My theory stands as firm as a rock; every arrow directed against it will quickly return to the archer. How do I know this? Because I have studied it from all sides for many years; because I have examined all objections which have ever been made against the infinite numbers; and above all because I have followed its roots, so to speak, to the first infallible cause of all created things. – Georg Cantor (1845-1918)

Allegory. I can’t see past it. And I made a mistake. I tried to eliminate it from my work. A certain determination took hold and I tried to prove what I was doing. I should have known better but in spite of myself I tried to cobble together a synthesis that could move through one gate to another, gliding through a proposition so that a final statement of undeniable truth would emerge after years of work.

And I placed the Georg Cantor quote at the beginning of this piece because of the sacrifice and toll that proof put on him. (And when he took a hiatus from his mathematics, he devoted his effort in trying to prove that the bulk of Shakespeare’s work was actually penned by Francis Bacon.) It seemed that whenever he could not see or hold the thread of his overall thesis, he would end up in a mental institution, paralyzed by depression. In fact, he eventually died in one.

I have seen his work and all I can see is that very few have cast the kind of light that he has on the infinities that abound, how they abound. The dynamics of infinity. And he gave us the aleph; the notation that allows us work within these dynamics. And when you read his original texts you can see how he carved his thesis out of the depths of his mind…

Unfortunately, there is a serious drawback to being a front-liner in this sort of game. Latent epistemologies still abound and there is nothing to suggest that there are any others. In a real sense, it is a matter of style and the role of iconoclast can be very unforgiving in a human sense. And in the modernist sense, concepts of “proof” require serious examination.

Thesis. Antithesis. Synthesis. The nuts of the German proof. However, we have come to learn that the synthesis is merely another thesis with its own child antithesis and synthesis and so the merry dance continues ad infinitum until the decision is made to stop. This can be seen as a dogmatic decision and the “proof” in its entirety timewise can be viewed as an unconsciously reverse engineered dogma; this adheres to the Bohm doctrine (explored in an earlier article) that the universe will reflect the thesis.

And in terms of the axiomatic departure of a proof system we have Gödel wobbles (as described here)

In taking the respective doctrines of Bohm and Gödel when examining the overall space of the proof, what we have is a series of binary logic devices hemmed in at all sides by allegory. In no way can proof exist as a general, covering absolute.
I am a third generation modernist mathematician and glad to be so. I can look back on the anatomy of proof and view it like the human appendix – something that has been superannuated by evolution, still lingers and in some cases needs to be surgically removed to protect the rest of the organism.

I am no longer concerned with proof.
Time is particularly harsh on false things.
I will leave it to time.
My compassion for Cantor is sometimes tempered by the recognition of hubris. Ahab had something to prove as well. Ahab would “smite the sun” if it insulted him.
The fatality of pride.
The fatality of proof.
Proof was Cantor’s white whale. He was a first generation modernist mathematician.