Listen in as Robert J. Marks picks the mind of Professor Gregory Chaitin about Chaitin’s number – a number that has been called “mystical and magical”. How does this number work? Why do some people call it “Chaitin’s constant”? What is the usefulness of philosophizing in mathematics?

Show Notes

• 00:27 | Introducing Gregory Chaitin and Chaitin’s number
• 01:32 | Chaitin’s number or Chaitin’s constant?
• 07:16 | Must the halting problem be solved for smaller programs in order to get Chaitin’s number?
• 09:50 | The usefulness of philosophy and the impractical
• 17:17 | Could Chaitin’s number be calculated to a precision which would allow for a proof or disproof of something like Goldbach’s Conjecture?
• 19:20 | 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
• Elements of Information Theory by Thomas Cover and Joy Thomas
• “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).
• Chris Calude, professor at the University of Auckland
• Gottfried Wilhelm Leibniz, German Enlightenment philosopher, mathematician, and political adviser
• Stephen Wolfram, computer scientist and physicist
• Goldbach Conjecture
• Collatz Conjecture
• Legendre’s Conjecture
• Elon Musk, engineer and entrepreneur 
• G.H. Hardy, English mathematician
• Ray Solomonoff, one of the founders of algorithmic information theory
• Hector Zenil, computational natural scientist
• Automacoin
• Bitcoin
• Marvin Minsky, cognitive and computer scientist
• George Gilder, economist and co-founder of the Discovery Institute
• Twin Prime Conjecture
• Georg Cantor, mathematician
• BBC 4’s Dangerous Knowledge