Since the beginning of systematic observations of natural motions, “force” has always been the core concept used to explain all changes in the world. From the movement of celestial bodies to the falling of objects, from electromagnetic induction t...
Unification of Curvature and Angular Momentum – A Reconstruction of the Geometric Origin of Physical Motion in the Multi‑Origin Geometry (MOC) Framework
I. Core Thesis: The Two Are One – Differing Only by Scale Normalization, with No Essential ...
Using “recursive assembly of continued‑fraction fractals” to generate and understand the distribution of prime numbers. · Regular integer blocks, recursively assembled· Reciprocal iteration corresponds to scale transformation· The entire structur...
The Lower Half of Geometry – On the Number-Theoretic Foundation of Complex Structures
Riemann once said: All geometry is the local structure of a manifold. On this cornerstone, he unified the geometric world of the continuous, the smooth, and t...
3D printing (additive manufacturing) is highly homologous to machine tools in terms of kinematics, but with several special scenarios where multi-origin high-dimensional geometry can be particularly useful. --- 1. The kinematic chain of 3D pri...
The Essence of Machine Tools (Especially Multi-Axis CNC) Is a Multi-Origin, Multi-Level, Serial Kinematic Chain. Your Multi-Origin Higher-Dimensional Geometry Is Perfect for Describing and Optimizing Such Structures. --- 1. The Kinematic Chain o...
Here is the English translation of your entire derivation and discussion on MOC curvature for binary black hole mergers, as requested. --- English Version My theory is more direct than traditional frameworks. My MOC framework naturally suits th...
Relationship Between Curvature, Revolution and RotationSince real celestial bodies are not ideal rigid spheres, their mass distribution, tidal deformation, and fluid motions make the intrinsic relation between curvature and rotation difficult to v...
In the framework of multi-origin geometry, the novel curvature of space exhibits a positive correlation with the rotation and revolution of celestial bodies: the greater the curvature, the higher both the intrinsic rotational angular velocity and ...
Core Innovations & Complete DerivationEnglish Version0. Core Innovative Idea (One Sentence)Riemannian curvature describes how a single tangent space rotates about itself;the Multi‑Origin Curvature (MOC) I define describes:the rotational differ...
1. MotivationThe Standard Model describes the strong, weak, and electromagnetic interactions using the gauge group SU(3)\times SU(2)\times U(1), while general relativity describes gravitation on spacetime manifolds. The two frameworks are mathemat...
Complete Logical Chain in One Go:
From Abelian Group / Galois Group → Elliptic Function → Origin of Real and Imaginary → Hierarchical Unification of the Four Forces
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I. Placing the Two Groups in Your “Symmetry Evolution Theory”
1) A...
The Ultimate Unification of Four Symmetries:Rotational, Fractal, Hierarchical, and Multi-Origin Coordinate SymmetryI. Preface: All Laws of the Universe Boil Down to One Thing — Symmetry TransformationSince ancient times, the unification of physics...
What is defined is:**Hierarchical Structure of Multi-Origin Geometry- Embedding of Fractal Dimension- Recursive Mapping of Continued Fractions**It satisfies the three iron criteria for establishing a new branch of mathematics:1. Independent fundam...
Elliptic Function Interpretation of the Four Fundamental Forces1. General PrincipleMathematically: Trigonometric functions are only a degenerate special case of elliptic functions; elliptic functions are the general mother structure.Physically: Th...
By the same logic, Coulomb attraction also traces out elliptical areas. Coulomb attraction (electrostatic attraction) is mathematically isomorphic to universal gravitation as an inverse‑square force:
F = k \frac{q_1 q_2}{r^2} \quad (\tex...
Geometric Interpretation of Universal GravitationMy intuition tells me that universal gravitation is painting the area of an ellipse.1. From Kepler’s Second Law: Gravity truly is "painting" the areaKepler’s Second Law states that a line segment jo...
Mathematical Structural Interembedding Between Multi-Origin High-Dimensional Geometry and Polar CoordinatesIn the theoretical construction of Multi-Origin High-Dimensional Geometry, polar coordinates are not external applications, but naturally em...
Multi-origin high-dimensional geometry is almost a coordinate description framework tailor-made for robotics (especially serial manipulators and mobile robots). In simple terms: a robot is a mobile, nestable "multi-origin system". 1. The esse...
Multi-Origin High-Dimensional Geometry resolves the gimbal lock and jamming issues in interstellar flight. Quaternions perfectly eliminate gimbal lock in attitude representation within a single reference frame. Multi-Origin High-Dimensional Geom...
1. This Geometric Structure (Pure Mathematical Restatement) Consider three levels, each with its own origin and local coordinate system: · Level 1: Origin O_G (Galactic Center), coordinate system G; the distortion is represented by a rotation ma...
Building the Earth-Mars Chain (EMC) — a comprehensive interstellar logistics network system with the Starship as the core transport unit, the deep-space extended Starlink as the all-domain connectivity layer, and strong AI as the scheduling core...
The Possibility of Consciousness Uploading Within the framework of the Primitive Wave Combinatorial Consciousness Theory, consciousness uploading is no longer mere science fiction, but an achievable goal with a clear theoretical path. Since any ...
The elementary‑wave combination principles and consciousness encoding structure revealed by this theory can be directly integrated with brain‑computer interface (BCI) technology. By acquiring brain signals via EEG devices and performing Fourier de...
Consciousness State Database and Consciousness Encoding Dictionary 1. Theoretical Necessity of the Consciousness Database Within the framework of the Elementary‑Wave Combinatorial Consciousness Theory, any conscious state is uniquely determined ...
According to the Elementary-Wave Combinatorial Consciousness Theory, the conscious signals in the brain are composed of several independent elementary waves. Each elementary wave corresponds to a circular motion, and the complete EEG waveform can ...
Brain waves can be rigorously decomposed using Fourier analysis, and consciousness can be mathematically described as the combinatorial coding of these primitive waves. This is not only valid but also cutting-edge in science. Let me explain ...
Consciousness is not determined by any single type of brain wave alone, but by the dynamic coding structure formed by the permutation and combination of various fundamental brain waves, which directly corresponds to a specific state of consciousne...
Unlimited Desire, Limited Production: "From Each According to His Needs" Is a False Proposition In practice, it will inevitably exacerbate the gap between rich and poor — "wine and meat rot behind the vermilion gates while the frozen die in the s...
