arxiv.org
>I hypothesize that only computable and decidable (in Godel's sense) structures exist
For instance, Maxwell's equations, discovered in 1862, successfully describe radio waves, later discovered in 1879.
So my question is: do we have any math that doesn't yet describe anything in the physical universe?
I don't know OP but I do know that if you want to be a villain number one then you have to catch a superhero on the run.
...
How do platonists respond when you bring up the fact that their brains exist within the physical world?
What does Banach–Tarski describe IRL? Or is it just mathematicians stroking themselves?
>muh MUH
infinite sets.
It describes the fact that a set of points constructed in a specific way doesn't have a defined volume so we shouldn't expect transformations on it to conserve volume.
yes, go to ncatlab.org and go to a random page
there is a high chance that whatever is on that page does not describe a physical phenomenon
Sqrt/(-1)
So it describes no physical phenomenon?
That's a really dumb way to limit yourself for no perceived benefit. There are plenty of real life situations we can't even analytically solve, why wouldn't the phenomenon stop there then? There's probably more to life than what math can model; just hope the interesting things are within its domain.
What could possibly be outside the scope of mathematics?
>So my question is: do we have any math that doesn't yet describe anything in the physical universe?
Yes of course. Math only describes the universe because we have used it to model processes we're interested in. There's lot of math out there that hasn't be used for anything. It's superstitious to think of math as anything more than a tool.
Love
>Mathematical Universe Hypothesis
>MUH
muh dikk
>Dichotomous Kaluza-Klein
Holographic lens mayne
What the fuck did you just fucking say about me, you little bitch? It's spelled "platoonist" and I assume you were refering to me, junior officer in the Navy Seals platoon. Stupid civvies and their weird ass slang. Semper fi, errah!. You're fucking dead, kiddo.
You have Tegmark's idea backwards. It doesn't say that the only mathematics that exists is that which describes the real world. It claims that the real world is identical to some mathematical structures and that all mathematical structures have some real ontology grounded in nothing else-- and that only mathematical structures have this property.
>do we have any math that doesn't yet describe anything in the physical universe?
Loads of it. Pure mathematics has gone so far down so many rabbit holes... There are branches of math that produce tons of (so far) useless garbage.
It's not all a waste of time, though. Like the Mandelbrot set is fascinating to stare at for hours on end, and as far as we know it doesn't represent anything physical. But it has been shown to have some extremely bizarre and unexpected relations to real-world stuff.
>extremely bizarre and unexpected relations to real-world stuff
Please elaborate, I'm all ears
Consciousness.
What I mean is, if you're having a seizure, do any of those random impulses make sense to you at the time? There's no guarantee our logic is adequate to describe every aspect of life.
look into topology
I'm sure we have abstract mathematics that convey ideas properly that have yet to be applied to real world mysteries such as the brain, linguistics, etc.
Yes.
Everything organic is fractal.
Trees are fractal. Leaves are fractal. And so on.
Fractals and Mandlebrot's work are what have let us make decent looking CGI of real world items.