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I wonder if it's the opposite. Like electromagnetism behaves a certain way because of fundamental properties of numbers.
by fooker 3y ago
I wonder if it's the opposite.
Like electromagnetism behaves a certain way because of fundamental properties of numbers.
- diogenes4 3y agoSorry, opposite of what? You seemed to have inserted causation where none is implied.
- smokel 3y agoThere 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.
- 3y ago
- mjan22640 3y agoIt is the third actually, because of fundamental properties of human thinking.
- Koshkin 3y agoNature doesn't care what (and how) we humans think.
- Koshkin 3y agoIndeed! (Numbers themselves lie at the foundation of Nature.)