Tales about Thales

I apologize for bringing bad news. I hope no one wants to kill me.

We all know that Thales was ‘the father’ of mathematical knowledge, the great origin of the ‘Greek miracle’ in geometry and philosophy. ‘We all know’? Let’s see if it turns out that fake news is not such a recent invention… So I propose to deconstruct a little bit the great myth of Thales, one of the Seven Wise Men of ancient Greece.

Looking at the web, I read in an encyclopedia: “Thales was born in Miletus, a restless traveller [in effect, he visited the grandiose Egypt]. His main passions were mathematics, astronomy and politics. He is considered the first of the physicist-philosophers. However, little is known of his philosophy, in which water is considered to be the principle of all things, although it is not clear whether this means that all things are made up of water or that the Earth comes from it and floats on it. He is also credited with a mysterious claim that “everything is full of gods”. One interpretation is that water is endowed with life and movement of its own, and therefore everything is alive and animated. Two theorems bear his name, the theorems of Thales:

• on the similarity of triangles, applicable in measurements of land [or of pyramids];
• that the triangle inscribed in a semi-circle, whose side is the diameter, has a right angle.”

 

A short and rather good text. But what is the truth in all this? Applying a critical and ruthless look, we could say “nothing”. It’s not even certain that he was born in Miletus, although he is said to have settled there, and he had followers. None of the works that have been attributed to him were really his own. This picture is also fake, of course.

Thales is a legendary figure — it is well known that every culture needs its myths, its “founding fathers” (or mothers). Someone at some point decided to name him as one of the Seven Wise Men — by the way, do any of us know the name of any other of the seven — and Plato already spoke of them in one of his dialogues. But the Vedas in India have their ‘seven sages’ too, and this was long before… Aristotle speaks of Thales, but only to attribute to him the idea of water as a physical principle, and to tell the story of how he became rich by renting out mills, having foreseen that the year would be one of great abundance in crops (the moral is: he had deep knowledge and knew, if he wanted, how to make the most of his wisdom). It is interesting that, when Aristotle talks about “the first people who devoted themselves to the cultivation of mathematics”, he says it was the Pythagoreans. Not Thales! Going on to what most interests us, no document (which is not very distant from Thales in time) supports attributing the two famous geometric theorems to him. It may be that all his knowledge of geometrical results, and of astronomy, came from what he learned from the Egyptian sages; and there is no reason to think that Thales ever gave the proof — or anything like it — of any result. The story of how he was able to measure the height of a pyramid without using any instrument is legendary, but this feat — incredible for peasants from Miletus — was perfectly feasible for a Babylonian scribe or an Egyptian measurer. (Wait until your shadow is approximately equal to your height; measure the shadow of the pyramid then. If we use a gnomon, the thing is even easier).

If you want to find the first Greek mathematician, it is certainly safer to bet on Hippocrates of Chios, author of the first book of ‘Elements of Geometry’, or perhaps on Oenopides from the same island, who is said to have solved geometrical problems using ruler and compass (both in the fifth century BC). Pythagoras was a mysterious type who wrote nothing, a vegetarian occultist; so, in any case, it would be some disciple of his sect (and also an infidel, for betraying the rule of silence) who would spread mathematical knowledge.

I will add a few more scholarly details. Many people speak of Thales: Herodotus in his History, Plato, Aristotle in Metaphysics and in Politics, Plutarch, Diogenes Laertius, Proclus in his Commentary on Book I of Euclid, etc. But of course, Herodotus in the fifth century B.C. (about 150 years after the fact) or Aristotle in the fourth century, is not the same as the good old Proclus writing a thousand years after Thales (!), or Pliny and Plutarch around the year 80. Ironically, these doxographers know more about the famous Wise Man as time goes by.

Herodotus tells us how Thales managed to predict (approx.) an eclipse; Plato gives us the story of the distracted wise man looking at the stars, who falls into a hole. On the other hand, Diogenes Laertius (in his Lives of the Philosophers, 3rd century AD) is already able to tell us about the life and miracles of the wise man of Miletus, but not precisely because documents have been found buried anywhere. And finally, Proclus gives us a series of details about ideas and propositions established by Thales: that the diameter divides the circle into two equal parts; that the angles of the base of an isosceles triangle are equal; the angle-side-angle criterion of equality of triangles; that two straight lines which intersect make angles (opposed by the vertex) equal to each other. But Proclus clarifies that this last proposition was not rigorously demonstrated, and suggests that Thales treated some problems in a general way and others empirically (which, by the way, is very bad for a Platonic author).

I do not want to finish this note in a negative way. Proclus was a very wise man and a true scholar: if we pay special attention to his account, it’s because he was careful and based it on the History of Geometry written by a disciple of Aristotle, Eudemus of Rhodes (circa 370-300 BC). This work is unfortunately lost today — we know that many cultures and many peoples have had a predilection for throwing books into the flames! So it’s possible that some of the attributions that Proclo makes are correct. We will never really know.  

PS: I am grateful to Manuel García-Pérez, who will soon be a PhD, for having given me the idea for this entry, and for many of the details that are told.