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TagGregory Chaitin

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Castaway in bureaucracy

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 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: https://episodes.castos.com/mindmatters/Mind-Matters-126-Gregory-Chaitin.mp3 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…

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Online education concept

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

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 math or engineering geniuses (Elon Musk came to mind, of course) can’t just follow the rules. This week, we look at Stephen Wolfram’s new program that checks your hard math. What can — and can’t — it do for mathematicians? https://episodes.castos.com/mindmatters/Mind-Matters-126-Gregory-Chaitin.mp3 This portion begins at 13:22 min. A partial transcript, Show Notes, and Additional Resources follow. Gregory Chaitin: Now, there is what I regard as a piece of AI, so it might be interesting to talk about it. My friend Stephen Wolfram (pictured), the system he’s created,…

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SpaceX Concept Spacecraft in orbit of the Earth. SpaceX Elon Musk Mars programm 3d render

Why Elon Musk and Other Geniuses Can’t Afford To Follow Rules

Mathematician Gregory Chaitin explains why Elon Musk is, perhaps unexpectedly, his hero

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: https://episodes.castos.com/mindmatters/Mind-Matters-126-Gregory-Chaitin.mp3 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,…

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black mathematics board with formulas

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.

In our most recent 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 whether math is invented or discovered. This time out, Chaitin talks about why he thinks great books on math, advancing new theorems, aren’t written much any more: https://episodes.castos.com/mindmatters/Mind-Matters-126-Gregory-Chaitin.mp3 This portion begins at 02:49 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks: You don’t hear the word “scholarship” very much anymore in academia. Gregory Chaitin: And people don’t write books. In the past, some wonderful mathematicians like G. H. Hardy (1877–1947, pictured in 1927) would write wonderful books like A Mathematician’s Apology (1940)…

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Red and Blue Spiral Fractal Background Image, Illustration - Vortex repeating spiral pattern, Symmetrical repeating geometric patterns. Abstract background

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?

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 (pictured) on how math presents us with a challenging philosophical question: Does math image deep truth about our universe? Or do we just make up these math rules in our own minds to help us understand nature? https://episodes.castos.com/mindmatters/Mind-Matters-126-Gregory-Chaitin.mp3 This portion begins at 00:39 min. A partial transcript, Show Notes, and Additional Resources follow. Gregory Chaitin: Deep philosophical questions have many answers, sometimes contradictory answers even, that different people believe in. Some mathematics, I think, is definitely invented, not discovered. That tends to be trivial mathematics — papers that fill in much-needed gaps because…

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Spiral Background.

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

In last week’s podcast,, “The Chaitin Interview II: Defining Randomness,” Walter Bradley Center director Robert J. Marks interviewed mathematician and computer scientist Gregory Chaitin on his method of describing true randomness:. If no theory is simpler than the data you are trying to explain, then the data is random. They also discussed the work of true randomness but also on how Ray Solomonoff (1926–2009), another algorithmic information theory founder, who pursued the “shortest effective string of information that describes an object.” But now, for a lighter touch, we learn that a musical comedy was made of Fermat’s Last Theorem. https://episodes.castos.com/mindmatters/Mind-Matters-125-Gregory-Chaitin.mp3 This portion begins at 19:24 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks: If you…

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Real Php code developing screen. Programing workflow abstract algorithm concept. Lines of Php code visible under magnifying lens.

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

In last week’s podcast,, “The Chaitin Interview II: Defining Randomness,” Walter Bradley Center director Robert J. Marks interviewed mathematician and computer scientist Gregory Chaitin on how best to describe true randomness but also on what he recalls of Ray Solomonoff (1926–2009), described in his obit as the “Founding Father of algorithmic information theory.” https://episodes.castos.com/mindmatters/Mind-Matters-125-Gregory-Chaitin.mp3 This portion begins at 10:30 min. A partial transcript, Show Notes, and Additional Resources follow. Gregory Chaitin (pictured): Ray Solomonoff was interested in prediction but I was more interested in looking at a given string of bits and asking, does it have structure or not, and the incompleteness results regarding this question. For example, most strings of bits have no structure, according to this definition. They…

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Infinite random numbers, original 3d rendering background, technology and science concepts

Chaitin’s Discovery of a Way of Describing True Randomness

He found that concepts from computer programming worked well because, if the data is not random, the program should be smaller than the data

In this week’s podcast, “The Chaitin Interview II: Defining Randomness,” Walter Bradley Center director Robert J. Marks interviewed mathematician and computer scientist Gregory Chaitin on randomness. It’s a subject on which Chaitin has thought deeply since his teenage years (!), when he published a journal paper on the subject. How do we measure randomness? Chaitin begins by reflecting on his 1969 paper: https://episodes.castos.com/mindmatters/Mind-Matters-125-Gregory-Chaitin.mp3 This portion begins at 1:12 min. A partial transcript, Show Notes, and Additional Resources follow. Gregory Chaitin: In particular, my paper looks at the size of computer programs in bits. More technically you ask, what is the size in bits of the smallest computer program you need to calculate a given digital object? That’s called the program…

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Close up cute little child girl spinning a coin to make decision. Heads or tails game.

The Chaitin Interview II: Defining Randomness

In the 1960s, mathematician and computer scientist Gregory Chaitin published a landmark paper in the field of algorithmic information theory in the Journal of the ACM – and he was only a teenager. Listen in as Robert J. Marks explores that paper with Chaitin, covering Chaitin’s definition of randomness and his philosophical interest in algorithmic information theory. Show Notes 00:27…

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White, grey and pink mandelbrot fractal.

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

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. Earlier, 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. Yesterday, we heard Chaitin’s recollection of how he (almost) met the eccentric genius Kurt Gödel (1906–1978). One way that Gödel stood out from many of his contemporaries was that he believed in God. He even wrote a mathematical proof of the existence of God. https://episodes.castos.com/mindmatters/Mind-Matters-124-Gregory-Chaitin.mp3 This portion begins at 17:16 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks: One of the things…

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mandelbrot set abstract mathematics computer generated

Gregory Chaitin’s “Almost” Meeting With Kurt Gödel

This hard-to-find anecdote gives some sense of the encouraging but eccentric math genius

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): https://episodes.castos.com/mindmatters/Mind-Matters-124-Gregory-Chaitin.mp3 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…

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Silhouette of human with universe and physical, mathematical formulas

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

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 on the almost supernatural awareness that the great mathematicians had of the foundations of reality in the mathematics of our universe: https://episodes.castos.com/mindmatters/Mind-Matters-124-Gregory-Chaitin.mp3 This discussion begins at 8:26 min. A partial transcript, Show Notes and Additional Resources follow. Robert J. Marks: There are few people who can be credited without any controversy with the founding of a game changing field of mathematics. We are really fortunate today to talk to Gregory Chaitin (pictured) who has that distinction. Professor Chaitin is a co-founder of the Field of Algorithmic Information Theory that explores the properties of…

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Close-up Shot of a Hand Holding Chalk and Writing Complex and Sophisticated Mathematical Formula/ Equation on the Blackboard.

The Chaitin Interview I: Chaitin Chats with Kurt Gödel

In this week’s Mind Matters episode, Robert J. Marks begins a conversation with mathematician and computer scientist Gregory Chaitin. The two discuss Chaitin’s beginnings in computer science, his thoughts on historic scientists in his field such as Leonard Euler and Kurt Gödel, and even the story of how a cold call to Gödel almost led to Chaitin meeting the famed…

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Bitcoin statistics

Artificial Intelligence Gaming the Stock Market

What are some assumptions about artificial intelligence? How does artificial intelligence affect the stock market? George Gilder and Robert J. Marks discuss assumptions about artificial intelligence, the stock market, and George Gilder’s new book Gaming AI: Why AI Can’t Think but Can Transform Jobs (which you can get for free here). Show Notes 00:30 | Introducing George Gilder 01:02 |…