Classical non-determinism in relation to holography, memory and the realization of intentional action in the TGD Universe

Gary Ehlenberg sent a link to an interesting article with title “‘Next-Level’ Chaos Traces the True Limit of Predictability” (see this).

Holography, as it is realized in the TGD framework, allows an interesting point of view to the notion of classical chaos. This view is not considered in the article. In the TGD framework, there is also a close relation to the question about how intentions are realized as actions.

1. Holography reduces the initial data at the fundamental level (space-times as surfaces) roughly by one half and space-time surfaces as orbits of 3-surfaces identified as particle like entities are analogous to Bohr orbits for which only initial positions or momenta can be fixed. This increases predictability dramatically. See (see this and this).
2. Holography= holomorphy principle reduces the extremely nonlinear field equations of TGD to algebraic extensions and one obtains minimal surfaces irrespective of action principle if it is general coordinate invariant and involves only the induced geometry. The space-time surfaces are roots of pairs of polynomials or even analytic functions f= (f₁,f₂) of one hyper complex coordinate and 3 complex coordinates of H=M⁴× CP₂. Field equations are more like rules of logic rather than an axiom system. This implies enormous simplification. Solutions are coded by the Taylor coefficients of f₁ and f₂ in an extension E or rationals and for polynomials their number is finite (see this) and this) .

One obtains new solutions as roots of maps g_º f , where g: C²–>C² is analytic. The iterations of g give rise to the analogs of Mandelbrot fractals and Julia sets so that in this sense classical chaos, or not actually chaos but complexity, emerges. For the iteration of hierarchies P = g_º g …. _º f the complexity increases exponentially since the degree P and the dimension of the corresponding algebraic extension increases exponentially. The roots for the iterates can be however calculated explicitly. The interpretation could be as a classical geometric correlate for an abstraction hierarchy.

This is expected to give rise to a finite classical non-determinism. It would be essential for the quantum realization of conscious memory since small state function reductions (SSFRs) do not destroy the classical information about the previous SSFRs (see this). The information is carried by the loci of classical non-determinism having as a counterpart quantal non-determinism assignable to conscious experience. How could classical non-determinism relate to p-adic non-determinism and to the realization of intentions as transformation of intentions as p-adic space-time surfaces to real space-time surfaces?

1. In adelic physics real and p-adic space-time surfaces are assumed to satisfy essentially the same algebraic field equations. The p-adic and real Taylor coefficients of f=(f₁,f₂) might however relate by canonical identification to guarantee continuous correspondence (see this).

The conjecture is that ramified primes of polynomials (and their generalization) correspond to preferred p-adic primes appearing in p-adic mass calculations and satisfying p-adic length scale hypothesis (see this) and (see this) .

Is it also possible to obtain real solutions with piece-wise constant Taylor coefficients of f? Is it possible to glue together solutions defined by different f? Does this pose additional conditions to the pseudo constants? If so, realizable intentions correspond to p-adic space-time surfaces, which also have real counterparts. Also real space-time surfaced with Taylor coefficients of f which are constant inside a given space-time region but they could change at the interfaces of two regions.

A concrete guess is that the gluing of solutions with different choices of f can take place along light-like surfaces since in classical field theories light-like surfaces are seats of non-determinism. Partonic orbits are such surfaces and wormhole contact could define one possible mechanism of gluing together two Minkowskian space-time sheets defined by different choices f.

The hierarchy of g_º g…g_º f would give exponentially increasing complexity and dimension of extension of rationals if g(0,0)= (0,0) so that also f =0. would define one of the roots. Reflective levels would make it easier to realize the intentions by increasing exponentially the number of roots which are in fact disjoint space-time surfaces. One obtains a disjoint union of space-time surfaces as roots unless f is not a prime in the sense that it does not allow a decomposition f = g_º h. Fundamenta space-time surfaces and intentions would be primes in this sense. For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.