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 how Stephen Wolfram’s software has taken much of the drudgery out of math. At the same time, in Chaitin’s view, a threat looms: A new, more bureaucratic, mindset threatens to take the creativity out of science, technology, and math:

This portion begins at 19:45 min. A partial transcript, Show Notes, and Additional Resources follow.

Robert J. Marks: I was sitting down tallying, I think, the intellectual giants that have introduced new mathematical ideas, brand new. I was thinking of people like Claude Shannon, Lotfi Zadeh, yourself… I don’t know if we see the introduction of new, great ideas today. At least I don’t see them. Do you have any thoughts on that?

Gregory Chaitin: I think the bureaucracy is killing the golden goose. There’s too much control. You have to get research funds, you have to publish lots of trivial papers, and you spend too much time filling out grant proposals.

They’re managing to make it impossible for anybody to do any real research. You have to say in advance what you’re going to accomplish. You have to have milestones, reports.

And the European community has made it worse. I was talking to a scientist in Europe and she told me, “I have to spend all the time interfacing with the bureaucracy in Brussels. I put together a research team but they are the only ones really doing the research because my time is all taken with this administrivia.” So if you give the bureaucrats a chance, they’ll grow and grow and grow and eventually sink the ship. But this seems to be the way this society is working.

The Chinese seem to be innovating and engineering in a remarkable way. They have a different system. I don’t know what it’s like there. I’ve seen videos of them putting up a building in amazing speed, with amazing speed, for example.

Robert J. Marks: There’s an old saying that only rich countries can afford poets. We used to have these great research centers such as Bell Labs, which dissolved after divestiture, I guess.

Gregory Chaitin: Yeah. They got so many Nobel prizes. They got so many Nobel prizes.

Robert J. Marks: It was incredible. But they dissolved. It was a rich country so they could have these poets where they got together some of the greatest engineers and scientists of all time. Maybe they would only make one big breakthrough in their lifetimes, but they employed them for their lifetimes, for their scholarship.

Google is making available to people all of this wonderful artificial intelligence software. That’s where I see the innovation coming from and not so much from academia.

Gregory Chaitin: Right. Well the universities were always very conservative. Elon Musk makes, I think, this remark in an interview he gave, maybe a few days before the remarkable flight of the Starship SN8 that if you don’t have a lot of research projects that fail, you are not doing enough research.

The problem is, if failure is unacceptable, then you’re in trouble. For example, the legacy aerospace companies that make rockets take years to design a rocket and it’s got to work on its first flight. Whereas Elon does rocket engineering the way you develop software, by using it.

The software I worked on, we were constantly using our own software. We were doing compiling and we kept compiling the compiler through itself, so we were constantly eating our own cooking. We had many prototypes, and if there was something wrong we would fix it and try again.

Elon is doing that. He’s doing his rockets very fast and breaking them and learning from each. So if you don’t have a lot of research projects …

But failure is now unacceptable. That means the research projects have to be very conservative. You
can’t try something really crazy.

Robert J. Marks (pictured): Yeah. If you try to do a project and you fail, you can’t publish it. That’s bad for the bean counters.

Gregory Chaitin: Yeah. Well the bean counters should get out of our way.

Robert J. Marks: Let me ask you this. What is the solution? Do we have any solutions?

One of which — this is very controversial to me — I think that some of the government funding is not good. I know that in Japan and Germany they require, well this is one solution, they require interface of the professors with industry so that they can work on more interesting problems. But that doesn’t clear people up to pursue pure creativity. So what’s the answer? How can we fix this?

Gregory Chaitin: It’s tough. I have a pessimistic vision which I hope is completely wrong, that the bureaucracies are like a cancer — the ones that control research and funding for research and counting how much you’ve been publishing. I’ve noticed that at universities, for example, the administrative personnel are gradually taking all the best buildings and expanding. So I think that the bureaucracy and the rules and regulations increases to the point that it sinks the society.

At that point, basically, I expect, as with companies, the country will collapse because it will fail in a competition with a younger, more vigorous, more daring country. So nations and corporations seem to have a life cycle like human beings do: Vigorous youth where they think they can do anything and then they get very conservative. They don’t want to come up with a new product which competes with their existing product line because you can’t predict how much it’s going to earn in advance.

At IBM it used to happen. The salespeople would — with a completely new technology, a new kind of computer — make a very low estimate of how many are going to sell. So we have to charge a lot for each one because we had a lot of development costs and we weren’t allowed to dump products.

So the result is that it’s a lost cause. If you want to try some daring new product, it’s going to be so expensive that no one is going to buy it.

Robert J. Marks: Yeah. It’s frustrating.

Gregory Chaitin: It’s more than frustrating. I think it’s the end. When our society reaches that point, their innovation is going to go down.

I remember when I was a kid, Scientific American every month was very thick. Why was it thick? Because it had lots of ads from General Dynamics, from other aerospace companies that were trying to hire wonderful engineers. Things were more dynamic.

Next: A question every scientist dreads: Has science passed the peak?

You may also wish to read these earlier posts in the series of conversations with Gregory Chaitin (of Chaitin’s unknowable number):

How Stephen Wolfram revolutionized math computing. Wolfram has not made computers creative but he certainly took a lot of the drudgery out of the profession. Gregory Chaitin also discusses the amazing ideas early mathematicians developed without the software-based methods we are so lucky to have today.

Why Elon Musk, and others like him, can’t afford to follow rules. Mathematician Gregory Chaitin explains why Elon Musk is, perhaps unexpectedly, his hero. Very creative people like Musk often have quirks and strange ideas (Gödel and Cantor, for example) which do not prevent them from making major advances.

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

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