Saturday, October 20, 2012

Heaven would be hell. Why? Infinity

Infinity is not an intuitive concept. For reasons that I think I detail rather well in God Doesn't; We Do (rather an arms-race of memes), the religious really like to use, which almost universally means to misuse, this non-intuitive and yet tantalizing concept in their formulations:
  • God is infinite (nonsense);
  • God's love is infinite (what does that mean, and how is it measured?);
  • God is infinitely powerful (how?);
  • God is infinitely knowledgeable and wise (how?);
  • ...that he who believes in him will have eternal (read: infinitely long) life (in the kingdom of heaven).
This last bit is what I want to focus on here. The afterlife in heaven is supposed to be eternal, meaning infinitely long? That means it will be hell, even without the multitude of other reasons that it would be (like having to manage forever knowing that your loved ones that didn't make it are being tortured beyond endurance and there's literally nothing you can do about it).

To get why forever, wherever, would be a hell, we've got to understand infinity a little bit better. I covered this in pretty good detail in chapters five and six in God Doesn't; We Do, but I'll elaborate here a little for those without a copy of the book. In particular, we need to understand "how big" infinity is. A good way to approach the idea is to notice that every number is smaller than most.

What we have to understand is the scale of infinity, and as it turns out, the simple and naive understanding that most people have is sufficient for the job here. If we think only about the positive whole numbers, the numbers we count things with, the intuitive notion that the numbers never end is the functional concept we need. Now normally I have a real knee-jerk to this "never end" business because it unnecessarily and inaccurately introduces the notion of time into the enumeration of the numbers (with which we enumerate). It's a real problem, normally, to conceive of having this number now, the next number later, and the next one sometime after that. All of the numbers simply "exist," in the abstract sense of the word, and they "exist" now and always, again in the abstract sense of existence. Here, though, we're lucky. Since we're talking about an infinite scope of time, eternity, the naive one now, two later, three after that, and so on, construction actually helps make our argument, when we get to it.

So, if we look at the positive whole numbers, we know that they go off without end. We often write things like 1, 2, 3, ..., where the three dots (known as ellipsis) indicate "going off without end." If we think about it, though, we also realize that where we decide to place the dots is pretty arbitrary. For examples, we might write,
  • 1, 2, 3, ... 
  • 1, 2, 3, 4, 5, ...
  • 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
In principle, if we wanted to take the time to do it or to introduce some other notation to facilitate it, we could put the ellipsis after whatever number we want. This is how big infinity is, though! If we put the ellipsis after the number 3, we know there are infinitely many numbers after 3 (and only 3 up to 3). If we put it after 5, we know there are infinitely many numbers after 5 (and only 5 up to 5). If we put it after 12, we know there are infinitely many numbers after 12 (and only 12 up to 12). If we were to put it instead after one billion, we know there are infinitely many numbers after one billion (and only one billion up to one billion).

This point is huge and non-intuitive, at least once you see what it implies, so you might want to re-read it and let it sink in. When we talk about an infinite collection of numbers like this one, literally all of the weight is in the ellipsis. We can even show it more rigorously. Take the example above where we stick the ellipsis after the number 12. Imagine we decide to elaborate upon the ellipsis, to uncover what is there. Obviously, we all know it would be the numbers 13, 14, 15, .... Now imagine we decide to number the numbers masked by the ellipsis. Thirteen is first, so we number it 1, fourteen is second, so we number it 2, fifteen is third, so we number it 3, and so on. The result is that we get 1, 2, 3, ....

But that's... yeah, all of them.

Weird, huh? Mathematicians can easily construct a fully rigorous argument that is beyond argument that exactly the same number of positive whole numbers are tied up in the ellipsis as there are positive whole numbers entirely. In other words, the ones we lay out explicitly before the ellipsis constitute effectively nothing (and this is the foundation of that almost surely concept that sits firmly at the center of my argument that God doesn't exist, almost surely).

So, we arrive at the claim I laid out above, then: every number is smaller than most, since the infinitely many numbers larger than any given number is immeasurably bigger than the finitely many numbers up to that specific number.

Now back to the argument for time and the horribleness of eternity, even if that eternity is in "heaven." People who argue for heaven being great and eternal are simply proving that they don't "get" infinity. If they did, they'd never make such a stupid claim. Nothing could possibly entertain a consciousness, particularly a provincial little ape consciousness like ours, for an eternity. Imagine one number, then the next number, then the next number, and so on, but where no matter how many numbers you have been through, once you get to "and so on," you're effectively still at the beginning.

The thing these religious folks need to "get" about infinity is that every number is smaller than most, and in fact, every number is smaller than almost every number. In other words, if you're sent to heaven, however much time you've done, however long it's been, you haven't even started your sentence of eternity yet, and you never will.

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