John Horton Conway's passing, stolen from us by Covid-19 four days ago, at 82 -- inspires me to damn omniscience, since a curious almighty would've displayed their addiction to this great man's life.
Also, it made me view JHC's answer on Numberphile, five years back, to the question, what would be your pick if you were to come back centuries from now with the right to the up-to-date answer to a single question?
First he answers, the Riemann Hypothesis I guess, buts that's not original,
Later on he rectifies himself, and says, "I'd like to know the why of the Monster".
He expands a bit, but remains vague. Tells this is a question he comes back to every 5 years or so, but tbh has left lingering longer than that in the last instance.
Prompts me to claim: The Monster is to Mars like curiosity to Curiosity
So, today, I know why I really the regret John Horton Conway.
I'll get no chance to ask him the kind of questions I'd ask him if neither of us had better to do.
M, the Monster. M-at-large is good at manifesting by intriguing numerical coincidences way down the ladder of mathematical complexity. 1^2^+2^2^+...24^2^ = 71^2^ for instance, or 41,43,47... 1601 and then exp(pi*sqrt(163)) that can spew out the famous monstrous moonshine expansion of the j-function.
But how good is M itself at doing the converse, at stealthiness? Is M, or any other sporadic, specially good at implying a paraconsistent mathematical subuniverse of interest, where it wouldn't exist?
Shouldn't it be within reach for paraconsistent logic to protect from defeat a rule falsely claiming to no exception? Especially if the paraconsistent logic, the rule, and the monstrous exception are hand-picked to fit the purpose together?
I rehearsed how JHC's relationship to the Monster came out of his fruitful meeting with Leech's Lattice... and how the Leech Lattice itself most sticks out from a distance, as an extraordinary form of trap for layered lattices enumeration algorithms.
So what I would beg JHC for, is a game in the generalized sense he excelled with.
The game would describe a class of rhetorical disputes where one player ends up beaten because fails their expectation to trap the other player as the other escapes the trap by virtue of Leech's lattice. The game could associate the nth layered lattice to the nth move. For the first 23 moves, the extrovert is rewarded for overreach, but at move 24, bang!, the introvert is vindicated when the extrovert believes they'll catch the introvert at a door... when (by exception) there's another door.
Paint convoluted exceptional structures as traps for arrogance. Design the arrogance as a function of the trap. The shape of the trap parsimoniously encodes a specialty of the particular sporadic. It's meant to trap tactics designed for a universe where the particular sporadic or structure wouldn't exist and its specialty, impossible.