Mathematical Physics

   

CMOSpacetime: Geometric/Algebraic Complex Analysis of Intelligence/Quantum Entanglement/Convergent Evolution

Authors: Yang Zhang

No truth is truly true, the more we reveal the more we revere nature on our voyage of unprecedented discovery. We argue that the soul or anti-soul of Complex Multiscale Orbifold Spacetime (CMOSpacetime) in higher dimensional Non-Euclidean geometry, is the origin of intelligence, and the metric of metrizable intelligence is the sectional curvature's absolute value of CMOSpacetime's soul or anti-soul. We also argue that the intersecting souls and/or anti-souls , when their sectional curvatures approaching positive infinity and/or negative infinity as singularity, is the origin of quantum entanglement. We further argue that the sectional curvatures of CMOSpacetime's intersecting souls and/or anti-souls , is the origin of convergent evolution through conformal transformation. We derive CMOSpacetime, a N-dimensional orbifold $\mathbb{O}=\mathbb{M}/\mathbb{F_g}$ ($\mathbb {M}$ as manifold)/degree N projective algebraic variety $\mathbb X$ over $\mathbb{C}^{N}$ defined by degree N non-linear polynomial function $\mathbb{F_g}(X_1, ..., X_N) = \sum_{i,j=1}^N(w_iX_i^j+b_i)$ in hypercomplex number system with $X = x_1 + \sum_{m=2}^{N}(x_mi_m)$ on Non-Abelian quotient group \begin{math} SO(\frac{N}{2}, \frac{N}{2}) \end{math} (\begin{math} 8 \leq N \to \infty, N = 2^n \end{math}), neural networks by correlating general relativity and quantum mechanics based on mutual extensions from 3+1 dimensional spacetime $\mathbb{R}^{4}$ to N-dimensional CMOSpacetime $\mathbb{C}^{N}$. CMOSpacetime addresses both singularity and non-linearity as common issues faced by physics, AI and biology, and enables curvature-based second order optimization in orbifold-equivalent neural networks beyond gradient-based first order optimization in manifold-approximated a adopted in AI. We build CMOSpacetime theoretical framework based on General equivalence principle, a combination of Poincar\'{e} conjecture, Fermat's last theorem, Galois theory, Hodge conjecture, BSD conjecture, Riemann hypothesis, universal approximation theorem, and soul theorem. We also propose experiments on measuring intelligence of convolutional neural networks and transformers, as well as new ways of conducting Young's double-slit interference experiment. We believe that CMOSpacetime acting as a universal PDE, not only qualitatively and quantitatively tackles the black box puzzle in AI, quantum entanglement and convergent evolution, but also paves the way for CMOSpacetime synthesis to achieve true singularity.

Comments: 12 Pages.

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Submission history

[v1] 2020-03-10 03:32:02

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