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?
- 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
- 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
- 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