Math and Reality

[Purple Rabbit]

To use the color of blue as an example... it is just a hue, but upon perceiving it we turned that hue into a concept, and later into a word. Logic (upon which math is based) has been continually observed in nature... that we can use that base to consider things we haven't even seen yet is due to our trust in logic. If logic is how reality "follows" (at least "here"), then what is based off of it is probably true. However, if math is wrong at a point, it would only be because logic does not apply to the scenario. Mathematical concepts are derived from logic, which is an unprovable assumption we've made to reality. It may not be the "true" reality, but it is the reality as we can see it.

Well said Sae. But my hesitation is with all the math that was thought up with no physical correlate whtsoever. Will it ever be put to use in a model of reality?

If math is ultimately a representation of reality, then following the math would be following the reality.

How could we ever know? IOW, can this be made into a falsifiable statement? Is it not falsified already by the fact that there is a whole lot of mathematics that does not in any way apply to reality?

For all we know, infinites might be real (see singularities?).

But if we are to guess, to fabulate away, we're not better of than the supernaturalists.

Logic itself is an assumption made... but it remains that it could all be one outlandishly ridiculous coincidence. Following the math would be entirely logical given that it hasn't really let us down yet when describing, and we can see no reason for it to do so. But all of math blows up if the illogical starts occurring. Logic is simply an observation we've made of 'reality'... and there is no way we can test it's validity without using itself.

I agree it could all be a ridiculous coincidence.

But I propose the following alternative explanation for the observed coherence between nature and (parts of) math. It's just my hypothesis but I can give you a few qualitative arguments for it. And maybe it's just a matter of rephrasing your words: math and nature match so well because they are both necessarily founded on symmetries. The more we discover about nature the more it becomes manifest that symmetry is what fuels our models of nature. Symmetry is everywhere in physics. In the structure of the atom, in the standard model of fundamental particles, in the way forces act, in the relativeness of viewpoints, in the immunity for spatial translation, in rotation of objects, in the spin of particles, in the particle wave duality, in the creation of matter-antimatter. Symmetry was what Einstein drove to general relativity. Hell the LHC is rigged to find supersymmetry! We seem to finally get it: symmetry, symmetry, symmetry! Like in circles, like in the building blocks of algebra, like in the mathematical equivalents of translation, transformation, rotations. Like in balance on both sides of the equation. Like in the order of natural numbers. Like in projections from one set of co-ordinates to another one. Mathematics is imagination restricted to consistency and symmetry. And why is symmetry a necessary essence of reality? Because only symmetry can ensure some sort of stability.