In the 1960s, mathematician and computer scientist Gregory Chaitin published a landmark paper in the field of algorithmic information theory in the Journal of the ACM – and he was only a teenager. Since then he’s explored mathematics, computer science, and even gotten a mathematical constant named after him. Robert J. Marks leads the discussion with Professor Gregory Chaitin on algorithmic information theory, randomness, unknowability, and philosophy in this bingecast.

Show Notes

• 0:00:09 | Introducing Gregory Chaitin
• 0:05:12 | Chaitin’s Youth
• 0:06:44 | Chaitin’s journey to computer science
• 0:08:38 | Chaitin’s thoughts on Leonard Euler
• 0:12:53 | Chaitin’s near brush with Kurt Gödel
• 0:17:21 | The quirks of Gödel
• 0:21:00 | Chaitin’s landmark paper published in his teen years
• 0:21:51 | Chaitin’s definition of randomness
• 0:28:30 | Metaphysics
• 0:30:07 | Chaitin’s philosophical interest
• 0:39:46 | Fermat’s Last Theorem
• 0:43:55 | Is Math Discovered or Invented
• 0:45:08 | The Pressure or Publish Papers
• 0:53:18 | A human-computer symbiosis?
• 0:56:40 | Computer Software Proofing Mathematics
• 1:03:26 | Bureaucratic Obstacles to Genuine Research
• 1:10:57 | A Simple Explanation
• 1:13:39 | Is Creativity Non-Computable?
• 1:15:07 | Defining Creativity
• 1:20:20 | Chaitin’s number of Chaitin’s Constant?
• 1:42:49 | Panpsychism
• 1:45:58 | The usefulness of philosophy and the impractical
• 2:04:30 | Could Chaitin’s number be calculated to a precision which would allow for a proof or disproof of something like Goldbach’s Conjecture?
• 2:06:33 | The Jump of the Omega Number

Additional Resources

• Gregory Chaitin’s Website
• Unravelling Complexity: The Life and Work of Gregory Chaitin, edited by Shyam Wuppuluri and Francisco Antonio Doria
• Meta Math!: The Quest for Omega by Gregory Chaitin
• Thinking About Gödel and Turing: Essays on Complexity by Gregory J. Chaitin
• Proving Darwin: Making Biology Mathematical by Gregory Chaitin
• Leonard Euler, Swiss mathematician and physicist
• Kurt Gödel, Austrian-born mathematician
• Georg Cantor, German mathematician
• Dr. Robert J. Marks’ critiques of Gregory Chaitin’s ideas on Youtube
• “Active Information in Metabiology“: Winston Ewert’s, William Dembski’s, and Robert J. Marks’ paper on Chaitin’s metabiology
• “On the length of programs for computing finite binary sequences,” by Gregory Chaitin, published when he as a teenager. (Journal of the ACM (JACM) 13, no. 4 (1966): 547-569).
• Karl Popper
• The Logic of Scientific Discovery by Karl Popper
• Hermann Weyl
• Gottfried Wilhelm Leibniz
• Leibniz’s Discours de Métaphysique (in English)
• “A Theory of Program Size Formally Identical to Information Theory” by Gregory Chaitin (Journal of the ACM (JACM) 22, no. 3 (1975): 309-440).
• Ray Solomonoff, one of the founders of algorithmic information theory
• Marvin Minsky, cognitive and computer scientist
• Fermat’s Last Tango on YouTube
• Henri Poincaré, 19th century French mathematician
• A Mathematician’s Apology by G.H. Hardy
• Claude Shannon, mathematician, “the father of information theory”
• Lofti Zadeh, world-renowned computer scientist
• Andrew Wiles, English mathematician
• William Sealy Gosset, statistician and chemist
• Elon Musk, engineer and entrepreneur
• Neuralink
• Alan Turing, mathematician and philosopher
• Stephen Wolfram, computer scientist and physicist
• WolframAlpha
• Mathematica
• Carl Friedrich Gauss, German mathematician and physicist
• Srinivasa Ramanujan, Indian mathematician
• The Unknowable by Gregory Chaitin
• Paul Erdős, Hungarian mathematician
• Chaitin’s Constant
• Jack Schwartz, American mathematician
• Roger Penrose, British mathematician and Nobel Prize winner
• The Emperor’s New Mind by Roger Penrose
• Shadows of the Mind by Roger Penrose
• Stephen Hawking, British theoretical physicist
• Selmer Bringsjord, engineer and computer scientist
• The Lovelace Test, a discussion between Robert J. Marks and Selmer Bringsjord at Mind Matters
• Giulio Tononi, neuroscientist and psychiatrist
• Christof Koch, German-American neuroscientist
• David J. Chalmers, philosopher and cognitive scientist
• The Conscious Mind by David J. Chalmers
• Gottfried Wilhelm Leibniz’s monads
• “Consciousness and Information, Classical Quantum or Algorithmic?” by Gregory Chaitin
• Bit Bang. La nascita della filosofia digitale by Giuseppe O. Longo (translation: Bit Bang: The birth of digital philosophy)
• Elements of Information Theory by Thomas Cover and Joy Thomas
• Chris Calude, professor at the University of Auckland
• Goldbach Conjecture
• Collatz Conjecture
• Legendre’s Conjecture
• G.H. Hardy, English mathematician
• Hector Zenil, computational natural scientist
• Automacoin
• Bitcoin
• George Gilder, economist and co-founder of the Discovery Institute
• Twin Prime Conjecture
• BBC 4’s Dangerous Knowledge