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> Mathematics is a part of physics. It's probably treading close to the don't be dismissive rule, but I confess it's really hard to keep reading when the piece
by User23 6y ago
> Mathematics is a part of physics.
It's probably treading close to the don't be dismissive rule, but I confess it's really hard to keep reading when the piece opens with something so obviously wrong.
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- bitdizzy 6y agoWhy is this obviously wrong?
- drdeca 6y agoBecause mathematics doesn’t have to be about the world?
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- bitdizzy 6y agoFor Arnold, mathematics is rooted in physical intuition and experimental inquiry. Can you name some math that is completely disconnected from that intuition?
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- dooglius 6y agoMathematics may be rooted in that, in a historical or pedagogical sense, but areas of math can certainly be disconnected from physical intuition. Non-measurable sets (e.g. those in Banach-Tarski) and transfinite numbers cone to mind.
- bitdizzy 6y agoNon-measurable sets are precisely the kinds of things Arnold wanted marginalized in mathematical pedagogy, instead of placed front and center. They are necessary auxiliaries to the main theory, that of measures and integration but auxiliary nonetheless. I disagree that transfinite numbers are detached from physical intuition since most of the ones you or I could write down can be easily visualized with a few ellipses here or there. But i do think Arnold would consider them marginal players. Perhaps he thought set theory was a formalist distraction from the main of mathematics!
- oytis 6y agoE.g. logic? A pretty important part of mathematics that is hard to marginalize, but that can't be observed experimentally. Rather scientific observation presupposes logic ability.
- Koshkin 6y agoBecause physics is part of mathematics.
- idolaspecus 6y agoToo close, in my opinion. If I said "Communication is a part of physics", it would be clear that I don't mean "all of communication is a subset of physics" and that I do mean "doing physics involves communicating your findings". I think this is the author's intention. Edit: Actually, it does seem like the author claims mathematics is a proper subset of physics.
- erdos4d 6y agoHistorically, this is accurate. The whole concept of "pure math" is actually very recent and before that math was almost exclusively tied to real world problems that often came directly from physics.
- mettamage 6y agoHow about having some understanding of complex numbers? Wasn't it an Italian who started to use sqrt(-1)? I don't see how that'd be practical. Disclaimer: I'm not a mathematician.
- bitdizzy 6y agoThe first use of complex numbers was as intermediate quantities in the calculation of the roots of cubic polynomial functions. This use is analogous to using negative numbers in a ledger even though negative amounts of physical things don't make sense. Edit: I meant physical things like apples fam. This is an important philosophical point we don't appreciate because we are so used to them. De Morgan once wrote: "It is not our intention to follow the earlier algebraists through their different uses of negative numbers. These creations of algebra retained their existence, in the face of the obvious deficiency of rational explanation which characterized every attempt at their theory."
- Koshkin 6y agoThe complex numbers enjoy a widespread use in physics (and electrical engineering).
- Koshkin 6y agoFor geometric algebraists, mathematics is part of physics; for algebraic geometers, it is the other way around.
- cassepipe 6y agoI am fascinated by geometric algebra but what I have seen so far seems like mathematicians trying to convince physicists and programmers to use their system, which to be honest seems much better, but is also harder to build an intuition of. I would love to read a geometric algebra for dummies/from the ground up.