In this week’s podcast, “The Chaitin interview I: Chaitin chats with Kurt Gödel,” Walter Bradley Center director Robert J. Marks interviewed mathematician and computer scientist Gregory Chaitin. Yesterday, we noted his comments on the almost supernatural awareness that the great mathematicians had of the foundations of reality in the mathematics of our universe. This time out, Chaitin recounts how he (almost) met the eccentric genius Kurt Gödel (1906–1978):

This portion begins at 12:42 min. A partial transcript, Show Notes and Additional Resources follow.

Robert J. Marks: You mentioned that you read the article about Gödel’s Incompleteness Theorem in Scientific American I also know that you had a near brush with Gödel and I’ve heard the story from you. But I’ve never seen it published. I wonder if you could share that.

Gregory Chaitin (pictured): I think the story is somewhere, maybe in a paper based on a lecture. Well, I had been in Argentina for a number of years and IBM sent me to the US. In the early 1970s, I was invited to be a summer visitor at the IBM Watson Research Center. I was living in the YMCA in White Plains. I had the proofs of one of my first papers on incompleteness, from IEEE Transactions on Information Theory. And I sent him the proofs. Well, I looked up Godel’s phone number in the telephone book and called him up.

Robert J. Marks: So you cold called him then.

Gregory Chaitin: Yeah. Out of the blue. Instead of basing my work on the paradox of the liar, Epimenides’ paradox, my approach is based on the Berry paradox. And Godel answered, “Well, it doesn’t matter which paradox you use.” He had said that in his 1931 paper. I was familiar with his paper. So I said, “Of course, but this suggests to me,” I don’t remember what I said, something like a whole new approach. I don’t know. What did I say? “I would very much like to talk to you about and get your reaction.”

So he said, “Okay, send me a paper of yours on this topic. I’ll take a look at it. And if like it, maybe I’ll give you an appointment to visit.” So I sent him the proofs. I had the proofs of that IEEE paper. It was my second IEEE Information for Transactions paper actually.

Note: Epimenides’ Paradox Also called the Liar’s Paradox: The paradox of a man who states “I am lying.” If he is lying, then he is telling the truth, and vice versa. Wolfram’s Mathworld

Berry Paradox: “The least integer not nameable in fewer than nineteen syllables” is itself a name consisting of eighteen syllables; hence the least integer not nameable in fewer than nineteen syllables can be named in eighteen syllables, which is a contradiction. Wolfram’s Mathworld

Gregory Chaitin: I called him up and I think I remember he said, “Very interesting. Your notion of complexity is an absolute notion.” Now this was a distinction he made between the idea of what you can compute is absolute. It doesn’t depend on the axioms, whereas what you can prove does. So he had taken a look at it and immediately perceived a crucial aspect of the definition of complexity that I was proposing. And he gave me an appointment.

I did some research to figure out. I was without a car. I would take the train into New York City. From New York City I would take the train out to, I don’t know, Princeton Junction or something. I would get there. Nothing could stop me, right?

Gregory Chaitin: I was all set for the great day — and it snowed! And this was the week before Easter. So that’s unusual, a spring snowstorm but it wasn’t a big snowstorm. Nothing was going to stop me from visiting my hero. So there I am in my office at the IBM Watson Center, about to leave. I figured out how much time I needed. About to leave and unfortunately — very unfortunately — the phone rang. It was Gödel ’s secretary saying Gödel is very careful with his health. And because it snowed, he’s not coming in to his office today. And therefore your appointment is canceled.

So that was a surreal experience. And there was no way to reschedule because I was going to leave just in a few days, heading back to Argentina, to Buenos Aires. But actually this surreal story actually fits better Gödel and his legend, because for example, when Gödel died, they found lots of answers typed up to letters he received, but were never sent. They were never mailed. So there was a surreal quality to Gödel and to communicating with Gödel.

Robert J. Marks (pictured): He was a quirky guy and a germophobe, if I recall correctly.

Gregory Chaitin: Yeah. He was from what, at the time, was the Austro-Hungarian Empire. And he didn’t accept being made a member of the Austrian Academy of Sciences. He never went back to Europe, never visited Europe. He turned down the offer to be a member of the Austrian Academy of Sciences. So he’s an interesting guy.

One of the books I like about Gödel is in French, it’s called Gödel’s Demons, Logic, and Madness. And this was by a gentleman in France who actually went through the Gödel archive at Princeton. Half the book was also devoted to Emil Post, a forgotten genius.

Note: Emil Post (1897–1954) was a Polish-born American mathematician and logician who is best known for his work on polyadic groups, recursively enumerable sets, and degrees of unsolvability, as well as for his contribution to the unsolvability of problems in combinatorial mathematics. – MacTutor

Next: How Kurt Gödel destroyed a popular form of atheism We don’t hear much about logical positivism now but it was very fashionable in the early twentieth century. Gödel’s incompleteness theorems showed that we cannot devise a complete set of axioms that accounts for all of reality — bad news for positivism.

The previous podcast in this series with Gregory Chaitin: Chaitin on the great mathematicians, East and West: Himself a “game-changer” in mathematics, Chaitin muses on what made the great thinkers stand out. He discusses the almost supernatural awareness some mathematicians have had of the foundations of our shared reality in the mathematics of the universe.

You may also wish to read: Things exist that are unknowable: A tutorial on Chaitin’s number (Robert J. Marks)

Show Notes

• 00:23 | Introducing Gregory Chaitin
• 05:00 | Chaitin’s Youth
• 06:33 | Chaitin’s journey to computer science
• 08:26 | Chaitin’s thoughts on Leonard Euler
• 12:42 | Chaitin’s near brush with Kurt Gödel
• 17:16 | The quirks of Gödel

Additional Resources

• Gregory Chaitin’s Website
• Unravelling Complexity: The Life and Work of Gregory Chaitin, edited by Shyam Wuppuluri and Francisco Antonio Doria
• Conversations with a Mathematician: Math, Art, Science and the Limits of Reason by Gregory J. Chaitin
• 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
• “On the Length of Programs for Computing Finite Binary Sequences” by Gregory J. Chaitin, written and published when he was a teenager
• 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

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