Could the physical limits of light affect maths in our universe?

Question

The speed of light is understood to be constant in the universe. This limits the speed at which information can be transmitted. Could this also affect numbers and functions in our universe? Like For example what If we had avogadros number 6.02214129 x 1023 and then put it in the function X to the power of itself . That's a tremendous amount of information. Could the physical limits of transmitting information "bend" this new number so that if able to be measured directly; the new number might actually be minutely larger or smaller than would be expected? Could there actually be a minute difference between the number represented by a function and the number returned by actually processing the function? Conceptually we understand infinite sets to be.. infinite... But could there be an upper limit to how "long" it takes to count a set based on the physical limit of information exchange in our universe? So conceptually an infinite set would be infinite. But maybe in our universe infinite sets could have a practical upper limit that could be named?

Answer 1

It's an interesting question. I think the answer is: no, the physical limits of light could not affect math in our universe (aside from making certain computations impossible or impractical to carry out).

But why do I say this?

Math could be defined as the study of computations. Of course, there are several ways of doing computations: they can be done mentally, mechanically, electronically, or in other ways.

Through centuries of experimenting with performing computations in a variety of ways, humans have discovered something very interesting: Essentially, computations behave in exactly the same way regardless of how they are implemented.

(There are some caveats. For example, if you have both a computer and a human compute $7 \cdot 13$, perhaps the computer will say $91$ while the human will say $93$. But we don't consider this to be an indication that in "human mathematics", $7 \cdot 13$ is sometimes $93$; instead, we consider the human to have made a mistake. Another example is that some computers can compute things that other computers cannot. But all of these differences between ways of computing seem to be "inessential".)

So, computations behave in the same way regardless of how they are implemented. This strongly suggests that the laws of physics really have no effect on computations (and, therefore, on mathematics) whatsoever, and so mathematics would be exactly the same even if the laws of physics were slightly—or dramatically—different.