New Mathematics

As General Physics merges with new companies and integrates with various manufacturing and industrial partners, we seek to formulate new concepts regarding the most fundamental mathematics and physics as it relates to the development of our ethos. Motivating this move, is a metadata tensor product built into calculus or what is a new Riemann zeta function attached to the calculus. It means evolution's punctuated equilibrium, prime numbers in cryptography, bitcoin mining using elliptic functions, Hubble inflation, RJ and KH instabilities, plasma turbulence, financial markets, and complex adaptive systems are all deterministic structures based in a new zeta calculus metadata basis relating uncertainty and volatility to a prime numbered distribution in the zeta. Let's delve into the history.

Calculus emerged in the mid-to-late 17th century as mathematicians and natural philosophers sought tools to handle continuous change, curves, and motion. Sir Isaac Newton developed his method of "fluxions" around 1665–1666 to solve problems in mechanics, viewing quantities as generated by continuous motion (such as a point tracing a curve). Concurrently and independently, Gottfried Wilhelm Leibniz developed differential and integral calculus in the 1670s, introducing notation that emphasized operational rules and algebraic manipulation. While Newton focused on kinematic applications and rates of change, Leibniz focused on geometric tangents and sums of infinitesimal rectangles. Their independent convergence on the Fundamental Theorem of Calculus—bridging the gap between instantaneous rates of change (derivatives) and accumulated totals (integrals)—transformed physics and mathematics from a static geometry into a dynamic science capable of modeling planetary orbits, fluid dynamics, and changing forces. We at General Physics are influenced by the irenical beliefs of Leibniz and want to create new Riemann zeta calculus to modify with metadata the integration and differentiation of dimension.

In the early 19th century, French mathematician Jean-Baptiste Joseph Fourier tackled the physics of heat conduction. In his 1822 treatise Théorie analytique de la chaleur, Fourier asserted that any arbitrary periodic function—no matter how jagged or irregular—could be represented as an infinite sum of simple sine and cosine waves (harmonic oscillations). This proposition was initially met with skepticism by contemporary mathematicians like Joseph-Louis Lagrange and Pierre-Simon Laplace because it challenged classical definitions of functions. However, Fourier’s intuition birthed harmonic analysis. The Fourier transform generalized this concept from periodic functions to non-periodic ones, mapping a function from its original domain (typically time or space) into a frequency domain. This shift from physical space to spectral space became foundational to modern signal processing, quantum mechanics, acoustics, and partial differential equations. At General Physics we want to apply Fourier transforms to the backbone of AI's interconnections to optimize chip architecture. We think in the AI diagrams there is a hidden zeta prime basis. Our wave analysis is also innovative with new Hilbert space filling curves rather than traditional eikonals of the O(2) PDE generating the sines and cosines. We use a space filling curve.

By the turn of the 20th century, physics faced a crisis reconciling James Clerk Maxwell’s equations of electromagnetism with Newtonian mechanics. Albert Einstein resolved this impasse in 1905 with his special theory of relativity. Einstein built his theory on two postulates: the principle of relativity (the laws of physics are the same in all inertial frames of reference) and the constancy of the speed of light in a vacuum for all observers, regardless of their relative motion. By abandoning the Newtonian notions of absolute space and absolute time, special relativity forced a radical restructuring of kinematics. Space and time were no longer independent stages upon which physical events unfolded; they were fused into a single four-dimensional continuum known as spacetime, where measurements of time dilation and length contraction depend entirely on the observer's coordinate system. At General Physics, we describe the interaction quantum in spacetime to delineate the nature of frames of reference as creating such effects as magnetism and turbulence. The zeta imparts the pseudo-randomness in the mathematics.

In the late 1940s, theoretical physics was bogged down by monumental computational bottlenecks in quantum electrodynamics (QED). Calculating the probabilities of particle interactions required evaluating endless, highly complex perturbation expansions. Richard Feynman short-circuited this complexity by introducing a visual, graphical notation. Feynman diagrams translated complex mathematical integrals into topological line drawings where incoming and outgoing particles are represented by lines, and interactions occur at vertices. Crucially, the perturbation expansion in quantum field theory organizes terms into "connected" and "disconnected" diagrams, where connected diagrams represent pure, irreducible multiparticle interactions. By treating graphs as algebraic blueprints, Feynman transformed an arcane, nearly impenetrable calculation method into an intuitive tool that allowed ordinary physicists to compute scattering amplitudes with unprecedented accuracy. Now General Physics applies laws of the Riemann zeta function and Fourier analysis to characterize the patterns in the connected diagram from transistor architecture to particle Standard Model physics.

Underpinning each of these historical breakthroughs is the ecumenical nature of mathematical language. Mathematics operates as a universal, cross-cultural, and cross-disciplinary framework. Its syntax does not depend on natural human languages, local idioms, or political borders; equations written in Tokyo, London, or a satellite in deep space share an identical logical grammar. This translatability allows math to act as an epistemological bridge, transferring concepts seamlessly from mechanics to thermodynamics, and from classical electrodynamics to quantum field theory. The bridge from universal unity to infinite complexity is zeta calculus. Unity from multiplicity is an Enlightenment ideal and we support the belief in prime numbered approaches to determinism.

A primary vehicle for this universality is the concept of coordinates. Whether it is René Descartes’ algebraic grid fixing points in geometric space, Fourier mapping time domains into frequency spectra, Minkowski and Einstein anchoring physical events in a four-dimensional spacetime metric, or Feynman tracing particle paths across abstract interaction spaces, coordinates provide the scaffolding that abstracts raw physical reality into manipulable structures. By turning concrete physical dimensions into abstract mathematical coordinates, scientists gain the power to calculate, predict, and manipulate phenomena far beyond the reach of human intuition.

Let General Physics be your guide as we navigate the new zeta calculus.