Thales, the "Pythagorean Theorem", and Technological Context (original) (raw)

2022, Dialogues d'histoire ancienne

In order to take a fresh look at Thales geometrical insights, I will place him in the broader, technological context of 6th century BCE Ionia. I start with Aristotle’s report about Thales and the early philosophers who he claims were – to use my terms – source and substance monists. I argue that this view is testimony of their modular thinking. I defend the reliability of Aristotle’s report by a new set of arguments pointing out that examples of modular thinking were all around Thales, Anaximander, Anaximenes, Heraclitus, Pythagoras/Pythagoreans and interpenetrated their thoughts -- in monumental stone temple architecture, in the production of coins in the monetization of their society, in the use of the gnomon, and even connected with the production of industrial textiles. Could it be that Thales inferred an underlying module of all things – he called it ‘water’ [ὕδωρ] -- by analogy with these other examples surrounding him? Everything that appears, according to Aristotle, are only alterations or modifications of this underlying nature or unity, because this unity always persists – this is the principle of modular thinking. Now, had Thales held such a view, it seems difficult to avoid the question “How does this happen – how does ‘water’ flow shapelessly in a cup at one moment, then invisible as air, as fire at the stove, and yet sometimes hard as marble?” And what I propose to explore is the possibility that Thales’ forays in geometry sought to identify the underlying structure of ‘water’ out of which all other appearances were built, re-packaged and re-combined, and that Thales’ plausibly reached the conclusion it was the right triangle. Accordingly, I will invite us to imagine the diagrams corresponding to the reports that Thales in Egypt measured the height of a pyramid, measured the distance of a ship at sea, and place them alongside the diagrams that display the geometrical propositions with which Thales is also credited. Having done this, the reader can see that all, or mostly all, deal not only with right triangles but with similar right-angled triangles. And since one line of proof, preserved by Euclid [VI.31], demonstrates the so-called Pythagorean theorem by similar right triangles, I argue it is plausible that Thales visualized, in a less sophisticated form, this line of reasoning for the famous theorem because it is a consequence of similar right triangles. And the ‘Pythagorean theorem’ by this line of reasoning shows that the right triangle is the fundamental geometrical figure. So, the case I explore is what I have been calling the “Lost Narrative,” the one that connects the reports about Thales’ geometrical insights with his speculations about the underlying unity of nature.