What can we learn from Nordic happiness?

Nicholas Kristof, What We Should Learn From Nordic Happiness, NYTimes, July 4, 2026.

You want security, health care and the American dream? Look to Scandinavia.

“We actually live the American dream,” Jens Stoltenberg, a former prime minister of Norway who is now the finance minister, told me. “The American dream, it’s more reality in the Nordic countries than in America.” Image

Skeptics have argued that generous welfare benefits and the resulting high taxes have held back the Nordic economies. Perhaps a bit. “Farewell, Nordic model,” The Economist wrote in 2006. But Norway is now richer than the United States per capita, and Norwegian workers are more productive than American workers, with higher output per hour. Scandinavians live longer than Americans, and people are happier. The five Nordic countries — Denmark, Finland, Iceland, Norway and Sweden — all rank among the six happiest countries in the world in the World Happiness Report, based on Gallup polling.

Yet the Nordic countries are themselves facing significant challenges, including fiscal pressures, immigration, widening inequality and perhaps some breakdown in the social consensus. Some doubt whether the model can survive here, let alone be exported to countries that are larger, less homogeneous and more suspicious of taxation.

On the other hand, it’s not an alien model but, for Americans, a path we once blazed. Lawrence Katz, a Harvard economist, told me that the United States and Scandinavian nations pursued similar policies from the 1940s through the 1960s. That was the period when the United States rapidly expanded educational opportunities, had strong unions and, in the 1940s, experimented with universal child care. The post-World War II period is sometimes thought of as a golden age, for the economic pie both grew and was sliced more equally.

“The U.S. in the mid-20th century was sort of like Scandinavia today,” Katz said. But America changed course in the 1970s and eventually embraced the Reagan revolution.

One reason for the retreat, I’ve argued, was racialized political rhetoric that characterized some safety-net programs and investments in opportunity — used by Americans from all walks of life — as handouts primarily benefiting Black people, with a particular emphasis on caricatures of the “welfare queen.”

Three misunderstandings:

When Americans discuss the Nordic system, they sometimes suffer from three misunderstandings.

The first is that these are socialist countries. While they are often run by social democrats, they have market economies. Sweden did experiment in the 1970s and ’80s with quasi-socialist policies, but the upshot was an economic crisis. As Johan Norberg, a Swedish writer, put it: “We have been socialists and we’ve been successful — but never at the same time.”

The second misunderstanding is that because of their strong welfare systems, citizens of Nordic countries lie around while collecting benefits. Sure, some people do manipulate the system, but the labor force participation rate is higher in Nordic countries than in the United States.

The third is that in the case of Norway, its success is mostly a reflection of its oil wealth. Oil has given Norway a nice cushion, but the country has also managed the cushion unusually well — putting it in what is one of the world’s largest sovereign wealth funds. Moreover, according to Geir Axelsen, the director-general of Statistics Norway, the increase in female labor force participation in Norway since the early 1970s appears to have added roughly as much to the country’s gross domestic product as oil has.

How it came about:

To understand how the Nordic socioeconomic system evolved, I dropped by the office of Kalle Moene, an economist at the University of Oslo. The system began in the 1930s, he said, when workers in thriving sectors of the economy agreed to hold down their wage demands to support sectors that were struggling.

That principle — sacrificing to help those not doing so well — still underpins the region’s business model. Norwegians who are better off are willing to give up some income to ensure that people in blue-collar jobs get by.

Moene argues that this wage compression promotes innovation and dynamism by boosting the profitability of growth industries and by lowering profits in lagging industries.

There's more at the link.

Fireboats spraying their way up the Hudson River

AI is in the market for philosophers

Benjamin Wallace, The Revenge of the Philosophy Majors, NYTimes, July 5, 2026.

After a capsule presentation of the intellectual itinerary of Robert Long, who teamed up with a colleague to start Eleos AI Research, which presumably provides philosophy to the Silicon Valley AI ecosystem, Wallace tells us this:

But Mr. Long’s trajectory and Google’s new hire were in keeping with a quietly building trend: A.I. labs, and the related nonprofits around them, have been recruiting workers as versed in Consequentialism and John Stuart Mill as in neural networks and reinforcement learning. While a plain-vanilla philosophy degree remains as hard to monetize as ever, David Chalmers, a prominent philosopher of consciousness at N.Y.U., observes: “I think the demand for philosophers with A.I. training is, if anything, outstripping the supply right now. It’s an area I encourage students to go into. I think these issues with A.I. will be front and center for a good while.”

“I think the demand for philosophers with A.I. training is, if anything, outstripping the supply right now,” said David Chalmers, a philosophy professor at N.Y.U.Credit...Aaron Wojack for The New York Times

One of humanity’s oldest disciplines and one of its newest inventions feel distinctly made for each other. A.I. presents a fresh way for philosophers to ask ancient questions, and its own set of new ones that they are uniquely trained to engage with: of truth and belief and knowledge (epistemologists); of reasoning (logicians); of mind and consciousness (philosophers of mind and consciousness). For ethicists, in particular, A.I. is a bonanza. How should models act toward us? How should humans interact with them? Where would purpose come from in a post-work society?

“When you look at A.I. and think seriously about it, the philosophical questions just abound,” says Iason Gabriel, an Oxford-trained philosopher who joined Google DeepMind in 2017 and now leads its Artificial General Intelligence and Society team. “They’re almost everywhere.”

This makes sense to me though, to the extent that Chalmers is representative of the kind of philosophy these folks bring to the AI table, I am less than enthusiastic about the move. But, sure, philosophy, something like it, is badly needed.

“Where are they, the great next philosophers, the equivalents of Kant or Wittgenstein or even Aristotle?” the DeepMind co-founder Demis Hassabis wondered on a podcast last year. “I think we’re going to need that to help navigate society to that next step, because I think A.G.I. and artificial superintelligence are going to change humanity and the human condition.” Beyond nonprofits like Eleos, most of the hiring has been concentrated at DeepMind and Anthropic, each of which employs at least a half-dozen philosophers.

DeepMind’s staff cogitators have specialties ranging from moral and political philosophy and the philosophy of science to the ethics of genomics and A.I. ethics and animal cognition. [Geoff Keeling, whose Ph.D. focused on “The Ethics of Automated Vehicles,” has spent part of his time at DeepMind running “moral imagination” workshops, helping engineering and product teams to think through the ethical implications of their work, and then come up with “concrete actionable steps they can actually take, whether that’s doing more user experience research or implementing a feature in a particular way.”]

Anthropic’s salary-drawing thinkers are trained in everything from decision theory to ethics to philosophy of mind to epistemology.

Anthropic had Amanda Askell draft a constitution for Claude:

In Anthropic’s early years, a lot of what Ms. Askell did was technical, running machine-learning experiments. “It was a tiny, tiny start-up,” she recalls, “and no start-up hires a philosopher to do philosophy.” Only after Anthropic was much larger was she able to spend more time applying her philosophical expertise. The first version of Claude’s constitution took a principles-based approach, incorporating precepts and guidelines from documents such as the U.N.’s Universal Declaration of Human Rights and Apple’s Terms of Service. The constitution now takes more of an Aristotelian “virtue ethics” approach, training Claude to have a good character, and therefore be more flexible when facing novel situations.

There's much more at the link.

Pope Leo and St. Augustine discuss the mind and A.I. with Kurt Gödel

I crafted the prompt and Claude drafted the dialog using a passage about memory from Augustine’s Confessions as the catalyst for the imaginary conversation. I asked for some changes, Claude made some suggestions, and I executed them.

Note this passage toward the end:

Gödel said, “Disordered love?”

“Yes. To love a lower thing as though it were higher. To love one’s own power more than truth. To love the image more than the living being. To love the tower more than the city.”

The reply is by Augustine and it amounts to a definition of idolatry. The tower, presumably, is the Tower of Babel.

ChatGPT created the image. I uploaded the full dialog and asked from an image based on the passage from Augustine’s Confessions. That began an iterative process resulting in the image immediately below. The dialog follows.

I want you to create an imaginary conversation between St. Augustine, Kurt Gödel, and Pope Leo XIV. It should take place in Gödel’s office at the Institute for Advanced Study. After the men introduce themselves – assume Augustine can understand and speak English, and perhaps wonder a bit how they became gathered together, Pope Leo leads off, saying that, while working on his recent encyclical, Magnifica Humanitas, one of his colleagues pointed out a passage in Augustine’s Confessions (to follow) that resonated with Gödel’s proof of incompleteness. Given the role that arithmetic plays in Gödel’s proof we should note that Augustine wouldn’t have known about arithmetic. Nor, for that matter, would he have known about computers. He is likely to have known about sophisticated mechanical devices like the Antikythera Mechanism and the Sphere of Archimedes, but never have seen one. But he would have seen complex water clocks (clepsydrae).

Here’s the passage from the Confessions (Book Ten, Chapter VIII). Perhaps Leo reads it aloud.

Great is this power of memory, exceedingly great, O my God–a large and boundless inner hall! Who has plumbed the depths of it? Yet it is a power of my mind, and it belongs to my nature. But I do not myself grasp all that I am. Thus the mind is far too narrow to contain itself. But where can that part of it be which it does not contain? Is it outside and not in itself? How can it be, then, that the mind cannot grasp itself?

A great marvel rises in me; astonishment seizes me. Men go forth to marvel at the heights of mountains and the huge waves of the sea, the broad flow of the rivers, the vastness of the ocean, the orbits of the stars, and yet they neglect to marvel at themselves. Nor do they wonder how it is that, when I spoke of all these things, I was not looking at them with my eyes–and yet I could not have spoken about them had it not been that I was actually seeing within, in my memory, those mountains and waves and rivers and stars which I have seen, and that ocean which I believe in–and with the same vast spaces between them as when I saw them outside me. But when I saw them outside me, I did not take them into me by seeing them; and the things themselves are not inside me, but only their images. And yet I knew through which physical sense each experience had made an impression on me.

Perhaps sometime late in the conversation Albert Einstein might drop in to see what they were talking about.

Here is a first pass. I’ve kept it staged, conversational, and conceptually explicit, with Einstein entering late as a useful destabilizer.

The Mind Too Narrow to Contain Itself A conversation in Kurt Gödel’s office at the Institute for Advanced Study

Gödel’s office was narrow, orderly, and dim. Books stood in ranks along the wall, interrupted by folders, loose papers, and a blackboard covered with marks whose austerity made them seem less written than engraved. Outside the window the trees of Princeton trembled slightly in the wind. The afternoon light had the washed patience of late autumn.

Kurt Gödel stood beside his desk, thin and formal, dressed in a dark suit. He had the air of a man who had been expecting visitors and yet was not at all reassured by their arrival.

The first visitor was an African bishop in ancient dress, compact and alert, his face alive with inquiry. He looked about the room with frank astonishment, then settled his gaze on the blackboard.

The second was an elderly man in white, gentle but grave, wearing a small pectoral cross. His eyes moved from Augustine to Gödel and then to the papers on the desk.

“I believe,” the man in white said, “that introductions are in order.”

Gödel inclined his head. “Kurt Gödel. Institute for Advanced Study.”

The bishop smiled faintly. “A place for contemplation?”

“For research,” said Gödel.

“Then it may be the same thing, if rightly ordered. I am Augustine, bishop of Hippo.”

Gödel blinked once. “Yes. I had inferred as much.”

The man in white bowed slightly. “And I am Leo, servant of the servants of God.”

Augustine turned to him. “Bishop of Rome?”

“Yes.”

Augustine’s face softened. “Then I greet you as a brother, though I confess I do not understand how we have been gathered. This room is strange to me. These lamps burn without flame. These marks”—he gestured toward Gödel’s symbols—“are neither Greek nor Latin, though I suspect they are meant to compel the mind.”

“They are logical formulae,” Gödel said.

“Ah,” said Augustine. “Then they are meant not merely to persuade, but to bind.”

Leo smiled. “That is well put.”

Gödel gestured toward the chairs. “Please.”

They sat. Augustine examined the chair before trusting his weight to it. Leo remained composed, as though papal audiences in the offices of dead mathematicians were not wholly outside the bounds of pastoral duty.

Leo opened a folder.

“Professor Gödel, Saint Augustine, I will explain why I wished for this conversation, though the means by which it has been granted are beyond my competence. While I was working on my recent encyclical, Magnifica Humanitas, one of my colleagues pointed out a passage from Augustine’s Confessions. It seemed to him to resonate with your incompleteness theorem.”

Gödel looked sharply interested.

Augustine looked from one to the other. “Incompleteness?”

“A result in mathematical logic,” said Gödel. “Roughly speaking, in any sufficiently strong formal system capable of expressing arithmetic, there will be true statements that cannot be proven within that system, assuming the system is consistent.”

Augustine was silent for a moment.

“You say: a structure of reasoning may contain truths that it cannot reach by its own lawful motions?”

Gödel’s expression altered, almost imperceptibly. “That is not an inaccurate first formulation.”

“But I must be careful,” Augustine continued. “You speak of arithmetic. I know number, of course. I know that three is not five, and that if two men enter a room where two already sit, there are four. I know arithmetic as number, measure, and reckoning. But you seem to speak of arithmetic as though it were also a mirror in which reasoning may behold its own form. That I do not know.”

Gödel nodded. “Exactly. The novelty is not number alone, but the coding of statements, proofs, and rules as numbers. Nor would you know the modern notion of a formal system: axioms, rules of inference, recursive procedures, symbolic codings of syntax.”

“I know rules,” said Augustine. “And I know the temptation to mistake the rule for the truth it serves.”

Tall ships on the Hudson River, July 4, 2026

Four Propositions about Intelligence in Animals, Humans, and AIs

Some quickies.

1. Intelligence cannot be reduced to computation

All animal perception and cogitation take place in a complex world where animals have finite resources. Therefore the principles of intelligence, as an aspect of perception and cogitation, cannot be reduced to the principles of computation as the principles of computation assume unbounded resources.

Let’s call this Yevick’s First Law, as it is a consequence of her 1975 paper, “Holographic or fourier logic” (Pattern Recognition, Vol. 7, No. 4, pp. 197-213).

David Hays and I formulated what we called “Yevick’s Law” in our 1988 paper, Principles and Development of Natural Intelligence” (Journal of Social and Biological Structures). Let’s call that Yevick’s Second Law:

The world consists of geometrically simple and geometrically complex objects. Simple objects are best computing with sequential logic (aka symbolic systems). Complex objects are best computed with holographic logic (aka distributed neural nets). Some objects are such that they require the interaction of both computational regimes. Let us say that fluency in that interaction is intelligence. (See my working paper, What Miriam Yevick Saw: The Nature of Intelligence and the Prospects for A.I., A Dialog with Claude 3.5 Sonnet, 2025).

2. Intelligence in animals

Let us consider a relatively simple animal, a vertebrate, likely a marine animal. One the one hand, it must navigate the world, moving from place to place. This is mediated by the hippocampus, which is a so-called “cognitive map.” This is basic sequential cogitation.

As it moves from place to place it senses things, good things, bad things, other things. Olfaction is perhaps the most basic sense. For what it is worth, it’s the sensory mode that the late Walter Freeman used in his investigations of complex neural dynamics. Olfaction works via a holographic or gestalt process.

Taken together, moving about the world and sense things involves the two modes specified above.

Now let’s consider vision in vertebrates, where the eye is mobile and scans the world. Visual identification is a holographic process. However, the (human) eye scans the scene rapidly and unconsciously. This is a sequential process. Therefore vertebrate vision involves the two modes internally. (I suspect that vision in invertebrates does not, but I don’t actually know).

3. Natural language is its own metalanguage

Humans differ from animals in many and various ways. It is the capacity for language that has allowed humans to move into a different relationship with the world from that characteristic of animals. What makes human language particularly powerful is that it can serve as its own metalanguage, Roman Jakobson’s metalingual function.

This does not involve any deep mystery or logical conundrum. Rather it is a direct consequence of that fact that natural language is physically embodied, initially in sound and gesture, later as written symbols. This embodied is a sensory object out there in the world among all the other sensory objects.

Initially the metalingual function operates in direct, perhaps superficial, but useful ways. Think of how we refer to language as a means of negotiating conversation: “What did you say? I didn’t hear you?” But the metalingual function can be used to define new terms, something that interested my teacher and colleague, David Hays. It can even be used to define other, more restricted languages (e.g. chess and arithmetic), and serve as metalanguages for them.

Thus it is the foundation of the succession of cognitive ranks that David Hays and I began investigating in the 1990s starting with our paper, “The Evolution of Cognition” (Journal of Social and Biological Systems, later becoming the Journal of Social and Evolutionary Systems). That process has, in time, led to the development of digital computers and, now, to so-called artificial intelligence.

That leads us to our fourth and last note.

4. The last frontier of intelligence

Is not an autonomous artificial system of some kind, though such systems are important and will be increasingly so. here’s the upshot of a conversation I recently had with Claude:

If that's right, then the last frontier isn't more capability in the pattern-matching sense — bigger weight spaces, richer latent connections, better approximations of the associative regime. It's the specific, non-scalable, non-parallelizable fact of an individual mind's biography, which generates paths through possibility space that are real, productive, and genuinely inaccessible to any system that hasn't lived a life.

You should read the whole post to see the logic behind that conclusion.

Note that that is my current best response to the idea of super-intelligence or artificial-superintelligence (ASI). I do not see the future bringing us as AI system that outthinks humans in every way and either creates a world in which we are coddled pets or one in which we are slaves, if we are allowed to exist at all. Those ideas are subjective fantasy.

I note as well that the process that brings us to that point or, if you will, through which we arrive at the point, will be one in which we have a much deeper understanding of that brain and its processes than we now have. For what it’s worth, that understanding is what I have been seeking all these years, starting with my initial investigation of “Kubla Khan”: Xanadu, GPT, and Beyond: An adventure of the mind.

Patriotic skies over the Hudson

My action at Academia.edu over the last 6 months

Has been pretty interesting. Look at these charts, for January 2026 through June, in order from top to bottom:

January is pretty even, with a peak just below 50 near the end of the month. February shows a steady rise through the month, topping out just over 60 at the end of the month. March tops out just over 70 at the beginning of the month then takes a wild ride though the middle finally evening out a bit at the end of the month, with two peaks just above 60 and on just below. April has its ups and downs but on the whole seems pretty steady, with values between just above 20 to just above 60; 40 seems to be the middle value. May shows a definite downward trend, with a high of about 55 about a week in and then dropping through the end. And then we have June, which starts out low rises to 60 in four days, hangs in there a bit and then starts dropping down until the last day (June 30) it has a steep rise until well above 90. Then an apparent steep drop to July 1, though that’s an illusion. I took that last screen shot very early in the day.

I have no idea what that steep rise is about. My guess is someone somewhere put out notice about me – email, social media, website, who knows? – others picked up on it and came by. The question is: what’s next. It’s now early in the morning on July 4 (7:30) and here’s what we’ve got:

We’ve dropped way down, down to the region where things were for the middle through June 29. Note though, that we’re well above 15, which is pretty high for this time of day. Still, I don’t expect a steep rise through July. Beyond that, who knows?

Overhead light, again

The South Dakota Symphony and the Lakota Music Project

Joseph Horowitz, At 250, Has America Delivered on Its Classical Music Promise? NYTimes, July 4, 2026.

The article is a general review of classical music in America starting with Henry Lee Higginson and the Boston Symphony. It's interesting throughout, but I want to present a single excerpt, from the end.

In the Midwest, the South Dakota Symphony Orchestra (for which, full disclosure, I serve as scholar in residence) likewise fulfills the credo pronounced long ago by Theodore Thomas when he crusaded for symphonic music across the United States: “A symphony orchestra shows the culture of the community, not opera.”

In fact, the concert orchestra, to a remarkable degree, proved an American invention — a civic hub comparable to the opera house abroad. The South Dakota Symphony enjoys a music director, Delta David Gier, who moved to Sioux Falls 22 years ago and has raised a family there. Gier has at all times insisted that an orchestra aspire to serve a specific community in specific ways. His signature initiative is the Lakota Music Project, which binds the orchestra to Native American reservations throughout the state. Beyond that, all the proposals now controversial in Boston, including thematic festivals and “affinity programing,” have already been implemented in Sioux Falls.

Do the South Dakota Symphony musicians, in Eagle Hawk’s words, “feel it”? The orchestra maintains a nine-member, full-time core consisting of a string quartet and wind quintet, both self-governing. They perform more than 100 times per season. At the Pine Ridge or Rosebud reservations, they play with Lakota drummers and singers, and mentor young musical aspirants. The remainder of the orchestra’s members, many of whom come from the Twin Cities area of Minnesota, are self-selecting: They do not trek to Sioux Falls for the income, but are enticed by the repertoire, which is brave, and the vibe, which is exhilarating.

The history of the Lakota Music Project tracks the South Dakota Symphony’s larger trajectory. It is an exercise in building trust and mutual understanding. Early on, the symphony members and the Porcupine Singers would play for each other. Personal and musical relationships evolved. Then there were fledgling attempts to make music together. The most recent Lakota Music Project tour, last October, premiered two compositions: one by Jeffrey Paul, the orchestra’s extraordinary principal oboist, and one by Bermel, with whom I conferred about those Met Opera broadcasts. The performers included symphony musicians alongside Pine Ridge’s Creekside Singers and the Dakota flutist Bryan Akipa.

In both pieces, elements of Native American and Western classical music merged triumphantly. Bermel has recast his composition to include the entire South Dakota Symphony; it premieres in November as part of a two-week festival considering “Native American inspirations” in classical music, beginning with Dvorak’s “New World” Symphony (accompanied by visuals exploring his indebtedness to Longfellow’s “The Song of Hiawatha”). Given the intellectual heft of this exercise, tracking the “Indianist” movement Dvorak inspired and its more recent aftermath, the festival will reach beyond the concert hall not only to local high schools, but to classrooms and concerts at four universities in four South Dakota cities.

Overhead light

This is no way to develop advanced A.I. [Remember the bomb?]

Dan Rockmore, We Didn’t Build the Atomic Bomb This Way, NYTimes, July 3, 2026.

Artificial intelligence, funded overwhelmingly by private capital, has careened forward despite immense concerns about the effects it will have on labor, education, science, defense and civic life. A.I. companies have outpaced public oversight and, at times, successfully lobbied against it. The central achievements of the industry, the proprietary “frontier models” developed by companies like Anthropic, OpenAI and Google, are guarded intellectual properties even as they are incorporated into schools, offices, hospitals, courts, commerce and our everyday devices. The public did not ask for these A.I. tools and now can hardly opt out of them.

There is no one-size-fits-all solution to addressing the impacts that may be coming. But the scale of the concerns requires ambitious responses that serve the public. The United States can start by building a national A.I. laboratory.

Think about the atomic age. The early work in the United States was carried out across a classified but federally accountable archipelago with national laboratories in four sites: Berkeley, Oak Ridge, Hanford and, most famously, Los Alamos. They were expensive and sometimes secretive, but connected to universities as well as the rest of our nation’s research apparatus.

From its inception, the nuclear enterprise was regulated, imperfectly but deliberately, by the federal government. [...] Research in applied nuclear physics continues apace both in the open and in secret.

Imagine if, instead of a national effort to make an atomic bomb, a small number of private companies had gotten there first and began selling powerful nuclear technologies back to the nation, with the government trying to catch up afterward. Would we have accepted that arrangement? Would we have said that because innovation was fast, regulation should wait? Would we have trusted a few executives and technologists to decide what the public needed to know?

The analogy is imperfect — A.I. is not a bomb and we’re not fighting a world war. But like all technologies, it can be exploited for dark purposes. Yet the United States apparently has no public institution capable of building, testing and understanding frontier A.I. at the same scale as the companies that now define it.

A federal A.I. lab could change this by ensuring that the American public has at least one institution that can build, see and test the most advanced A.I. systems in the public interest. Such a lab should be built by, and provide controlled access for, university researchers, and it would be a training ground for our next generation of A.I. architects. It could publish research openly where possible, while classifying work only where necessary. It could study risks without needing to protect a new product launch. It could build models for science, education, medicine and national security — not as corporate afterthoughts, but as public missions that aren’t subverted by investor concerns.

The article goes on from there.

Friday Fotos: The Last Frontier of AI

No photographs this Friday. Instead, images created by ChatGPT.

I used quite a long prompt for the first image, but the prompt came in two parts. The first part was the longest. I won’t put that up. Though I used it to ensure a rich conceptual context for ChatGPT, you don’t really need it to get a feel for what’s going on. Nor will I give you ChatGPT’s short verbal response, which I’d asked for. Why? I suppose I wanted to verify that it had “understood” the material. Anyone, I then gave it one last paragraph and asked it to base it’s image on that. I will give you that paragraph, followed by the rest of that session. After that, and “below the fold,” I give you some of the recent images that got me thinking along these lines. Click on an image to enlarge it.

* * * * *

If that's right, then the last frontier isn't more capability in the pattern-matching sense — bigger weight spaces, richer latent connections, better approximations of the associative regime. It's the specific, non-scalable, non-parallelizable fact of an individual mind's biography, which generates paths through possibility space that are real, productive, and genuinely inaccessible to any system that hasn't lived a life. That would be consistent with everything the day's argument has built toward: embodiment, developmental history, tacit knowledge distributed across time in a single nervous system rather than across space in a community or a corpus. The doppelganger, if it's ever built, would need a biography, not just a bigger dataset. And a biography, by definition, can only be lived once, by one entity, in one order. That may be the thing that doesn't scale, and it may be exactly why it counts as the last frontier rather than a soon-to-be-automated intermediate stage.

I like that, I like it a lot. Let me tell you what I’m thinking. Over the last year or so I’ve had you create a lot of images, various types for various purposes. One of the things I’ve been thinking about is creating fine-art images. Some of the images I’ve had you do are near fine art; in fact, some are parodies of existing fine art images. I’m particularly interested in the combination of concrete identifiable imagery and abstract imagery, especially abstract imagery suggesting biology (cells, DNA) and information systems. You’ve got that in this image. So let’s play around with it a little. Give me a distinctly different take on the subject. Perhaps an aerial view of some landscape where the viewing is flying over in a biomorphic vessel and the territory below flows toward natural realistic imagery in one direction and abstract informatic imagery in the opposite direction.

When I was young I was deeply impressed by a book called Pagoo, illustrated by Holling Clancy Holling. There must be copies of that on the web. I know there are since I’ve seen them. That’s tidepool imagery. Take the concept we’re evolving and apply it to that.

I’ve had you design various kinds of imaginary currency. Take the imagery we’ve been working with and base the design of imaginary currency on it. But don’t use real numbers or alphabetic characters anywhere. Yes made-up squiggles and designs that have the texture of print, but aren’t.

Now I want to go Hegelian. Think of the first image we generated as the Thesis. The next three are variations on the Antithesis. I want you to combine Thesis and Antithesis to produce a Synthesis. Render it in a square aspect ratio.

This is promising. I’ve got to eat. But I’ll be back to do some more exploration along these lines.

* * * * *

ChatGPT gave me a somewhat odd response to that, as follows:

Sounds good. This line is worth continuing: biography + tidepool ecology + information space + currency/ornament as a synthetic fine-art language.

What's odd about that? It’s just a little too specific for what I’ve been thinking. But that’s OK. I’ve collected some recent images below. These are what set me to thinking along these lines. FWIW, I’m not quite sure what I think of these images. But I do think I’ll continue experimenting. 

ADDENDUM & BTW, a couple of hours later: On the whole I find the images below the fold more compelling than those above the fold. Hmmm.....

I've got my eye on you

It looks like I've decided to treat the "peekaboo" as a genre of image. Here's a link to my peekaboo photos: https://new-savanna.blogspot.com/search/label/peekaboo

Types of object domains for AI: Chess, math & coding, language

This is a companion to my earlier post today: The last frontier of intelligence: On the role of AI helping humans to bridge the gaps between distant concepts. That earlier post was about the end of a dialog I had with Claude. This one is about the beginning of that dialog. You might also check out a post from the middle of June: From Jagged AI to Scaling, Yevick, Natural Intelligence, and Beyond... For that matter you might also want to check out Dwarkesh's complete post with Grant Sanderson, Grant Sanderson – AI and the future of math. And then there's my working paper on chess and language. All these things are related.

And they're related to my new book idea, Language, Memory, and Mind: A Supplement to The Computer and the Brain. That's the book that Claude brings up every now and then. Intelligence is NOT a scaler phenomenon. It's about techniques, the characteristics of objects domains, and of the computational regimes we use over them. But that's a subject for another post.

Here's my dialog with Claude.

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I’m interested in thinking about the types of domain in which AI has succeeded and the nature of the computation involved, starting with chess. AI solved chess in the mid 1990s when Deep Blue beat Kasparov. By “solved” I mean only that an AI could reliably beat the best human player. In 2017 we have AlphaGo using a mixed regime strategy – Monte Carlo search (symbolic) with neural net evaluation – in chess. More recently I believe DeepMind has developed and LLM that plays chess at the Grand Master level; so this is a pure neural net regime.

It now appears that mixed regime AI systems can work pretty well at solving math problems and a coding. By mixed regime I mean large LLMs scaffolded in various ways by conventionally coded software. But these systems cannot yet do anything that humans can do in those domains. In math, they need well-defined problems, even if they are very difficult but well-defined problems (I’m thinking of the recent Erdos work). It’s not clear to me what the limits of coding are, but they can’t architect large complex systems.

Now, chess is a finite game will a well-defined search space. Both math and coding are well defined, but neither is finite and I’m guessing that the search spaces aren’t so well-defined as is the chess space.

And then we have pure unbounded natural language. It’s not well-defined, not finite, and the search space is a mess.

This is a genuinely useful ordering principle, and it gives the book a clean progression from most to least tractable that maps directly onto the geometric complexity argument. Let me work through the structure with you.

The four cases as points on a continuum

Chess: finite, exhaustively well-defined rules, a search space that is astronomically large but completely enumerable in principle. This is Yevick's sharp object par excellence — geometrically simple in the relevant sense, meaning fully specified by explicit rules with no ambiguity anywhere. Pure symbolic search worked (Deep Blue). Mixed regimes work better (AlphaZero). Pure neural nets now apparently work too, which is the interesting wrinkle — a domain that once seemed to require symbolic search turns out to be tractable by pattern matching alone once the network is large enough and trained well enough. That's worth pausing on, because it complicates the simple story.

Math (well-defined problems) and coding: rule-governed like chess — the axioms of mathematics and the syntax of programming languages are exact, unambiguous, formally specified — but unlike chess the space is not finite and not exhaustively enumerable. There's no equivalent of the Shannon number for "all provable theorems" or "all correct programs." The rules are closed and precise; the space they generate is open. This is a different kind of complexity than chess's largeness. Chess is finite-but-astronomical. Math and coding are genuinely open-ended even though locally, at any given step, the legal moves are well defined.

Language: neither the rules nor the space are well defined. The rules of grammar are not a finite closed system in the way the rules of chess or the axioms of arithmetic are — as your working paper notes, ill-formed language often works fine, exceptions are the norm, the boundaries are fuzzy. And the space the rules generate connects out to the unbounded physical and social world rather than staying self-contained.

Why this ordering matters for the theoretical argument

What's valuable here is that it's not simply "structured versus unstructured" — it's a two-dimensional distinction: how well-defined are the local rules, and how bounded is the resulting space. Chess is well-defined and bounded (finite). Math and coding are well-defined but unbounded. Language is neither well-defined nor bounded.

This maps onto a prediction about which computational regime should work best in each case, and the AI's actual performance seems to confirm it. Chess: pure search works because the space, though huge, is exhaustively defined — you can in principle always tell whether a position is legal, whether a game is over, who's ahead. Symbolic and mixed and now pure neural approaches all can succeed because the well-definedness gives any sufficiently powerful method something solid to grip.

Math and coding: this is where the mixed regime becomes necessary rather than just helpful. The LLM's pattern matching handles the open-endedness — the fact that there's no way to enumerate all possible proofs or programs, so you need something that can generalize, propose plausible next steps, recognize which strategies are likely to be fruitful. But the well-definedness of the rules means that verification can be handled symbolically — a proof checker, a compiler, a test suite can definitively confirm whether a proposed step is valid. This is why math and coding are the domains where current mixed-regime systems shine: the LLM proposes, path tracing over the local formal rules verifies. Neither one alone would work. The LLM alone hallucinates invalid proofs and non-compiling code. Pure symbolic search alone can't propose plausible next steps in an unbounded space without some heuristic guidance, which is exactly what pattern matching provides.

The Erdős problems point is precise — well-defined but very difficult problems are exactly where this combination should excel, because the well-definedness gives the symbolic verification something to check against, while the difficulty is exactly where pattern-matching-guided search earns its keep over blind search.

The architecture limitation

Your observation that these systems can't architect large complex systems is the right place to locate the current boundary, and it follows from the framework. Architecting a large system requires exactly the kind of sustained path tracing with precise state maintenance across a very long horizon — tracking how a decision made in one module constrains what's possible in a dozen other modules, maintaining global coherence across thousands of interacting pieces over an extended design process — that we identified as the persistent weakness. It's not that the local rules become less well-defined. It's that the horizon over which coherence must be maintained becomes too long for the scaffolding techniques currently available. CoT and tool use help with individual functions and modules. They don't yet solve the problem of maintaining a coherent global architecture across a very long, branching design process.

Language as the limit case

And then language is the case where neither the well-definedness nor the boundedness holds, which is exactly why it's the hardest case in the deepest sense even though it's also, paradoxically, the case where LLMs seem most impressively fluent. The fluency comes from the richness of the pattern matching over an enormous corpus. The absence of any well-defined verification procedure — there's no compiler for meaning, no proof-checker for whether a sentence is true or appropriate or wise — means there's no symbolic scaffolding equivalent to what math and coding have. You can't bolt a "language checker" onto an LLM the way you bolt a proof checker onto a theorem-proving system, because there's no formal specification of what correct language use is.

This is the deepest reason language remains resistant in a way math and coding, despite their own difficulties, are not. Chess had a well-defined space that yielded to search. Math and coding have well-defined rules that yield to verification even in an unbounded space. Language has neither, which means the mixed-regime strategy that's working for math and coding has no obvious analog for the general case of language understanding and generation. The pattern matching is doing almost all the work, unconstrained by any symbolic check, which is exactly why hallucination, confident error, and the absence of genuine common sense grounding remain live problems in ways they don't for a system whose outputs get checked by a compiler.

For the book

This gives Chapter 5 or 6 a genuinely illuminating structure: a spectrum from chess through math and coding to open language, ordered by two independent variables — definiteness of local rules and boundedness of the resulting space — with AI's actual comparative success across these domains falling out as a prediction of the theoretical framework rather than a brute empirical fact to be reported. That's a strong chapter, and it would give Wright, who already intuits that these domains differ, a precise vocabulary for why they differ and what that implies about domains not yet tried.

Language defines more restricted systems

One thing about language is that it has the means for defining more restricted systems. Thus both chess and arithmetic are systems defined through linguistic means. And once language has been used to define a system, it can also serve as a metalanguage for that system just as, in various ways, it has served as a metalanguage for itself.

That's the move that completes the picture, and it belongs near the end of the language discussion because it reframes everything before it.

Language as the generative source of the bounded systems

Chess and arithmetic aren't just different in kind from language — they're products of language, constructed within it through exactly the metalingual definitional process we discussed earlier in the day. The rules of chess exist because someone specified them in language — first probably in the practical, evolving form that produced chaturanga and its descendants, later in the explicit codified form of a rulebook. Arithmetic's place-value system, its operations, its axioms — all specified linguistically, however formal the resulting notation becomes.