How to Find the Height of Heaven

How the Chinese discovered the Pythagorean Theorem hundreds of years before Pythagoras

Discoveries are often made by multiple people, but we tend to only celebrate one of those folks.

This is just as true for the theory of evolution (Wallace, but also Darwin), as it is for lightning rods (Diviš, but also Franklin), as it is for the electrical telegraph — invented by Wheatstone but also Morse, whose first message is a favorite of trivianauts and bibliophiles alike (“what hath god wrought”, Numbers 23:23).

The concept of multiple discovery also happens to apply to a favorite hobbyhorse of mine, the Pythagorean Theorem — i.e., that natty formula that allows you to deduce the area of a square alongside a triangle’s hypotenuse, which in turn allows you to develop trigonometry, which in turn allows you to (eventually) navigate the ocean using a sextant and (even further eventually) calculate things like the height of Mount Everest without climbing it and the fastest route via Google Maps.

Now any Tom, Dick, or Platonist can tell you that the Pythagorean Theorem was first set down as an axiomatic proof in The Elements around 300BCE. It is slightly less well known (tho very wikipediable) that parts of the theorem were known as early as 3000 BCE as far away as India and China. As with all multiple discoveries, the interesting question is…how? How did multiple people discover the same thing? And in this case, given that the theorem, y’know, empirically describes geometric reality, was there any similarity in the thought process that led people thousands of miles distant and thousands of years apart to discover it? I mean, everyone was just trying to create, like, wagon wheels…right?

Hoo boy, not at all! The triangles in Babylon were the triangles in Punjab were the triangles in Zhou, but the reason for developing those triangles was wildly different. Those differences reveal quite a lot about how different cultures pursued knowledge, and even how they valued the practice of learning. My favorite example comes by way of China.