Graph, Wall, Tome: Difference between revisions

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== Background ==
{{InfoboxProject
|project=Graph, Wall, Tome
|image=[[File:Ascending and Descending.jpg]]
|topic=Graph, Wall, Tome
|leader=[https://twitter.com/AardvarkLaurant Aardvark (Aardvark#5610)]<br>[https://twitter.com/Tim_Melon Tim (TimFH#7940)]
|startdate=27 January 2020
|customlabel1=<!-- Placeholder -->
|customdata1=<!-- Placeholder -->
|customlabel2=Google Drive
|customdata2=[https://drive.google.com/drive/folders/1706CBEJQEMppV60OU8OtcXxicluk2T3Y?usp=sharing Drive]
|customlabel3=Master Planning
|customdata3=[https://docs.google.com/document/d/1t9AvvFZzODw1WiGRZwRsFFZdPdBzYVJGLHiqWNrMtIA/edit?usp=sharing Doc]
|customlabel4=Reference Material
|customdata4=[https://docs.google.com/document/d/18rN-zfv41xeH3WFNOrZNb7Clz-yu1dgulP4bcEPKbcY/edit?usp=sharing Doc]
|link1title=Website
|link1=[https://graphwalltome.com/ Homepage]
|link2title=<!-- Projects Page -->
|link2=<!-- Projects Page Link -->
|link3title=
|link3=
|link4title=Discord
|link4=[https://discord.gg/Z3u3pPm Invite]
}}


'''Imagine:''' It's 1915, and you've made one of the greatest discoveries in hundreds of years. You visit your mother and show her your work:
The knowledge of fundamental physics and the mathematics necessary to perform and understand it are known to few, maybe some tens of thousands of people at most, and commitment to reach those levels entails almost a decade of graduate and post-graduate study. Yet what if it was all much easier and much harder to understand? What if the necessary knowledge was finite and more rapidly attainable to a broader population than those select few? What if there was a way to identify and abstract the most basic physical structures, a list of all the tools to build and operate on those structures, and a user's guide to describe how to use those tools?


The '''Graph, Wall, Tome''' project demonstrates that these resources exist and already cover much of the necessary ground, but also that they are still flawed and need refinement. Edward Witten, perhaps the most intelligent living physicist, wrote a [[#Graph|paragraph]] in 1987 (from his address at the International Congress of Mathematicians, Berkeley, August 1986) that linguistically encodes and abstracts the most basic structures underlying physics, such that their function can still be understood even if the particular underlying equation may change. This is the '''Graph'''. Jim Simons, billionaire physicist, commissioned the [[#Wall|iconic Wall at State University of New York Stony Brook]] which has inscribed upon it the equations of what Witten says in addition to some of history's most important mathematical and physical results. This is the '''Wall'''. [[Sir Roger Penrose]], Nobel laureate and intellectual descendant of Albert Einstein’s school of geometric physics, wrote a book titled [[#Tome|''The Road to Reality'']], which describes and summarizes how to use the mathematics and physics contained within the Wall and the Graph. This is the '''Tome'''.


$$R_{\mu v}-\frac{1}{2}Rg_{\mu v} = 8 \pi T_{\mu v}$$
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 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. -->


'That's nice dear', she responds, unaware of the implications of your discovery.
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.


The problem, is that although this equation carries with it the secrets of gravity, to a layman it is merely a bunch of letters and symbols.
__TOC__


Now, consider this single image.
=== Prime Directive ===
<blockquote style="width: 600px; text-align: center; margin-left: auto; margin-right: auto; font-size: 125%;>
A request:


Try to draw the lines through the three. View it as a unified idea:


[[File:sheetsunx.gif||Curved Space-Time]]
The Paragraph gets edited,


Instantly, the meaning becomes clear. Gravity warps space(time), and matter, planets, and even light follows a path that is curved by the warped geometry.
The Wall gets defaced and graffitied,


Fundamental physics is an unknown world to most people. Equations, symbols, and incomprehensible terms abound, and unless you've studied post-grad mathematics and physics, this world is inaccessible to you.
The Sacred Tome gets rewritten.


Although there are several great resources to map the way toward complete understanding. Most people will not undertake the journey to understand the source code to the world that we all inhabit.
But follow the skeins through each.


== The GWT Project ==
The Graph points to the Wall,


Bringing an understanding of fundamental physics is one aim of The Portal.
And the Wall to the Tome,


There currently exist 3 resources that themselves contain all that you need for an almost complete understanding of the world.
And the Tome leads to the Search.
</blockquote>


# '''The Graph''' - A paragraph written by Edward Witten
=== Graph ===
# '''The Wall''' - The iconic wall of Stony Brook University
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 Tome''' - The book 'The Road to Reality' by Roger Penrose


These resources are available to everyone, but will be sought by almost none. The aim of the GWT project to convert these resources into a medium that can be widely disseminated, and which can not be ignored.
<blockquote style="font-size: 125%;">
If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations:


This project will require bi-directional information transfer, and the minds of people with many different aptitudes.
(i) Spacetime is a pseudo-Riemannian manifold <math>M</math>, endowed with a metric tensor and governed by geometrical laws.


* We need mathematicians, topologists, geometers, and physicists to understand these resources, and all of their implications.
(ii) Over <math>M</math> is a vector bundle <math>X</math> with a non-abelian gauge group <math>G</math>.
* We need explainers and educators, to convey this information to a wider audience, and
* We need artists, linguists, and programmers to create intuitive visualisations.


The Portal will create a community of people, working together to that achieve these aims.  
(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 representation difference <math>\Delta</math> in some underlying theory.


Success will generate yet further insights, opening up a more fundamental understanding of the nature of reality - for the individuals involved, and - for humanity as a whole.
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.
 
 
 
This was first collected in a Google Doc titled [https://docs.google.com/document/d/1Bo5ny0UyC8gEHiAaDR2Al2OSGscUWPS8NFI-hvB1z4o/edit?pli=1 Graph, Wall, Tome - Problem Solving].
 
== The Graph ==
 
<blockquote>
If one wants to summarise our knowledge of physics in the briefest possible terms, there are three really fundamental observations:
 
# [https://en.wikipedia.org/wiki/Spacetime Spacetime] is a [https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold pseudo-Riemannian manifold] M, endowed with a [https://en.wikipedia.org/wiki/Metric_tensor metric tensor] and governed by [https://en.wikipedia.org/wiki/Geometry geometrical laws].
# Over M is a [https://en.wikipedia.org/wiki/Principal_bundle principal bundle] $$P_{G}$$ with a [https://en.wikipedia.org/wiki/Non-abelian_group non-abelian structure group] G.
# [https://en.wikipedia.org/wiki/Fermion Fermions] are sections of $$(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}\_ \otimes V_{\bar{R}})$$. $$R$$ and $$\bar{R}$$ are not [https://en.wikipedia.org/wiki/Isomorphism isomorphic]; their failure to be isomorphic explains why the light fermions are light.
# Add something about Higgs
 
All of this must be supplemented with the understanding that the geometrical laws obeyed by the metric tensor, the [https://en.wikipedia.org/wiki/Introduction_to_gauge_theory gauge fields], and the fermions are to be interpreted in [https://en.wikipedia.org/wiki/Quantum_mechanics quantum mechanical] terms.
</blockquote>
</blockquote>


=== Origin ===
<div style="text-align: center">
This is a modified version of the paragraph by Edward Witten as [https://twitter.com/EricRWeinstein/status/928296366853328896?s=20 posted by Eric via Twitter].
Scan of the original paragraph:
 
[[File:The-graph.png|class=shadow|650px]]
[[file:The-graph.png|600px]]
</div>
 
Eric Weinstein suggested several alterations, that have been included above:
 
* In (ii), “vector bundle X” should be changed to principal G-bundle.
* Also in (ii), “nonabelian gauge group G” should be changed to nonabelian structure group G.
* In (iii), <math>\ R</math> and <math>\tilde R</math> should be (complex) linear representations of G and so they are not equivalent.
* He mentioned that some info was not required, and that higgs is remarkably absent.
 
== The Wall ==
 
[[File:The-wall.png|right|class=shadow|400px]]
 
This [http://www.math.stonybrook.edu/~tony/scgp/wall-story/wall-story.html image is carved into a wall at Stony Brook University]. It contains many of the most fundamental equations of physics, providing a formulaic representation of all reality.
 
Several of the equations have been identified as having direct connections to statements in 'The Graph' (identified by numbers)
 
=== Equations ===
 
'''1: Einstein's General Relativity equation:'''
: $$R_{\mu v}-\frac{1}{2}Rg_{\mu v} = 8 \pi T_{\mu v}$$
 
'''2: Maxwell's equations:'''
: $$\nabla \times \mathbf{B} = \frac{1}{c} \frac{\partial \mathbf{E}}{\partial t}$$
: $$\nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \mathbf{B}}{\partial t}$$
: $$\nabla \cdot \mathbf{B} = 0$$
: $$\nabla \cdot \mathbf{E} = 0$$
 
'''2: Yang-Mills equations:'''
: $$d^*_A F_A \propto J$$
 
'''3: Dirac equation''':
: $$(i \not{D}_A - m)\psi = 0$$
 
'''4: Klein-Gordon equation:''' (this is not included in 'The Wall', but it has been suggested that perhaps it should have been)
: $$\frac{1}{c^2} \frac{\partial^2}{\partial t^2} \psi - \nabla^2 \psi + \frac{m^2 c^2}{\hbar^2} \psi = 0$$
 
Einstein's mass-energy equation:
: $$E = mc^2$$
 
Kepler's 2nd law:
: $$\frac{d\theta}{dt} \propto \frac{1}{r^2}$$
 
Newton's force-acceleration equation:
: $$\mathbf{F} = m\mathbf{a}$$
 
Kepler's 3rd law:
: $$T^2 \propto a^3$$
 
Newton's gravitational law:
: $$F = \frac{G m_1 m_2}{r^2}$$
 
Schrödinger's equation:
: $$i \hbar \frac{\partial \psi}{\partial t} = - \frac{\hbar^2)}{2 m} \nabla^2 \psi + V \psi$$
 
Atiyah-Singer theorem:
: $$dim\, ker \not{D}_E - dim \, coker \not{D}_E = \int_M \hat{A}(M) \cdot ch(E)$$
 
Defining relation of supersymmetry:
: $$\{Q,Q\} = P$$
 
Stokes' theorem:
: $$\int_M d\omega = \int_{\partial M}\omega$$
 
The boundary of a boundary is zero:
: $$\partial\partial = 0$$
 
Heisenberg's indeterminacy relation:
: $$\Delta x \Delta p \geq \frac{\hbar}{2}$$
 
Euler's formula for Zeta-function:
: $$\sum\limits_{n=1}^{\infty} \frac{1}{n^{s}} =  \prod\limits_{p} \frac{1}{1 - \frac{1}{p^s}}$$
 
 
Eric talked about some of the important equations on the wall. There are 2 different recorded versions of the conversation if you want to listen to it.
 
== The Tome ==


[[File:The-tome.png|right|class=shadow|250px]]
Implicit in each respective section is:
# Spin-2 Force Field for Gravity, the Einstein Field Equations
# Spin-1 Vector Boson Theory, Yang-Mills-Maxwell Equations
# Spin-1/2 Matter Theory, Dirac Equation


This book by Roger Penrose constains a comprehensive account of the physical universe.  
These are the gauge fields referred to by the last sentence.


To gain an understanding and intuition for the information contained in 'The Graph', and 'The Wall', reading this book will provide a great head-start.
Note that the quantum (e.g. quantum mechanics, quantum field theory, quantum measurement, etc...) is mentioned only after the key geometric insights.


With 34 chapters spread over 1000 pages, including diagrams, equations, and descriptions, there are multiple avenues for understanding all concepts.
=== 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).
<div style="text-align: center;">'''[https://dev.theportal.dev/wall/ Click here for an interactive version of the Wall]'''</div>


=== Book Details ===  
<gallery mode="packed" heights=600px>
File:Newwall.png|center|class=shadow|400px|The Wall
File:Key-to-wall.png|center|class=shadow|800px|Legend
</gallery>


* ISBN: 978-0679776314
=== Tome ===
* [https://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679776311 Road to Reality by Roger Penrose (2004)]
{{InfoboxBook
* There appears to be a [https://www.amazon.com/Road-Reality-Complete-Guide-Universe-ebook/dp/B01BS7NTA6 Kindle Edition] that isn't available in the US. If anyone in the community has a way to get a Kindle version of the book, please add it here.
|title=The Road to Reality
* Purchase the book somehow, then get the [https://www.academia.edu/351112/The_Road_to_Reality_Sir_Roger_Penrose pdf here]
|image=[[File:The-tome.png|150px]]
|author=[[Sir Roger Penrose]]
|language=English
|genre=Physics
|publisher=Vintage
|publicationdate=9 January 2007
|pages=1136
|isbn13=978-0679776314
}}


== Methodology ==
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]


* Create/assemble resources that allow uninitiated to quickly and easily get up to speed with state of project.
The community is reading through the tome and gathering relevant resources on the wiki.
* Create/assemble resources that provide analogies for more complex principles - to demonstrate a key feature of the principle.
* [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!
* Create/assemble resources that provide a geometric intuition for the equations of fundamental physics - Geometric interpretations are most amenable to being visually represented.
* [[The_Road_to_Reality_Study_Notes|Community study notes]]
* Create/assemble resources that allow the geometric visualisation/intuition for principles of foundational physics.
* [[The Road to Reality|Reference material by chapter]]
* Rinse and repeat.


=== Project Files ===  
== Core Sub-projects ==
The essence of Graph, Wall, Tome is viewing each as part of a singular idea. What content is common among them is what should be expanded, and their unique content should be promoted if it is a part of fundamental physics toolkit, or removed if it isn't.
=== Graph-Wall-Tome Connection ===
* [[Decoding the Graph-Wall-Tome Connection]] - What are the common themes that appear in the Graph, the Wall, and the Tome? What do they point to?


A working area for the project is located in a [https://drive.google.com/drive/folders/1yPZHTNy47jUpmD-RMRCVtitfD-gQBRhP google drive].
<div class="projects-container">
{{GenericBoxWithHeader
|header=
===Editing the Graph===
|content='''[[Editing the Graph]]''' - Though the original Graph aptly summarizes our physical knowledge, there are some minor alterations and additions to be made in order for it to accurately capture current physics.}}
{{GenericBoxWithHeader
|header=
===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 relations between underlying principles.}}
{{GenericBoxWithHeader
|header=
===Rewriting the Tome===
|content='''[[Rewriting the Tome]]''' - For everything that is in the new Graph and Wall, write their elaboration and explanation. Received wisdom does not need to be accepted wholesale, the original Tome is a good example but not the ideal solution.}}
</div>


It includes a [https://docs.google.com/document/d/1sB_LTltdq8J6mIKyPRaHQWKEuLk0ZXuwYQZb78BnNuk/edit?usp=sharing list of tasks] that can be worked on by individuals or groups of individuals. (add a comment to let people know if you're working on something)
=== Resources ===
* [https://docs.google.com/document/d/1t9AvvFZzODw1WiGRZwRsFFZdPdBzYVJGLHiqWNrMtIA/edit?usp=sharing Master Planning Doc]
* [https://drive.google.com/drive/folders/1706CBEJQEMppV60OU8OtcXxicluk2T3Y?usp=sharing Drive Folder]
* [https://docs.google.com/document/d/18rN-zfv41xeH3WFNOrZNb7Clz-yu1dgulP4bcEPKbcY/edit?usp=sharing List of Reference Material]


This file also has an area to list specific areas of aptitude or interest.
== Other Sub-projects ==
* [[The Road to Reality Study Notes|Studying the Tome]] - The Tome can be intimidating. This problem can be solved 1) by creating resources that make it easier to digest its content and 2) by going through the chapters together.
* [[Holonomy Project]] (Stalled) - The goal is to create visualizations for the effect known as "holonomy", whereby parallel transporting a vector around a loop in a curved space leads to the vector changing upon returning to the start of the loop. How the vector changes orientation/position in space is the holonomy of that loop in that space. This effect reveals deep information about the curvature of the space itself.


== Accelerators ==
== Archived Sub-projects ==
* [[Climbing the Cliff]] (Archived) - Create a learning guide through ''The Road to Reality''.
* [[Deface the Wall]] (Completed) - Cam and boqu made a new wall that's interactive.
* [[Geometry|Geometry Project]] (Archived) - The aim is to create and collect resources related to Frederic P. Schuller's lecture series titled "Lectures on Geometrical Anatomy of Theoretical Physics" that provides a great introduction to geometrical concepts that are essential for the Graph, Wall, Tome project.
* [[Interactive Wall]] (Completed) - Demp and boqu made a wall that you can pan and zoom and click on! It also pulls information from the wiki based on what is in view.


[[Accelerators:|Accelerators: 2 minute guides to fundamental principles.]]
== Reference ==
* [https://cds.cern.ch/record/181783/files/cer-000093203.pdf Physics & Geometry by Ed Witten]
* [http://www.math.stonybrook.edu/~tony/scgp/wall-story/wall-story.html The Wall at the Simons Center for Geometry and Physics, Stony Brook University]
* [https://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679776311 The Road to Reality by Sir Roger Penrose]


== Resources &amp; References ==
== Related Material ==
* [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]]
* [[15: Garrett Lisi - My Arch-nemesis, Myself|Garrett Lisi on The Portal Podcast]]
* [[14: London Tsai - The Reclusive Dean of The New Escherians|London Tsai on The Portal Podcast]]
* [[A Portal Special Presentation- Geometric Unity: A First Look|Geometric Unity First Presentation]]
* [[Theory of Geometric Unity]]
* [https://www.youtube.com/watch?v=o2nG7-eXxko Eric on the Lex Fridman Podcast 134]
* [https://www.youtube.com/watch?v=rIAZJNe7YtE Eric on the Lex Fridman Podcast 88]
* [https://www.youtube.com/watch?v=wf0_nMaQ6tA Eric on JRE 1453]
* [https://www.youtube.com/watch?v=_EWCN3CPhTI Eric on JRE 1320]
* [https://www.youtube.com/watch?v=X9JLij1obHY Eric on JRE 1203]
* [https://www.youtube.com/watch?v=CJx3gLkebIA Theories of Everything on PBS Space Time]
* [https://www.youtube.com/watch?v=OI0AZ4Y4Ip4 Eric and Stephen Wolfram with Brian Keating on Into the Impossible]
* [https://www.youtube.com/watch?v=YjsPb3kBGnk Eric on Into the Impossible]
* [https://youtu.be/57SMQj3lOm0?t=4376 Into the Impossible – Sir Roger Penrose: Conformal Cyclic Cosmology, Black Holes Nobel Prize w/ Eric Weinstein Janna Levin]
* [https://www.youtube.com/watch?v=DvPvFDF9dAE Into the Impossible - Eric Weinstein: Imposter Syndrome, Donald Trump, & the Future of Theoretical Physics]
[[Category:Graph, Wall, Tome]]
[[Category:Projects]]
[[Category:Requested Project]]


* [https://drive.google.com/open?id=1sB_LTltdq8J6mIKyPRaHQWKEuLk0ZXuwYQZb78BnNuk Working folder for Projects]
{{SHORTDESC:A holistic view of math and physics}}
* [https://www.dropbox.com/s/xdickldblj574mf/eric%20wall%20-%20tome%20-%20graph.m4a?dl=0| Recording of original call w/ Eric]
* [https://www.youtube.com/playlist?list=PL5TiDYF_g45BA3abSyNl7M4pFzihZdoHT| Conversations with Eric on The Portal Discord Server]
* [https://www.youtube.com/playlist?list=PL5TiDYF_g45Az5qgAP5Lj8Y3qKPSib1eP| Misc recordings on The Portal Server for project and other notable conversations]
* <span class="highlight">[[Eric’s Most Important Set of Books]]<span>

Latest revision as of 14:48, 20 February 2023

Graph, Wall, Tome
Ascending and Descending.jpg
Information
Topic Graph, Wall, Tome
Leader Aardvark (Aardvark#5610)
Tim (TimFH#7940)
Start Date 27 January 2020
Google Drive Drive
Master Planning Doc
Reference Material Doc
Links
Website Homepage
Discord Invite
All Projects

The knowledge of fundamental physics and the mathematics necessary to perform and understand it are known to few, maybe some tens of thousands of people at most, and commitment to reach those levels entails almost a decade of graduate and post-graduate study. Yet what if it was all much easier and much harder to understand? What if the necessary knowledge was finite and more rapidly attainable to a broader population than those select few? What if there was a way to identify and abstract the most basic physical structures, a list of all the tools to build and operate on those structures, and a user's guide to describe how to use those tools?

The Graph, Wall, Tome project demonstrates that these resources exist and already cover much of the necessary ground, but also that they are still flawed and need refinement. Edward Witten, perhaps the most intelligent living physicist, wrote a paragraph in 1987 (from his address at the International Congress of Mathematicians, Berkeley, August 1986) that linguistically encodes and abstracts the most basic structures underlying physics, such that their function can still be understood even if the particular underlying equation may change. This is the Graph. Jim Simons, billionaire physicist, commissioned the iconic Wall at State University of New York Stony Brook which has inscribed upon it the equations of what Witten says in addition to some of history's most important mathematical and physical results. This is the Wall. Sir Roger Penrose, Nobel laureate and intellectual descendant of Albert Einstein’s school of geometric physics, wrote a book titled The Road to Reality, which describes and summarizes how to use the mathematics and physics contained within the Wall and the Graph. This is the Tome.

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 Madame Wu, and we didn't know the 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 chart the path to learning fundamental physics for as many willing people as can be reached.

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's 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.

Prime Directive[edit]

A request:

Try to draw the lines through the three. View it as a unified idea:

The Paragraph gets edited,

The Wall gets defaced and graffitied,

The Sacred Tome gets rewritten.

But follow the skeins through each.

The Graph points to the Wall,

And the Wall to the Tome,

And the Tome leads to the Search.

Graph[edit]

The Graph is a paragraph from Edward Witten's 1987 paper Physics and Geometry at the bottom of page 20. In language it concisely encodes the general structure of reality:

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 [math]\displaystyle{ M }[/math], endowed with a metric tensor and governed by geometrical laws.

(ii) Over [math]\displaystyle{ M }[/math] is a vector bundle [math]\displaystyle{ X }[/math] with a non-abelian gauge group [math]\displaystyle{ G }[/math].

(iii) Fermions are sections of [math]\displaystyle{ (\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}_{-} \otimes V_{\tilde{R}}) }[/math]. [math]\displaystyle{ R }[/math] and [math]\displaystyle{ \tilde{R} }[/math] are not isomorphic; their failure to be isomorphic explains why the light fermions are light and presumably has its origins in representation difference [math]\displaystyle{ \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.

Scan of the original paragraph: The-graph.png

Implicit in each respective section is:

  1. Spin-2 Force Field for Gravity, the Einstein Field Equations
  2. Spin-1 Vector Boson Theory, Yang-Mills-Maxwell Equations
  3. Spin-1/2 Matter Theory, Dirac Equation

These are the gauge fields referred to by the last sentence.

Note that the quantum (e.g. quantum mechanics, quantum field theory, quantum measurement, etc...) is mentioned only after the key geometric insights.

Wall[edit]

The 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 Wall

    The Wall

  • Legend

    Legend

Tome[edit]

The Road to Reality
The-tome.png
Information
Author Sir Roger Penrose
Language English
Genre Physics
Publisher Vintage
Publication Date 9 January 2007
Pages 1136
ISBN-13 978-0679776314

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 and the 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.

The community is reading through the tome and gathering relevant resources on the wiki.

Core Sub-projects[edit]

The essence of Graph, Wall, Tome is viewing each as part of a singular idea. What content is common among them is what should be expanded, and their unique content should be promoted if it is a part of fundamental physics toolkit, or removed if it isn't.

Graph-Wall-Tome Connection[edit]

Editing the Graph

Editing the Graph - Though the original Graph aptly summarizes our physical knowledge, there are some minor alterations and additions to be made in order for it to accurately capture current physics.

Defacing the Wall

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.

Rewriting the Tome

Rewriting the Tome - For everything that is in the new Graph and Wall, write their elaboration and explanation. Received wisdom does not need to be accepted wholesale, the original Tome is a good example but not the ideal solution.

Resources[edit]

Other Sub-projects[edit]

  • Studying the Tome - The Tome can be intimidating. This problem can be solved 1) by creating resources that make it easier to digest its content and 2) by going through the chapters together.
  • Holonomy Project (Stalled) - The goal is to create visualizations for the effect known as "holonomy", whereby parallel transporting a vector around a loop in a curved space leads to the vector changing upon returning to the start of the loop. How the vector changes orientation/position in space is the holonomy of that loop in that space. This effect reveals deep information about the curvature of the space itself.

Archived Sub-projects[edit]

  • Climbing the Cliff (Archived) - Create a learning guide through The Road to Reality.
  • Deface the Wall (Completed) - Cam and boqu made a new wall that's interactive.
  • Geometry Project (Archived) - The aim is to create and collect resources related to Frederic P. Schuller's lecture series titled "Lectures on Geometrical Anatomy of Theoretical Physics" that provides a great introduction to geometrical concepts that are essential for the Graph, Wall, Tome project.
  • Interactive Wall (Completed) - Demp and boqu made a wall that you can pan and zoom and click on! It also pulls information from the wiki based on what is in view.

Reference[edit]

Related Material[edit]


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