Why Ruler and Compass?
The fifth and final guest video
In this fifth and final guest video, Ben Syversen discusses a question anyone who has done ruler and compass constructions for a geometry class may have wondered: What’s the point?
There is a lot about Euclid’s Elements that is easily misunderstood. Arguments that seem to have logical gaps, some constructions that seem pointless, others that seem needlessly convoluted. But each of these actually provides a window into how the ancient Greeks thought about math, and the philosophical role that geometry played.
[12:34] Well yes, but actually no. Today we might say that mathematicians left philosophers in the dust, but at that time this isn’t quite right, mathematicians *were* philosophers. The very word mathematician comes from the Greek 'mathematikos', and the 'mathematikoi' were a group within the Pythagorean philosophical school (Pythagoras himself being a philosopher).
This is a mistake we often make when looking into the past: we set figures like Pythagoras, Newton, or Adam Smith against “the philosophers” of their time, when in reality they *were* philosophers, even as they pioneered things in what would later consider the separate branches mathematics, physics, or economics. One of the main roles of philosophy is to refine difficult or fuzzy problems so that they can eventually become part of science. That’s still true today; e.g. I work on a philosophical problem that may one day fall into the realm of mathematics (if I’m successful) but that doesn’t make me a mathematician, it still makes me a philosopher.
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