In last week’s podcast, “The Chaitin Interview III: The Changing Landscape for Mathematics,” Walter Bradley Center director Robert J. Marks interviewed mathematician and computer scientist Gregory Chaitin on many things mathematical, including why great books on math, advancing new theorems, aren’t written much any more. This week, we look at why geniuses like Musk (whose proposed Mars Orbiter is our featured image above) simply can’t just follow the rules, for better or worse:

This portion begins at 7:57 min. A partial transcript, Show Notes, and Additional Resources follow.

Gregory Chaitin: Look at Elon Musk (pictured). He’s my great hero. He’s a wonderful engineer and he’s a wonderful entrepreneur and he doesn’t follow the rules.

Robert J. Marks: He doesn’t, and innovators don’t follow the rules. I think that’s one of the elements and one of the characteristics of creativity.

Gregory Chaitin: That’s tough. Elon is clearly a genius, amazing engineer, incredibly talented and innovative. But he also has to figure out a way to do this in the real world, and he has managed to do it. So that’s a remarkable achievement also and I admire him greatly.

Robert J. Marks: But then again, we were talking offline about the relationship between genius and creativity. We talked about, for example, the quirkiness of Kurt Gödel and about Georg Cantor spending a lot of his life in a sanatorium because of mental anguish.

Note: “Gödel’s mental problems tormented him until his death: Obsessed with the fear of being poisoned, he only ate what his wife prepared for him. When she had to stay in a hospital for a while, Gödel refused to eat, eventually starving to death in 1978.” Phys.org

“As he aged, Cantor suffered from more and more recurrences of mental illness, which some have directly linked to his constant contemplation of such complex, abstract and paradoxical concepts. In the last decades of his life, he did no mathematical work at all, but wrote extensively on his two obsessions: that Shakespeare’s plays were actually written by the English philosopher Sir Francis Bacon, and that Christ was the natural son of Joseph of Arimathea. He spent long periods in the Halle sanatorium recovering from attacks of manic depression and paranoia, and it was there, alone in his room, that he finally died in 1918, his great project still unfinished.” – Story of Mathematics

Robert J. Marks: Elon Musk has his quirks too. He has opined that we are all computer simulations.

Gregory Chaitin: He has? Well that’s a popular view now. The computer has replaced God in a lot of people’s minds, and I think we’re all the poorer for it, but it’s the fashion now. So we’re machines. We’re machines. AIs are going to be better than us. Human beings will be obsolete. This is the fashionable view, and of course I don’t appreciate it very much.

Note: Neil deGrasse Tyson also thinks so, telling NBC News in an e-mail that he gives “better than 50-50 odds” that the simulation hypothesis is correct. “I wish I could summon a strong argument against it, but I can find none.” Well-known British astronomer Martin Rees
treats the idea with sympathy. The thought that our universe is a giant simulation created by advanced extraterrestrials is meant to account for the remarkable fine-tuning of the universe for life, without the need for belief in God.

Robert J. Marks: Mind Matters and our podcast is part of the Bradley Center, the Walter Bradley Center for Natural and Artificial Intelligence and that’s one of the things that we push back on, is the idea that there are things that machines can’t do that humans will always be able to do. We actually use some algorithmic information theory to back the theories.

I’m glad you’re not a proponent that machines are going to replace people. We still have some attributes that I think will never be duplicated.

Gregory Chaitin (pictured): Computers might replace people if they’re cheaper and better at uninteresting tasks. But I think human beings will always be better at creativity, at doing art. As Turing said, “A computer is likely to write poetry that only another computer would enjoy reading.”

Robert J. Marks: That assumes that another computer can enjoy. I don’t think computers have the capability of enjoying.

Gregory Chaitin: Yeah, I don’t know. Elon Musk is worried that AI will get out of control, and he also has his personal project to not let computers replace humans by coupling computers and humans into a symbiosis where both can contribute what they’re best at.

Robert J. Marks: It’s called Neuralink, I believe. Where he implants a chip in the brain. I think I’m going to wait awhile before I do that. I don’t think I want a chip in my brain.

Gregory Chaitin: To justify doing that, they’re doing it for people who are quadriplegic, for example, who need help. But trying to make a symbiosis between humans and computers. Elon thinks you need to do that so the human beings aren’t left behind. So if you give a high bandwidth link between computers and people he thinks that’ll help people to not feel obsolete, but to participate.

Human beings use machinery, and we don’t think that just because I can’t run as fast as a sports car or lift as much weight as a steam shovel, we don’t think that that means that human beings are valueless. We invented those devices.

Similarly, some things computers certainly are better at than humans, like remembering precisely large quantities of information unless you have a photographic memory.

So a symbiotic relationship between the two of us, each one might contribute what they’re better at and people will not feel that they have become obsolete. It’ll just be like using a steam shovel or using an airplane instead of trying to fly by flapping your arms.

Robert J. Marks (pictured): The comedian Emo Philips says that computers might be able to beat him at chess, but he can always win a game of spirited, kickboxing. So I think that, yeah, there are things which computers can do, they can do well. But there are limitations on them.

Gregory Chaitin: On the other hand, we invented the computer. So we can take the credit for whatever they do well.

Robert J. Marks: Well yes, and you’ll notice this idea of Elon Musk’s fear — and I don’t want to detract from Elon Musk because he’s clearly a genius. But this assumption that computer software is going to write more creative computer software that’s going to write more creative computer software, and you’re going to have an AI which reaches just this hyper intelligence, has the assumption that computers can write programs that are creatively more able to do things than the original computer programs…

Note: It would be difficult to create computers that are intrinsically smarter than ourselves, as opposed to simply faster at one specific job or another. However, some thinkers hope that, with advancing technology, AI can evolve into a superintelligence all by itself. That hope runs into the problem created by the No Free Lunch theorems, as summarized by Jonathan Bartlett: “If someone were to invent a universally good search through a search space, it would have to be done on something that isn’t a computer.” Roman Yampolskiy, looking at the literature, notes“Although, on the surface, the results may seem impressive, deeper analysis shows complete absence of success in evolving nontrivial software from scratch and without human assistance…”

Gregory Chaitin: Yeah, I would think a team of brilliant engineers might write an amazing piece of AI software, but the AI software doesn’t write itself.

Robert J. Marks: Exactly. This actually dovetails, this is something I think I read that you wrote, and you have to correct me if I’m wrong. But you were talking about computer programs and software that was able to prove meaningful theorems, that is insightful theorems of the type that a brilliant mathematician would write. I believe you said that there’s no evidence of that happening.

Gregory Chaitin:Well I made that remark some years back. What they have now are proof checkers. You write the proof in a special language, in a precise mathematical notation, and there’s software that can check if the proof is correct or ask you to provide more steps if it doesn’t understand how one thing followed from another. That technology is improving, so there are mathematicians who claim that at least that all of math should be written up this way and submitted to checking like this. But these computers are not doing wonderful new mathematics.

Robert J. Marks: Exactly. There’s a difference between checking the proof and originating the proof.

Gregory Chaitin: Yeah, there’s an enormous difference.

Next: Does Stephen Wolfram’s amazing math program beat math nerds?

—

You may also enjoy:

Why don’t we see many great books on math any more? Decades ago, Gregory Chaitin reminds us, mathematicians were not forced by the rules of the academic establishment to keep producing papers, so they could write key books. Chaitin himself succeeded with significant work (see Chaitin’s Unknowable Number) by working in time spared from IBM research rather than the academic rat race.

Mathematics: Did we invent it or did we merely discover it? What does it say about our universe if the deeper mathematics has always been there for us to find, if we can? Gregory Chaitin, best known for Chaitin’s Unknowable Number, discusses the way deep math is discovered whereas trivial math is merely invented.

From the transcripts of the second podcast: Hard math can be entertaining — with the right musical score! Gregory Chaitin discusses with Robert J. Marks the fun side of solving hard math problems, some of which come with million-dollar prizes. The musical Fermat’s Last Tango features the ghost of mathematician Pierre de Fermat pestering the math nerd who solved his unfinished Last Conjecture.

Chaitin’s discovery of a way of describing true randomness. He found that concepts f rom computer programming worked well because, if the data is not random, the program should be smaller than the data. So, Chaitin on randomness: The simplest theory is best; if no theory is simpler than the data you are trying to explain, then the data is random.

and

How did Ray Solomonoff kickstart algorithmic information theory? He started off the long pursuit of the shortest effective string of information that describes an object. Gregory Chaitin reminisces on his interactions with Ray Solomonoff and Marvin Minsky, fellow founders of Algorithmic Information Theory.

Here are the stories, with links, to an earlier recent podcast discussion with Gregory Chaitin:

Gregory Chaitin’s “almost” meeting with Kurt Gödel. This hard-to-find anecdote gives some sense of the encouraging but eccentric math genius. Chaitin recalls, based on this and other episodes, “There was a surreal quality to Gödel and to communicating with Gödel.”

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

and

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 positivist atheism.

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

and

Five surprising facts about famous scientists we bet you never knew: How about juggling, riding a unicycle, and playing bongo? Or catching criminals or cracking safes? Or believing devoutly in God… (Robert J. Marks)

Show Notes

• 00:23 | Introducing Gregory Chaitin
• 00:39 | Is math discovered or invented?
• 02:49 | The pressure to publish papers
• 08:31 | A human-computer symbiosis?
• 13:22 | Computer software proofing mathematics
• 19:45 | Bureaucratic obstacles to genuine research

Additional Resources

• The Chaitin Interview Part I
• The Chaitin Interview Part II
• Gregory Chaitin’s Website
• Unravelling Complexity: The Life and Work of Gregory Chaitin, edited by Shyam Wuppuluri and Francisco Antonio Doria
• Proving Darwin: Making Biology Mathematical by Gregory Chaitin
• Henri Poincaré, 19th century French mathematician
• Georg Cantor, German 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
• Karl Popper, Austrian-British philosopher
• William Sealy Gosset, statistician and chemist
• Elon Musk, engineer and entrepreneur
• Neuralink
• Kurt Gödel, Austrian-born mathematician
• Alan Turing, mathematician and philosopher
• Stephen Wolfram, computer scientist and physicist
• WolframAlpha
• Mathematica
• Leonard Euler, Swiss mathematician and physicist
• Carl Friedrich Gauss, German mathematician and physicist
• Srinivasa Ramanujan, Indian mathematician

Podcast Transcript Download