Difference between revisions of "Annotating the Wall"

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<gallery mode="packed" heights=400px>
File:Newwall.png|center|class=shadow|400px|The Wall
File:Key-to-wall.png|center|class=shadow|400px|Explanations for the Wall
</gallery>


* A [https://dev.theportal.dev/wall/ High Resolution Interactive Version of the Wall] has been created


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.
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; [https://theportal.wiki/wiki/Jones_polynomial Witten’s path-integral formulation] for Jones polynomial using Chern-Simons action
*I.  [[Jones polynomial]] for right trefoil knot; [https://theportal.wiki/wiki/Jones_polynomial Witten’s path-integral formulation] for Jones polynomial using Chern-Simons action
*II.  [[Feynmann Diagram]] illustrating [[Associativity]] equation in [[Quantum Field Theory]]  
*II.  [[Feynman Diagram]] illustrating associativity equation in [[Quantum Field Theory]]  
*III. [[Yang-Baxter equation]]
*III. [[Yang-Baxter equation]]
*IV.  [[Lorenz Attractor]]: Lorenz equations with orbit
*IV.  [[Lorenz Attractor]]: Lorenz equations with orbit
*V.  Diagram of a black hole with [[Schwarzschild radius]]
*V.  Diagram of a black hole with [[Schwarzschild radius]]
*VI.  The five [[regular polyhedra]]
*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.
*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]]
*VIII.[[Babylonian computation of the square root of 2]]
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*X.  [[Cell decomposition of torus; Euler characteristic; Gauss-Bonnet formula.]]
*X.  [[Cell decomposition of torus; Euler characteristic; Gauss-Bonnet formula.]]
*XI.  Archimedes: [[On the Sphere and Cylinder]].
*XI.  Archimedes: [[On the Sphere and Cylinder]].
*XII. [[Aharanov-Bohm effect]]
*XII. [[Aharanov-Bohm Effect]]
*XIII.[[Supergravity Langangian]]; root diagramm for [[Lie group E8]]
*XIII.[https://en.wikipedia.org/wiki/Supergravity Supergravity] Langangian; root diagram for [[Lie group E8|Lie Group E8]]
*XIV. [[Navier-Stokes equation]] with flow around cylinder.
*XIV. [[Navier-Stokes equation]] with flow around cylinder.


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*E. [[Heisenberg's indeterminacy relation]]
*E. [[Heisenberg's indeterminacy relation]]
*F. [[Euler's formula for Zeta-function]]
*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.
*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 ==
<div class="toccolours mw-collapsible mw-collapsed" style="width:400px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">What is $$F_A$$ geometrically?</div>
<div class="mw-collapsible-content">
$$F_A$$ is the curvature tensor associated to the connection or vector potential $$A$$.
</div></div>
<div class="toccolours mw-collapsible mw-collapsed" style="width:400px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">What are $$R_{\mu v}$$ and $$R$$ geometrically?</div>
<div class="mw-collapsible-content">
[https://www.youtube.com/watch?v=UfThVvBWZxM&t=12m6s Explanation of $$R$$]
$$R$$ 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.
</div></div>
<div class="toccolours mw-collapsible mw-collapsed" style="width:400px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">How do they relate?</div>
<div class="mw-collapsible-content">
[https://en.wikipedia.org/wiki/Cohomology Cohomology]
</div></div>
<div class="toccolours mw-collapsible mw-collapsed" style="width:400px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">What does this have to do with Penrose Stairs?</div>
<div class="mw-collapsible-content">
* [https://en.wikipedia.org/wiki/Penrose_stairs Penrose stairs]
* [https://en.wikipedia.org/wiki/Spinor Spinor]
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.
</div></div>
<div class="toccolours mw-collapsible mw-collapsed" style="width:400px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">What are “Horizontal Subspaces” and what do they have to do with Vector Potentials or Gauge fields?</div>
<div class="mw-collapsible-content">
* [https://en.wikipedia.org/wiki/Vertical_and_horizontal_bundles Vertical and horizontal bundles]
* [https://en.wikipedia.org/wiki/Introduction_to_gauge_theory Introduction to gauge theory]
* [https://en.wikipedia.org/wiki/Symmetry_(physics) Symmetry]
From '''theplebistocrat''':
<blockquote>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.
</blockquote>
</div></div>


== Further Resources ==
== Further Resources ==
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* [https://www.youtube.com/playlist?list=PL5TiDYF_g45CyK7w7ZXH24FiuASYes2VO Youtube playlist with helpful videos]
* [https://www.youtube.com/playlist?list=PL5TiDYF_g45CyK7w7ZXH24FiuASYes2VO Youtube playlist with helpful videos]
* [http://scgp.stonybrook.edu/archives/6264 List of elements on the Wall at Stony Brook]
* [http://scgp.stonybrook.edu/archives/6264 List of elements on the Wall at Stony Brook]
[[Category:Graph, Wall, Tome]]
[[Category:Projects]]
[[Category:Archive]]

Latest revision as of 00:27, 20 October 2022

  • The Wall

  • Explanations for 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.




Further Resources

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