In 2000 I wrote my first and only good academic paper on Hodge theory on noncompact manifolds with Daniel Stroock and realize talking to my acquaintance Jeff who is a professor of philosophy that I need tons of references etc. to be taken seriously and realize that my inspired genius is but a spark for a new life. The right path might be to consider fractional differential equations on smooth riemannian manifolds where, like the graph network of the market, is defined intrinsically. Recall that Riemann laid down in 1854 a vision of study of curved spaces by equipping a topological space– a point set where a certain set of subsets are distinguished with some useful mathematical properties called ‘open’ sets, with a ‘riemannian metric’ which amounts to putting a smoothly varying inner product on the ‘tangent space’ abstractly defined for each point of the space. Formal definition of this smoothly varying inner product is called a riemannian metric, often denoted by the letter ‘g’ with a couple of indices ‘g_{ij}$ where indices refer to the matrix components with respect to a basis of the tangent space at a point: T_xM. The Laplace-Beltrami operator is defined in terms of this metric in such a way that integration by parts holds on closed compact manifold M:

<Laplacian(u),u> = < gradient(u), gradient(u)>

We’ve been looking at the Laplacian of a graph but this Laplace-Beltrami operator on a manifold M is quite classical for its study and in a compact manifold it has, like finite dimensional situations a DISCRETE INFINITE set of eigenvalues due to the fact that the Laplacian has a compact self-adjoint resolvent (I – Laplacian)^{-1} which is standard material in functional analysis. Now fractional differential equations of form

D^alpha_t + (-Laplacian)^beta = F

can be studied on manifolds both compact and noncompact, for forms as well as functions. I think this sort of study I can do in the next few months after I get my shit together a bit better — get off the streets, get another laptop, get comfortably settled into Muddy’s without getting thrown out, etc.

Now S4 theory originated with the clear analysis of the heat equation on a noncompact manifold (open infinite static universe) and its impossibility in producing an equilibrium thermal distribution that never dips below 2.7 Kelvin, and my idea is that the material universe is an evolving three dimensional hypersurface. We want, I think, to study FDE of Navier-Stokes type on such manifolds for purely MATHEMATICAL interest in order for us to produce credible steps (to scientists and mathematicians doing detailed work which must be addressed and studied by me in the process) and then try to understand the real basis of why determinisitic models can displace Quantum Mechanics.

Dearest, Quantum Mechanics’ interpretations are all I believe fabricated based on two LINEAR PDE essentially; QM is the only ‘linear theory’ in physics almost. The equations are Paul Dirac’s equation and Erwin Schroedinger’s. These are wave equations which are hyperbolic: the power of d/dt is 2 rather than 1 and written in the form:

on June 17, 2015 at 11:31 am |ReaderYou need a laptop?

How much do you need?

– Let me know. –