Hofstadter’s Gödel Escher Bach Fooled Us

Scott Aaronson writes:

A central thesis that many readers, including me, took from Douglas Hofstadter’s Gödel Escher Bach when young was that the secret of intelligence (and therefore, of AI) was going to have a lot to do with self-referentiality and “strange loops.” ...

Now, in 2026, we’ve succeeded at building AIs that outperform most humans at most intellectual tasks that are well-defined enough to judge. And at no point in the tech stack of those AIs — neither in the transformer neural nets, nor in the GPU clusters they run on, nor in the training process, nor anywhere else — did anyone need to build in anything about self-reference. ...

But the idea that you’d need explicit self-referentiality before you could get convincing and world-changing conversational intelligence? Let it be buried in a Westminster Abbey or Arlington National Cemetery for the most important wrong ideas in human history — geocentrism, Aristotle’s teleological physics, aether, phlogiston, Freud’s psychology, Marx’s prediction of a workers’ uprising followed by a classless utopia, etc. But buried it needs to be.

He could make a similar comment about fractals. Textbooks give examples using self-reference, and then say that the weather is also an example. But self-reference is not used to model the weather.

There is a distinction between the mathematical tool used for proof/pedagogy and the actual mechanisms that generate the phenomena in the real world.

Diagonalization can be used to construct irrational or transcendental numbers, but most transcendental numbers are not obtained or studied this way.

(I tried to post this comment on his blog.)

Quantum Nonlocality Explained FROM SCRATCH

A month ago, Curt Jaimungal interviewed Tim Maudlin on Can Quantum Mechanics Be Explained FROM SCRATCH?. Now, Part II just dropped, for another 3+ hours.

Maudlin is an expert on this subject, and he discusses in detail the work of von Neumann, Einstein, Bohm, Bell, and others saying that the concepts of locality, classical hidden variables, and quantum mechanics predictions are in conflict. One must be rejected.

What is not so clear is how Maudlin differs from textbook Copenhagen interpretation. Copenhagen says that the classical hidden variables are to be rejected. That is what von Neumann proved, under some assumptions. Then we have locality and predictions of quantum mechanics, with no problem.

Maudlin has some philosphical reasons for subscribing to classical hidden variables, so he ends up rejecting locality.

To me, no one has ever observed spooky action at a distance, so local theories are very much preferred. Bohm's pilot wave theory is crazy, because the theory is nonlocal, but all the observations magically turn out to be local.

Maudlin explains that all the great physicists rejected quantum nonlocality.

Tim: But they never straightforwardly acknowledged the nonlocality. And if you don’t believe that, 1:58:07 go read Bohr’s response to the EPR paper and see whether he straightforwardly says, “Yes, I believe in nonlocality. I believe in spooky action at a distance.” He denies it. ...

So I think Einstein saw correctly that if you accept this spooky action 1:59:25 at a distance, relativity itself is at risk. And he didn’t wanna put, you know, relativity at risk without good reason, and he couldn’t see any reason to accept the spooky action at a distance.

Now, he may not have liked it for other reasons. I mean, we, Newton didn’t like it, right? He says, he says, “No rational person would believe in it.” I mean, there are lots of people who find that just intuitively ugly or unacceptable or whatever. Curt: Mm-hmm.

Tim: And, and, and, and to this day, there are people who don’t wanna accept nonlocality, and they’ll more or less clutch at any straw to try to avoid it, as we’ll see. The psychology of that I can’t quite explain.

I can explain it. The entire scientific enterprise for millennia has been to figure out cause and effect, by tracing events to nearby actions. If that is all wrong, and our lives are controlled by the spooky astrology of far-away stars, then we need to reconsider all the known laws of science.

In fact, no such nonlocality has ever been discovered, and we can continue with what has worked for centuries.

Bell and Maudlin claim that all the great geniuses and textbooks are wrong. They have a belief in what a quantum theory ought to be, and they say that quantum mechanics, as understood by Bohr and von Neumann, does not qualify.

I agree with Newton. No rational person would believe in spooky action at a distance. Unless it is proved, of course.

Professor Dave Rants against Dr. Bee again

Professor Dave has attacked Sabine Hossenfelder again.

Dave Farina has one of the top science Youtube channels, with 4.4 million subscribers. That is enough to make a living. He is not a real professor, but has a large number of expository videos, mostly on elementary science. He also likes to debunk Flat Earthers and others he considers pseudoscientific or religious.

Hossenfelder is closer to being a real professor, and posts lots of videos, mostly on theoretical physics. She also does science news, and likes to cover cutting edge research. She does not do elementary expository videos. She avoids politics, except that she often criticizes research projects she considers unproductive.

So they would seem to have little or nothing to do with each other. But Dave regularly trashes Sabine in the harshest terms. It is strange, as it is unlikely that he even understands most of her videos.

Dave's politics are Woke Leftist and anti-Zionist. He recites Woke lines about race not existing, Whites being evil, LGBTQ talking points, etc. He wants Israel destroyed, and taken over by Arabs. His rants on these topics are filled with obscenities, and lack any scientific reasoning. He subscribes to weird conspiracy theories about Peter Thiel and the Jews. He strongly suspects that Thiel is funding Sabine.

Dave's latest video is 40 minutes of calling Sabine a racist. Odd, and she hardly ever says anything about race or politics.

It was all provoked by the Jason Arday scandal. He was a Cambridge U. professor who got exposed as a charlatan, and committed suicide. Dave explained the issue as some dubious accusations of plagiarism that might have been overlooked if he had been White, but which caused White racists to harass him to death.

No, I do not think the plagiarism is what got him in trouble with his employer. His problems were much deeper. He had lied about almost everything, including his childhood, his life story, his academic credential, his teaching, and his research. His autobiography was being published, and it was all lies. His research was garbage, and he had no ability to do academic work. And yet he was promoted as a great genius.

So what does any of this have to do Sabine? She tweeted a couple of times that one of the whistleblowers should not be fired for exposing Arday. Yes, that's all.

Dave is a culture warrior where he stands with the right-minded people who believe is Science, Atheism, and Wokism. He sides with whatever is published in respectable science journals, and he hates Sabine for throwing cold water on some big science projects. He loves whatever science government and universities are doing, and hates whatever Elon Musk and other billionaires do.

I have sometimes criticed Sabine myself, on this blog. But Dave is just an ideological and dishonest jerk. There is no way he can really believe what he says about race, Arday, and the whistleblower. He is like the woke activists who say that a transgender woman is just as much a woman as any other woman, or that a man can get pregnant. It is not science. It is an extreme ideological stance in order to support certain progressive objectives.

Palmer says Irrational Numbers Not Real

New tweet:

Quantum mechanics works perfectly in experiments, but Oxford physicist Tim Palmer argues it rests on a mathematical fiction: irrational numbers like √2 have no basis in physical reality.

Strip them out, and quantum's strangest mysteries disappear.

Palmer's theory makes a testable prediction: quantum computers will fail beyond 400 qubits, hitting a fundamental limit set by the discrete structure of nature itself.

The coming quantum computing race will determine whether our most successful physical theory contains a basic mistake.

Paywalled article. No, I do not think he is correct. I am just posting because I think it is amusing.

Possible AI Proof of Complex S6 Manifold

A new Claude AI LLM assisted paper claims to find a complex manifold structure on the six-dimensional sphere, S⁶. There are videos here and here.

The opposite result was claimed in 2016, but the argument was faulty.

If verified, this will probably be the biggest AI math accomplishment to date. So far, the biggest success are the Jacobian conjecture counterexample, and the Erdox unit distance problem.

Notes on Minkowski's Geometric Relativity

Einstein scholar Tilman Sauer writes a new paper:

Minkowski's Geometric Explanation of Lorentz Contraction

Hermann Minkowski's original explanation of relativistic length contraction using a space-time diagram and conic section geometry of a standard hyperbola is reconstructed on the basis of unpublished manuscript notes dated to the spring of 1908. The manuscript notes likely reflect Minkowski's preparation of a lecture to physics and mathematics teachers. They reveal Minkowski as an educator as well as a promoter of a mathematization of the physical sciences. I also comment on his interpretation of Einstein's work and on the use of language in his popularization of mathematics.

He did not find anything particularly interesting in the notes.

It is not clear that Einstein's work had much influence on Minkowski, if any.

He mentions Einstein’s work on the relativity principle as a continuation of Lorentz’s work. ...

He did not identify the principle of relativity and the principle of the constancy of the speed of light as the two defining principles for the special theory of relativity. Instead, he singled out Lorentz’s contraction hypothesis as a fundamental postulate, and the existence of a limiting velocity as an axiom. ...

He then stated his impression that Einstein had not yet achieved “full understanding of the facts” (“volle Einsicht der gegebenen Tatsachen”).

Minkowski mentions crediting Einstein for this:

Lorentz himself told me in a conversation in Rome that Einstein’s merit is to have recognized that the time of one electron is just as good as that of the other, i.e. to have recognized the equivalence of t and t′.

That may be Einstein's merit, but Lorentz surely understood that in 1895, because he used it to explain the Michelson-Morley experiment. And Poincare believed that Lorentz understood it, because it was part of the recommendation for Lorentz to get the 1902 Nobel Prize.

The whole point of the Lorentz 1895 theory was that Maxwell's equations held in the moving frame, for the transformed coordinates. For that to work, the transformed time has to be genuine time in the moving frame. Perhaps Lorentz was missing some conceptual details, but he had to believe that what he called "local time" was the locally observed time.

Discussion of Poincare is strangely absent. Minkowski wrote two papers on relativity, citing Poincare prominently in the first but not the second. Some of Minkowski work, such as the 4d spacetime, indefinite metric, and Lorentz covariance, appear to be straight out of Poincare. Minkowski died shortly afterwards, so we got no more explanation.

Sauer is loyal to Einstein, as evidenced by:

Minkowski knew about and cited Einstein’s famous paper from 1905 on the Electrodynamics of Moving Bodies (3), which introduced the special theory of relativity.

It is pretty clear that Minkowski would not have said that Einstein introduced the theory. If anyone, it was Lorentz, Poincare, and Minkowski.

Update: I happened to see a 2013 Sauer paper:

As is well-known,12 Einstein’s attempts to obtain an assistantship any- where failed flatly despite various letters of application. To make matters more difficult, Einstein and his fellow student Mileva Mari´c had fallen in love and, unfortunately, Mari´c had become pregnant in the spring of 1901, an unplanned circumstance that surely contributed to her failing the final examinations again at her second attempt in summer 1901. ...

Since Einstein now had a tenured job, he was able to marry Mileva Mari´c in January 1903.

This is such a strange way of describing the situation. The daughter Lieserl is believed to have been abandoned. He could have married and taken responsibility for the child, even without a tenured job.

The 1969 Book that Killed AI Research

The neural nets at the core of AI were invented in 1943, and popularized in 1957-60 as the Perceptron. It had the basic idea that was later developed into today's AI LLMs.

But not everyone recognized it. Prominent MIT professors wrote a 1969 book, Perceptrons: An Introduction to Computational Geometry, trashing the concept.

Reports by the New York Times and statements by Rosenblatt claimed that neural nets would soon be able to see images, beat humans at chess, and reproduce. ...

This book is the center of a long-standing controversy in the study of artificial intelligence. It is claimed that pessimistic predictions made by the authors were responsible for a change in the direction of research in AI, concentrating efforts on so-called "symbolic" systems, a line of research that petered out and contributed to the so-called AI winter of the 1980s, when AI's promise was not realized.

The book claimed to prove that perceptrons were hopelessly limited, as they could not even approximate a simple xor function.

The authors doubled down in 1988 updated edition, saying "little of significance [has] changed since 1969". At the time there was a revival of interest in neural nets, but the authors said they would fail to scale up.

We now know that those neural nets of the 1940s, 50s, and 80s do scale up, and perform spectacularly well. The bold predictions of the perceptron inventor must have been seen as wildly optimistic at the time, but they turned out to be correct.

I post this as an example of how smart people can be wrong about what is possible, and how brilliant research could be sidetracked.

Rosenblatt made a hardware computer perceptron in 1960, and that is now in the Smithsonian Museum. What no one knew until about 2012 was that video game chips would be the key to scaling up neural nets. [date corrected]

Here is a recent video that tries to relate these old ideas about neural nets to current research.