Of course no one nowadays would rest the case for the Oriental origin of Greek philosophy on the evidence of Clement or Eusebios; the favourite argument in recent times has been the analogy of the arts and religion. We are seeing more and more, it is said, that the Greeks derived their art and many of their religious ideas from the East; and it is urged that the same will in all probability prove true of their philosophy. This is a specious argument, but not in the least conclusive. It ignores altogether the essential difference in the way these things are transmitted from people to people. Material civilisation and the arts may pass easily from one people to another, though they have not a common language, and certain simple religious ideas can be conveyed by ritual better than in any other way. Philosophy, on the other hand, can only be expressed in abstract language, and it can only be transmitted by educated men, whether by means of books or oral teaching. Now we know of no Greek, in the times we are dealing with, who knew enough of any Oriental language to read an Egyptian book or even to listen to the discourse of an Egyptian priest, and we never hear till a late date of Oriental teachers who wrote or spoke in Greek. The Greek traveller in Egypt would no doubt pick up a few words of Egyptian, and it is certain that somehow or other the priests could make themselves understood by the Greeks. They were able to rebuke Hekataios for his family pride, and Plato tells a story of the same sort at the beginning of the Timaeus.[[28]] But they must have made use of interpreters, and it is impossible to conceive of philosophical ideas being communicated through an uneducated dragoman.[[29]]
But really it is not worth while to ask whether the communication of philosophical ideas was possible or not, till some evidence has been produced that any of these peoples had a philosophy to communicate. No such evidence has yet been discovered, and, so far as we know, the Indians were the only people besides the Greeks who ever had anything that deserves the name. No one now will suggest that Greek philosophy came from India, and indeed everything points to the conclusion that Indian philosophy came from Greece. The chronology of Sanskrit literature is an extremely difficult subject; but, so far as we can see, the great Indian systems are later in date than the Greek philosophies which they most nearly resemble. Of course the mysticism of the Upanishads and of Buddhism were of native growth and profoundly influenced philosophy, but they were not themselves philosophy in any true sense of the word.[[30]]
Egyptian mathematics.
XI. It would, however, be another thing to say that Greek philosophy originated quite independently of Oriental influences. The Greeks themselves believed their mathematical science to be of Egyptian origin, and they must also have known something of Babylonian astronomy. It cannot be an accident that philosophy originated in Ionia just at the time when communication with these two countries was easiest, and it is significant that the very man who was said to have introduced geometry from Egypt is also regarded as the first of the philosophers. It thus becomes very important for us to discover, if we can, what Egyptian mathematics meant. We shall see that, even here, the Greeks were really original.
There is a papyrus in the Rhind collection at the British Museum[[31]] which gives us an instructive glimpse of arithmetic and geometry as these sciences were understood on the banks of the Nile. It is the work of one Aahmes, and contains rules for calculations both of an arithmetical and a geometrical character. The arithmetical problems mostly concern measures of corn and fruit, and deal particularly with such questions as the division of a number of measures among a given number of persons, the number of loaves or jars of beer that certain measures will yield, and the wages due to the workmen for a certain piece of work. It corresponds exactly, in fact, to the description of Egyptian arithmetic which Plato has given us in the Laws, where he tells us that the children learnt along with their letters to solve problems in the distribution of apples and wreaths to greater or smaller numbers of people, the pairing of boxers and wrestlers, and so forth.[[32]] This is clearly the origin of the art which the Greeks called λογιστική, and they certainly borrowed that from Egypt; but there is not the slightest trace of what the Greeks called ἀριθμητική, or the scientific study of numbers.
The geometry of the Rhind papyrus is of a similarly utilitarian character, and Herodotos, who tells us that Egyptian geometry arose from the necessity of measuring the land afresh after the inundations, is obviously far nearer the mark than Aristotle, who says that it grew out of the leisure enjoyed by the priestly caste.[[33]] We find, accordingly, that the rules given for calculating areas are only exact when these are rectangular. As fields are usually more or less rectangular, this would be sufficient for practical purposes. The rule for finding what is called the seqt of a pyramid is, however, on a rather higher level, as we should expect; for the angles of the Egyptian pyramids really are equal, and there must have been some method for obtaining this result. It comes to this. Given the “length across the sole of the foot,” that is, the diagonal of the base, and that of the piremus or “ridge,” to find a number which represents the ratio between them. This is done by dividing half the diagonal of the base by the “ridge,” and it is obvious that such a method might quite well be discovered empirically. It seems an anachronism to speak of elementary trigonometry in connexion with a rule like this, and there is nothing to suggest that the Egyptians went any further.[[34]] That the Greeks learnt as much from them, we shall see to be highly probable, though we shall see also that, from a comparatively early period, they generalised it so as to make it of use in measuring the distances of inaccessible objects, such as ships at sea. It was probably this generalisation that suggested the idea of a science of geometry, which was really the creation of the Pythagoreans, and we can see how far the Greeks soon surpassed their teachers from a remark of Demokritos which has been preserved. He says (fr. 299): “I have listened to many learned men, but no one has yet surpassed me in the construction of figures out of lines accompanied by demonstration, not even the Egyptian harpedonapts, as they call them.”[[35]] Now the word ἁρπεδονάπτης is not Egyptian but Greek. It means “cord-fastener,”[[36]] and it is a striking coincidence that the oldest Indian geometrical treatise is called the Çulvasutras or “rules of the cord.” These things point to the use of the triangle of which the sides are 3, 4, 5, and which has always a right angle. We know that this triangle was used from an early date among the Chinese and the Hindus, who doubtless got it from Babylon, and we shall see that Thales probably learnt the use of it in Egypt.[[37]] There is no reason whatever for supposing that any of these peoples had in any degree troubled themselves to give a theoretical demonstration of its properties, though Demokritos would certainly have been able to do so. Finally, we must note the highly significant fact that all mathematical terms are of purely Greek origin.[[38]]
Babylonian astronomy.
XII. The other source from which the Ionians directly or indirectly derived material for their cosmology was the Babylonian astronomy. There is no doubt that the Babylonians from a very early date had recorded all celestial phenomena like eclipses. They had also studied the planetary motions, and determined the signs of the zodiac. Further, they were able to predict the recurrence of the phenomena they had observed with considerable accuracy by means of cycles based on their recorded observations. I can see no reason for doubting that they had observed the phenomenon of precession. Indeed, they could hardly have failed to notice it; for their observations went back over so many centuries, that it would be quite appreciable. We know that, at a later date, Ptolemy estimated the precession of the equinoxes at one degree in a hundred years, and it is extremely probable that this is just the Babylonian value. At any rate, it agrees very well with their division of the celestial circle into 360 degrees, and made it possible for a century to be regarded as a day in the “Great Year,” a conception we shall meet with later on.[[39]]
We shall see that Thales probably knew the cycle which the Babylonians used to predict eclipses ([§ 3]); but it would be a mistake to suppose that the pioneers of Greek science had any detailed knowledge of the Babylonian astronomy. It was not till the time of Plato that even the names of the planets were known,[[40]] and the recorded observations were only made available in Alexandrian times. But, even if they had known these, their originality would remain. The Babylonians studied and recorded celestial phenomena for what we call astrological purposes, not from any scientific interest. There is no evidence at all that their accumulated observations ever suggested to them the least dissatisfaction with the primitive view of the world, or that they attempted to account for what they saw in any but the crudest way. The Greeks, on the other hand, with far fewer data to go upon, made at least three discoveries of capital importance in the course of two or three generations. In the first place, they discovered that the earth is a sphere and does not rest on anything. In the second place, they discovered the true theory of lunar and solar eclipses; and, in close connexion with this, they came to see, in the third place, that the earth is not the centre of our system, but revolves round it like the other planets. Not very much later, certain Greeks even took, at least tentatively, the final step of identifying the centre round which the earth and the planets revolve with the sun. These discoveries will be discussed in their proper place; they are only mentioned here to show the gulf between Greek astronomy and everything that had preceded it. The Babylonians had as many thousand years as the Greeks had centuries to make these discoveries, and it does not appear that they ever thought of one of them. The originality of the Greeks cannot be successfully questioned till it can be shown that the Babylonians had even an incorrect idea of what we call the solar system.
We may sum up all this by saying that the Greeks did not borrow either their philosophy or their science from the East. They did, however, get from Egypt certain rules of mensuration which, when generalised, gave birth to geometry; while from Babylon they learnt that the phenomena of the heavens recur in cycles with the greatest regularity. This piece of knowledge undoubtedly had a great deal to do with the rise of science; for to the Greek it suggested further questions such as the Babylonian did not dream of.[[41]]