Ripheus23

Hmm...

• []()[]()()()()[][]()()[][][][][][][][][][]()[][][]()()()()[]...
• [][]()()[][][]()()()[][]()[][]()[][]()()()[]()()()[][]()[]()...
• &c. ...

Don't these potentially map to nonrepeating decimals, except represented in the equivalent of binary? That also suggests a gloss on binary, I suspect: instead of 0/1::true/false, we have 0/1::possible/actual. I think that's probably even more fitting since false does not = 0, but -1 (I know in propositional space by itself, the absence of truth+ is equivalent to the presence of truth-, and true/false is a propositional opposition, but...).

At any rate, this would imply that the cardinality of the set of sigma-actuations is equivalent (as such) to the cardinality of the continuum. Allowing that every sigma-actuation represents a possible world, this would imply the abstract existence of at least aleph-C worlds. [This would be a far more massive multiverse than the string-theoretic one by itself, then... Not sure about Everett's or Tegmark's, though. Tegmark's seems to contain universes whose component cardinalities (if that description makes sense!) are whichever aleph-X there could be, in which event these self-transfinite universes would have to contain infinite stacks of systems of multiverses or what, individually. So who knows!] Now I'm in the camp that believes aleph-C = aleph-1, and so that 2 to the power of aleph-0 = aleph-1. [I think those beliefs go together...] So I don't have to suppose that the cardinality of the known universe's mathematical equations (the level of infinity from which the numbers for the equations are drawn) is greater than aleph-1, at least not as such. Indeed, it appears that irrational numbers occur in physics equations so it would appear that the universe is thus condensed at least from the ether of the continuum, so to speak. [Btw, this means both (A) finite/mortal/w/e beings can grasp infinity but also that (B) this turns out to be a potential let-down as there are still infinite numbers of infinities that we can't (yet/easily) grasp, and so on.]