Different Sizes of Infinity: Woo Masters, Unite

I misunderstood the lengths at which people who’ve never studied something in their lives would go to nonetheless spew and spatter about that something. I can almost imagine the spittle spraying from their mouths as they rave.

The article in question attempts to explain, in as inviting of terms as possible, the mathematical concepts of infinity and cardinality. It attempts to explain that yes, there are different “sizes” of infinite sets. It even goes so far as to present a watered-down version of Cantor’s diagonalization proof that the set of real numbers and the set of natural numbers, both infinite, nonetheless have different sizes.

But in a fervor that’s reminiscent of, and equally intellectually dishonest as, the Intelligent Design movement, some people just won’t have it. One commenter writes, “If anyone thinks that this article about one infinity being bigger than another infinity actually is worthwhile or describes anything useful I urge you to continue to follow your slavish devotion to Mathematics and go jump off a building.”. Another writes, abusing technical terms all the while, “Infinity is something that is completely uncountable. If value A is infinite and bigger than value B, then B is not infinite.”

All of these commentators have two things in common: they don’t appear to have ever studied a smidgen of calculus or set theory, and they don’t appear to ever read the responses to their arguments. And all the while, an aura of religious woo-woo pervades the discussion. Infinity, they say, is unsurpassable, the biggest there is. It is Everything! It is the Universe! Oh my god, hallelujah!

How Pythagorean of them.

But I’ve met these sorts of people before, mostly way back when in my introductory calculus classes. They’re the types who fail utterly, and then end up blaming the subject for being too esoteric. You can tell them apart, because they’re usually the first to insinuate that the professor is a Nazi or a Fascist. They don’t get it, and so they project. And then, if you’ll allow me to imagine, years later they plop onto Digg and release their frustrations and their bile in a complete, comforting anonymity. The kind of anonymity where it’s difficult to question whether they’re truly interested in discussing the subject, or whether they’re campaigning against it, despite the evidence. Do they really care about this? Or are they determined to vindicate their lack of understanding?

If experience means anything, I’d say the latter.