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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

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 a number of things, including whether computers can show creativity. Chaitin has thought a lot about that:

This portion begins at 21:34 min. A partial transcript, Show Notes, and Additional Resources follow.

Robert J. Marks: We’re talking, just in general, about the unknowable. Roger Penrose recently won a Nobel Prize for his work with Stephen Hawking on black hole theory. He also wrote a book called The Emperor’s New Mind: Concerning Computers, Minds and The Laws of Physics (1989) and he followed it up with The Shadows of the Mind: a Search for the Missing Science of Consciousness (1996).

He says that “creativity is non-computable.” He uses your work, along with Turing’s work and Gödel’s work, to make an argument that creativity is non-computable. Therefore, if we’re to pursue it by artificial intelligence, it’s something that will never be done. Now he refers to quantum as possibly the only non-algorithmic thing which occurs in nature. So he says all of this stuff must be due to quantum tubules in our brain and quantum collapse or something like that.

Note: Sir Roger Penrose (Nobel Prize, 2020 ) “posits that the noncomputable characteristics of human thinking spring from quantum effects in microtubules in the brain. The quantum collapse of a wave function to a deterministic state, reasoned Penrose, is nonalgorithmic and thus might be the source of noncomputable creativity.” – Robert J. Marks, “Advice to Physicists: Shut Up and Do Physics (May 25, 2020)

Robert J. Marks: I’m wondering if you have any thoughts on whether creativity is computable or not computable. Or do we know yet?

Gregory Chaitin: Yeah. I do have thoughts on this, and one or two remarks. One remark is that I did meet Penrose at Cambridge at a meeting. We were both speakers, and I went to him and I said, “Is the reason you think that a machine can’t equal human intelligence because you believe that we have a divine spark and computers don’t have a divine spark?” And he answered, a trifle annoyed I think, “Not at all.” Well, he did revert to a materialistic solution, which is quantum-mechanical,.

I’d been worried a lot about creativity when I started working on biological creativity and I connected it with mathematical creativity. There is this paradox — just like the first uninteresting number is, ipso facto, interesting. There’s a problem with creativity with having an algorithm for creativity, a computer program for creativity. The problem is that if you know how to do something, ipso facto, it’s not creative anymore.

Robert J. Marks: Yes. That’s the problem with identifying creativity. One can have a creative spark and you explain it to somebody. They sit there and rub their chin and say, “Well, that’s obvious.”

Gregory Chaitin: Well, creativity is what we don’t know how to do. And so, it looks like it’s a hard thing to program because, if we try to program productivity, that just becomes something mechanical and the frontier between what’s creative and what isn’t just moves a little forward. It’s a problem.

I think that my attempts at a little toy model of biological evolution… this is a controversial point… is a first step in the direction of a mathematical theory of creativity. I believe that Gödel’s incompleteness theorems and Turing’s work on computability and the halting problem are baby steps… well, they’re big, big baby steps… in the direction of a theory of creativity. That’s normally not how you view them, but I feel they feed into my little attempts at looking at biological creativity with a painfully simplified toy model.

So there is a paradoxical aspect to creativity. You could have a mathematical theory of creativity that enables you to prove theorems about creativity, but is not implemented in software. That doesn’t give you an algorithm for being creative. Because if it’s an algorithm, it’s not creative, right? But you might be able to prove theorems about creativity.

Like I can prove theorems that most numbers are random or unstructured. I can’t produce individual examples that I’m certain are. So it might be that you could prove theorems about creativity. But the theory wouldn’t give you a formula, a recipe, for being creative. Because once it does that, then it’s not creative. You see? There’s this paradox.

Robert J. Marks: Yeah. And also, those theorems that you’re talking about are kind of meta. You’re using creativity to write theorems about creativity. And one of the important things is to define creativity.

Selmer Bringsjord, has something called the Lovelace test, which is a lot better than the Turing test. He says that a computer program will be creative if and only if that computer program does something which is outside of the intent or explanation of the programmer. The Lovelace test is one that I believe that hasn’t been passed yet. So it’s going to be interesting to see if in the future AI does anything creative.

Note: The Turing test of whether a computer has achieved human-like intelligence assesses whether it can imitate humans to the extent that it fools humans. George Montañez of Harvey Mudd College notes that the test was based on a popular mid-twentieth century party game.

The central weakness of the Turing test is that the question doesn’t come down to whether people are fooled but rather what is really happening in the computer. The Lovelace test requires evidence that the computer acts independently of its programming. It is not known to have been passed.

Dr. Marks offers a simpler way to tell whether one is talking to a human or a computer: “It’s very easy to determine if who you’re talking to is a computer. You just ask them to compute the square root of 30 or something because a human would take a while to get the square root of 30.”

Gregory Chaitin: Turing says he will believe that a computer is intelligent if the computer will punish him for saying that computers aren’t intelligent.

Robert J. Marks: What did what did he mean by “punish” you? Come up and whack you across the head?

Gregory Chaitin: I guess Turing is referring to a notion of truth based on political considerations. People will say something’s true if society will fire you from your job if you disagree.

Presumably, Turing thought that a computer that can independently fathom such issues and act according to its own interests has achieved some type of creative intelligence

Next: Can mathematics help us understand consciousness? Chaitin offers a somewhat unorthodox approach.

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

From Podcast 4: 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.

Omega, the letter of a Greek alphabet. Greek numerals, mathematical eight hundred number concept. Abstract, digital, wireframe, low poly mesh, Raster blue neon 3d illustration. Triangle, line dot

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 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.

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.


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)


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

Podcast Transcript Download

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Why Human Creativity Is Not Computable