[moritzwarhier]

I would never ask this in a trolling way, but I'm a bit floored (ha), so I'm asking it seriously:

> Effectively, I am interested in a mathematical representation of any conceivable structure in space-time, with operations that allow for transformations of those structures in space-time.

Are you serious about that?

If so, this is not really about maths. It's the classical "theory of everything" question in physics.

But you can't say anything meaningful about space and time using only maths. It makes no sense.

[andoando]

Haha yeah I am very serious. I spent a ridiculous amount of time the last 3-4 years thinking about this. It might all be junk but I find it very interesting.

>But you can't say anything meaningful about space and time using only maths. It makes no sense.

Why do you think that? I am talking about entirely abstract mental conceptions. I am not saying anything about how real physical processes work. Theres several mathemathic formulations of space-time, so I am confused as to what your bewilderment is.

Also keep in mind this is not too different from the Turing machine, which is a row or a multidimensional row of squares, with operations that allow for manipulating any one starting configuration to another.

[moritzwarhier]

> > But you can't say anything meaningful about space and time using only maths. It makes no sense.

> Why do you think that? I am talking about entirely abstract mental conceptions. I am not saying anything about how real physical processes work.

When considering if something is "real", maths and physics are OTOH deeply related (physics desribes the world using maths) and OTOH fundamentally different.

Maths builds systems of logical deduction based on self-evident axioms. "Pure Logic", ideally, if you will. The point is if the deduction is sound and how far logic can take you regarding abstract structure.

The simplest example is indeed the natural numbers, defined by the unit 1 and the rule that every natural number has a successor.

Physics, like other sciences, uses maths as a tool, for example statistics.

Physics is special in a way, because it applies stricter rules to what is a sounds and falsifiable theory.

But the basics are the same in every scientific discipline excluding Maths and/or Philosophy: a theory is only worth considering if it allows itself to be proven wrong. And the benefits of a theory or a theoretical model of physical reality lie in "predictions". A theory that does not make any prediction is not science, it's not a theory either. It's non-falsifiable; at best called metaphysics or religion.

[andoando]

Hmm, I am not really sure how any of that relates. I am not proposing a model that explains all of physical reality, just one that can formally represent mental observations. Different mathematics aim to do this in different ways.