Lyndon LaRouche recently described classical Greece as the “child of Egypt.” The great figures of the sixth century B.C., Solon, Thales and Pythagoras, were, in fact, the children of Egypt, each having travelled to Egypt and studied under the Egyptian astronomer- and geometer-priests. Through them, and others, Egypt transmitted a science — a method of knowing the universe which has reached its current height in the works of Gauss, Riemann and LaRouche. Yet, the role of Egypt in relation to science, astronomy and mathematics has been almost universally rejected by modern historians of science, as the following samples show:
” … looking at Egyptian mathematics as a whole, one cannot escape the feeling of disappointment at the general mathematical level. … Babylonian mathematics … did supply a basis for Greek mathematics. … We do not need to set up a hypothesis concerning a lost Egyptian higher mathematics.” from Science Awakening, Van der Waerdan
” … mathematics and astronomy played a uniformly insignificant role in all periods of Egyptian history … mathematics and astronomy had practically no effect on the realities of life in ancient civilizations.” from Exact Sciences in Antiquity, Neuegebauer
” … The Greeks owed much more to the Babylonians than to the Egyptians.” from Greek Astronomy, Heath
Nor will one find much literal evidence of Egypt’s role in these fields in available, ancient writings. There are only a few written mathematical-scientific papyri that have been discovered, most dating from Egypt’s Middle Kingdom (2000-1800 B.C), and none from the great Pyramid Age of the Old Kingdom. Of Pythagoras, the central figure in this transmission, there are no extant writings. Nor are there any from other Pythagoreans of his generation.
But, if you look with your mind, instead of with your senses, the evidence is abundant.
A comparison of a passage from Kepler, to one from Plato, begins the journey. Kepler, in the introduction of Book 5 of the “Harmonici Mundi,” pays homage to the importance of Egypt, “I am free to taunt the mortals with the frank confession that I am stealing the golden vessels of the Egyptians, in order to build of them a temple for my God, far from the territory of Egypt. If you pardon me, I shall rejoice; if you are enraged, I shall bear up. The die is cast and I am writing this book — whether to be read by my contemporaries or not. Let it await its reader for a hundred years, if God himself has been ready for his contemplator for six thousand years.”
Kepler’s is echoing a passage from Plato’s “Laws,” during which Plato, in the person of the Athenian Stranger, cites the same Egyptian golden vessels: “Then there are, of course, still three subjects for the freeborn to study. Calculations and the theory of numbers form one subject: the measurement of length and surface and depth make a second; and the third is the true relation of the movement of the stars to one another … Well then, the freeborn ought to learn as much of these things as a vast multitude of boys in Egypt learn along with their letters… The boys should play with bowls containing gold, bronze, silver and the like mixed together, or the bowls may be distributed as wholes.”
What is the subject of this boys’ play?: the incommensurable, as the Stranger elaborates next. In questioning Cleinias, he establishes that Cleinias believes he knows what is meant by “line,” “surface,” and “volume.” Then:
“Ath: Now does not it appear to you that they are all commensurable (measurable) one with another?
Clein: Most assuredly.
Ath: But suppose this cannot be said of some of them, neither with more asurance nor with less, but is in some cases true, in others not, and suppose you think it is true in all cases: what do you think of your state of mind in this matter?
Clein: Clearly, that it is unsatisfactory.
Ath: Again, what of the relations of line and surface to volume, or of surface and line one to another; do not all we Greeks imagine that they are commensurable in some way or other?
Clein: We do indeed.
Ath: Then if this is absolutely impossible, though all we Greeks, imagine it possible, are we not bound to blush for them all as we say to them: Worthy Greeks, this is one of the things of which we said that ignorance is a disgrace?”
With this brief section of the “Laws,” Plato has given us the essence of the “who” and the “what” behind the development of classical Greece: the “who” is Egypt, the “what” is a geometrically-grounded mathematics, for which the questions involving the incommensurable were primary. Plato unpacks the various paradoxes which deal with the incommensurable in the Meno, the Theaetetus, and the Timaeus.
Most readers will be familiar with Plato’s “introduction” of the problem in the Meno, that the diagonal of the square is incommensurable with its side. That Socrates is threatened for his method, in the course of the dialogue, by Anytus (who later helps precipitate his trial and execution), perhaps foreshadows Kepler’s recognition that some will be “enraged” by such ideas.
But it is in the Theaetetus and the Timaeus that Plato establishes, directly, the debt to Egypt. The Theaetetus begins to introduce the necessary concept of “power” or dunamis. The power which creates a square or a cube is an action in the universe, an action knowable to the mind, but not reducible to the sense-certainty numbers of the visible domain. The two characters in this dialogue, besides Plato, are two real geometers who made fundamental breakthroughs. The older of the two, Theodorus, comes from the Greek-Egyptian city of Cyrene, a city on the western edge of Egypt, and dominated by the Temple of the Egyptian god, Zeus Ammon. Theodorus is the teacher of the young Theaetetus who goes on to discover the uniqueness of the five Platonic solids.
In his masterwork, the Timaeus, Plato is even more direct in identifying Greece’s debt to Egypt. Plato opens the dialogue by having Critias tell of Solon’s trip to Egypt and his instruction by the priests of Heliopolis. When the priests chide Solon, that the Greeks are children, and have no knowledge of ancient things, the tell Solon that Egyptian knowledge and civilization extend back 9000 years (hence, 9600 B.C.). With that introduction, Plato unfolds his composition on the universe, in a very Pythagorean discussion of astronomy, harmony and geometry.
Indeed, Pythagoras was the key figure in the transmission of Egyptian knowledge to Greece. The sixth century B.C. was the century of Solon, Thales and Pythagoras, and was the century in which the leadership in this method of thinking, passed from Egypt to Greece. Iamblichus, a third century A.D. biographer of Pythagoras wrote that it was Thales, the Ionian scientist, who deployed Pythagoras to Egypt:
“When he had attained his eighteenth year, there arose the tyranny of Polycrates: and Pythagoras foresaw that under such a government, his studies might be impeded .. So by night he privately departed (from the island of Samos) … going to Pherecydes, to Anaximander the natural philosopher and to Thales at Miletus…. After increasing the reputation Pythagoras had already acquired, by communicating to him the utmost he was able to impart to him, Thales, laying stress on his advanced age, advised him to go to Egypt, to get in touch with the priests of Memphis and Zeus (priests of Ammon, ed.). Thales confessed that the instruction of these priests was the source of his own reputation for wisdom, while neither his own endowments nor achievements equalled those which were so evident in Pythagoras. Thales insisted that, in view of all this, if Pythagoras should study with those priests, he was certain of becoming the wisest and most divine of men…. He (Pythagoras) visited all of the Egyptian priests, acquiring all the wisdom each possessed. He thus passed twenty-two years in the sanctuaries of the temples, studying astronomy and geometry, and being initiated in no casual or superficial manner in all the mysteries of the Gods.”
Working back from Plato’s various identifications of Egypt as the wellspring of a geometrical, astronomical and harmonic tradition which is embedded in the study of incommensurables, to the history of the sixth-century B.C. travels and studies of Solon, Thales and Pythagoras, one might ask Van der Waerden and his cothinkers, why they think that Egyptian higher mathematics is either “lost” or non-existent. Perhaps, as Kepler suggests, it is the rage induced by living inside a reductionist’s mind that can only see the shadow’s cast on the cave wall.
A future pedagogical will “let the stones speak” of Egyptian astronomy.