[MarcelOlsz]

What level of math do I need to be at to "compute" this comment?

[ben_w]

> function from {0,1}^N -> {0,1}^M

"{0,1}": the set containing the values 0 and 1

"{0,1}^N": a discrete n-dimensional space, where the possible values in each dimension are 0 or 1

So they're saying a computer takes a length N binary sequence input and produces a length M binary output.

(As for "what level is this", I didn't cover any of this in my double A-level[0] in maths/further maths, but I am covering it in brilliant.org and some popular maths books, so my best guess is it's first or second year degree level?)

[0] https://en.wikipedia.org/wiki/A-Level

[mjburgess]

Very little.

A computer is an abstract mathematical description (eg., like "prime") of a certain mathematical object, a function.

A computer is a way of specifying a discrete function (ie., one which maps a finite number of bits to a finite number of bits), in terms of a sequence of mathematical transitions.

It's an "algorithmic" way of specifying the domain and codomain of a discrete function.

Electrical digital computers aren't actually computers in this sense, and are extremely aproximately described by them. Inasmuch as the shape of the earth is aproximately "spherical".

In any case, pretty much all of physics does not use discrete functions (indeed, I can't think of a single case). In every way physics describes reality, ie., parameterised on space and time, functions are continuous.

They map an infinite amount of spatio-temporal information to an infinite amount of spatio-temporal information.

And there is yet no reason whatsoever, other than the AI PR machine, to suppose that all of physics is wrong in this regard, and the universe is describable by anything else.

This is relevant here, since the problem that cannot be represented to the machine uses ordinary equations of physics, none of which are computable.