Zeta Calculus

Since Leibniz and Newton created calculus, with the help of Jakob Bernoulli and his integral sign, in the latter part of the 17th century, there has been a consistent effort to describe with the first and second spatial derivates, a sort of symmetry-based approach to a physical-mental-mathematical world. Advancements in the endeavor of human thought have led to the description of topological space (Weyl) and conscious neural networks (Turing). General Physics is hard at work describing the nature of reality as topological and connectionist (A.I.'s interpretation is connectionism) rather than strictly Cartesian or Euclidean. This move to describe histories, events, spacetime points etc. as topological and connected means moving beyond the nature of grids to a diagram of points that are weighted and distinguishable with a partition function summation for their ensemble properties. What is interesting about the second derivative (and the culmination of physics with the quadrature) is that the reality of acceleration and force connected to the work-energy theorem is built from a picture of symmetry again. The factor of two is critical, however, the nature of the quadrature is in the binary system and the dual reality of everything. Matter-antimatter, fermion-boson, positive-negative, even-odd, and so forth. One of the only systems that does not fit into the symmetric quadrature picture is the prime numbered index so easily found in the Riemann zeta function expansion.

This leads into the next discussion of how the zeta parameter is part of a logical framework that builds integral calculus with metadata correlated to inflationary and evolutionary points. Such as the Hubble constant determines the rate of expansion, and the inflationary acceleration, the zeta index patterns prime turbulence and a fundamental non-Cartesian and non-spacetime approach to connectionist topology. In essence, the Fourier transform of the connected diagram reduces through row echelon formation into a zeta pattern of primes, a prime basis.

Implications are that the patterns that define the world are a mix of hard determinism and structural physical-mental-mathematics. Astounding as it may seem, the ideas of fractional dimension, scale invariance, and emergence, are parts of a system that requires new metadata correlated zeta prime indices on the fundamental integration constant of calculus. Thus, the nature of mathematics becomes physical. Relating the nature of points to other points is done through the second derivative, however, the corresponding coefficients are based in a prime numbered zeta from a new calculus (interior and exterior). To describe the nature of calculus requires a mathematical uniqueness theorem which is again self-referential and based in an evolutionary and inflationary cycle that could be repeating according to Sakharov's rule's for cyclic universal models. I am hesitant to recall Andrei Sakharov, but the work is undoubtedly interesting and political. The repeating nature of things is a social outgrowth, a mental outgrowth, of the ideology of Marx and Lenin. Their concepts harken an equivalence and equilibrium of all things. Politics influences math and math influences politics. The social Darwinism of modern societies in the pay to play arena have a more fractional dimensional mathematics. The points are not all the same.

Nobel prize winner Murrary Gell-Mann, who theorized about quarks, likened all the particles in the jungle as different and uniquely distinguishable. No point in spacetime is like the one previous. Here a Fourier transform would be of the points and their defining characteristics, based in a deterministic zeta prime pattern from the Riemann function. The inspiration was the California condor, from afar appearing alike, from up close completely distinguishable.

Zeta function forms tacked on to the calculus will create a metadata approach to the inflationary model, to the evolutionary model, to biological systems, and ecologies. It describes the complexity of systems, and the nature of reality as built from a physical turbulent and chaotic world. General Physics is a few years into its work in advanced manufacturing, mathematical modeling of markets, and simulation of complex adaptive systems. From plasma physics to advanced shipbuilding (new magnetic coupling propulsion) we are looking to pave the wave from incremental growth and progress, between nodes of prime numbered zeta indices. Although there is a fear of determinism, the spacing of prime numbers determines a pseudo-random patterning that allows for accurate prediction of events with minimal error.

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