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Comment by nategri | Hacker News Reader

From a physics perspective, I think you could actually get most of classical physics to hang together without the number 6. I suspect you could re-formulate or re-normalize yourself out of many potentially sticky situations.

Anything to do with quantum mechanics and particles falls utterly and immediately apart though.

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I don't think so. If you follow the logic of the article to eliminate 6, you essentially have to turn everything too big into integers mod 6. I guess you could also no longer have rational or real numbers or only really limited versions of them without access to all the integers. Losing the real numbers kills classical physics.

It seems space could be at most a 6 x 6 x 6 lattice, maybe forming a hyper-torus or something like that. And time, only 6 possible points in time, too. Hopefully nobody starts walking around in that tiny universe and discovers that there are more than 5 distinct places to visit. To really get rid of 6, you probably have to limit the entire universe to 6 states, but even then I am not really confident that 6 remains out of reach.

Note that there is also a tension between ordinals and cardinals, you can number points in each dimension of the lattice universe with 0 to 5 but that are of course 6 numbers. But I decided to ignore that, it just makes the idea even harder to realize.

Ah yeah I was working on the assumption that we could keep the real numbers (article makes no mention of them), since for classical problems they're all you really need (maybe we can keep 5.9(repeating)?)

Nope. No 9 for you. Also what do you mean with repeating, you aren't suggesting strings with more than 5 symbols, are you?

A further weird problem with this, even given the one-dimensional universe with only six locations, is to form the power set of points in the universe. Now it's true that there's nowhere in the universe to write down the elements of the power set because no representation of them fits anywhere in the universe at a single time. But one might still feel that this power set is well defined. (You could try to describe it as "How many groups of places in the universe are there?", although indeed no useful representation of that question can fit into the universe either.)

It contains 64 elements. ... oops!

In a sense it's not a weird problem so much as the entire concept of forbidding a 6 is inconsistent with the axioms of mathematics. Reasoning about a universe without 6 will inherently include contradictions because you can always redefine something equivalent to 6 given our axioms.

I think that's a very reasonable way to put it.

For example,

https://en.wikipedia.org/wiki/Peano_axioms#Set-theoretic_mod...

does not depend on having any pre-existing set of 6 objects that you can point out by ostension. Instead, you can construct one, given the concepts of ∅, ∪, and {}!

Why do you assume that without the number 6, all dimensions would be a lattice? There's nothing that forbids them from being dense (at least until Planck scale).

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