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Graph, Wall, Tome (edit)

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=== Prime Directive ===
=== Prime Directive ===
<blockquote style="width: 600px; text-align: center; margin-left: auto; margin-right: auto; font-size: 125%; background: #f3f3ff; border-color: #ddd;">
<blockquote style="width: 600px; text-align: center; margin-left: auto; margin-right: auto; font-size: 125%;>
A request:
A request:


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=== Graph ===
=== Graph ===
The Graph is a paragraph from Edward Witten's 1987 paper [https://cds.cern.ch/record/181783/files/cer-000093203.pdf Physics and Geometry] at the bottom of page 20. In language it concisely encodes the general structure of reality:
The Graph is a paragraph from Edward Witten's 1987 paper [https://cds.cern.ch/record/181783/files/cer-000093203.pdf Physics and Geometry] at the bottom of page 20. In language it concisely encodes the general structure of reality:
<div class="projects-container">
 
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<blockquote style="font-size: 125%;">
<blockquote style="max-width:575px; min-width:300px; font-size: 125%; background: #f3f3ff; border-color: #ddd;">
If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations:
If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations:


(i) Spacetime is a pseudo-Riemannian manifold $$M$$, endowed with a metric tensor and governed by geometrical laws.
(i) Spacetime is a pseudo-Riemannian manifold <math>M</math>, endowed with a metric tensor and governed by geometrical laws.


(ii) Over $$M$$ is a vector bundle $$X$$ with a non-abelian gauge group $$G$$.
(ii) Over <math>M</math> is a vector bundle <math>X</math> with a non-abelian gauge group <math>G</math>.


(iii) Fermions are sections of $$(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}_{-} \otimes V_{\tilde{R}})$$. $$R$$ and $$\tilde{R}$$ are not isomorphic; their failure to be isomorphic explains why the light fermions are light and presumably has its origins in representation difference $$\Delta$$ in some underlying theory.
(iii) Fermions are sections of <math>(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}_{-} \otimes V_{\tilde{R}})</math>. <math>R</math> and <math>\tilde{R}</math> are not isomorphic; their failure to be isomorphic explains why the light fermions are light and presumably has its origins in a representation difference <math>\Delta</math> in some underlying theory.


All of this must be supplemented with the understanding that the geometrical laws obeyed by the metric tensor, the gauge fields, and the fermions are to be interpreted in quantum mechanical terms.
All of this must be supplemented with the understanding that the geometrical laws obeyed by the metric tensor, the gauge fields, and the fermions are to be interpreted in quantum mechanical terms.
</blockquote>
</blockquote>
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    <div class="grid-column" style="display: flex; align-items: center; justify-content: center;">
<div style="text-align: center">
Scan of the original paragraph:
[[File:The-graph.png|class=shadow|650px]]
[[File:The-graph.png|class=shadow|650px]]
    </div>
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Implicit in each respective section is:
Implicit in each respective section is:
# Spin-2 Force Field for Gravity, the Einstein Field Equations
# Spin-2 Force Field for Gravity, the Einstein Field Equations
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=== Wall ===
=== Wall ===
The [http://www.math.stonybrook.edu/~tony/scgp/wall-story/wall-story.html following image] is carved into a wall at Stony Brook University, completed and unveiled in May 2015. It contains many equations and mathematical results that have contributed to the human understanding of reality. In specific relation to the Graph, there are the Einstein Field Equations (item 5), the Yang-Mills Equations (item 9), and the Dirac Equation (item 7).
The image below is [http://www.math.stonybrook.edu/~tony/scgp/wall-story/wall-story.html carved into a wall at Stony Brook University], completed and unveiled in May 2015. It contains many equations and mathematical results that have contributed to the human understanding of reality. In specific relation to the Graph, there are the Einstein Field Equations (item 5), the Yang-Mills Equations (item 9), and the Dirac Equation (item 7).
<div style="text-align: center;">'''[https://dev.theportal.dev/wall/ Click here for an interactive version of the Wall]'''</div>
 
<!-- <div style="text-align: center;">'''[https://dev.theportal.dev/wall/ Click here for an interactive version of the Wall]'''</div> -->


<gallery mode="packed" heights=600px>
<gallery mode="packed" heights=600px>
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* [https://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679776311 The Road to Reality by Sir Roger Penrose]
* [https://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679776311 The Road to Reality by Sir Roger Penrose]


== Related Material ==
== Related Pages ==
* [[Cell decomposition of torus; Euler characteristic; Gauss-Bonnet formula.]]
* [https://twitter.com/EricRWeinstein/status/928296366853328896 Eric's tweets about the Graph]
* [https://twitter.com/EricRWeinstein/status/928296366853328896 Eric's tweets about the Graph]
* [[20: Sir Roger Penrose - Plotting the Twist of Einstein’s Legacy|Roger Penrose on The Portal Podcast]]
* [[20: Sir Roger Penrose - Plotting the Twist of Einstein’s Legacy|Roger Penrose on The Portal Podcast]]
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[[Category:Projects]]
[[Category:Projects]]
[[Category:Requested Project]]
[[Category:Requested Project]]
{{SHORTDESC:A holistic view of math and physics}}
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