Step 1: Imagine a slug. Okay, that should be no problem.
Step 2: Now imagine a slimy slug. You probably already did that, in step 1, but just in case, now you're imagining a slug with a thin, shiny veneer of ooze. Great.
Step 3: Imagine a super-slimy slug. I mean, really, really slimy. So much slime. Not just a thin veneer, but a thick wad of slime. Imagine more slime than slug. Like, the slime of the slug is double the width of the slug. Triple. Quintuple. Imagine a giant ball of slime rolling down the street with a slug in the middle of it. Imagine a wad of slime the size of Cleveland, with a slug at its center.
Step 4: Imagine the slimiest slug you could possibly imagine. Hmmm.
Step 5: Imagine a slug so slimy that you can't imagine it. This is what's known as a super-imaginary super-slimy slug. "Super-imaginary" in the sense of "beyond your wildest imagination," or more accurately, "beyond all possible imagination." Hm. Can you do it?
Well, on the one hand, no. You can't imagine a slug so slimy that you can't imagine it. That's a flat contradiction. Obviously, if you can't imagine it, then you can't imagine it. Period.
But just because you can't imagine it, doesn't mean it can't exist. There could be super-imaginary super-slimy slugs out there.
So, consider, for instance, a slug with an infinite amount of slime. Let's be more precise and say, an infinite volume of slime. You can't imagine that, right? No one can imagine an infinite volume of anything. It's beyond the capacity of our finite brains to comprehend the concept of an infinite volume of anything. Isn't it? (Or is it?)
Like, maybe you could step through a portal and travel to an alternate universe - a universe that consists of nothing but a slug surrounded by infinite slime in every direction. (And you, and the portal....) There are some theories of physics that say that alternate universes exist. Trillions of them. And they're real. So, maybe, one of those universes is a slug surrounded by an infinite amount of slime.
Now this slug with infinite slime, which exists in a real universe out there, is unimaginable by you. Even if you traveled to this alternate universe and saw the slug, face to face, you wouldn't be able to imagine it. At best, you would be able to have a hyperbolic representation of the infinite slime in your finite mind, somewhat like the way that we can have a hyperbolic representation of three dimensions in two dimensions.
Wait a minute. But the fact that we are discussing the concept of super-imaginary super-slimy slugs - and we think they could possibly actually exist - implies that we can imagine them, doesn't it? We're imagining them right now. (Or are we?)
Maybe there's an ambiguity here in the word "imagine". Like, what we're doing now is entertaining the possibility of super-imaginary super-slimy slugs. We're not actually imagining them. Wait... but what, exactly, is the difference between entertaining the possibility of something, and actually imagining that thing? Is there a difference between considering the concept of something, and imagining it?
So maybe we should go back to step 4. Is this possible? Can we imagine the slimiest slug that we can possibly imagine? Well, if it were, then we would only need to imagine something slightly slimier, and then we would be imagining a slug slimier than we could possibly imagine. And that's obviously a contradiction. So apparently, step 4 is the boundary between what is possible and what is impossible. But the more you think about it, the harder this becomes to imagine. So maybe step 4 is impossible. But if that's the case, then we're in trouble. If we can't imagine the slimiest slug possible for us to imagine, then we can't imagine any slimy slug at all. Why not? Well, here's a proof-by-induction, of sorts: if we can't imagine the slimiest slug possible for us to imagine - which, I'd like to point out, seems to be just as much of a contradiction as saying that we can imagine a slug slimier than we can possibly imagine - then, would we be able to imagine a slug a little less slimy than the slimiest slug we could possibly imagine? Well, if so, then that's the slimiest slug we can possibly imagine. So we would run into the same problems with that that we would run into with the previous slug we were considering. But then we could go through the same kind of argument about a slug slightly less slimy than that, and a slug less slimy than that, and so on and so on.... and pretty soon we have proved the impossibility of imagining any slug with any degree of sliminess. Or have we?
Pretty soon, we are asking ourselves - what does it mean to imagine anything? How do you know if you are actually imagining something? Is it possible that you aren't actually imagining what you think you're imagining - you just think you're imagining it? (You're just imagining that you're imagining it? Or maybe you're just imagining that you're imagining that you're imagining it....)
Back to the real world. There's the universe out there, right? Well, but... there's an ambiguity with this word, universe. There's the observable universe, which is about 94 billion light years across. But that's just the observable universe. Then there's the rest of the universe, which is... much bigger. How big? We don't really know. It might be infinite. But it's probably much, much bigger than the observable universe. Okay. Actually, there's three levels here: the actual universe, which is... who knows how large. Then, smaller than that, the observable universe- meaning, observable in theory. It's theoretically possible to observe this much of the universe, which is 94 billion light years across. Then there's the actually observed universe. The furthest we've seen through our telescopes is only a little more than 13 billion light years away. And we've only seen a little bit of the universe at that distance. There's still a whole lot of the universe, within a radius of 13 or 14 billion light years, that we haven't seen. And we may never see much further than that, even though it is, in some sense, theoretically "observable".
Well, we can add some layers here. How large is the part of the universe that we can imagine ourselves observing? How big is the imaginable universe? How about the portion of the universe that we can conceive of, or the part that we can entertain the existence of? They're all pretty big, right? But ultimately, they must be finite, because we have finite brains. How big are they, exactly? Are they bigger than the observable universe? Smaller? How big are they in relation to each other?
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