It seems fully convincing that “proof” of RH (and other prime problems)are inseparable from First philosophy, ie. metaphysical problems.

In a way, it can be said that RH was allready “proven” by Gödels proof of death of the formalist dream, proof of formally unprovable mathematical fenomenological invariants aka “truths” – and hence the birth of proof theory, category theory etc.

I’m unable to fully follow Gödel’s technical proof, but it appears (from Gödel numbers) that the “truth” of Gödels proof is codependant on the fenomenologically invariant “truth” of prime numbers and/or ordinality. Others hopefully understand it better and can correct my impression, if needed.

So, with the very convincing presuppositions that

1) RH is unprovable or “false” inside the axioms of set theory; 2) statistical distribution of primes is fenomenological invariant at least in this “anthropocentric” universe

and taking in consideration the quite likely platonic possibility that our actualized thoughts *are* p-adic numbers,

then how does one (pun intended) proceed in formulating the metaphysical proof of RH?

The strategy that suggests itself is a version of proof by negation, diving blindly. If it is possible, by help of category theory, to “mindlessly as possible” to generate nonnatural sets of “N” with nonnatural distributions of primes, which however satisfy certain axiomatic requirements (set of mofphed axioms for arithmetics etc. that universes (with observers) can be build by) and if it then can be shown that these nonnatural sets of “N” (ie. with alternate distributions of primes) don’t produce universes with similar phenomenological invariants (e.g. “laws” of physics) that are obvious to observers like us, perhaps this could be considered a metaphysical proof or RH (etc)?

Needles to say, methinks, such a task is a tall order and requires an utter madman or a bunch.

]]>1 – Could a dioid algebra be a type of dimer?

‘The Max Plus approach in a few words’:

“… the so-called “Max Plus” algebra (essentially, the addition of two numbers consists of their maximum, whereas the multiplication of two numbers is the usual plus; for example 3 plus 5 equals 5, and 3 times 5 equals 8), or more generally, the dioid algebra (or idempotent semiring) …”

http://cermics.enpc.fr/~cohen-g//SED/index-e.html

2 – Please also see comment #12 in ‘Strings in Two Minutes or Less’ of U-Duality.

https://www.blogger.com/comment.g?blogID=33076818&postID=3868822281206142299

]]>I get it, that’s it – honeycomb dimers, yeah. ]]>