In last week’s podcast, “The Chaitin Interview IV: Knowability and Unknowability,” Walter Bradley Center director Robert J. Marks interviewed mathematician Gregory Chaitin, best known for Chaitin’s Unknowable Number, on, among other things, consciousness. What can mathematics contribute to the discussion. Also, what does Chaitin think about panpsychism (everything is conscious”)?

The discussion began with reference to David Chalmers’s 1996 book, The Conscious Mind: In Search of a Fundamental Theory, in which Chalmers coined the term “Hard Problem of Consciousness.” The term acknowledged what everyone knew, that human consciousness is a very difficult problem to understand, especially from a materialist perspective.
Are there other approaches? Chaitin offers a look at the challenge panpsychism presents to materialism:

This portion begins at 28:25 min. A partial transcript, Show Notes, and Additional Resources follow.

Gregory Chaitin: Everything has some degree of consciousness. It may be greater. It may be smaller. The maximum monad corresponds to God, whose consciousness is the largest possible conscious of everything, right? A rock doesn’t have that much consciousness. But he believes a physical system has n bits of consciousness if it has n bits of memory and processes, these n bits. So that would mean that an on-off light switch would have one bit of consciousness, and a human being would have a lot of bits of consciousness. It’s hard to have a cutoff. For example, if humans are conscious and the people who love dogs are certain that dogs are conscious, so is there a sudden place where consciousness blanks off as you go to more primitive life-forms… bacteria, viruses, light switches? So it looks a little implausible from a philosophical point of view. It seems more like it’ll just be gradually less and less consciousness, right? And you can go in the other direction. You can have a corporation. Does that have the consciousness? Does the internet have consciousness? Does the whole universe of consciousness, which presumably would be God?

Note: A monad, (the term originated in ancient Greek philosophy) is an indivisible unit. The term has sometimes been used with reference to God, e.g., “Monad of Monads.” Gottfried Wilhelm Leibniz (1646–1716), who was a mathematician as well as many other things, popularized the idea.

Leibniz had some interesting things to say about consciousness as well:

“If we were magically shrunk and put into someone’s brain while she was thinking, we would see all the pumps, pistons, gears and levers working away and we would be able to describe the workings completely, in mechanical terms, thereby completely describing the thought processes of the brain. But that description would not contain any mention of thought! It would contain nothing but descriptions of pumps, pistons, levers!” – Discussion of automatons, c. 1700

The difficulty of arriving at a materialist solution to the hard problem of consciousness is leading some thinkers, including prominent neuroscientist Christof Koch, to look favorably at panpsychism (everything is conscious). It is an alternative to the “nothing is conscious” approach, according to which the mind is what the brain does and consciousness is a user illusion generated by the brain.

Gregory Chaitin: My latest (and hopefully not last) paper is on consciousness, and it’s just being published in a book in honor of one of my distinguished colleagues here in Brazil. It’s “Consciousness and Information, Classical Quantum or Algorithmic”?

Chalmers didn’t know [in 1996] that maybe at the time, there were three, at least more than three, definitions of information. There’s Shannon information, entropy. There’s quantum information theory, which maybe didn’t exist in 1996 or was very incipient and now it’s a very big, fashionable topic. And there’s algorithmic information. And I’m sort of looking at Chalmers, is it 25 years later? It’s a philosophical essay.

Robert J. Marks: I’ve always looked at panpsychism as kind of a weird philosophy. I’m wondering if there’s any way that it can be tested. I doubt it. It’s going to be interesting to see if it can. But it is the position that consciousness is part of the universe just like mass and energy and all of the other stuff.

Gregory Chaitin: Well, they’re idealistic philosophies, which say that the universe is spirit really and matter is sort of an illusion. So that’s sort of related to an idea that I’ve been backing, which is the universe is made from information, that that’s the basic ontological basis.

The normal view if you dabble in metaphysics is that the universe is made from mathematics. That’s a Pythagorean idea, that God is a mathematician. And I prefer to say God is a … a computer programmer or a programmer.

There’s a book by a theologian, an Italian theologian, a priest, on this subject called Bit Bang. La nascita della filosofia digitale [2013]. It’s a wonderful book. Unfortunately, it’s only in Italian.

It’s saying that the universe is built out of information is like saying that the universe is really built out of spirit or the universe is in the mind of God; it’s not a material object. And the new version that physicists love is to say the universe is built out of quantum information. They want to try to get everything out of quantum information, including spacetime due to entanglement between qubits, for example. That’s a fashionable topic.

Note: The idea that the universe is, at bottom, information rather than matter has been expressed by well-known theoretical physicists. As George Gilder notes in Gaming AI, “John Archibald Wheeler [1911–2008] provocatively spoke of ‘it from bit’ and ‘the elementary act of observer-participancy’: in short… all things physical are information-theoretic in origin and this is a participatory universe.” (p. 41) James Jeans (1877–1946) held that “The stream of knowledge is heading towards a non-mechanical reality; the Universe begins to look more like a great thought than like a great machine. Mind no longer appears to be an accidental intruder into the realm of matter… we ought rather hail it as the creator and governor of the realm of matter.” (The Mysterious Universe, 1944, p. 137.)

On the other hand, some argue that information, as well as consciousness, is material. Melvin Vopson argues that information is the missing dark matter of the universe and Max Tegmark thinks “consciousness can be understood as yet another state of matter. Just as there are many types of liquids, there are many types of consciousness.”

Both could be wrong but both can’t be right.

Gregory Chaitin: But in a way, where we’re looking at an old idea, which is the universe is in the mind of God or the universe is spirit and matter is… It’s idealism as opposed to materialism, which is why this theologian was interested and put together a wonderful book surveying all of this work.

Robert J. Marks: Maybe. I think that still has a long way to go.

Don’t miss the stories and links from the previous podcasts:

From Podcast 4:

Why human creativity is not computable. There is a paradox involved with computers and human creativity, something like Gödel’s Incompleteness Theorems or the Smallest Uninteresting Number. Creativity is what we don’t know. Once it is reduced to a formula a computer can use, it is not creative any more, by definition.

The paradox of the first uninteresting number. Robert J. Marks sometimes uses the paradox of the smallest “uninteresting” number to illustrate proof by contradiction — that is, by creating paradoxes. Gregory Chaitin: You can sort of go step by step from the paradox of the smallest “uninteresting” number to a proof very similar to mine.

Why the unknowable number exists but is uncomputable. Sensing that a computer program is “elegant” requires discernment. Proving mathematically that it is elegant is, Chaitin shows, impossible. Gregory Chaitin walks readers through his proof of unknowability, which is based on the Law of Non-Contradiction.

Getting to know the unknowable number (more or less). Only an infinite mind could calculate each bit. Gregory Chaitin’s unknowable number, the “halting probability omega,” shows why, in general, we can’t prove that programs are “elegant.”

From Podcast 3:

A question every scientist dreads: Has science passed the peak? Gregory Chaitin worries about the growth of bureaucracy in science: You have to learn from your failures. If you don’t fail, it means you’re not innovating enough. Robert J. Marks and Gregory Chaitin discuss the reasons high tech companies are leaving Silicon Valley for Texas and elsewhere.

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 from 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.

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.

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
• 00:40 | What is unknowability?
• 06:07 | Does non-computable mean unknowable?
• 09:43 | A simple explanation
• 21:34 | Is creativity non-computable?
• 25:55 | Defining creativity
• 28:19 | Panpsychism

Additional Resources

• Gregory Chaitin’s Website
• The Unknowable by Gregory Chaitin
• Unravelling Complexity: The Life and Work of Gregory Chaitin, edited by Shyam Wuppuluri and Francisco Antonio Doria
• Mathematica
• Paul Erdős, Hungarian mathematician
• Chaitin’s Constant
• Jack Schwartz, American mathematician
• Roger Penrose, British mathematician and Nobel Prize winner
• The Emperor’s New Mind by Roger Penrose
• Shadows of the Mind by Roger Penrose
• Stephen Hawking, British theoretical physicist
• Selmer Bringsjord, engineer and computer scientist
• The Lovelace Test, a discussion between Robert J. Marks and Selmer Bringsjord at Mind Matters
• Giulio Tononi, neuroscientist and psychiatrist
• Christof Koch, German-American neuroscientist
• David J. Chalmers, philosopher and cognitive scientist
• The Conscious Mind by David J. Chalmers
• Panpsychism
• Gottfried Wilhelm Leibniz’s monads
• “Consciousness and Information, Classical Quantum or Algorithmic?” by Gregory Chaitin
• Bit Bang. La nascita della filosofia digitale by Giuseppe O. Longo (translation: Bit Bang: The birth of digital philosophy)

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