes on many prehistoric motives. We might say that there are as many prehistoric relics embedded in the language of forms as there are in the language of words; it is one of the delights of art historians as well as of philologists to detect these immortal witnesses of the distant past.

PREHISTORIC MEDICINE

We have already referred to the prehistoric knowledge of herbs and other drugs, knowledge distilled from immemorial empiricism, trial and error doggedly continued for hundreds and thousands of years. It is impossible for us to understand how such vague and casual experiments could be repeated long enough, their results taken note of and transmitted from generation to generation, but the fact is there: our prehistoric ancestors, like the primitive people who can still be observed, had managed to try many plants and other objects and to classify them in various groups according to their utility or danger.¹⁶ Shepherds must have learned simple ways of setting broken or dislocated bones. Midwifery was necessarily practiced and the more intelligent midwives improved their methods and taught them to younger helpers. In all such cases the best as well as the hardest of teachers was always close at hand: necessity. If a man had his arm mauled by a wild beast or a falling rock, if he broke his leg, if a woman experienced unusual trouble in her travail, something had to be done, quickly. Other pathologic disturbances called for immediate solutions. Healing was probably one of the earliest vocations and professions. Sometimes the healer succeeded, and his successes were more likely to be remembered than his failures; he became famous and was imitated. Prehistoric medicine may be understood by comparison with the practice, half empirical, half magical, of primitive medicine men or shamans. It is possible that the extraordinary success of some of those shamans was due to their mediumistic power or to the popular belief in such a power. We may assume that faith healing began, at least in some places, at the very dawn of civilization.

All this is necessarily conjectural, but in at least one case we have direct and abundant evidences of a peculiarly daring kind of procedure. Many of the prehistoric skulls that have come down to us show signs of trepanation. The reader will ask: “How do you know that the operation was made on living men, not simply, for some ritual purpose, on empty skulls?” We know it well, because the hole made in the skull of a living man tended to heal itself and the growth of new bone can be recognized without ambiguity.¹⁷Why was the skull perforated? That question cannot be answered. It is possible that the surgeon tried to relieve unendurable pressure due to concussion of the brain. One may also ask, How was it done? Some kinds of drills were already used by paleolithic craftsmen; witness the existence of perforated stones and of actual drills in ancient sites.¹⁸ The perforation of a stone with a stone drill must have been a very long task; trepanning must have been rela tively easy, at least for the surgeon; not so easy for the patient.¹⁹

PREHISTORIC MATHEMATICS

The transition from empiricism to rational knowledge was necessarily very slow in medicine, because the number of independent variables was very great and each ailment might vary considerably from one individual to another. Let us pass to another field, mathematics, where some humble kind of rationalization was possible, and abstraction natural, at an early stage. One of the fundamental ideas of mathematics is the idea of number, which, in its simplest form, may have occurred to very early men. The first mathematician — a great unknown genius — was perhaps the man who adumbrated that idea.

How did that happen? We can only guess, but our guesses are neither arbitrary nor futile. The first theologian adumbrated the idea of oneness or wholeness, one cause, one world, one self, one God. The idea of twoness or duality must have occurred almost as early, for there are many obvious pairs in nature. We have two eyes, two nostrils, two ears, two hands, two feet; women have two breasts. The hands were particularly instructive, for man must have used them unequally from the very beginning. The simplest acts, such as eating, drinking, using tools, loving, or fighting, imply different tasks for each hand. The two hands revealed the right and left sides of everything, not a simple duality but a polarity wherein one side is different from, and preferable to, the other. Above all, dominating everything, is the polarity of sex. Not only all men, but also every animal that they could observe, was either male or female. That was not only obvious, but imperative, obsessing, unavoidable. Moreover, every quality appears necessarily under a dual aspect; things are hot or cold, dry or moist, large or small, pleasant or unpleasant, good or evil.

Larger groups, though less universal, were noticeable enough. A father and mother with their first baby — that is a trinity. On a river there are two directions, up and down, but to the man standing in a plain there are many more. Let him stand with outstretched arms; there are revealed to his mind four privileged positions — straight ahead, backward, and the directions of either arm. His language will soon express this with four significant words, such as front, back, right, left. If his hands were stretched out, the right toward the place of the rising sun and the left toward that of the setting one, the idea of four cardinal points was emerging. To those four elements might be added a fifth, the center, the very place where he stood, or two others, the sky above and the earth below. Hence arise the categories of fiveness, sixness, sevenness. The first of these categories was strongly reinforced by the existence of five fingers. When counting things on one hand or one foot, it was natural enough to group them in fives and to speak of so many “hands.” Larger groups, such as ten or twenty, were almost equally natural, but a little more difficult to recognize.

Most people, almost all of them, took these categories for granted and did not give a thought to them, but if there was a born mathematician among them — and why should there not have been? — he must have realized the existence of numbers, abstract numbers, independent of the objects counted. The fiveness of hand or of foot or of Cassiopeia, he must have thought, is essentially the same thing. As to the theologians or the cosmologists, they may have been hypnotized by the number one, generative of all others, or by two, expressing the universal polarity, or even by three, the mystic triangle. Dualism, such as was elaborated in the Zoroastrian religion, is rooted in the deepest recesses of the human conscience.

These numerical categories were the seeds of arithmetic, that is, of pure science, but also of number mysticism, or pure nonsense. The two roots grew exuberantly. Let us consider the situation in China; we can do this without abandoning the prehistoric level, for the numerical groupings of which the Chinese mind is so fond are immemorial, and if we could trace them to their origins they would very probably take us back to the most remote antiquity. Chinese ideology is dominated by the universal polarity of yang and yin , the male and female, positive and negative, principles of life. Yang is male, light, hot, active, it is heaven, the sun, rocks and mountains, goodness . . .; yin is female, dark, cold, passive, it is the earth, the moon, water, trouble and evil ... (It is clear enough that the earliest Chinese cosmologists were men, not women!) Every example of duality can be expressed in terms of yang and yin. The sexual origin of every form of life, the fact that each child needs two parents, is extended to the whole universe. What is most curious is that that sexual cosmology received very early a mathematical interpretation. Not only is negative opposed to positive (a fundamental distinction to be developed later on in geometry as well as in arithmetic), but yang is represented by a solid line and yin by a broken one. Take these lines three by three, and eight combinations, the eight diagrams pa kua , are possible, neither more nor less (Fig. 1). The discovery of that mystery was ascribed to the legendary founder of Chinese culture, Fu hsi , the first emperor, supposed to have ruled from 2953 to 2838 B.C. Such an ascription is simply a patent of hoary antiquity. If the yang and yin lines are combined six by six there are 64 possible hexagrams, each of which was given a definite meaning; this process might be continued and was indeed continued (the mathematical mind at work!), but we need not worry about that. It is interesting to realize that those early Chinese savants and mystics were playing, without being aware of it, with combinatorial analysis. It would be foolish to expect that they should have realized the mathematical implications of their thinking at that early stage, but their instinctive tendency in that direction is confirmed by their invention of a sexagenary period (a “cycle of Cathay”) obtained by combining, two by two, the twelve earthly branches (shih êrh ti chih ) with the ten heavenly stems (shih t’ien kan ).²⁰ As 12 × 5 = 10 × 6 = 60, sixty different combinations are possible (Fig. 2). This discovery is ascribed to another mythical emperor, Huang Ti , who ruled from 2698 to 2598. At first, it was applied only to days and hours; the application to years occurred only later under the Han dynasty (let us say, about the time of Christ), but we are concerned here only with the fundamental idea of a sexagenary cycle, not with its applications.²¹

Fig. 1. Symbols of yang (white, male) and yin (dark, female) in the center and the eight diagrams around.

The average Chinese did not indulge in such speculations; he accepted the pa kua and the chia tz as naturally as the seasons or the phases of the moon, yet the habit of numerical categories was deeply ingrained in his mind. Some such desire of grouping things by twos or threes and so forth exists in every mind (it expresses an instinctive need of order and symmetry, fundamental to science as well as to art), but the Chinese allowed it to expand more freely than any other people. Thus a large collection of groupings are as familiar to them, as, let us say, the four cardinal points to us, groupings by twos, threes, fours, fives,²² sixes, sevens, eights, nines, tens, twelves, thirteens, seventeens, eighteens, twenty-fours, twenty-eights, thirty-twos, seventy-twos, hundreds. William Frederick Mayers²³ listed 317 such groupings, and I am confident that his list could be extended. Of course, many of these groups are of late origin, others will be added in the future, but the primary idea is almost as old as Chinese culture.

We have come very close to mathematics and then drifted away. This must have happened many times in the past; it continues to happen within our experience. Any scientific idea may be, and often is, perverted; that cannot be helped. It is like a tool that may be used for good purposes or for evil ones.

To return from fancy to reality, the progress of arithmetic was probably due to the fact that people could not stop at small and familiar categories, but were obliged to count things and faced relatively large numbers at a very early stage. A chieftain, wanting, as was natural enough, to assess his resources, would ask himself how many men he could depend upon, how many horses, sheep, and goats. In short, he would need a census, and, even if his tribe were small, that census would quickly lead to numbers too large to be counted on one’s fingers. How would he do it? In his delightful account of how the rajah of Lombok took the census,²⁴ Wallace gives us the diplomatic side of the story and stops at the point where the mathematical difficulties begin; those difficulties could not be evaded. The tangible result of the rajah’s survey was many bundles of needles. How did he count the needles? Now grouping is the very basis of counting. Every language betrays the presence of what mathematicians call a number base, which was often five (among many American tribes), sometimes twenty (among the Mayas), but more often ten.²⁵ These bases were more popular than others, because almost every primitive man used the same counting machine, to wit, his fingers or toes. He might stop at one hand (or foot) in which case his base was five, or use both hands (or both feet) when the base was ten, or use the whole outfit, when the base was twenty.²⁶ In medio virtus! The peoples whose culture patterns were destined to dominate all others agreed unconsciously on the use of ten. How do we know the number bases of primitive people? We can easily deduce it from their language, even as our own decimal base is clearly represented by our number words. Indeed, it was partly because of the words themselves that a base was needed and was instinctively created. The base makes it possible to use periodically the same few words, with slight modifications, if any; without it an infinity of words would be required.²⁷

The spontaneous agreement of the leading nations on the decimal base is wonderful, but not more so after all than the marvelous symmetry of each language. These things pass our understanding. How is it possible to account for the unconscious development of such complex and symmetric structures, not in one place, but wherever men flourished? Each language evidences not a perfect symmetry, like that of a geometric drawing, but one that is imperfect in many ways, like that of a tree or of a beautiful body — a living symmetry.

How were the returns of a primitive census enumerated? Let us assume that each item to be counted was represented by a twig²⁸ and that the base was decimal. One made bundles of ten twigs each, then the total number of twigs was ten times that of the bundles. If there were too many bundles, it may have occurred to the computer to consider each bundle as a single twig, a kind of superior twig, and make new bundles of ten bundles each. If the computer had done that much and was mathematically minded, there was nothing to stop him from repeating that operation as often as necessary. After having recognized tens, he might recognize hundreds, thousands, tens of thousands, and so on, creating new words, as well as new symbols if he had already reached that particular stage. Please note that the number of new words (or symbols) which are needed decreases rapidly. It took probably a long time before the word million was actually needed and we are but just beginning to use with any frequency the word billion.²⁹

Fig. 2. Sexagenary cycle (“a cycle of Cathay”). The ten symbols of each first column are alike; they are ten celestial stems. The twelve earthly branches are written in the second columns, from 1 to 12, 13 to 24, 25 to 36, 37 to 48, 49 to 60. Each group of two characters is different from every other. [Herbert A. Giles, Chinese-English dictionary (Shanghai, ed. 2, 1912), vol. 1, p. 32.]

What we call the fundamental operations (addition, subtraction, multiplication, division) emerged naturally, if not explicitly, from the very process of enumerating collections and sharing them. The idea of subtraction arose also from the fact that when numbers are a little smaller than round numbers it is easier to approach them from above than from below, to say, for example, that there are 2 less than 20 rather than 18, 100 less 1 rather than 99, 10,000 less 300 rather than 9700.³⁰

We have assumed thus far that early accounts were made by means of twigs or other objects, say pebbles (calculi in Latin, hence our words calculus, calculation, etc.) ; it might be done and was done as well by means of knots in strings or notches in tallies. The same periodicities would naturally reappear. Anyone having in his mind, however unconsciously, the decimal rhythm, would carve a longer notch for a ten, and one still longer for a hundred; numbers approaching the longer notches would be grasped more easily by retrogression from those notches, that is, subtractively.

The concepts of rhythm and pattern awakened by the necessity of counting reappeared more tangibly in the process of ornamentation. The simplest measurements, such as were needed to build an altar or a house, may have inspired the earliest geometric ideas, but the love of beauty innate in most men was probably the real cradle of geometry, for in order to decorate pleasantly various objects or one’s body, not only were some measurements required but a whole gamut of them, plus as many symmetric and periodic combinations of decorative elements as fancy would suggest. Mother Nature was the best art teacher; the infinite patterns evidenced in natural objects, such as trees, leaves, flowers, birds, snakes, were a continual source of inspiration to the men who had in them the love of beauty. Some of the paleolithic drawings that have come down to us were made by genuine artists. The decorations of ceramics and textiles that may be viewed in anthropologic museums reveal an astonishing amount of imagination and sensitiveness. Not only were the craftsmen able to create patterns of great complexity, but they rang the changes on them with virtuosity and were subtle enough to realize the value of little deviations. Any such composition implied the solution, however crude, of many geometric problems.

It was easy enough to measure a distance and to divide it — let us say by means of a string which could be folded twice or more often — but a more difficult problem arose when early “scientists” tried to estimate the relative distances of the stars of a familiar constellation, or the change of distance of a moving star (planet) approaching a fixed one (that is, one moving regularly with all the others), or the changes of distances between the Moon and the constellations through which it never ceased to proceed. They may have tried to measure such a distance with a string, but if so, they must have promptly noticed that the length to be measured diminished when the string was brought closer to the eyes. It finally dawned upon the mind of a prehistoric Newton that astronomic distances were not linear but angular; the idea of angle was a geometric and astronomic invention of fundamental importance.

It did not suffice to make measurements; such measurements had to be expressed and that expression implied a choice of units. Nor did it suffice to choose units; it was necessary to keep them. The preservation of standard units was perhaps one of the first steps in scientific organization, though this was naturally as unconscious as were all the other early steps. It would seem that almost every nation agreed upon selecting as units parts of the adult body (cubit,³¹ foot, span, etc.). Our earliest ancestors realized as naturally as we do that many units are needed, small ones for small distances, larger ones for longer distances, and so on, but they did not try to establish fixed relations between those units. We should not blame them, bearing humbly in mind that highly civilized peoples of our own days have not yet understood that need.

PREHISTORIC ASTRONOMY

We have already spoken of the stars. It was impossible for any reflective man to observe them night after night without asking himself a number of questions, which were primarily scientific questions. Early people, especially those encouraged by a hot climate to spend nights out of doors, cannot fail to have observed the changing places throughout the year of sunrise and sunset, the phases of the Moon, the regular motion of the Moon to the left³² Among the stars at different altitudes of culmination but with about the same speed, the seasonal appearance and disappearance of some constellations, the more complex motions of the morning and evening stars ³³ and of other planets. They were aware in many ways of the march of time, for they could not help recognizing the ever-recurring periods of day and night, of moon phases, of meteorologic seasons, and years. They made for themselves calendars wherein those events were foretold on the basis of past experience, calendars based on meteorologic events, on the Moon cycle, or the Sun cycle, or on many of these events combined. Those calendars might be gradually improved as the observations from which they were derived were repeated and refined.

We need not continue this enumeration. It is certain that at least a few privileged peoples, favored by better opportunities of climate or site or by greater intelligence, had already accumulated a large amount of knowledge before the invention of writing. Prehistoric knowledge was so vast and varied in some parts of the earth that a complete catalogue of it, if it were possible to reconstruct it, would occupy considerable space.

PURE SCIENCES

Some readers will object that whatever knowledge there was, was purely practical, empirical, too raw and rough to deserve the name of science. Why should we not call it science? It was a very poor science, very imperfect, yet perfectible; our science is decidedly deeper and richer, yet the same general description applies to it — it is very imperfect yet perfectible. Or one might say, There was no pure science. Why not again? How pure must science be to be called pure? If pure science is disinterested science, knowledge obtained for its own sake without thought of immediate use, surely the early astronomers were or might be as pure as our own. It is possible that astrologic fancies had already developed, but it is equally possible that they had not, for that would have implied a degree of sophistication which those astronomers had not yet reached. Their main reason for observing the strange behavior of certain planets may have been simply curiosity.

Curiosity, one of the deepest of human traits, indeed far more ancient than mankind itself, was perhaps the mainspring of scientific knowledge in the past as it still is today. Necessity has been called the mother of invention, of technology, but curiosity was the mother of science. The motives of primitive scientists (as opposed to those of primitive technicians and shamans) were perhaps not very different from those of our contemporaries; they varied considerably from man to man and time to time and then as now covered the whole gamut from complete selflessness, reckless curiosity, and spirit of adventure down to personal ambition, vainglory, covetousness.

If research had not been inspired and informed from the beginning by a certain amount of disinterestedness and adventurousness, and by what its enemies would later call indiscretion and impiety, the progress of science would have been considerably slower than it was. The amount of knowledge attained by some primitive men can be deduced from anthropologic records and also from the amount observable in the most ancient civilizations. When man appears on the scene of history, we find him already a master of many arts, expert in many crafts, as full of lore as of cunning.

Then as now the true scientist, even as the true artist, was likely to be or to seem a bit queer and secretive; it is highly probable that his more practical neighbors already made jokes about his absent-mindedness. Of course, he was not more absent-minded than they were, but their minds were focused on different interests. He was engrossed in his own reflections; his motives being less tangible, his life seemed mysterious. Sometimes he may have wished for praise and recognition, or he may already have discovered that such praise was futile and that it was better not to try for it. If he were selfish and jealous, the primitive inventor might prefer to keep his new idea — say a better hook, or a better ax, or better materials for the making of either — to himself and his family. In almost every case the scientist or the inventor tended to be reticent. The growth of science was always entangled in psychologic and social accidents.

Not only was the development of primitive invention somewhat confidential and secret, it was also of necessity antagonistic to the regular habits and traditions that it tended to subvert. Every invention, however useful it may turn out to be (and it cannot be useful before it is used), is disturbing, and the more pregnant it is, the more disturbing. There were vested interests in prehistoric times as well as now, though they could not be described in exactly the same way and were perhaps less blatant. There was, then as now, a strong inertia impeding progress, the inertia of habit and complacency, distrust and contempt of everything novel or foreign. That inertia, however, was not simply a hindrance, but a necessity, like a flywheel or a brake, to steady and warrant mankind’s invasion of the unknown. Men’s resistance to new tools or newfangled ideas was useful, because novelties should be thoroughly tested before being adopted. Every accepted tool was the fruit of a very long process of trial and error, of a very long tussle between inventors, innovators, reformers at one end and conservatives at the other. The latter were far more numerous; the former were more enthusiastic and aggressive.

DIFFUSION AND CONVERGENCE

Some anthropologists (the “diffusionists”) seem to believe that each invention was made in but one place, and that this sufficed to spread it elsewhere, if it was worth while. Sir Grafton Elliot Smith (1871–1937) and William James Perry, arguing in that way, would have us consider Egypt the cradle of civilization. A generalization of such boldness is not susceptible of proof, and the history of science tends to disprove it. Simultaneous discoveries, that is, identical or similar discoveries made at about the same time by different people in separate places, are not uncommon in modern times, and their circumstances have been investigated. They are generally explained by a common ancestry of problems or instruments; the inventors were trying to solve the same problems, and drew their information from the same sources and their inspiration from similar needs; the simultaneity (or quasi simultaneity) of their triumphs is accounted for by the simultaneity of their needs. “The idea was in the air,” as we say. Moreover, each problem, as soon as it is solved, creates new problems; each discovery entails a logical sequence of other discoveries. Why should it not have been the same in prehistoric times? The only difference in this respect between the distant past and the present is that, everything being much slower in the past than now, the simultaneities would be counted in centuries instead of in years or months as they are now.

The most impressive example of convergence (as opposed to imitation) is the independent invention of a decimal system of numeration in distant parts of the world, its almost unanimous (yet unconscious) acceptance by the very nations whose cultures became the dominating ones. That is one of the miracles of the dawn of science. The anatomic explanation given above is convincing enough as far as it goes, but it is far from complete. Why did men unite on ten, rather than on five or twenty?

The theory of convergent evolution, or convergence (as the anthropologists call it), does not deny the frequent occurence of borrowings and imitation between one people and another; it claims that similarities between different cultures are not necessarily the result of imitation but may be and often are due to independent inventions. Even when a people borrows a cultural trait, a tool, a word, or an idea from another, the imitation is more often active than passive. Indeed, the tool or the idea must be acceptable to the new people; if not immediately acceptable, it must be put in an acceptable shape; and even when acceptable, it must still be accepted and that may involve as long and painful a struggle as was needed for the acceptance of the original invention. The cultural trait is not really a trait of the new people until it has been thoroughly understood (or misunderstood!), liked, assimilated. Its introduction is never a process of simple addition, but one of biological intussusception, re-creation. In order to use metal tools or weapons instead of stone ones, men had to discard old notions and become — to use modern slang — metal conscious. That sort of thing did not happen in a day, nor in a year, nor perhaps in a century.

Even if mankind originated in but a single place, so many millennia elapsed between its emergence and the dawn of culture that men had had innumerable opportunities of spreading in many directions as fate and circumstances pushed them hither and thither. Though modified by climatic and geographic conditions, the problems that they had to solve were essentially the same. Is it surprising, then, that they hit upon the same or similar solutions? Were they not essentially the same people? Sometimes they would find a solution unaided by others; sometimes another solution having reached their eyes or ears would be accepted by them, stolen, or reinvented. The borrowing could be interpreted in various ways, and it would vary considerably from all to almost nothing, or from servile imitation to the taking of the least hint.

Each settlement had its men of genius, its dullards, and its great majority of “average” people. The average varied from settlement to settlement not only for hereditary reasons, but also because the climatic and geographic conditions (including the availability of definite plants and animals) were more favorable in some places than in others. There was from the beginning a great variety of men and women as well as a great variety of opportunities. People who had settled at the edge of a lake or of the sea had different opportunities from their distant cousins who had found a refuge in mountain caves or in desert oases. Each gift of nature created distinctive needs. Some of those needs vanished in the course of time, and this accounts for the “lost arts.” Primitive man could do a great many things that we would be incapable of, and he managed to survive in the midst of dangers that we could not face any more.

Even as some people excelled among other people, some communities excelled among other communities, and were able to accomplish certain tasks that those others did not even think of, and thus to help mankind rise a step higher. The next step was made possible by another community, at another time, in another place. Thus it was at the beginning and thus it has always been. The student of human evolution cannot escape feeling that mankind is working in shifts. There is no privileged “race” or community in any absolute way, but for each task and for each time some people or some nations may excel all others.

The dawn of science did not break out everywhere with the same beauty and the same hopefulness. There were probably precocious peoples, as there are precocious children, who began very early but did not go very far. We shall concern ourselves in the following chapters with the ancient peoples whose cultural dawn was only the prelude to the greatest achievements of the third and second millennia before Christ.³⁴

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