If you're happy for mathematical structures to be infinite, why can't our universe (including ourselves) just be one infinite mathematical structure?

Yes, it's very complex, but there's plenty of room in infinity.

It doesn't need to have a "real" physical instantiation anywhere. It's like the simulation hypothesis, except you don't need the simulation. We're just the inside of an infinite self-experiencing mathematical structure, with nothing on the outside.

It's an assumption that someone is happy with mathematical structures being infinite.

There are mathematicians unhappy with the notion even while being well versed in the Cantor (and other) arguments.

You can wander down that rabbit hole via (say) [1] as a starting point.

[1] https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_...

Because universe is a physical structure, not mathematical, e.g. you can't define things into existence.

Is it? Says who? This is an untirely unfalsifiable assumption. I personally don't share it. "It from bit"[0], I say, mathematics is fundamental, physical reality is just our perception of the underlying math.

[0] Title of a paper by John Wheeler. Can't find it right now, but if you google "it from bit" you'll find a lot of commentary on it.

The concept of fundamentality doesn't exist in mathematics, and it's by design. What is fundamental, Tailor series or Fourier transform? Mathematics doesn't care, it simply has no such concept.

Found commentary on "it from bit". It looks like an attempt to resurrect antirealism (participatory universe). The reason why antirealism was buried is because there's too much realism in quantum physics, so it won't fly.

This is exactly the position I'm trying to argue against.

What does it mean for something to be a physical structure? That you perceive it to be physical? But aren't your perceptions part of the universe? So how would you know if it actually "exists" anywhere?

Physical structure works by its own rules, mathematical structures work by our rules. For example, in mathematics you can complete an infinite process, because there's no time in mathematics, it can just be assumed out of existence. It can't be done with physics, because physics isn't affected by our assumptions.

Time and physics are just things you experience. They're parts of the universe, they're within the universe. The mathematical universe itself can quite easily be infinite in both space and time, you just can't experience all of it.

Physical systems have finite information storage capacity. Our infinities are descriptions of recursive processes (either iteration or subdivision). The quantization we've observed in the universe is a strike against infinities of subdivision, and it's literally impossible to observe a macro-infinity, so from a scientific perspective physical infinity is unsupported and seems unlikely.

Space might appear "infinite" if you set up a word problem where you fire two photons off in opposite directions and track the distance between them over time, but without an observer the only place information exists is in those photons, and space is meaningless. Infinities of time are likewise artificial constructs of measurement, there is only the current moment.

>infinity seems impossible to me

"Me," in this case, is a microcontroller that evolved to move muscles on a primate body effectively.

Do we have any reason to believe such a system should be capable of grasping the true nature of the universe? After all, it's far outside the design spec!

>"Me," in this case, is a microcontroller that evolved to move muscles on a primate body effectively.

Distinction between brain and body not really a thing though, yeah?

The universe being finite in any way is even harder to grasp for me. How can existence itself have a beginning?

That's a great point. I don't know (obviously). But I tend to think that there is actually a point in space beyond which it does not make sense to ask the question "What is beyond this". Just like when we are at North Pole, the question "Which way is North" does not make sense.

Based on his talks Penrose doesn't either.

It's just that we are talking about googolplex timescales.

But it can’t NOT be infinite! If space were three dimensionally finite, then there must be a boundary. But if there were a boundary, then there must be something beyond that boundary. And now we have a paradox that infinitely regresses. Same goes for time. Same goes for distance. How can there be both a finite distance, as well as an infinite number of points between two distinct points? To me, infinity seems to be everywhere I look

> If space were three dimensionally finite, then there must be a boundary.

Not true, space might just repeat in all directions - a finite volume but with no boundaries. Maybe if you go far enough you always end up back where you came from.

That may be true. But if that we’re the case, then a fourth spatial must exist for the entire 3rd dimension to wrap in on itself. And then we find ourselves in the same infinite regression, wondering about the boundaries of the parent dimension.

That seems to be a personal problem. There's nothing inconsistent about either space or time being infinite.

It's a personal outlook, not a problem. It's not a statement of fact. It's an opinion at best.

I can't think about these things too hard... stresses me out. What's a quark made up of again? 'Tiny rubber bands' :)

All "Infinities" are not the same, you are using the word in a colloquial sense (i.e. non-converging) while there actually are different definitions/interpretations.

See wikipedia : https://en.wikipedia.org/wiki/Infinity "Cosmology" section; the key point being The question of being infinite is logically separate from the question of having boundaries.