Why I think the universe is finite

#1

I was talking with Kyle and Thomas the other day about how I think the universe is finite, but is expanding and at such a rate (speed of light?) that nothing can observe the boundary. Kyle called this a cop out. Here’s the way I think about it, and in a fun physics move I will connect this physics on the largest possible scale with physics on the smallest possible scale.

The Heisenberg Uncertainty Principle basically says that once you zoom in far enough on a particle you can’t really be quite sure where it is, up to like 10^-36 m. The way I think about this is that god wanted to make his universe infinite, and dense, like the real numbers, but he just couldn’t get it that way. Infinity is a concept we’re very used to by now, but to me the concept of there actually being anything infinite in our universe is weird. How do you get to infinity? I think god wanted to but couldn’t. So he made the universe as close to dense as he could, but density requires having infinite positions and he couldn’t do that, so once you look too close things get fuzzy.

And on the large scale, he wanted the universe to be infinite, but again couldn’t get that so just made it effectively infinite, i.e. it’s finite but with a boundary that’s moving away so fast no one can observe it and the universe looks infinite.

#2

I didn’t realize your argument was religious. I like the idea of a non omnipotent god, since that’s what we are and always will be. What do you think about the simulation hypothesis? Is it too much about computers for your taste?

On that, a finite but infinitely increasing universe would require infinite memory.

#3

Idk if I would call my argument religious although it certainly does sound that way doesn’t it. It’s more like, when I think about the laws of the universe it seems so cool and works so well with math that it feels like it has to purposeful, so I think about it in terms of a creator trying to make a universe that would work out great like ours does. And uncertainty leads me to imagine that the creator couldn’t actually get infinity into the universe, and the more I think about it, why should that be possible? There actually being infinity of anything seems weird to me.

#4

I don’t know anything about the simulation hypothesis, besides the basic premise now that I’ve googled it (obviously I’ve sort of heard that idea thrown around before also). But it sounds like it’s basically the same as my creator picture, although I don’t really picture it happening on a computer, at least not a computer like the ones we have now. Would it require infinite memory or an unbounded amount of energy? Maybe there’s not really a meaningful difference? Also I might be fine with whatever world this hypothetical creator lives in having access to infinite memory.

#5

Yeah the simulation hypothesis is like your creator picture. But it’s also a statistical argument. If you assume that someday we will be able to simulate a reality like our own and that we will have the proclivity to do so, then we are statistically likely to be one of those simulations now. This follows from the fact that there can be orders of magnitude more simulations than the single “reality”.

So in regards to your idea, the creator might be in a universe not unlike our own and so would be bound by our same constraints on energy, information, and computation.

You need infinite memory to have an unbounded universe. And if you have infinite memory you can have infinite precision. So you wouldn’t need to make things fuzzy. I don’t think you like that. So maybe you can add finite memory and a finite universe to your assumptions.

You might be interested in thinking about this more from the perspective of computation. It adds another interesting dimension to all this metaphysics. But first you need to overcome your fear of computers. (And thinking about simulations and AI might not help there…)

#6

Oh! And relevant to our discussion of realizable uncountable sets: There are only a countable number of computable numbers (numbers which a finite but arbitrarily large computer could generate to arbitrary precision).

Maybe we should embrace your idea and get rid of uncountable sets all together! From the above wikipedia article:

The computable numbers include many of the specific real numbers which appear in practice, including all real algebraic numbers, as well as e , π , and many other transcendental numbers. Though the computable reals exhaust those reals we can calculate or approximate, the assumption that all reals are computable leads to substantially different conclusions about the real numbers. The question naturally arises of whether it is possible to dispose of the full set of reals and use computable numbers for all of mathematics. This idea is appealing from a constructivist point of view, and has been pursued by what Bishop and Richman call the Russian school of constructive mathematics.

To actually develop analysis over computable numbers, some care must be taken. For example, if one uses the classical definition of a sequence, the set of computable numbers is not closed under the basic operation of taking the supremum of a bounded sequence (for example, consider a Specker sequence). This difficulty is addressed by considering only sequences which have a computable modulus of convergence. The resulting mathematical theory is called computable analysis.

1 Like
#7

@ethan haven’t you talked about this computable analysis thing before?

#8

I’d always thought computable analysis (or whatever @ethan had talked about previously, something about doing calculus on computable numbers or rationals) sounded ridiculous (in the specific instance I’m remembering Ryan was involved in the conversation so that probably didn’t help), but in light of this thread I’m into the idea/working it in with physics.

I don’t think uncountable sets have a place in the physical universe.

#9

going back to simulation hypothesis, I’m not really into the statistical argument cause I don’t really think we’ll be able to simulate a reality like our own. My creator idea I think has the creator in a universe probably not quite like ours and I’m probably fine with letting them blow by some constraints that we have.

Overcoming my fear of computers might be a good idea. I’ll think about it.

#10

I don’t know if it has to be religious, or if Alan is just personifying aspects of our universe that exist. We know stuff gets smaller (ie, is smaller than, say, my hand). What possible bottom could that have for a universe that follows rules? Would it even be possible to construct a self-consistent universe that was “turtles all the way down” so to speak?

What I’ve said here does not play well with Alan’s argument that there is a link between the very big and the very small, because as far as we can tell, there are self-consistent models for both a finite and infinite universe.

I think theres something to be said for this personification of the universe “wanting” things, as each is clearly an issue of existence that needs to be resolved, and then it “settles” on a way that is possible without breaking its own rules. I have often thought this way on wave functions, etc, which are not intuitive to me.

1 Like