"Infinite:" I Do Not Think That Word Means What You Think It Means

Some of you may have noticed the megawoo troll Ghislain in the comments at my old Life Technology post, polluting the thread with line after line of clichéd woo nonsense and a healthy smattering of multiple-posts-cum-deleted-posts (by his hand, not mine; it's really fucking annoying).

In his first extra-long post, he said:

when you are able to understand we live in an infinite universe with infinite possibilities your mind will become free from any boundaries and limitations...(sic)

Well, he's totally wrong all over the place. I explained it in a response to that comment, but I feel its a topic upon which it is worth expanding.

In short, people don't understand the concept of infinity. That's nothing new; our monkey-brains can hardly deal with billions and trillions much less infinity. It's not easy to wrap our heads around the concept. Some people (like Ghislain), however, redefine infinity into something it very much is not, either out of total ignorance or malice aforethought, and this post is about those people.

Bronze Dog already did a doggerel on Infinite, and everything he said is good and true. He deals with misuses of infinity when folks use it more as a buzzword without a real definition. I am, on the other hand, going to attempt to tackle what morons actually think about infinity, when they think anything at all.

BD says in his doggerel "There's a difference between 'a really, really big number' and infinity." There's also a difference between "infinity" and "everything." But, essentially, that's what woos, religiosos, and run-of-the-mill shitheads (but I repeat myself), think "infinity" means.

"God is infinite," for example, is essentially synonymous with "God is omnipresent, omniscient, and omnipotent."

Ghislain, above, talking about an "infinite universe with infinite possibilities," perhaps demonstrating a bit of later Wittgenstein, doesn't really mean what his words literally say. In fact, he's using the word "infinite" to mean two different things at different points in the sentence.

The first, "infinite universe," is closer to what "infinite" actually means, as in "an unbounded universe." Unfortunately for him, while he's using the word more correctly here (but still not really correctly), he's wrong. The universe is of finite age and maybe even finite size. We know its age with less than a 1% margin of error and we now have a bead on its shape, which might allow an infinite amount of space, but 50% does not an "infinite universe" make. Even should a final heat death occur leaving the universe in an incredibly low-energy state, filled with nothing but loose, speeding photons for all time (should "time" even retain meaning at that point), the universe would still never be infinite. It would always be of a finite age, with a very distinct beginning and a present that keeps it from being infinite. 1 with a trillion zeroes after is very far away on the number line from 0, but it's still finite.

The second "infinite," "infinite possibilities," is being used to mean "anything and everything is possible." This is very, very incorrect. "Infinity" just plain doesn't mean either "anything" or "everything."

It can kind of mean, in a different sense, "every thing," when you define "thing" very specifically, like "real number between 1 and 2," as in "every real number between 1 and 2." That represents an infinite set of numbers. "Every natural number" is also an infinite set. Strangely enough, the set of naturals is a subset of the set of reals; there are more reals than there are naturals, even though they are both infinite. Rather counterintuitive, really, and it just goes to show what a weird concept infinity really is.

Now, despite both of these sets being, quite properly, infinite, in no sense does either set contain "anything" or "everything," whereby both essentially amount to "all things that are logically and physically possible," or, in woo, "whatever you can possibly imagine." Both infinite sets only contain the numbers that they contain, albeit an infinite amount. As Magus put it while we discussed this very thing, "There may be an infinity of numbers between 1 and 2, but that doesn't mean that any of them is 3."

I prefer to paint an even greater relief against "woo infinity:" just because there are an infinity of numbers between 1 and 2 doesn't mean that any of them is a unicorn.

To make it relevant to Ghislain's claim, even if the universe was, in every sense of the word, infinite, it still does not follow that "whatever you can possibly imagine" would exist, or even could exist, somewhere in the universe. Just because a universe is infinitely large and exists from infinity in the past to infinity in the future thus allowing an infinite number of distinct events doesn't mean that its natural laws can be broken.

Is this "infinity as everything" misconception brought about by poor math education? Probably at least partially. I would, though, rather than call out math teachers, indict the students themselves who think that math is stupid, boring, and irrelevant and the society that created and reinforced such views. We currently have a "war on illiteracy." What about the much-needed "war on innumeracy?" Oh, yeah, I forgot: math is for nerds in their ivory towers, just like science. The rest of us have calculators.

A good way for laymen like myself to think of infinity is, quite apart from "everything," as "always one more," or even just "always more." That's why, in mathematics, limits approach infinity without ever actually reaching it. You always need more, no matter how much you have, to reach infinity.

If I plug Mario 3's infinite lives code into my Game Genie, I could play indefinitely and still not reach the code's full utility, because after my current life there would always be one more. And one more. And one more after that.

But none of those lives would allow me to play as Sonic the Hedgehog.