Comment by gjm11

My apologies to ikrima for being critical, but I think anyone who thinks "aleph/beth/Betti numbers" is a coherent set of things to put together is just very confused.

Aleph and beth numbers are related things, in the field of set theory. (Two sequences[1] of infinite cardinal numbers. The alephs are all the infinite cardinals, if the axiom of choice holds. The beth numbers are the specific ones you get by repeatedly taking powersets. They're only all the cardinals if the "generalized continuum hypothesis" holds, a much stronger condition.)

[1] It's not clear that this is quite the right word, but no matter.

Betti numbers are something totally different. (If you have a topological space, you can compute a sequence[2] of numbers called Betti numbers that describe some of its features. (They are the ranks of its homology groups. The usual handwavy thing to say is that they describe how many d-dimensional "holes" the space has, for each d.)

[2] This time in exactly the usual sense.

It's not quite true that there is no connection between these things, because there are connections between any two things in pure mathematics and that's one of its delights. But so far as I can see the only connections are very indirect. (Aleph and beth numbers have to do with set theory. Betti numbers have to do with topology. There is a thing called topos theory that connects set theory and topology in interesting ways. But so far as I know this relationship doesn't produce any particular connection between infinite cardinals and the homology groups of topological spaces.)

I think ikrima's sentence is mathematically-flavoured word salad. (I think "Betti" comes after "beth" mostly because they sound similar.) You could probably take ten years to get familiar with all the individual ideas it alludes to, but having done so you wouldn't understand that sentence because there isn't anything there to understand.

BUT I am not myself a topos theorist, nor an expert in "our human brain's sensory instruments". Maybe there's more "there" there than it looks like to me and I'm just too stupid to understand. My guess would be not, but you doubtless already worked that out.

[EDITED to add:] On reflection, "word salad" is a bit much. E.g., it's reasonable to suggest that our senses are doing something like discrete sampling of a continuous world. (Or something like bandwidth-limited sampling, which is kinda only a Fourier transform away from being discrete.) But I continue to think the details look more like buzzword-slinging than like actual insight, and that "aleph/beth/Betti" thing really rings alarm bells.