A starting point is what I believe GR (General Relativity) is in simple -
It is a theory where we think that gravity and space can be plotted on a four dimensional graph. In this graph, we have xyz for space. And then we have a separate axis for time.
Celestial objects interact on these graphs with the equations of physics - and it shows us things like curved spaces are the cause of some forces (gravity in particular!)
Edit: I asked a Facebook member on the physics society page if he’d like to be friends (not the first time I’ve tried this with others) and he never responded. It’s surprisingly difficult to find enthusiasts for Physical Science even on university society’s and groups sometimes!
I know it’s why I said physical science empirically not maths bc I don’t view maths as a science overall - oh it seems I didn’t word it that way at all!!! My mistake
I think Feynman made a solution for this paradox, but I don’t remember the details as the experiment itself I’m not even comfortable with. Double slit I mean, the idea that a photon is a particle and a wave is hard for me to imagine, it makes me think - well what if you break it down further - what is it then? lol
The type of maths used in physics is usually Euclidean/Geometry based - so it is based on shapes therefore that side is definitely scientific because it all measurable and validated by shape positions and things
Pure maths only really comes to use in things like cryptography and other abstract shapes connections so it does get pretty empirical too tbh
I don’t know any maths that’s more on the art side - I believe it’s usually things like probability or philosophical abstracts
Edit - I’m by no means proficient at proofs and abstract maths though, as it’s not fun for me lol
Similarly, basic arithmetic might be thought to be ‘validated’ simply by counting. Count 2 apples, count 2 more apples, and you count 4 apples, so here we have an experiment that proves 2 + 2 = 4 right? But then why should counting 2 apples and then counting 2 more apples make you say there is 4 apples? That is because (as a math statement) 2 + 2 = 4, regardless of apples or whatever.
And so even in geometry, no proof goes about observing some number of shapes and then validating any theorem, think of how Pythagoras is proven, not by measuring some number of triangles. Rather, on a plane, by measuring the angles 3,4,5 you can deduce, rather than hypothesize the right angle.
There’s no data/observation in math - well most of it. There is some niche called experimental math I think which basically runs computers to try out stuff.
Edit: unrelated note. I’m still working through integration by substitution (mentioned in the say anything thread but I’ll mention the progress here now as it ties into this thread more neatly and won’t clog conversation on the other thread)
Pretty good! Still a lot of fun and pretty close to finishing now. Probably end up just over 4 years, but then next to my full time job so I am happy with that
Integration by substitution and then integration by parts and then matrices and networks. I think that’s all I have left to do. After that I have sequences and some Taylor polynomials and I think complex numbers and I’m done with this years syllabus. Have to prep for the exam.
Exam is in September. That stats stuff I’ve decided will be sorted on itself, if I pass, hooray. If I don’t pass stats I’ll talk to them about doing something else or retaking it
Was reading about free will from a physical science perspective. In some ways, it really does feel/seem like it’s all just a chain of events connected by deep mathematics