So there is a deeper reality it would seem - the vagueness that is the boundless Apeiron. A sea of pure formless fluctuation. — apokrisis
I’m here addressing differences, not agreements. We may, and me thinks most likely will, choose to yet disagree. But so I may, hopefully, better elucidate the root difference between us on a metaphysical scale:
First off, once again, my realm of expertise is not that of maths. I don’t intend to purport otherwise. Still, I know enough so that the contents of your latest post to me are readily understandable to me – albeit, not in the “shut up and calculate” sense as regards the specifics. To each their own fields of interest.
As to the metaphysical issue:
You choose the Apeiron as the deeper/est reality: “boundless/formless fluctuation”. I so far further interpret you as expressing that one day all shall be Apeiron once again, aka end in a Heat Death. Correct me if needed.
To the extent I’m correct in so interpreting, the Apeiron then serves as the final telos.
Yet, in nevertheless yet holding “fluctuation”, this notion is not one of
perfect symmetry.
The final telos (for there are innumerable more proximate teloi) is for me one of
perfect symmetry. I think, thus expressed, you may then understand why I also at times state it is technically ineffable / inexpressible (if one seeks accuracy of expression), and impossible to represent via ideas, notions, etc., for none would accurately and fully correlate to its reality. (I don’t deny this correlative aspect of truth)
While it is true that for me this final telos is also, in part, that of absolute metaphysical objectivity (impartiality, hence fairness, hence justice) of which we are all (freewill-endowed) subjects to, absolute coherency/harmony/lack-of-conflict/peace/love (which brings about coherency, harmony, lack-of-conflict, etc.), absolute beauty/sublimity (which, complex as this topic in itself is, in part draws us to the unknown), and absolute selflessness of being, it is also true that—while inductively knowing, or at least believing, it to so be—I for logical reasons also know/uphold that what “it” in fact is is impossible to conceptualize, accurately represent, etc. (for technical metaphysical purposes, by anything that is endowed with selfhood; hence, by any psyche: be it ant, human, or (hypothetically) deity). Still, it, by definition, would likewise also need to be a state of perfect symmetry.
I don’t place this state at the metaphysical beginning, in part, because it is of no personal concern to do so.
At a metaphysical level, to me this end-state is not idealized but actual and obtainable. I’m not here addressing awareness of it, nor alignment with it, nor some kind of mystical vision of it, etc., but, rather, obtainable as a final state of being … which, maybe needless to add, prior to this is always in a state of becoming.
Again, focusing in on our differences:
To keep things relatively concrete and particular, the referents to the symbols of 0 and 1 are then, to me, in a sense, Platonic universals that emerge from this perfect symmetry’s reality in conjunction with the plurality of beings—quantifiable things (as becoming)—that occur. The referents to 0 and 1 are then (very intentionally so stated)
more eternal/immortal than the referent to far more complex and context-specific mathematics that hold 0s and 1a as axiomatic givens. Though, upon eventual and contingent obtainment of this final end-state of perfect symmetry, the referents to 0 and 1 too will vanish.
[As to thermodynamics, different debates can ensue. Including those of: is information equivalent to energy? And: can information be created and nullified/erased, such as within the very center of a black hole? Different tangential topics, though.]
Back to the basic concept, though: The maths to me—again, in a simplified sense—emerge from this perfect symmetry as telos, which is itself a non-maths reality (again, not an idealization which is metaphysically impossible to obtain/actualize; but, rather, a metaphysical reality) ((I think we can both understand that minds, within this point of reference, are maths)). Whereas, to you, as far as I so far understand you as saying, this deepest reality of perfect symmetry is itself one of maths.
My contention is that the maths applicable to the physical world will work regardless of metaphysical outlook chosen. For instance, I so far know of no modern maths not in some way reliant upon the referents to 0 and 1. These two referents, then, can be explained to be both via they notion of the Apeiron you uphold and the notion of the factually ineffable final telos of non-maths, which I've previous expressed via its various faces (including that of perfect symmetry).