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## Thales, the “Pythagorean Theorem”, and Technological Context

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Hahn Robert. Thales, the “Pythagorean Theorem”, and Technological Context. In: Dialogues d'histoire ancienne, vol. 48, n°2, 2022. pp. 25-51.

DOI : 10.3917/dha.482.0025

www.persee.fr/doc/dha_0755-7256_2022_num_48_2_5250

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DHA, 48/ 2, 2022 – CC-BY Dialogues d’ histoire ancienne, 48/ 2, 2022, 25‑51 – CC-BY

Thales, the “ Pythagorean Theorem”, and Technological Context

Robert Hahn Southern Illinois University Carbondale, USA hahnrprof@ gmail. com

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 arguments1 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, repackaged and re-combined, and that Thales’ plausibly reached the conclusion it was the

1 These case studies are examined in greater detail in my essay, Hahn (forthcoming).