Hacker News Reader

Comment by lolinder | Hacker News Reader

They don't recommending Euclid as a way to learn geometry, they recommend him because his book has been the foundation of the scientific dialog for the last several millennia. Regardless of whether his formalization of geometry is the most up-to-date, every subsequent mathematician and logician has been building on The Elements. That fact alone makes it valuable to read, not as a way to learn geometry, but as a way to understand where we came from.

View on HN

There's a little story told about the philosopher Thomas Hobbes, by John Aubrey:

"He was (vide his life) 40 yeares old before he looked on geometry; which happened accidentally. Being in a gentleman's library in ..., Euclid's Elements lay open, and 'twas the 47 El. libri I[Pythagorean theorem]. He read the proposition. 'By G--,' sayd he, 'this is impossible!' So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that trueth. This made him in love with geometry."

Reading all of Euclid's Elements is a big undertaking, though I think you can get a sufficient taste and appreciation of iron-clad logical reasoning and demonstration from going through some subset of it. Perhaps working through a single proposition back through its base propositions, definitions, common notions, and postulates will be enough to alter your thinking and at least see what's possible. Unlike the author I can't tell from discussion sampling if people are ignorant of Euclid, but I have been frustrated by 1-on-1 failures to win arguments by mathematical proof (e.g. that 0.999.... = 1) and such an unwillingness to accept such things shows a profound disconnect in how we look at the world. Reading Euclid may help that.

On the other hand, lots of software developers are exposed to proofs as part of their formal education (those who received one), so how much Euclid can add here is questionable, vs. actually putting proofs into practice by learning things like TLA+, or learning about probabilistic inference which is more needed outside crisp and clear worlds like Euclidean geometry. Personally I'd sooner have software developers take a few minutes to learn and reflect on Chesterton's Fence, than working through examples of geometry proofs, and maybe some can learn to reduce their bad habit of sloppily "reconstructing things from first principles" (where "first" is frequently "first thought of").

Then you, as Moicanu below, didn't understood my point: You learn less from the Elements than from later, curated sources. Analogously, no one would advocate reading Newton's Principia to "understand where we came from". You would first learn the theory (geometry resp physics) with up-to-date sources, then read a commentary of the original (which is often longer than the original), and only then you'd be able to get something out of reading a translation of the original.

Thus, by reading the original works you will confuse yourself with the obscure notation you will encounter, semi-circular arguments and other problems (both the Elements and the Principia are riddled with problems), which actually have prompted many many scholarly works commenting and fixing these.

I've read the 'original' Elements, indeed. Apart from the geometric figures which were not even available in the original form of the manuscript, but added later as an aid, there is no obscure notation whatsoever. Indeed, there is no notation at all. It's all prose.

If you want to read it more as a historical piece of art I wouldn't object; if you want to actually get some mathematical insight out of it on the other hand, this would be a good starting point:

https://math.stackexchange.com/questions/845288/has-any-erro...

One of missing pieces in education is surfacing problems, deadends and struggles of different sorts. Shame because it’s such an insightful part, often allows grasping underlying reason for why things are the way they are.

Nicely said.

Reply on news.ycombinator.com