In this 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, including whether the great discoveries in science are behind us — not due to lack of creativity or ability on the part of scientists — but to the growing power of corporate and government bureaucracies to stifle research. But then a question arises: Could science, succumbing to the swamp of bureaucracy, be losing that inventive edge?

This portion begins at 24:56 min. A partial transcript, Show Notes, and Additional Resources follow.

Gregory Chaitin: What did an airplane engineers say once in a speech I heard? He said, “In the old days, a bunch of engineers could go to a motel for the weekend, so they wouldn’t be distracted by their family, with a bunch of six packs of beer and design a new airplane.”

Robert J. Marks Uh-huh (affirmative).

Gregory Chaitin: That doesn’t happen anymore. Since I was working in industry, I could see all these forces at work at IBM, which in the early days was full of adventurers.

There was no computer engineering. The guy I worked with, I think his field was English literature originally. But he wanted to help make a new industry. He was fascinated by computers and he was one of the great contributors at IBM.

So IBM was very vigorous and innovative at first. But then it got more and more bureaucratic and afraid of competing with its own existing products. So you get to the point where a new kind of computer can only come from a new company because the existing company will never want to take a chance on something new.

Note: There is an active debate just now as to whether innovativeness in science is drying up.

In 2018, on the Yes side were Patrick Collison and Michael Nielsen at The Atlantic: Progress in science is “requiring larger teams, far more extensive scientific training, and the overall economic impact is getting smaller.”

On the No side was Chad Orzel at Forbes: “the arguable peak in importance comes in the 1920’s and 1930’s, during the development of quantum mechanics. I don’t think the revolutionary progress of that era is something we could reasonably expect to be sustainable”

The critical question is, how much progress depends on much earlier discoveries in science and technology and how much depends on the efforts of recent years?

Gregory Chaitin: Anyway, all this worries me. I hope I’m completely wrong and this doesn’t happen. Elon Musk certainly is an example that it’s still possible to be tremendously innovative in the field of technology.

But he also talks about bureaucracy and how it’s a question that worries him a lot — and the fact that failure is not allowed, whereas you have to learn from your failures. If you don’t fail, it means you’re not innovating enough.

That worries me a lot. I hope I’m wrong, but I have this vision of the life cycle of corporations and nation states. I saw what IBM was going through and a lot of people are worried that China is becoming more capitalist than we are in a funny way.

Here in South America I see US influence disappearing. China is now the leading trade partner for a lot of countries in South America rather than the United States.

On the other hand, the Elon Musk and Stephen Wolfram makes me think that the United States can still do basic innovation in spite of everything… That’s probably why Elon Musk wanted to come to the US. He went from South Africa.

Robert J. Marks (pictured): Now he’s moved from California to my backyard in Texas.

Note: Ever heard the old song, “From this valley they say you are going?” A number of media sources have noted a trend away from Silicon Valley:

● From the Chicago Tribune (December 16, 2020): “Tech workers are leaving California in droves, sending San Francisco rents tumbling by as much as 35%. Large companies have made the leap, too Oracle Corp. announced plans on Friday to leave the Bay Area for Austin, Texas, e-cigarette maker Juul said it would move to Washington, D.C., and cybersecurity firm Tanium is moving to a suburb of Seattle. Even Elon Musk has said he’s now a Texan.”

From Bloomberg Editorial Board: “Silicon Valley remains the world’s preeminent tech hub. But that won’t last if lawmakers there keep antagonizing businesses.” (December 29, 2020)

● From CNBC (January 23, 2021): In 2020, Oracle, Palantir and Hewlett-Packard Enterprise were among the companies that announced they’re relocating their headquarters out of the Golden State. Wealthy individuals from the tech industry moving recently include Larry Ellison, Drew Houston, Joe Lonsdale and Elon Musk, currently the world’s richest man.”

According to CNBC, concerns cited by exiting firms include “high taxes, cost of living and heavy regulations.”

Gregory Chaitin: Yeah. Probably because aerospace manufacturing is all gone from California. Too much bureaucracy. I think Texas is a freer place.

Robert J. Marks: So far. I hope we can keep it that way.

So Elon built his spaceport in Southern Texas and he’s moved his foundation there.

Gregory Chaitin: Fortunately there’s still Texas. Texas could be a separate country. You spend a year as a separate nation then, didn’t you?

Robert J. Marks: Yes. The Republic of Texas. In fact, I work at a place, Baylor University, that was founded when Texas was a Republic.

Gregory Chaitin: Yeah. Well, I worry about creativity. I have a chapter on that in my book, Proving Darwin. I make a remark that from the point of view of creativity, I think that the best thing to do would be to split up the European community in separate countries and split up the US in separate States. Because that would give more freedom of action to creative people instead of having a central bureaucracy.

Robert J. Marks: And it would set the free enterprise system into effect.

Gregory Chaitin: Yeah. I once asked a Greek how come ancient Greece was so innovative? He told me, “Well the ancient Greeks asked that question themselves. He said, “Because Greece was divided into separate city states, and actually it wasn’t Athens alone. The talented people would come from other city states and they would go to Athens. Whereas Egypt was very uncreative. And why was that? That was because it was flat and they weren’t split up in separate islands or on land divided by volcanoes as Greece, or mountains.”

So a central government was able to control all of Egypt and as a result ancient Egypt wasn’t very innovative. And the crazy Greeks were always fighting each other and always with these separate little nations, the city states.

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

Gregory Chaitin on how bureaucracy chokes science today. He complains, 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. In Chaitin’s view, a key problem is that the current system cannot afford failure — but the risk of some failures is often the price of later success.

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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