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I read the first few pages and will certainly want to dig into the rest. It is interesting insightful stuff from a true expert. Something I never realized as
by dzdt 10y ago
I read the first few pages and will certainly want to dig into the rest. It is interesting insightful stuff from a true expert.
Something I never realized as an undergradute math major/ physics minor was to what exent mathematics is arbitrary. We set certain axioms describing the real line, and then two, three, higher dimensional spaces. But the actual details are governed by arbitrary choices and culture as opposed to any reason of necessity.
A lot of advanced mathematics assumes the axiom of choice, but as far as the mathematics applies to the real world there is no known consequences to assuming the opposite. It is purely a cultural choice.
People have an idea that math is universal and absolute, but that isn't so much true!
- licebmi__at 10y agoWhen I was a physics undergrad, I loved discussing (both offline and online) about the arbitrary nature of math and also the logical holes in the scientific method. Despite providing reputable sources to my claims, I got called out for being anti-scientific, a creationist maybe. I felt disheartened not for the lack of knowledge, but because the refusal from some "skeptics" to challenge their beliefs. Nowdays I still love discussing about this stuff but only for amusement and with a somewhat trollish approach.
- empath75 10y agoThey assume the axiom of choice because it makes a lot of nice results possible. So, it's not exactly arbitrary.
- DigitalPhysics 10y agoLet Mathematicians frolic in the Platonic world if they wish, but should physicists be using continuous math if our universe ends up by being discrete and finite?