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Graph, Wall, Tome: Difference between revisions
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Already in these objects together is enough information to begin a serious study of physics at its most fundamental level and comprehend the deep connections between mathematics and physics. Yet, almost no one knows or seeks them. Further still, as recently as the 1950s we were confused about the structure of the universe: we didn't know the world is left-right asymmetric, as discovered by [https://en.wikipedia.org/wiki/Chien-Shiung_Wu Madame Wu], and we didn't know the [https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect Aharonov-Bohm effect], which demonstrated that the electromagnetic field is less important than the electromagnetic potential. In the mid-1970s as well, Jim Simons and C.N. Yang showed that particle theory is completely geometric. Both of these developments are little known among the public. That the Graph, the Wall, and the Tome and these recent foundational developments are unknown is evidence that something is off in how we communicate science and hand down our knowledge. | Already in these objects together is enough information to begin a serious study of physics at its most fundamental level and comprehend the deep connections between mathematics and physics. Yet, almost no one knows or seeks them. Further still, as recently as the 1950s we were confused about the structure of the universe: we didn't know the world is left-right asymmetric, as discovered by [https://en.wikipedia.org/wiki/Chien-Shiung_Wu Madame Wu], and we didn't know the [https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect Aharonov-Bohm effect], which demonstrated that the electromagnetic field is less important than the electromagnetic potential. In the mid-1970s as well, Jim Simons and C.N. Yang showed that particle theory is completely geometric. Both of these developments are little known among the public. That the Graph, the Wall, and the Tome and these recent foundational developments are unknown is evidence that something is off in how we communicate science and hand down our knowledge. | ||
The aims of Graph, Wall, Tome lie in an extremely focused presentation of its core elements, improving and expanding upon the originals where necessary, to | The aims of Graph, Wall, Tome lie in an extremely focused presentation of its core elements, improving and expanding upon the originals where necessary, to chart the path to learning fundamental physics for as many willing people as can be reached. <!-- It is not an easy road to travel, but it is one extremely rewarding, and it is the one that, in the past 100 years alone, is responsible for the comforts and relative peace we enjoy today. --> | ||
Beyond Graph, Wall, Tome is the '''Search''', the search for a theory of everything. Ventures that may be considered part of the search are String Theory, Loop Quantum Gravity, Garrett Lisi's E8, and [[Eric Weinstein|Eric Weinstein's]] [[Theory of Geometric Unity|Geometric Unity]]. Graph, Wall, Tome can serve as a road to participate in the Search, though it should not be confused for the Search, and the Search should not be confused for it. | Beyond Graph, Wall, Tome is the '''Search''', the search for a theory of everything. Ventures that may be considered part of the search are String Theory, Loop Quantum Gravity, Garrett Lisi's E8, and [[Eric Weinstein|Eric Weinstein's]] [[Theory of Geometric Unity|Geometric Unity]]. Graph, Wall, Tome can serve as a road to participate in the Search, though it should not be confused for the Search, and the Search should not be confused for it. | ||
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=== Prime Directive === | === Prime Directive === | ||
<blockquote style="width: 600px; text-align: center; margin-left: auto; margin-right: auto; font-size: 125%; | <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: | ||
<blockquote style="font-size: 125%;"> | |||
<blockquote style=" | |||
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 | (i) Spacetime is a pseudo-Riemannian manifold <math>M</math>, endowed with a metric tensor and governed by geometrical laws. | ||
(ii) Over | (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 | (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> | ||
<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> | </div> | ||
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 | 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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|publicationdate=9 January 2007 | |publicationdate=9 January 2007 | ||
|pages=1136 | |pages=1136 | ||
| | |isbn13=978-0679776314 | ||
}} | }} | ||
The Tome is ''[[The Road to Reality]]'' by Nobel laureate [[Sir Roger Penrose]], which contains a comprehensive account of the physical universe, as it was understood circa 2007, in 34 chapters spread over 1000 pages with diagrams and equations. For the information contained in the [[Graph, Wall, Tome#Graph|Graph]] and the [[Graph, Wall, Tome#Wall|Wall]], this book | The Tome is ''[[The Road to Reality]]'' by Nobel laureate [[Sir Roger Penrose]], which contains a comprehensive account of the physical universe, as it was understood circa 2007, in 34 chapters spread over 1000 pages with diagrams and equations. For the information contained in the [[Graph, Wall, Tome#Graph|Graph]] and the [[Graph, Wall, Tome#Wall|Wall]], this book serves as an index of concepts to chart a path of learning. It also demonstrates how these concepts can be explained and arranged to encourage productive learning. | ||
* [https://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679776311 Road to Reality by Sir Roger Penrose on Amazon] | * [https://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679776311 Road to Reality by Sir Roger Penrose on Amazon] | ||
The community is reading through the tome and gathering resources on the wiki. | The community is reading through the tome and gathering relevant resources on the wiki. | ||
* [https://discord.gg/3xgrNwJ The Portal Book Club] - We have a weekly group that meets to talk about this book. Come join us in Discord! | * [https://discord.gg/3xgrNwJ The Portal Book Club] - We have a weekly group that meets to talk about this book. Come join us in Discord! | ||
* [[The_Road_to_Reality_Study_Notes|Community study notes]] | * [[The_Road_to_Reality_Study_Notes|Community study notes]] | ||
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|header= | |header= | ||
===Defacing the Wall=== | ===Defacing the Wall=== | ||
|content='''[[Defacing the Wall]]''' - Update and improve the wall so that it is conciliant with fundamental theoretical physics. Remove extraneous information and reorganize to make clear the underlying principles.}} | |content='''[[Defacing the Wall]]''' - Update and improve the wall so that it is conciliant with fundamental theoretical physics. Remove extraneous information and reorganize to make clear the relations between underlying principles.}} | ||
{{GenericBoxWithHeader | {{GenericBoxWithHeader | ||
|header= | |header= | ||
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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 | == 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}} | |||