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Graph, Wall, Tome: Difference between revisions

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* Also in (ii), “nonabelian gauge group G” should be changed to nonabelian structure group G.
* Also in (ii), “nonabelian gauge group G” should be changed to nonabelian structure group G.
* In (iii), R and R should be (complex) linear representations of G and so they are not equivalent.
* In (iii), R and R should be (complex) linear representations of G and so they are not equivalent.
== The Wall ==
[[File:The-wall.png]]
[http://www.math.stonybrook.edu/~tony/scgp/wall-story/wall-story.html Source]
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 ==
[https://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679776311 Road to Reality by Roger Penrose (2004)]
ISBN: 978-0679776314
== Questions ==
Some questions Eric posed related to the assignment:
=== What is FA geometrically? ===
[https://en.wikipedia.org/wiki/Atiyah%E2%80%93Singer_index_theorem Atiyah-Singer index theorem]
=== What is R and R geometrically? ===
[https://en.wikipedia.org/wiki/Einstein_field_equations Einstein field equaitions]
Einstein’s original publication, Die Feldgleichungen der Gravitation, in English
=== How do they relate? ===
[https://en.wikipedia.org/wiki/Cohomology Cohomologhy]
=== What does this have to do with Penrose Steps? ===
* [https://en.wikipedia.org/wiki/Penrose_stairs Penrose stairs]
* [https://en.wikipedia.org/wiki/Spino Spino]
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.
=== What are “Horizontal Subspaces” and what do they have to do with Vector Potentials or Gauge fields? ===
* [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>