Jach's personal blog

(Largely containing a mind-dump to myselves: past, present, and future)
Current favorite quote: "Supposedly smart people are weirdly ignorant of Bayes' Rule." William B Vogt, 2010

Does studying math lead to learning more truth?

I think it does. I offer my friend as a case study. At one point he thought you could divide by 0; he finally gave that up I think. Now he believes 0.999.... does not in fact equal 1.0. Here's a list of proofs for a reader who also doubts the fact that 0.9999... = 1. Yes, my friend has seen these, can't find anything wrong with them, but still holds onto his belief.

He's not a math guy, he's not a science guy, and he's only recently become a philosophy guy. Okay, a single-philosophy guy. He knows some Objectivism, but that's it. He's become a Guardian of the Truth, instead of a truth-seeker.

This is why I think learning math (and science) will lead to more truth. If you accept a philosophy as absolutely true, you're going to be limited in how much you can discover afterward. Godel's Incompleteness Theorem states that not all truths can be derived from any finite set of axioms, and Objectivism has only three axioms (at least one of which isn't an axiom but a tautology). Also, when you don't accept something even after having it proved to you, you are no longer to be trusted as knowing any true statement when you can discard proofs for or against at whim.

There are many true statements that go against human intuition. The light speed limit is just one: if I'm traveling at 0.9c and shoot a bullet whose normal speed (from rest) is also 0.9c, then the bullet does not attain 1.8c. Also the Earth revolves around the Sun, not the other way around; the Earth is not flat, and not even spherical (it bulges at the middle so it's more pear-like); humans are capable of flight; there is no supernatural "you" outside of physics; centrifugal force is a fictitious force, only centripetal is real... I could go on and on.

Study as much math and science as possible to learn more truth. Even in cases where the math or science community thought itself was right, people came along and showed why existing proofs were incorrect and gave their own correct proofs to the contrary. The idea of falsifiable theories (and false-steps in theorem-making) is what keeps science and math respectively progressing. Be a Truth Seeker, don't degrade into a Guardian.

Posted on 2009-10-18 by Jach

Tags: rationality


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