x^3 + y^3 = 1729

“… my purpose to re-tell the story in class was to illustrate the use of addition on an elliptic curve as a mean to construct more rational solutions to the equation …” from ‘the taxicab curve’ on ‘NeverEndingBooks’ by lieven le bruyn.

Hello Carl and Matti:

Carl, do you have any other citations for Bohmian mechanics? I have only found the Stanford Encyclodpedia and Wiki references readable. But from what I gather, Bohm felt that position was a measureable quantity of a particle at all times and he believed in hidden variables. I also understand his theory was non local. I don’t mind the non locality because from viewpoint of ultrametric spaces, we get non locality as a result…However, the concept that all positions are measurable at any given time doesn’t sit well with me, if only for reason of measurement resolution. Has anyone references to elucidate? Thanks.

-dS/dt = V + Q + (1/2m)\sum (grad(S))^2

V is just potential for elementary theory is zero. Q is the quantum potential that disappears for no space dependence (i.e. qubit calculations). So this reduces to

E = (1/2m)\sum (grad(S))^2

and there you have energy as the square of a vector ala Kneemo.

]]>Not a very inspiring vision. One can try to deconstruct it by asking what “we” really means. A possible answer is based on quantum model of living matter. “We” would consist of macroscopically quantum coherent dark matter quantum controlling visible matter. Hierarchy of dark matter with levels characterized by increasing value of Planck constant would make cosmos a living organism since dark variants of elementary particles can have arbitrarily large Compton lengths (they scale as hbar).

Dark matter as a template for the formation of visible structures would reflect itself directly in the physics of visible matter. Bohr rules for planetary orbits is one implication and there is indeed empirical evidence for them.

One can go even further. Accept the generalization of the notion of number obtained by identifying reals and p-adics along common rationals (roughly). Identify correlates of cognition as p-adic space-time sheets. p-Adically smooth space-time sheets contain rational points with arbitrarily large distance from origin and have thus infinite size in the real sense. Therefore our “cognitive bodies”/”thought bubbles” would have size of entire Universe (also in the direction of geometric time).

Also this vision is experimentally testable. p-Adic continuity and smoothness imply via intersection with real space-time sheets p-adic fractality of the real dynamics reflecting itself as long range temporal and spatial correlations and local chaos. The presence of p-adic “thought bubbles” is therefore testable. The fact that p-adic thermodynamics works so well for elementary particle mass calculations supports the view that p-adic cognition is present already at elementary particle level.

Best,

Matti