Hacker News Reader

Comment by jgrahamc | Hacker News Reader

I don't know if this will help, but I believe that all of mathematics arises from an underlying fundamental structure to the universe and that this results in it both being "discoverable" (rather than invented) and "useful" (as in helpful for describing, expressing and calculating things).

View on HN

> but I believe that all of mathematics arises from an underlying fundamental structure to the universe and that this results in it both being "discoverable" (rather than invented) and "useful" (as in helpful for describing, expressing and calculating things).

That is an interesting idea. Can you elaborate? As in, us, that is our brains live in this physical universe so we’re sort of guided towards discovering certain mathematical properties and not others. Like we intuitively visualize 1d, 2d, 3d spaces but not higher ones? But we do operate on higher dimensional objects nevertheless?

Anyway, my immediate reaction is to disagree, since in theory I can imagine replacing the universe with another with different rules and still maintaining the same mathematical structures from this universe.

Why do you believe that the same mathematical properties hold everywhere in the universe?

Not the person you're replying too, but ... because it would be weird if they didn't.

There are legitimate questions if physical constants are constant everywhere in the universe, and also whether they are constant over time. Just because we conceive something "should" be a certain way doesn't make it true. The zero and negative numbers were also weird yet valid. How is the structure of mathematics different from fundamental constants, which we also cannot prove are invariant.

The constants don't have to be the same everywhere. It is sufficient that everywhere in the universe follows some structure and rules, that's all.

Otherwise we have a random universe, which does not seem to be the case.

> It is sufficient that everywhere in the universe follows some structure and rules, that's all.

What is that sufficient for?

>Otherwise we have a random universe, which does not seem to be the case.

Why jump to randomness, rather than to the possibility of undiscovered laws?

What the heck, how is "undiscovered laws" different from "structure and rules"?

Not OP but I think they are making a slightly different claim — that the universe sort of dictates or guides the mathematical structure we discover. Not whether they hold everywhere or not.

Reply on news.ycombinator.com