I'd love to ask you a question.
Can you please justify that Physics is 80% mathematics? What do you have to say to nominalists who present several strong arguments against this? What of, specifically, the arguments made by Field in Science Without Numbers? Where does this magic "80%" number come from, and what does it in actuality represent?
The 80% is more of a feeling than some test result or so. According to my experience and friends from higher semesters as well as professors I talked to, what we do most of the day is calculation. Be that solving differential equations or simpler problems, the vast majority of work is math.
That is because math is a tool which is mainly used to derive conclusions from known values.
As I said, math is pure logic, 1=1 is simply true, there are no conditions.
Actually, this depends on axiom. It is entirely conceivable to choose a set of axioms in which 1 != 1. The conditions are the axioms of choice.
Similarly nature is I guess per definition logic as well and physics is the study of nature. So the strong relationship between math and physics is obvious.
My argument is that such a tie is not obvious, especially given one can perform physics without the use of mathematics.
Personally I think there is an extreme misunderstanding about physics out there. People look to e.g. Neil DeGrasse Tyson (as I did) or Bill Nye or watch documentaries. But all they say is extremely boiled down and simplified. They tell you the conclusions and ideas that were inspired by long processes of actual experimentation and evaluation of test results but they couldn't explain the actual reasons even if the explanation took an entire week. Their job is more to inspire people, not to teach them.
I agree very strongly with this.
I mean sure, stuff like the many worlds theory, Schrödingers cat, and so on is awesome to think about but that's not what physics/ science is about. No one knows what happens during the double slit experiment and the math only tells you what happens before and after. One can wonder if new universes are created each time there is a seemingly random event but that's not the point. Science and especially physics is about explaining phenomena but also about simply predicting outcomes from given circumstances.
In actuality, science isn't about explaining phenomena. What you are thinking about is aristotelian science which predates the scientific revolution. Science aims to describe. One cannot find 'true cause.'
But that doesn't mean that it is boring. I personally find it extremely fascinating that you can more or less describe a (simplified version of) an entire storm system with an equation that fits in one line. (In the end it is more complicated than that but still).
I guess what I am trying to say is that yes, Physics is mostly math.
If physics is mostly math, how can it be performed without use of math? I am happy to provide justification here if necessary, just ask.
Yeah, how do you perform Physics without math? I personally think that math also serves as a kind of guide for when my intuition is no longer capable of working with physics problems...
Field did so by axiomizing Newton's laws with no reference to functions or numbers. He started with Hilberts Axioms and added extra relations between points to do the work formally done by calculation and vector fields - and he did so without use of hilbert's abstract points and instead had them refer to real physical points.
From there he used this to show that every fact provable in 'normal physics' is also provable in his system, making mathematical physics a conservative extension of his theory - and thus a useful fiction.
Ok, I guess this is somewhat out of my league yet, the deeper mathematics is something I will go through in future semsters, so I can't really say much about that. However as far as I understand it, there roughly are two "directions" that physics is "performed" in. One is experimental physics which more or less is what the name implies. The other is theoretical physics which is something I guess your statement would fit in. Here the point is no longer to figure out the value of G so to say but it is more about focusing on the mathematical side of physics. It is way more mathematics heavy than experimental physics.
I guess I also just want to clarify what I mean by "mathematics". Usually people think of the stuff you do at school when talking about math, which is doing calculations, solving functions etc. That is however more of a useful but small part of the thing. I'd be an idiot if I were to pretend to understand what mathematics is in its entirety but a big part is proving statements from given circumstances (as you already said) and building a sort of structure which can describe and handle patterns, relations etc. To be honest, I can't remember the last time I saw an actual number being used in a math lecture.
Also, to be honest I am kind of impressed that you seem to know quite a lot about mathematics (provided you understand what you wrote
, which I certainly do not entirely). What is your motivation to believe in the flat earth, if you do? Math isn't easy for anyone, so you must have put a lot of effort into learning it. With all the logic thinking necessary, I would think that you should also have a similar approach to physics and the real world in which (not only by my judgement) a flat earth would not be possible.
BTW, sorry for not responding for some time, the semester has started.