I'm back, baby. I've been away traveling for podcasts and am excited to bring you new ones with Michael Levin, William Hahn, Robin Hanson, and Emily Riehl, coming up shortly. They're already recorded. I've been recovering from a terrible flu but pushed through it to bring you today's episode with Urs Schreiber. This one is quite mind-blowing. It's quite hairy mathematics, something called higher category theory, and how using this math (which examines the structure of structure) allows one manner of finding "something" from "nothing." Here, "nothing" means the empty set, and "something" is defined as fermions and even 11D supergravity. It's the first time this material has been presented in this manner. Enjoy.
NOTE: Link to technical details are here from Urs Schreiber: https://ncatlab.org/schreiber/show/Peri+Pantheorias
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Links Mentioned:
- nLab website: https://ncatlab.org/nlab/show/HomePage
- Paper on category theory: https://people.math.osu.edu/cogdell.1/6112-Eilenberg&MacLane-www.pdf
- “Higher Topos Theory for Physics” (Urs’s talk): https://www.youtube.com/watch?v=GD20W6vxMI4
- “Higher Topos Theory for Physics” (Urs’s paper): https://arxiv.org/pdf/2311.11026
- Stephen Wolfram on TOE: https://www.youtube.com/watch?v=0YRlQQw0d-4
- Feynman’s thesis: https://faculty.washington.edu/seattle/physics541/2012-path-integrals/thesis.pdf
- Differential cohomology in a cohesive ∞-topos (Urs’s paper): https://arxiv.org/pdf/1310.7930
- M-Theory from the Superpoint (paper): https://arxiv.org/pdf/1702.01774
- Character Map in Non-Abelian Cohomology, The: Twisted, Differential, and Generalized (textbook): https://amzn.to/4bFuz7H
- TOE’s String Theory Iceberg: https://www.youtube.com/watch?v=X4PdPnQuwjY
Timestamps:
00:00 Introduction
01:27 The Creation of nLab
04:36 Philosophy Meets Physics
07:55 The Role of Mathematical Language
09:32 Emergence from Nothing
16:25 Towards a Theory of Everything
22:21 The Problem with Modern Physics
25:31 Diving into Category Theory
35:30 Understanding Adjunctions
41:46 The Significance of Duality
52:54 Exploring Toposes
1:14:20 The UNEDA Lemma and Generalized Spaces
1:16:37 Charts in Physics
1:20:55 Introduction to Infinitesimal Disks
1:23:56 The Emergence of Supergeometry
1:27:33 Transitioning to Gauge Theories
1:28:11 Exploring Singularities in Physics
1:32:50 The Role of Superformal Spaces
1:36:44 Functors and Their Implications
1:40:51 From Nothing to Emergent Structures
1:43:04 Hegel's Influence on Modern Physics
1:54:07 Discovering Higher-Dimensional Structures
1:56:30 The Path to 11-Dimensional Supergravity
1:57:21 Universal Central Extensions
2:03:21 The Journey to M-Theory
2:11:19 Globalizing the Structure of Supergravity
2:15:36 Understanding Global Charges in Physics
2:23:31 Dirac's Insights into Gauge Potentials
2:30:21 The Quest for Non-Perturbative Physics
2:39:04 Conclusion
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