Annotating the Wall
The following list contains the names of all equations, formulas, and illustrations that are shown on the Wall. The goal is to create a helpful explanation for each element of the list.
- I. Jones polynomial for right trefoil knot; Witten’s path-integral formulation for Jones polynomial using Chern-Simons action
- II. Feynmann Diagram illustrating Associativity equation in Quantum Field Theory
- III. Yang-Baxter equation
- IV. Lorenz Attractor: Lorenz equations with orbit
- V. Diagram of a black hole with Schwarzschild radius
- VI. The five regular polyhedra
- VII. Equiangular spiral drawn in "golden" rectangle (side ratio = golden mean g), ratio of consecutive Fibonacci numbers approaches g, represented by its continued fraction expansion.
- VIII.Babylonian computation of the square root of 2
- IX. Visual proof of the Pythagorean Theorem
- X. Cell decomposition of torus; Euler characteristic; Gauss-Bonnet formula.
- XI. Archimedes: On the Sphere and Cylinder.
- XII. Aharanov-Bohm effect
- XIII.Supergravity Langangian; root diagramm for Lie group E8
- XIV. Navier-Stokes equation with flow around cylinder.
- 0. In Ellipse: (Kepler's 1st law represented by star, ellipse, planet)
- 1. Kepler's 2nd law
- 2. Newton's force-acceleration equation
- 3. Kepler's 3rd law
- 4. Newton's gravitational law
- 5. Einstein's General Relativity equation
- 6. Schrödinger's equation
- 7. Dirac equation
- 8. Atiyah-Singer Theorem
- 9. Yang-Mills equations
- 10. Defining relation of Supersymmetry
- A. Einstein’s mass-energy equation
- B. Maxwell's Equations
- C. Stoke's Theorem
- D. The boundary of a boundary is zero
- E. Heisenberg's indeterminacy relation
- F. Euler's formula for Zeta-function
- G. Interaction between two string; Feynman diagram shows corresponding interaction of particles, here the Compton scattering of a photon off an electron.
Questions by Eric Weinstein
$$F_A$$ is the curvature tensor associated to the connection or vector potential $$A$$.
$$R$$ is a scalar value, describing the "curvature of the spacetime manifold" at each point along the manifold. It's based on a concept of 'parallel transport', where you move a vector around some path on the manifold.
$$R$$ can be computed at each point on the manifold, and describes the difference in the vector's angle after following an infinitesimally small path around the neighborhood of that point, vs. what it was originally. The video does a great job of visualizing when and why that vector angle change would happen, with flat vs. curved manifolds.
In the video, they focus first on the curvature of space. Hopefully they incorporate back in curvature in time, because that's less obvious.
The same video then proceeds to explain $$R_{\mu v}$$. It progresses through some concepts.
We’ve heard Eric talk about Penrose stairs and spinors - essentially phenomena where you cannot return to the original state through a 360 degree rotation, but require a 720 degree rotation.
From theplebistocrat:
Generally, we're wanting to understand how fermions arise from - or are embedded within / upon - topological "spaces" that have distinct rules which govern operations within those topological spaces, and then how those rules produce higher dimensional operations in corresponding spaces.
Just intuitively, and geometrically speaking, the image that I'm getting when describing all of this and trying to hold it in my head is the image of a sort of Penrose Tower of Babel, where the fundamental underlying structures reach upwards (but also downwards and inwards?) before reaching a critical rotation that corresponds to a collapse of structure into a higher dimensional fiber bundle.
But doesn't this require the symmetry break? How is left and right rotation in a subspace transformed into verticality? This is a crazy rabbit hole, friends. Keep your chins up. Let me know if this was helpful or leading astray.