Editing User:Aardvark/GWT

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 [[#Tome|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, and we didn't know the Aharonov-Bohm effect, which demonstrated that the electromagnetic field is less important than the electromagnetic potential. As recently as the mid-1970s, 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, Wall, and 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 open the world of fundamental physics to 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.

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

(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 <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.