OK, so if we have a distribution D (less nice than the average function) and a test function T (nicer than the average function), we have ⟨D,T⟩ = c: ℂ, so ⟨D,—⟩: test fn→ℂ and ⟨—,T⟩: distribution→ℂ ?
if there are no interiors (maybe edges but no faces nor volumes) then the vertices on the diagonals are truly independent: eg QM on small scales, GR on large ones.
[I'm currently pondering how the "main diagonal" of a transition matrix provides objects, while all the off-diagonal elements are the arrows. This implies that by rotating into an eigenframe (diagonalising), we're reducing the diversion to -∞ (generalised eigenvectors have nothing to lose but their Jordan chains) and hence back in the world of classical boolean logic?]
Is this sufficient relation: rel'ns (matrices which are particularly "irrreducible"/"simple" in that they've forgotten their weights to the point where these are either identity or zero) are concrete models of abstract quantales?
EDIT: I'm afraid I'm just learning fns vs distributions (curried fns?) myself.
I wonder how quasiparticles might relate to ideals (nuclei in quantale-speak I believe)? Note that something very much like quasiparticles is how regexen turn exponential searches into polynomial...
I ought to get overly emotional (in a bittersweet way) about all this, and i almost did, but Teddy reminded me to stay ataraxic (i.e. keeping his role in formulating key management policies purely in the cortex )
thank you for that blogpost about MPB (its one small step for fuzzablekind!)
thank you for EC ... as to thermidorian reactions, I haven't read tRB yet but it's on the slush pile now (and I have an ice pick —albeit full length— for set dressing while I read).
[My bad, it was Matvei, not Manuel, no idea how i mixed that up..
Checkout his childrens books, as well as
https://archive.is/eaYRs
Note how the independent diagonals are what i consider interesting]