[Dylan16807]

As far as we can tell, there is nothing resembling a number with infinite digits in the real world.

It's complicated in a completely different way from how the real world is complicated. I don't think that gives you useful intuition.

[Nevermark]

I agree but with a slightly different definition.

There are no numbers in the real world, that require and infinitely long definition.

1/3 has infinitely many digits in decimal, but has a finite definition. So its good.

I would write down the opposite, a definition of an uncomputable, unnameable real, but there are not enough atoms in the universe (multi-verse, ...) to being to do that.

[tialaramex]

Of course "having infinite digits" isn't from the real world because it's about an artifice, our choosing to represent numbers with digits. But the distinction between the Rationals and the Reals isn't about those digits. The discovery that there's some fixed ratio between the diameter of a circle and its circumference is fascinating and yet though we can't (AFAIK) prove it's normal that ratio sure looks normal and across mathematics we find this ratio again, and again, and again, it's something fundamental but it clearly isn't rational.

Likewise for the square root of 2 and for Euler's Number. These numbers are ever so real and yet they sure fucking look normal to me. If you assure me they are not normal, but you can't prove it, I shall not believe you.

[Dylan16807]

The real world doesn't have any of those numbers, only approximate matches.

My point isn't about digits, it's about precision. You can do math by hand with more precision than actually exists in the real world. And once you add any slack at all, even one part per googol, your numbers stop being normal and they can all be computed and represented in rational form.

[tialaramex]

> You can do math by hand with more precision than actually exists in the real world.

This claim can't mean anything because it disappears up its own backside. If you, here in the real world, can "do math by hand" that math is in the real world.

[Dylan16807]

All you have in the real world is scribbles on paper.

I'm sorry, what did you mean by "how complicated the world we inhabit is" because I thought you were talking about physical interactions of matter and energy.

If you're including all math as "real world", then I think the claim that math teaches you something useful about the complexity of the real world is what actually disappears up its own backside.

[singularity2001]

what he probably meant is that if you write down pi with 200 digits there's nowhere in the universe where you can find pi with that precision

[tialaramex]

Are you sure? Naively sure, you won't find sufficiently enormous circles and even if you could such a huge circle won't have the Pi ratio here, that's a property of Euclidean space and we don't live in a Euclidean space, ours is slightly off IIRC.

But Pi shows up in other places and I'm not at all sure you can show there are no such places which distinguish some arbitrary approximation from the actual ratio.

[Dylan16807]

The most precise situations I can think of involve impossibly perfect measurements of volume. And even there, okay a cubic meter is 10^105 cubic planck units and the visible universe is 10^186. Finite math can easily throw a million digits at any problem. How do you reach a point where you need reals to describe actual things?