3 ms·
There might well be a connection between the two. However, there are much more obvious connections between electromagnetism, or all of physics for that matter,
by smokel 3y ago
There might well be a connection between the two. However, there are much more obvious connections between electromagnetism, or all of physics for that matter, and numbers [1].
Even though I prefer to interpret things differently, the paper "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" [2] might be a good avenue to think about these things.
I wouldn't be surprised if numbers and physics go hand in hand, in the sense that we can only observe these, and not the more irregular patterns that make up the total chaos that we might exist in.
[1] https://en.m.wikipedia.org/wiki/Maxwell%27s_equations https://en.m.wikipedia.org/wiki/Maxwell%27s_equations
[2] https://en.m.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.m.wikipedia.org/wiki/The_Unreasonable_Effectivene...
- jiggawatts 3y agoMaxwell's equations are not the simplest formulation for electromagnetic theory, and they're not a foundation, but merely a formulation of the physics. The more elegant mathematical foundation for understand electromagnetism is Noether's theorem. The more elegant formulation of the physics is just: ∇F = J Which uses natural units and the geometric algebra of spacetime to encode everything contained in Maxwell's equations, but in a way that is coordinate-free and relativistic. See: https://en.wikipedia.org/wiki/Mathematical_descriptions_of_the_electromagnetic_field#Spacetime_algebra https://en.wikipedia.org/wiki/Mathematical_descriptions_of_t...
- computerfriend 3y agoBut ∇F = J is Maxwell's equations (written very concisely).
- jiggawatts 3y agoThat's like saying C++ is just machine code written very concisely.
- Koshkin 3y agoIn all fairness, it should be noted that, for better or worse, GA is not part of the mainstream; modern treatments use differential forms instead. For an accessible account, see, for example, https://www.jpier.org/ac_api/download.php?id=14063009 https://www.jpier.org/ac_api/download.php?id=14063009.
- jiggawatts 3y agoIMHO: Differential forms are just half-arsed GA. Physics is littered with incomplete implementations of GA using a mish-mash of random bits of mathematics because of a perverse insistence on refusing to use the appropriate algebra.
- tralarpa 3y ago> I wouldn't be surprised if numbers and physics go hand in hand, in the sense that we can only observe these, and not the more irregular patterns that make up the total chaos that we might exist in. I am curious to see how far we can get with the logic and mathematics that we understand (as humans). Perhaps there is a perfectly "logical", consistent and complete description of why the universe exists and what it looks like that is beyond our comprehension. Maybe we wouldn't even recognize the description as such if it were shown to us (comparable to an abstract painting with two lines and one dot that is supposed to depict a woman).
- smokel 3y agoThis kind of reasoning is slightly problematic. What does it mean if properties of "logic" are "logical"? Does that lead to tautology, recursion, symmetry, or worse? I notice that you put "logical" in quotes, so you seem to be aware of this problem. Any idea how to get around it?