Gregory Chaitin discusses algorithmic information theory, its relationship with Gödel incompleteness theorems, randomness, and the properties of Omega number.
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LINKS MENTIONED:
- Meta Math and the Quest for Omega (Gregory Chaitin): https://amzn.to/3stCFxH
- Visual math episode on Chaitin's constant: https://youtu.be/WLASHxChXKM
- Podcast w/ David Wolpert on TOE: https://youtu.be/qj_YUxg-qtY
- A Mathematician's Apology (G. H. Hardy): https://amzn.to/3qOEbtL
- The Physicalization of Metamathematics (Stephen Wolfram): https://amzn.to/3YUcGLL
- Podcast w/ Neil deGrasse Tyson on TOE: https://youtu.be/HhWWlJFwTqs
- Proving Darwin (Gregory Chaitin): https://amzn.to/3L0hSbs
- What is Life? (Erwin Schrödinger): https://amzn.to/3YVk8Xm
- "On Computable Numbers, with an Application to the Entscheidungsproblem" (Alan Turing): https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf
- "The Major Transitions in Evolution" (John Maynard Smith and Eörs Szathmáry): https://amzn.to/3PdzYci
- "The Origins of Life: From the Birth of Life to the Origin of Language" (John Maynard Smith and Eörs Szathmáry): https://amzn.to/3PeKFeM
- Podcast w/ Stephen Wolfram on TOE: https://youtu.be/1sXrRc3Bhrs
- Incompleteness: The Proof and Paradox of Kurt Gödel (Rebecca Goldstein): https://amzn.to/3Pf8Yt4
- Rebecca Goldstein on TOE on Godel's Incompleteness: https://youtu.be/VkL3BcKEB6Y
- Gödel's Proof (Ernest Nagel and James R. Newman): https://amzn.to/3QX89q1
- Giant Brains, or Machines That Think (Edmund Callis Berkeley): https://amzn.to/3QXniYj
- An Introduction to Probability Theory and Its Applications (William Feller): https://amzn.to/44tWjXI

TIMESTAMPS:
- 00:00:00 Introduction
- 00:02:27 Chaitin's Unconventional Self-Taught Journey
- 00:06:56 Chaitin's Incompleteness Theorem and Algorithmic Randomness
- 00:12:00 The Infinite Calculation Paradox and Omega Number's Complexity (Halting Probability)
- 00:27:38 God is a Mathematician: An Ontological Basis
- 00:37:06 Emergence of Information as a Fundamental Substance
- 00:53:10 Evolution and the Modern Synthesis (Physics-Based vs. Computational-Based Life)
- 01:08:43 Turing's Less Known Masterpiece
- 01:16:58 Extended Evolutionary Synthesis and Epigenetics
- 01:21:20 Renormalization and Tractability
- 01:28:15 The Infinite Fitness Function
- 01:42:03 Progress in Mathematics despite Incompleteness
- 01:48:38 Unconventional Academic Approach
- 01:50:35 Godel's Incompleteness, Mathematical Intuition, and the Platonic World
- 02:06:01 The Enigma of Creativity in Mathematics
- 02:15:37 Dark Matter: A More Stable Form of Hydrogen? (Hydrinos)
- 02:23:33 Stigma and the "Reputation Trap" in Science
- 02:28:43 Cold Fusion
- 02:29:28 The Stagnation of Physics
- 02:41:33 Defining Randomness: The Chaos of 0s and 1s
- 02:52:01 The Struggles For Young Mathematicians and Physicists (Advice)