#### IdleRich

##### IdleRich

So apparently he came up with a new way of doing things, he rejected the idea of infinite sets in favour of potentially infinite lists (I forget what he called them) - distinction seems slight but I think he's saying that instead of there being an infinitely large (countably infinite) number of natural numbers which form an infinite set, there is no such set, just a list that could go forever if we wanted it to. Without going into it too much that means that you don't get the Russell Paradox which was such a problem for Frege etc and you get a whole weird new kind of maths. In this new maths two big distinctions are the law of the excluded middle doesn't apply, and also the treatment of Irrational but Real numbers is different. The latter follows from the infinite thing, an irrational number being one with a non-recurring and infinitely long list of numbers following on behind a decimal point. Basically in Intuitionist Maths it seems that (apart from certain special irrational numbers that we can generate according to a given rule) most irrational numbers are not really described, or are not fully described. You can't necessarily say which is larger than the other at any given expansion and so you get this kind of indeterminism of which numbers are greater than or less than others, you lose the rule which says for any number, any other number is either less than it or the same as it or greater than it.

Anyway, this idea was invented early 20th century and although it never kinda became the main maths, it has been studied almost in parallel for a long time, it actually turns out to be more rigorous (ironically given its name) and require more conditions and so on for given theorems as you need to deal with approximations and so on, but turns out a lot of theorems in normal maths have a pretty decent equivalent in IM.

So, interesting stuff (I think), but, long story short, I read an article saying that some physicist read about this recently and was like hang on a minute, if I use this kind of maths with relativity it introduces a non-deterministic element that allows me to marry it with quantum physics. Now I don't know much about physics but I think that reconciling those two theories is THE problem in the field.

Another thing I like (mentioned in the article below) is that he argues it's an explanation of how we experience time. In physics you have the past and the future and so on, but the present is an instantaneous and infinitesimally small moment, yet we experience all our lives in a continuous present. I think he's arguing that irrational real numbers having this kind of fuzziness when described this way make the instant not infinitesimally small, cos that's not properly defined. Something seems intuitively right there somehow (although I've not explained it properly).

So... here's the article on the physics

https://www.theatlantic.com/science/archive/2020/04/passage-of-time-relativity-physics/609841/

Some background reading on Intuitionist Maths (what I read yesterday in other words)

https://en.wikipedia.org/wiki/Intuitionism

https://plato.stanford.edu/entries/intuitionism/ (this one is a bit complicated so I kinda skimmed it)