What's Up with Pythagoras?

The first time I read Bertrand Russell's History of Western Philosophy, I could not get over the chapter on Pythagoras. As Russell claims, "Pythagoras... was intellectually one of the most important men that ever lived, both when he was wise and when he was unwise. Mathematics, in the sense of demonstrative deductive argument, begins with him." This is probably the aspect of Pythagoras that's well known. The unwise part comes from his weird and wacky mysticism (which he managed to intertwine with his mathematics both to great success and to halt its own progress) and to his dogmatism: you did not want to upset the guy or threaten the beauty and perfection of his rational philosophy.

The guy who did, by pointing out the existence of irrational numbers as a logical consequence of Pythagoras' own rational theorem, angered Pythagoras and his posse, and got himself viciously killed by them.

So how do irrational numbers flow out of the Pythagorean theorem? Well, the awesome Vi Hart explains in her deliciously unique way in today's episode of the doodling in math series.

And if you're curious about some of the rules of the Pythagorean order, check these out:
  1. To abstain from beans
  2. Not to pick up what has fallen - sorry grandma!
  3. Not to touch a white cock - I guess once you go black... sorry, but isn't that racist :)
  4. Not to stir the fire with iron - being that iron is a metal, I'll let that slide

And if you want to inspire your friends, family, kids, students, co-workers, you can also show them how the late and beloved Jacob Bronowski explains the mathematical, philosophical and historical significance of this great discovery. Trust me, it's inspirational...
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