Category Archives: Science And Society

Innumeracy

I’m watching (in the background) The Wizard of Oz. I just noticed that when the wizard hands out the diploma to the scarecrow to give him a brain, the scarecrow says (apparently as evidence of his newfound knowledge) that “…the sum of the squares of the sides of an isosceles triangle is equal to the square of the other one.”

The problem being, of course, that it’s not true, at least not in Euclidean geometry. Pythagoras’ Theorem applies to right triangles, not isosceles triangles (triangles with two equal sides).

But then, perhaps the movie was making a subtle statement that having a diploma and spouting intelligent-sounding nonsense is all that constitutes smarts…

Math Is Hard

And not just for Barbie. This article says that math problems are getting too big for our brains.

Well, that’s one of the thing that transhumanism is for. This part bothers me, though:

Math has been the only sure form of knowledge since the ancient Greeks, 2,500 years ago.

You can’t prove the sun will rise tomorrow, but you can prove two plus two equals four, always and everywhere.

This begs the definition of the words “knowledge” and “prove.” Two plus two can be proven, I suppose (inductively from one plus one equals two), but only within the confines of the mathematics that you’re using. It’s not “sure” or “knowledge” in any absolute sense.

What they really mean is that some of the tougher mathematical problems are not amenable to classic deductive analytical proofs, but are more reliant on brute-force computations, possible now because we have machines that can perform them in a useful amount of time.