Struggles with the Continuum | Hacker News Reader

Struggles with the Continuum

arxiv.org

73 pointsraattgift9 comments

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!

When 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.

They assume the axiom of choice because it makes a lot of nice results possible. So, it's not exactly arbitrary.

Let 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?

Together with "There are no particles, only fields" (https://arxiv.org/abs/1204.4616) at the top of my web reading list.

While I agree with that paper, I was unsatisfied with it. He simply hand waved away the measurement problem, which is the single largest conceptual issue with the idea that everything is waves. To be fair, he explicitly says that he will not address the measurement problem, but I think if it weren't for the measurement problem there wouldn't be any issue believing that everything is made of waves. In particular, position eigenvector collapse is what causes the appearance that things are made of localized particles, but we don't actually know how it works. We have all sorts of interpretations, none of them confirmed, and many of them nonsensical. Plug for my favorite hypothetical mechanism, Einselection. It's so boring and straightforward-ish that I think it has a good chance of being the right idea.

Aha! Thank you for this, I had forgotten that it existed!

Some further discussion is available here: https://news.ycombinator.com/item?id=12377393

he blogged about this last week https://www.physicsforums.com/insights/author/john-baez/

For visitors from the future, the last post in the series is https://www.physicsforums.com/insights/struggles-continuum-c... . It links to the previous ones.

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