Without any basis whatsoever, and I really must one day put this idea out of its misery with some studying, I long suspected that quantum mechanics involved parallel universes where different bases more aptly fit with that other reality.
My thought is surely crackpot but I'll explain how my idea arose :
A fraction eg 1/3 describes a decimal number to infinite accuracy but creates a challenge for base 10 calculations.
I thought about the precision necessary for learning the math of the quantum particles and the experimental way we're trying to figure out how they behave to infer their properties. (Higgs was the other way around but I am optimistic that we'll predict much more in future instead of this convoluted observations rigmarole) and I started wondering if you could approximate extremely high precision decimals to fractions in non decimal bases and from there simplify calculations with far greater resolution.
How much more capable would Nyquist - Shannon sampling, if we could clock with the precision of infinite decimal fp digits but handle only a short simple "one third" input or do visor?
My silly mind wandered off to imagine particles jumping between different base based universes just as a sequential progression through the precision of their infinitessimal steps through space and time.
This is my favourite kind of pure speculation. You don't know what you're talking about, really, but you're clearly exploring vast areas of thought at the same time.
Remember, integers are integers are integers, because they represent the intrinsic "whole quantity" of something; this is as concrete as logic will get, the idea that there are "ones", it's pretty hard to imagine a universe that doesn't have that.
Once you have integers, then you're going to do math in an integer base; and making too high of a base has a diminishing value at at certain point, so it's unlikely we'd see higher than maybe 60. Non-integer bases exist - https://en.wikipedia.org/wiki/Non-integer_base_of_numeration - but it's clear to me that I'm too stupid to use them, and so probably most other people are too. This tells me that it's going to be a comparatively rare Many World that chooses to do this.
Choosing a number like 12 or 60 with a lot of divisors would have been nice. 1/3 in base 12 is "0.4", which is a lot nicer than 0.333... and would probably help make a lot of younger math education way easier.
Combining that with skipping "degrees" entirely and using radians from the start would probably have been wise choices. We'd have been much better equipped to divide things! I imagine a six-fingered being would have had an immediate advantage in that regard, but, alas.
Now, would some of those number constants look particularly different? Not really. Pi in base 12 is "3.184809493B91866", for instance, so it doesn't look like that would be much easier. E and other numbers similarly just end up with different expansions.
Remember, you can use whatever number base you want to, in this universe. The key is that it's just a way your brain interprets the symbols to represent a quantity; don't confuse the map for the territory. Five, the quality of having five whole entities, exists the same when it's 101 in binary or 10 in base 5 or 11 in base 4; either way it's all still just five, and so the right thing to do is to use the base system that most intuitively works for you so that it becomes transparent.
