Tom Griffiths - Laws of Thought: The Quest for a Mathematical Theory of the Mind

Summary

A Book With Legs | Smead Capital Management
Episode: Tom Griffiths – Laws of Thought: The Quest for a Mathematical Theory of the Mind
Date: March 2, 2026

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Episode Overview

In this episode, host Cole Smead sits down with Tom Griffiths, Henry R. Luce Professor at Princeton, to discuss his new book, Laws of Thought: The Quest for a Mathematical Theory of the Mind. Griffiths guides listeners through a sweeping intellectual history—from Leibniz’s earliest ambitions to mathematically formalize thought, through philosophers, logicians, computer scientists, and psychologists who tried to make sense of the mind using rules, symbols, and, ultimately, artificial intelligence (AI). The discussion explores the philosophical and mathematical journey to understand the mind, the emergence of computers and neural networks, and the enduring mystery of human intelligence versus AI. The episode blends philosophy, science, business, and investing, reinforcing the value of mental models and worldly wisdom.

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Key Discussion Points & Insights

The Origins of Mathematical Thought and the Mind

• The Ambition of Leibniz ([02:49])

  • Leibniz’s 1679 vision: A mathematical language to resolve debates and model thought.
  • Griffiths: "[Leibniz] had this vision of having some kind of a mathematical language that you could use to write down the thoughts that you had. ...Put them into a machine and turn a crank and then you'd be able to get out the answer about who was right and who was wrong..." ([03:19])
  • Leibniz failed to realize this vision, but inspired future generations.

• Philosophy and Formal Reasoning ([04:26])

  • The role of Aristotle’s syllogisms—identifying good arguments—and the later quest to formalize them mathematically.
  • Transition from philosophical speculation to scientific study of the mind.

Developing Formal Systems and Logic

• Wilkins and the Universal Language ([06:39])

  • Reverend Wilkins’ 17th century attempt to create a taxonomy-based artificial language with no room for falsehood.
  • The idea of mapping meaning through ontological structures, a precursor to modern knowledge ontologies.

• What is a Formal System? ([08:41])

  • Three pillars: Digital (discrete states), Medium independence, and Token Manipulation (rule-based transitions).

• Boole and Mathematical Logic ([10:17])

  • George Boole’s creation of algebraic logic that laid the groundwork for computers and later, psychological theories.
  • William Stanley Jevons critiqued Boole’s system, refining logical operations further.

• Boole's Family Legacy ([12:42])

  • Boole’s wife and daughters achieved remarkable scientific and literary success, influencing generations in science and mathematics.
  • Griffiths: “His wife...went on to teach psychology, philosophy, and logic at university...each of [his daughters] did remarkable things...” ([12:54])

Psychology, Behaviorism, and Scientific Challenges

• Behaviorism and Its Limits ([14:08])

  • Early 20th-century shift to behaviorism—studying observable behavior, not the mind.
  • The challenge: minds are not observable objects.
  • Jerome Bruner’s return to mentalist experiments showed that perception was shaped by context and expectation, not just stimulus.

• Example: Coin Value and Perception ([16:37])

  • Rich vs. poor children perceived coin size differently, revealing how values and experience bias perception.

Computation and the Birth of Modern Computing

• Turing and the Turing Machine ([20:30])

  • Alan Turing conceptualized computation as a set of discrete operations akin to a mathematician’s thought process.
  • Griffiths: "If you watch a mathematician solving a problem... that basic operation... you have something that you're thinking about already, it changes... You write something down and you move on. That's exactly what a Turing machine does." ([21:20])
  • Turing proved not all problems are solvable by machines, foreshadowing inherent computational limits.

• Von Neumann and Stored-Program Computers ([24:17])

  • Von Neumann’s architecture: an improvement on Turing’s abstract model, allowing practical, reprogrammable computers—true ancestors of all modern computers.

Mathematical Models of Mind: Logic, Language, and Cognition

• Bruner and Concept Learning ([27:53])

  • Mathematical rigor applied to cognition: using logic to model how people learn and distinguish categories.
  • Bruner’s experiments showed that conjunctions (“and”) are easier for people to learn than disjunctions (“or”), coining “intellectual nightmares” for the latter.

• Shannon’s Information Theory ([30:59])

  • Claude Shannon connected Boolean logic to practical electronics, enabling efficient information transmission—pivotal for both communication technology and cognitive modeling.

• Miller’s “Magic Number Seven” ([32:10])

  • George Miller demonstrated that human channel (memory or perception) capacity is limited, often to around seven chunks of information.

• Simon's Heuristics and the Path Model of Reasoning ([35:01])

  • Newell, Simon, and Shaw explored how humans navigate decision spaces using heuristics—leading to the modeling of problem-solving as navigating a search tree.

Language, Grammar, and Learning

• Chomsky and Generative Grammar ([37:48])

  • Noam Chomsky’s revolution: formal, mathematical systems can represent the underlying structure of language.
  • Demonstrated that natural language is more complex than finite-state systems; the mind constructs abstract, generative grammars.
  • Chomsky (quoted): "The child who learns a language has in some sense constructed the grammar for himself..." ([68:06])

• Induction vs. Deduction ([41:59])

  • Chomsky was skeptical that language could be learned just from data, positing “universal grammar” as an innate constraint.
  • Induction, unlike logic (deduction), deals with inference from incomplete info—Hume regarded it as habit, but Griffiths suggests systematizable cognitive bias.

• Rosch and Family Resemblance ([46:14])

  • Eleanor Rosch argued categories are fuzzy and based on similarity, not strict logical boundaries—updating the classical view of concepts.

• Tversky on Similarity and Dimensionality ([48:08])

  • Amos Tversky challenged the idea that mental similarity maps onto geometric/spatial rules like symmetry or the triangle inequality.

Neural Networks, Learning, and the Roots of AI

• Perceptrons and Neural Networks ([51:35])

  • Frank Rosenblatt’s Perceptron: an early neural network, capable of linear discrimination but limited—critiqued by Marvin Minsky for failing to solve non-linear tasks.
  • Ideas of spreading activation by Collins, Loftus, and Quillian modeled associative memory as a network of connected concepts.

• Hinton and Deep Learning ([56:20])

  • Geoffrey Hinton (a Boole descendant) helped revive neural networks with backpropagation (gradient descent) and led to breakthroughs in deep learning when more data/compute became available (2009, 2012).
  • Modern AI—massive data + deep neural nets—now solves previously “unsolvable” problems.

Probability, Bayesian Reasoning, and Human vs AI Intelligence

• Probability and Bayesian Inference ([61:37])

  • Cardano’s early probability theory developed into subjective (Bayesian) reasoning—modeling belief updating as data comes in.
  • Griffiths: “Probability theory gives us a tool for talking about... why [AI] are still not as efficient as humans at being able to learn from the data that they get.” ([62:36])

• Peter Wason’s Card Experiment and Human Logic ([64:34])

  • Human choices in logic puzzles (like Wason's selection task) reflect probability-based, not strictly logical, reasoning—clarifying the distinction between how humans and formal systems “think”.

Human Exceptionalism, AI, and the Limits of Computation

• Chomsky on Human Learning & "Divine" Abilities ([68:06])

  • Chomsky marveled at the child’s capacity to construct grammar with little input—the “remarkable type of theory construction”.
  • Cole Smead: “Doesn't that show you how incredibly unique the human is? ... a child doesn't have really much, if any, data ... and yet ... are able to do that.” ([68:55])
  • Griffiths: “This is really the biggest gap that I think remains between AI and human minds, right. Which is that humans are able to make these inferences from relatively small amounts of data...” ([69:16])
  • AI is “derivative”—dependent on training data—whereas human thinking is generative and bias-filled from evolution, embodiment, and social learning.

• Divinity, Plato, and the Soul ([74:00])

  • The discussion touches on the Platonic notion of innate knowledge, Chomsky's "biolinguistics," and whether human reasoning is “divine” or simply a product of evolved biases.

• The AI Singularity and Human Constraints ([77:42])

  • Griffiths characterizes AI intelligence as qualitatively different—not just “smarter”, but fundamentally “alien” due to different constraints and inductive biases.
  • Griffiths: “Intelligence is not a one-dimensional axis... humans are able to learn from small amounts of data because that's all they're going to get...” ([78:53])

• The Role of Metacognition in the AI Era ([81:41])

  • As cognition is increasingly automated, metacognitive skills—how we manage and direct thinking—become more essential.
  • Griffiths: “That metacognitive skill ... is made even more important by the power of these kinds of AI systems.” ([82:18])

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Notable Quotes & Memorable Moments

• “Leibniz was... trying to solve this problem of how to use math to understand the mind. What's interesting... is that he kind of failed...” —Tom Griffiths ([03:19])

• “If you said [a fish is a mammal], the words that you used for fish and mammal would tell you that they're not compatible with one another.” —Tom Griffiths ([08:07])

• “No one ever saw a thought or touched a feeling. And so that created this problem...” —Tom Griffiths ([15:28])

• “Turing was remarkably prescient...” —Tom Griffiths ([23:00])

• “Bruner called some disjunctive categories ‘intellectual nightmares’.” —Cole Smead ([27:53])

• “There's an effortlessness and a mystery to it [how children learn language] that the word divine captures well.” —AI Claude, paraphrased by Cole Smead ([76:00])

• “Humans are able to make these inferences from relatively small amounts of data... The rest of [what we know] needs to be what we call inductive bias.” —Tom Griffiths ([69:16])

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Timestamps for Key Segments

• AI as Historical Continuum, Not Sudden Arrival – [02:01]
• Leibniz, Calculus, Math and the Mind – [02:49]
• Wilkins' Universal Language and the Limits of Formal Systems – [06:39]
• Boolean Logic, Jevons, and the Rise of Mathematical Psychology – [10:17]
• Boole's Family Legacy – [12:42]
• Behaviorism and Bruner's Perception Experiments – [14:08] / [16:37]
• Alan Turing, the Turing Machine, and Unsolvable Problems – [20:30]
• Von Neumann and Practical Computing – [24:17]
• Information Theory (Shannon) – [30:59]
• Miller's Magic Number Seven – [32:10]
• Newell, Simon, and Search Trees in Reasoning – [35:01]
• Chomsky, Universal Grammar, and Language Learning – [37:48]
• Induction, Probability, and Bayesian Reasoning – [41:59]/[61:37]
• Neural Networks (Perceptron, Hinton, Deep Learning Revolution) – [51:35]/[56:20]
• AI versus Human Intellect, Divine/Innate Intelligence – [68:06]/[76:00]
• AI Singularity and Human Constraints – [77:42]
• Metacognition in the Age of Cognitive Automation – [81:41]

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Conclusion

Tom Griffiths provides a masterful, lucid storytelling thread that traces the quest to mathematically formalize the mind—from early philosophy to deep learning. While technology has delivered astonishingly capable machines, the human mind remains uniquely, irreducibly generative, shaped by evolution, bodily experience, and the mysterious capacity to learn from little. Investors, thinkers, and the curious are reminded that the most valuable insights often come from the convergence of disciplines and that true progress may depend not just on the power of computation, but on the art of critical, metacognitive thinking.

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Where to find Tom Griffiths:

• Princeton University Webpage
• His lab’s X/Twitter handle and official publications are also available online. ([82:21])

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Host Call to Action:
Buy Laws of Thought, review this podcast, and send book suggestions to [e-mail] or @smeadcap on X/Twitter.

Transcript

[Podcast Announcer]

You're listening to A Book with Legs, a podcast presented by Smead Capital Management. At Smead Capital Management, we advise investors who play the long game. You can learn [e-mail] or by calling your financial advisor.

[Cole Smead]

Welcome to A Book with Legs podcast. I'm Cole Smead, CEO and Portfolio Manager here at Smead Capital Management. At our firm, we are readers and we believe in the power of books to help shape informed investors. In this podcast, we speak to great authors about their writings the late, great Charlie Munger prescribed using multiple mental models and analysis. We analyze their work through the lens of business markets and people. In this episode, we will have a conversation that touches philosophy, mathematics. We will understand the history of this and we will, in my opinion, ask what is divine. Joining us for this episode is author Tom Griffiths to discuss his newly published book, the Laws of the Quest for a Mathematical Theory of the Mind for our listeners. I'll give you a little background on Tom. He's the Henry R. Luce. Henry R. Luce professor of Information Technology, Consciousness and Culture in the Department of Psychology and Computer Science at Princeton University, where he directs the Computational Cognitive Science Lab and and the New Princeton Laboratory for Artificial Intelligence. He has published other books, including Algorithms to Live by, which he co authored. Tom earned his BA from the University of Western Australia. He received a master's and a PhD from Stanford University. Tom, thanks for joining me today.

[Tom Griffiths]

Thanks. It's great to be here.

[Cole Smead]

Yeah. So I always ask authors this. You know, you do a lot of work in this, but this is like a short, it's a short history you're giving people. Kind of like, we're going to take you from the beginning of these thoughts to where we are today and how we really came to this date in, you know, in many respects, what we call AI today. What inspired you to go tell this story?

[Tom Griffiths]

I think for a lot of people, AI maybe started a couple of years ago when, you know, there was suddenly this moment where you could interact with a computer in the same way that you interacted with a human. And so it sort of came out of nowhere. And in writing this book, I wanted to provide a lot of the context for that. Right. So where does these ideas start? How is it that they evolved? What were all of the paths that people have tried and what were the challenges that they encountered along the way? Because having some of that history gives us insight into the moment we're in now, but also gives us some tools for thinking about where these things might be going.

[Cole Smead]

Sure. I think it was like a calculus Question the rate of change, if you will. So let's start with Leibniz. What was important about his work in 1679? Because you really start the story with his work.

[Tom Griffiths]

Yeah. Speaking of the calculus. Right, yeah. So the place I decided to start the story is with a group of people who like 300 years ago, were really trying to understand how the world works. Right. And this was the time of the scientific revolution. It's when philosophers and proto scientists were starting to think about using math as a tool for understanding the world. And as much as they were interested in understanding the physical world using math, they were just as interested in understanding the mental world using math. Right. As much as they wanted to know, how can we describe the things that are going on in the world outside us? They want to know how we understand the things that go on inside us. Leibniz was one of these people. He was a mathematical prodigy. He co invented the calculus. He made contributions to a huge number of scientific fields, those fields just starting to exist. But he also tried to solve this problem of how to use math to understand the mind. And what's interesting about it is that he kind of failed when he was doing that. So he had this vision of having some kind of a mathematical language that you could use to write down the thoughts that you had. And maybe two people could write down their competing thoughts and you could just sort of put them into a machine and turn a crank and then you'd be able to get out the answer about who was right and who was wrong in the same way that you can for a math problem. Sure. And he tried to formalize this, tried to work out what the mathematical system was that could do this, and throughout his life tried various kinds of permutations and in the end wasn't able to crack that problem.

[Cole Smead]

So from there you go with his original kind of math work, but then you immediately pivot to philosophy. You take us to Aristotle with syllogisms. Why is the core reasoning of philosophy so important as we establish this work and all these people's work that you go through, but also as we study the mind? Because there's, you know, philosophy is a core issue at a lot of, in a lot of your story.

[Tom Griffiths]

So thinking about minds for a long time was the job of philosophers. Right. There's a kind of radical idea that's started with Leibniz and then really comes to fruition in the 20th century that maybe this isn't just the job of philosophers. Right. Maybe this is something that you can do scientifically using the kinds of methods that we associate with sciences. And so Leibniz was trying to do this with math. Right. So you have Aristotle saying, here are the good arguments. That's what Aristotle was doing. He was sort of saying, if you want to convince somebody of something, here's the set of arguments that work and here's the ones that don't work, and maybe here's a little bit of what differentiates them.

[Cole Smead]

Sure.

[Tom Griffiths]

And Alibna said, okay, Aristotle gave us this kind of target of, some arguments are good, some arguments are bad. Now I want to know the math behind that. I want to figure out the mathematical system which tells us which arguments are good and which arguments are bad. And then he didn't succeed in doing that. We had to wait another 150 years or so, and then George Boole comes along and actually has a solution to this problem. But Boole's solution then fed the development of things like computers, which fulfilled that vision that Leibniz had of having machines that could tell us what the right answers to certain kinds of questions are. And that in turn fed into psychologists who were really beginning to develop scientific approaches for studying minds by exploring people's behavior. Right. So using those same mathematical ideas as a way of being able to develop theories about what's going on inside people's heads that you could test out by running experiments, by asking people questions, by. By doing something that starts to look like a science.

[Cole Smead]

Sure. You bring up Wilkins early on, he had this idea of a universal language. As he's going to do this, though, isn't he really just building a framework or hierarchy to be modeled? Wasn't that his actual attempt?

[Tom Griffiths]

Yeah. So Reverend Wilkins is one of my favorite sort of underappreciated figures in the history of people trying to think about these kinds of questions, where his goal was a sort of wild goal of being able to come up with a language in which you couldn't say anything false.

[Cole Smead]

Right, sure.

[Tom Griffiths]

So his idea was create a language, some kind of artificial language, such that whatever you said in that language, you would know whether it was true or false just based on the words that you used. And so the trick that he used for doing this was creating something that we now sort of recognize as a. An ontology. Right. A sort of taxonomic structure for capturing all of the things in the world. And then the words that you would use to name those things would be based on their positions in that taxonomy. So you'd have, say, a word for fish and a word for cat, and those words would sort of share some Parts that would reflect the fact that these are both living things, but then have different parts that reflect the fact that one of them is a mammal and one of them is a fish. And so those differentiated parts would mean that you couldn't say a fish is a mammal.

[Cole Smead]

Sure.

[Tom Griffiths]

Because if you said that, the words that you used for fish and mammal would tell you that they're not compatible with one another.

[Cole Smead]

In other words, it would be inferred automatically by the person saying it. You wouldn't have to learn anything the system would tell you.

[Tom Griffiths]

Yeah, it's like. And you can kind of think about a good example of this is there's a part of English that works like this already, which is, and Descartes pointed this out, which is numbers. Right. So if I tell you 111 is less than 93, you know immediately that that's not the case because of the words that we've used to describe those numbers.

[Cole Smead]

Yeah, yeah. You mentioned what defines a formal system. If I remember correctly, there's three parts to a formal system. Can you explain that to our listeners?

[Tom Griffiths]

Yeah. So really what Leibniz was trying to do, what, you know, Wilkins was trying to do, what Descartes was thinking about, when thinking about, you know, can you make languages that have these sorts of properties, was trying to create a system of rules and symbols that you could use to characterize this part of, you know, how the mind or language worked. And so when we think about what makes something a system of rules and symbols, you can kind of think about it as being like a board game. Right. So you think about the rules that you have to describe a board game. That's kind of the things that they had in mind. So we think about those systems as being digital is one of the properties which is that you know exactly what state you're in.

[Cole Smead]

Sure.

[Tom Griffiths]

Right. So if you're in a board game, you know exactly, you know, what position, position the chess pieces are in. There's no sort of ambiguity about that.

[Cole Smead]

Okay.

[Tom Griffiths]

That they're medium independent, that it doesn't sort of matter that your knight looks like a horse or something like that. Right. The way that you build your chessboard is not. Is irrelevant. It's actually the rules that are governing it. And then those rules form what's called a token manipulation system. And that really is that sort of idea of a board game. You've got a starting position, you've got rules that tell you how you move from that starting position to other positions, that tell you about the positions that you can visit and so that is sort of abstractly a way that you can think about saying what a system of rules and symbols is. Right. It's something that has this abstract board game like structure.

[Cole Smead]

Sure. So. So you mentioned Boole. Boole was, I think, very bold based on your work. He tried to take syllogisms to understand the mind. I say bold because he does that, but not everyone necessarily agrees with him. I think you mentioned William Stanley Jevons, who we get the Jevons paradox from, pointed out what he thought were his errors.

[Tom Griffiths]

Yeah. So Boole was again, a sort of remarkable figure. He was a schoolteacher who made fundamental contributions to mathematics. He was sort of largely self taught. He kind of grew up reading French mathematics books that were very, very sort of complicated. Didn't have a lot of money. So he would buy mathematics books because they would take him the longest to work through. Right. So he was sort of looking for value for money in the books he was buying. And so he'd get these very obscure, very dense French mathematical texts.

[Cole Smead]

Sure.

[Tom Griffiths]

But as a consequence, he had this different perspective on math than a lot of the people who were living in England at the time, which was this algebraic perspective. So sort of thinking in terms of not just arithmetic, but how it is that you create something which is an algebra where you have symbols that stand for things and operations that those things can perform. And so that equipped him to actually solve the problem that Leibniz had been trying to solve. Leibniz was kind of living in this world that was sort of more sort of arithmetic, calculus, sort of, you know, and Boole has this insight that, ah, I need to create my own algebra to solve this problem. And he comes up with a solution and is able to then write out the syllogisms in sort of mathematical form. And that really provides the foundation for modern mathematical logic. That said, yeah, he wasn't perfect. His system was sort of overly complicated in a few ways. And Jevons pointed out one of those. Like the way that Boole had defined one of those mathematical operations sort of required some special cases. And Jevons was able to figure out how to get around that. But it really demonstrated how it was possible to have a mathematical theory that could capture at least some aspect of thought.

[Cole Smead]

Sure. I was also thinking, I think he's the only economist that you mentioned in your book. So I was like, leave it up to the economist to poke holes in something but never come up with something himself. So you also mentioned Boole's family and legacy was just incredibly unique relative to the other people in your story, what was so exceptional about his offspring and his wife?

[Tom Griffiths]

Yeah, I mentioned this because it's really a story that I think isn't necessarily emphasized when you hear this kind of history, which is the sort of great man history.

[Cole Smead]

Sure.

[Tom Griffiths]

But Boole's family was just as much of an important legacy as the work that he did in mathematics. So his wife, Mary Everest Boole was interested in these kinds of questions in her own right and went on to teach psychology, philosophy and logic at university. And together they had five daughters, each of whom did remarkable things. The youngest became a renowned novelist. The next youngest was the first woman to be elected to the Royal Society for Chemistry. The middle daughter trained herself to visualize the fourth dimension and was able to characterize four dimensional shapes in a way that was before a lot of mathematicians had figured out what those were. And then the oldest two became the matriarchs of two significant scientific families. One of which comes back later in the story.

[Cole Smead]

Yeah, the behaviors are next in your book. What was innovative about their work and also what was problematic about their findings, if you will.

[Tom Griffiths]

So so far we've been talking about this kind of like mathematical thread, right. And Boole was not particularly interested in what we today would recognize as psychology. He said, if you figured out one of these mathematical principles, you know you've got it right. Right. There's no need to go off and actually try and compare this to what human minds are doing. He's just interested in just being able to answer the questions about what the fundamental principles are. And so that changes in the end of the 19th century when we start to see the development of a scientific psychology. But what it meant to do scientific psychology at that time was you would carefully control what you show to people. So they built all sorts of clever devices for know, giving people particular sounds or showing them particular things or giving them particular sensations. And so they sort of very precisely controlled the stimulus that people would receive. But then the way that they got their data was relying on people's subjective reports of what those experiences were like. So people were just sort of saying, oh, this happened, this happened, you know, or pushing a button when they perceived something or something like that. There was sort of the subjectivity in the process. And, um, one of the big challenges of having a science of the mind is that unlike any other science, minds are not a physical thing. Right. It's not a thing that you can see or touch.

[Cole Smead]

Sure.

[Tom Griffiths]

So if you're a physicist, even if you're studying atoms, you can make a Microscope that lets you look at atoms. Right. And even if you're studying galaxies, you can make a telescope that lets you look at galaxies. Those things seem very remote, but thoughts and feelings are just even more remote. Right. No one ever saw a thought or touched a feeling. And so that created this problem where there was a group of psychologists that felt like relying on people's subjective reports made for something that was not very scientific. And if you wanted to have something that's a real science of the mind, maybe you should get rid of the mind and you should focus on the things you can see or touch, which are behavior and the environment that produces it. And so that's this idea of behaviourism, that what we're going to study is the kinds of behaviors people produce and the circumstances under which they produce them, using methods that are much more continuous with the kinds of methods that we might use to study non human animals. So, like using the kind of techniques you might use to study learning in rats or pigeons and trying to explain as much as possible of human behavior using those same simple sort of fundamental principles. Sure.

[Cole Smead]

And you used an example in the behavior section of the book where you talk about how they found out that people with different means saw coins, different sizes. And to your point. So if we're trying to understand the mind, how do we account for minds seeing and perceiving things differently?

[Tom Griffiths]

This is one of the big challenges for behaviorism. So I think there was sort of like the first half of the 20th century, it was quite hard to be a psychologist who was interested in minds. And then Jerome Bruner, who was a psychologist at Harvard, went off to, During World War II, he became a cultural attache to liberated France. And so while he was there, he was spending a lot of time hanging out with Jean Paul Sartre and Simone de Beauvoir and got this very different view of what the kinds of things were that you could ask questions about the kinds of things that should be part of a psychology, a science of the mind. So he comes back to the United States and he starts running these experiments where he shows that you can put people in the same situation and give them the same stimulus, but then they respond quite differently based on their expectations or the experiences that they've had. And so the study you mentioned is a sort of classic one of these, where he had, you know, sort of, in his characterization, rich children and poor children who were given coins, they would see a coin and they'd adjust a circle of light to match the size that they perceived the coin to be sure and his result was, first of all, as the coins increased in value, the children tended to overestimate the size of the coins to a greater extent. So you would overestimate the size of a quarter much more than you would the size of a nickel. And second, that that seemed to be even stronger for the kids who are coming from poorer backgrounds. Right. So the import of the value of the coin was something that was influencing the perception that they had of that experience. So it's worth noting that psychology has had its struggles with replicating different psychological phenomena, and that study was based on a pretty small sample. So it's one that we might be concerned about. But the basic idea that he demonstrated in a bunch of other experiments was that how people perceive the world, right, how we perceive the stimuli that are informing our behavior is influenced by those experiences that we have.

[Cole Smead]

Hi, I'm Cole Smead, CEO and Portfolio Manager here at Smead Capital Management and host of this podcast. If you enjoy this podcast, I'd like to invite you to check out smeedcap.com at our firm. We are stock market investors. We advise investors who play the long game with a discipline that has proven successful over long periods of time. Learn more about our [e-mail] Past performance is not indicative of future results. Investing involves risks, including loss of principal. Please refer to the prospectus for important information about the investment company, including objectives, risks, charges and expenses. Read and consider it carefully before investing Smead Funds distributed by Smead Funds Distributors llc. Not affiliated. So let's pivot next to the to Alan Turing and the Turing Machine. And I'm gonna put up here a slide. I thought this was really helpful in your book. You do a lot of you show a lot of pictures to describe the math. You also show a lot of different situational logic pictures for your readers to understand. And again, this is just you're giving people a short history. It's like being a well educated class. And so you're like my professor of math, which I'm glad because I tried to take little math class as I could in college, but I thought this was a really good picture for understanding the logic and math behind the Turing machine. So could you use this as a way to explain Alan Turing and what he brought to us?

[Tom Griffiths]

Yeah. So the Turing machine is our starting point for thinking about this idea of computation. Right. That's going to lead us to being able to make digital computers. And so Turing was trying to solve a problem of characterizing the limits of mathematics, trying to work out if there were Math problems that no mathematician would be able to solve. And the way that that was expressed was in terms of whether there were math problems that no machine could solve, where that machine was doing what a mathematician does. So he tried to sort of figure out what's a way of characterizing the things that a mathematician does. If you watch a mathematician solving a problem, you see they've got some things written down on the piece of paper that's like the problem that they're trying to solve. And then they are. You know, they have a pencil and an eraser, and they're looking at the particular part of the problem, and then something happens inside their head. They move their pencil, they write something down, and then they sort of maybe look back and forth, and they're sort of thinking about what the next step is. But that basic operation of seeing something, you have something that you're thinking about already, it changes the thing that you're thinking about. You write something down and you move on. That's exactly what a Turing machine does. So it's a way of automating what a mathematician's doing. And so if you simplify that down to the simplest form that it can take, you get something where you imagine that you have a machine which has some state that's like the mental state that the mathematician is in, that is looking at a sequence of numbers. We can sort of make it as simple as possible. We'll just have zeros and ones be the numbers. And then there are rules inside that machine which tell it if you're in this particular state in the picture at state number two, and you read the number one, then you write the number zero, change to state number three, and then move to the right, and then look at the next number which is on the right, and that's it. That's enough to be able to then characterize all the things that mathematicians do.

[Cole Smead]

So I'm going to use a quote here. You write about Turing's work in 1936. He showed that quote. He showed that no machine could determine whether something could be proved or not. In the same paper that he defined what a computer is. He thus established that there were questions that no computer could answer. End quote. How should Turing's statement that you're reiterating there inform our view? Or maybe another way of asking that is, how would Turing look at the world today if he had said that then?

[Tom Griffiths]

Well, so the first thing I'd say is Turing was remarkably prescient, and he wrote a paper in 1950 that was really about how he thought AI was going to shake out and all of the kinds of questions about it, and maybe we can come back to that and sort of talk about that.

[Cole Smead]

Sure.

[Tom Griffiths]

So I think a lot of the things that he saw today would not necessarily surprise him. He really had this clear vision of what the future was like. Sure. In terms of all of the things that computers can do, the kinds of constraints that he was proving on computers are not really things that prevent us from using computers to do the kinds of practical things that we want to do, or even using computers to do math. Because what he showed is that there exist problems that cannot be solved by a computer, but the kinds of problems that we've run into that have that structure are often things about what a computer might be doing. Right. They're sort of like these recursive meta problems. Right. So the one that you showed in that original paper was you can't build a machine that will tell you whether on a particular input a machine will halt. Right. So you can't build a computer that's going to tell you whether a computer can solve a problem.

[Cole Smead]

Sure.

[Tom Griffiths]

Which mostly there are certainly cases where we might like to be able to do something like that, but most of the time that's not a practical constraint on the things that we use computers for.

[Cole Smead]

Sure. John von Neumann was fundamental to modern computing, according to what you write. Explain what he did and why stored computing was so important. And again, you were just kind of touching on this. So, you know, another way of asking this question might be, was he just solving an engineering problem?

[Tom Griffiths]

It was a little bit of that. So Turing had described what a computer was, but in a very abstract way. Right. I sort of said, oh, so you know, Turing setup, you have this piece of paper, so you imagined an infinitely long tape with, you know, numbers that can be written on it.

[Cole Smead]

Yeah.

[Tom Griffiths]

Right. And then this machine that's moving backwards and forwards, that's not a very practical way of building something that's going to solve problems for you. Although Turing actually built tape based computers during World War II when he was doing code breaking, that resemble his ideas about a Turing machine.

[Cole Smead]

Sure.

[Tom Griffiths]

Von Neumann was trying to think about how do you turn this into a sort of practical device that you can use for solving problems. So now we're going to build something which is an electrical computer that's going to be representing information inside that computer in terms of using magnets and other kinds of tricks from electronics. And so to think about what the structure of that would look like. And in particular, he wanted to make A computer that could store its own program. So Turing had shown that you can create a kind of machine that can read in some information on that tape about what it's supposed to be doing and then execute that on the other part of the tape. Right. It sort of has this distinction between the. The hardware, the machine, and then the software, which is the instructions that are given to that machine on the tape. And he'd shown that you could make a machine that could simulate any other machine. Sort of remarkable idea. So Neumann wanted to be able to make a machine which was like that, that you could load a program into memory, and then the program would be able to be run on, you know, another set of information that you provide into it, which would be a big improvement over the other kinds of computers they had at the time, where you had to have a big rig of plugs that were going into an array of sockets in order to rewire the machine to solve every different problem that it's solving. And there was actually a team of women who was responsible for this first computer that did this with these plugs and so on. And they were sort of the experts on thinking about how do you connect everything up in order to make it work. So he wanted to be able to make something where you didn't have to do all that rewiring every time you wanted to run a different computation. And so he created something that's called the von Neumann architecture. It's a little controversial how much von Neumann wrote the report, but he might have, in doing so, undermined his collaborators, who helped come up with some of those ideas as well. But he was very inspired by how brains work. And so he kind of thought about this in terms of different organs that you have inside the computer. There's one organ that's doing sort of the computation part. There's one organ that's where you're storing things in memory and you have an input and an output. And he sort of read these sorts of papers about how brains work, and that inspired him in thinking about how to make a computer.

[Cole Smead]

And effectively, what we just discussed is. I mean, that's the. What we, you know, as a kid, what a floppy disk drive or a hard disk drive. I mean, that's, in effect, what that did over time. Structurally, to compute.

[Tom Griffiths]

Yeah, no, that's right. So, you know, it's laying the foundation for what we now think of as a computer.

[Cole Smead]

Sure. You mentioned Bruner earlier. I was just caught by this. I loved the picture you used for this. Bruner called some disjunctive categories. He called these intellectual nightmares.

[Tom Griffiths]

Quote.

[Cole Smead]

Okay, I think I understood what you meant by this, but I want to make sure to kind of bring this. And I have a slide here that you had in that section. I'll go to Slide 2 here, where, you know, this is what he shows. And. And this is what you'd walk away as you're trying to study categories and learning to be. This is an intellectual nightmare.

[Tom Griffiths]

So. So there's this important moment that happens in this transition from psychologists not being able to talk about the mind to figuring out how to have our sort of rigorous science of the mind, which is the key insight is that the way to make that rigorous science is math, right? That you can use math to express hypotheses about how minds work and that are precise, and then you can test those out because they make predictions about people's behavior. And so Bruner, who'd been doing these experiments, had this insight that this might be possible because he goes to the Institute for Advanced Study down the road here in Princeton, and he runs into von Neumann, and von Neumann's trying to figure out, how do I represent information? How do I store things in memory? And Bruner is trying to figure out, how do I rigorously study the mind and sort of overcome the constraints of behaviorism. And it's this sort of perfect collision where Bruner comes away with that, with this idea, oh, I can use something like logic as a tool for characterizing people's mental representations. So he goes off and runs these experiments which are looking at how people learn concepts. And so he shows people cards like the ones that are shown in the figure. So they have, like, you know, white circles on them and two black squares. And they have, you know, two lines around the border or three lines around the border. They vary in these different dimensions that you can use for expressing a concept. And so the key idea that he has is then you can look at whether different logical formulas are easier or harder to learn. And one thing that he finds is that it's easier for people to learn a logical concept that has a conjunction. So an. And learning something is the square is part of the concept. If it has a black shape and it has three things on the border, that would be relatively easy to learn. It's really hard to learn things that are disjunctive concepts, so things that have an orbit. So learning it's in the concept, if it has a black shape or it has three lines on the border is very counterintuitive for people. And most of our natural concepts don't necessarily take that form. It seems like there's sort of more and like things. Right. Than there are, or like things that we sort of think about when we're thinking about how the world is organized.

[Cole Smead]

Sure, yeah. And it gets to your point. I always think about our brains thinking about in similes and analogies. And therefore that doesn't always follow a clean line. There are nonlinear relationships at times. Claude Shannon created the information theory. Why was this important to this story?

[Tom Griffiths]

Shannon was important in translating Boole's abstract ideas about logic into something that you could use to actually build electrical circuits. This is another sort of thread in this, thinking about how you go from the abstract mathematics to things that are kind of like brains. Right. And actually, some neuroscientists were inspired by this too, and sort of had a whole theory about how you could build circuits out of neurons that then turned into the kinds of things we think of now as neural networks. Shannon's other work was on information theory, which is thinking about how much information you can transmit along a channel. And so, again, this was influenced by World War II.

[Cole Smead]

Sure.

[Tom Griffiths]

People are trying to send messages. They have constraints on how much time they have to send a message using a radio or using another sort of mode of transmission. So they want to be able to do this as efficiently as possible. And so Shannon kind of works out what's the most efficient way of sending messages, and if you send things in the most efficient way, how long is it going to take you how much information you need to transmit?

[Cole Smead]

So George Miller came up with his magic number seven that you talk about in the book. Can you explain how he came to this? And I want to talk about this because I've really changed my mind on certain things to your point of how the mind works. So, for example, this is why I think Miller's work is interesting. If someone said to me, why do we have popular people in the culture? And things like that, like, why do humans allow that to happen in their mind? Okay. And I used to think to myself, oh, it's because we're jealous by nature, and therefore we need something to be jealous of. It's just kind of how we're made. And I think that is partly true, But I also think that the way the human mind processes is it's looking for efficiencies. And one of the ways it can create efficiencies is, is by having things it makes quicker determinations from. So, for example, the example used in a book that helped me change my mind on this was the little black dress. You know, the little black dress. Every woman has the little black dress. And up until a point, you know, for a woman, it was, what am I going to wear? What am I going to have in my wardrobe? But for the fact that that has become adopted, it means it created an efficiency in the mind of a woman as it pertains to her wardrobe. And when you talked about Miller's magic number, I thought of it as it shows you where the mind finds efficiency in processing, if that makes sense.

[Tom Griffiths]

Yeah. And Shannon had defined this kind of idea of what the capacity was of a channel, how you can measure the amount of information that the channel can process. And George Miller uses this idea to argue that there are capacity limits in human cognition, too. Sure. So, interestingly, he was doing two kinds of work. He was doing work on perception. So, like, how many different tones can you distinguish? Or how many different levels of light can you distinguish?

[Cole Smead]

Sure.

[Tom Griffiths]

And he was also doing work on memory. So how many things can you remember? And then he was asked to give a presentation that was an hour long presentation, and he didn't have an hour long presentation. So he put together these two presentations that were about, you know, capacity in these two different senses. And then they were unified by the fact that in both cases, the answer was basically seven, that you could sort of like differentiate about seven different pitches or seven different luminosities of light without seeming to lose information. And after that, you started to lose information, and you could remember about seven things, but then if you tried to go too much above that, you would start losing information. And so that was the origin of his sort of magical number seven was that it seemed like this number seven was occurring in these two different parts of his research life.

[Cole Smead]

Yeah. Let's see. Newell, Simon, and Shaw, they came to the idea of paths that the mind works in. Thus logic follows these paths. Can you explain this more to us?

[Tom Griffiths]

So we were now at this point where we have computers and we have this idea that maybe something like logic is a model for how people might be representing concepts. There are still problems that computers can't solve very well that humans can solve better. Right. And so one of these problems is just doing math, not arithmetic, but producing mathematical proofs. So if you want to discover a new fact in logic, the way you do that is by constructing a proof. And what a proof is, is you start with some statements and then you kind of follow a set of rules that tell you what you're allowed to conclude from those statements until you get to the point where you have the answer that you wanted. And so that problem of finding a proof, it's exactly the same problem as a problem of playing a good chess game. If you think about a chess game going back to our board game analogy, you've got a choice about what move you make as your first move, and then your opponent makes a move and you make another move, and then they make a move. You can kind of think about this as a branching tree of possibilities where at each point there are all of the things that you could do, and you're trying, when you're playing a game of chess, to follow your way through that tree to get to the point where you find the leaf that corresponds to you winning the game. Someone who's trying to prove a theorem in mathematics is following a path where they're trying to apply the mathematical rules to get to the point where they get to a leaf which corresponds to solving that mathematical theorem. And so Newell, Simon and Shor were interested in creating machines that were able to solve this problem, and they tried to do that using strategies that human mathematicians use. So, just like Turing was inspired by thinking about what is going on inside the head of a mathematician.

[Cole Smead]

Sure.

[Tom Griffiths]

Newell, Simon and Shaw looked at these kinds of strategies or heuristics that human mathematicians use that are things like, if you know that you can get to the solution for from some other place, then work towards that place. If you know, oh, if I could prove this, then I can prove this, then it's sufficient to just prove that first thing. Or if you are having trouble finding the path from the beginning of the problem, instead go to the end of the problem where you prove the result and work backwards in terms of the steps that you could take away from the endpoint. And that helps you to sort of constrain the space of solutions. And so they showed that if they built a computer that used these human heuristics, it could actually prove the kinds of mathematical theorems that human mathematicians could prove.

[Cole Smead]

So let's pivot to language. We're kind of back to the Wilkins idea, if you will, which Chomsky tried to tackle. What was novel about Chomsky's work at that time?

[Tom Griffiths]

Chomsky was a young linguist who had a very different view of what linguistics was from all of the other linguists at the time. So for a lot of the other linguists at the time, what it meant to be a linguist was you were going out and you were collecting information about what languages are like, and then maybe thinking about what some of the correspondences were across these languages, what some of the general principles were that characterized human languages.

[Cole Smead]

Sure.

[Tom Griffiths]

And Chomsky wanted something which was different from that. He wanted to have a way of characterizing, if you had a single language, could you come up with something like a mathematical system would allow you to characterize all of the sentences that were grammatical statements in that language? So trying to create a formal system that gives you a way of producing all the sentences that are in that language and nothing else. And so this approach, which is called generative grammar, led him to then ask this question, what kinds of formal systems do you need in order to capture the structure of human languages? And so he was able to show that some simple kinds of systems that were like things that the behaviorists and the information theorists had assumed were, would be sufficient to capture language weren't going to work. And in fact, you needed something much richer that had a sort of like internal structure. Right. Like ideas like noun phrases and verb phrases and so on, that then could capture the structure that sentences have in order to get even close to the structure of English.

[Cole Smead]

Sure. Explain what's a finite state language versus something that's not a finite state language.

[Tom Griffiths]

So this is the distinction that Chomsky was focused on in terms of ruling out a sort of simple model. So a finite state language. You could think about it again, going back to our board game analogy as a language that you could generate just by creating a board game where a bunch of positions that you're playing, pieces can be in, and you have moves that can take you from one position to another. And then as you move into each position, you produce a word. So I go from the start position to the next position, I produce the word the I go to another position, I produce the word dog, and so on. And then maybe I go from that position to the end of the game and I produce the word runs. And now I produced a sentence, the dog runs.

[Cole Smead]

Sure.

[Tom Griffiths]

That structure allows you to capture certain things about language. Right. You can imagine now you can capture the fact that you can have sentences like the dog runs and the dogs run and you're reusing parts of the board when you're producing those sentences. There's not a unique trajectory that you have to follow for every sentence. And so it allows you to capture some of the structure that exists in language. And for the behaviourists, that was nice because it suggested that you could learn language just by learning associations between words.

[Cole Smead]

Sure.

[Tom Griffiths]

So you could learn that after dog, then you're more likely to produce the word runs. Right. And after dogs, you're more likely to produce the word run. And, you know, you could sort of learn these associations between things. And it was good for the information theorists because they wanted to be able to estimate the probability of different pairs of words occurring next to one another. Sure. And so that's something which again is like sort of forming these associations between words. And so a finite state language is a language which can be captured just by creating a blog game like that.

[Cole Smead]

We hope you're enjoying the podcast. You know, we work hard putting together this show, but we work even harder for our investors at SMEAD Capital Management. At smead, we believe in disciplined investing, which is why the SMEAD funds have a proven track record of long term outperformance. If you're an investor who plays the long game and want to invest in wonderful companies to build wealth, we invite you to visit smeedcap.com Past performance is not indicative of future results. Investing involves risks, including loss of principal. Please refer to the prospectus for important information about the investment company, including objectives, risks, charges and expenses. Read and consider it carefully before investing. SMEAD funds distributed by Smead Funds Distributors llc. Not affiliated. Teach us about induction and who tried to prove and test the needs of induction.

[Tom Griffiths]

So the challenge that Chomsky ran into. So he showed that English was not a finite state language. There are sort of structures in English which are richer than the kinds of things that you can capture using those simple board games. And as he increased the complexity of his understanding of what language was, you start to run into a problem which is if language is something nice and simple, then there's a story about how you learn language, which is you just learn the associations between successive words and you can kind of string them together and you've learned how to produce sentences. But the more complex language turns out to be, the harder it's going to be for you to learn language. Sure. And Chomsky was a sort of skeptic about the possibility that children could learn language from the data that they saw and said that you needed to have some sort of strong constraints, what he called a universal grammar, on the kinds of things that you could learn. But part of that was that he was trying to think about learning a language in a way that looks a lot like logic. So his kind of intuitive idea of what it means to learn a language is you hear enough sentences that you get to the point where you know exactly what the language is. And that was the way that sort of early on, people were thinking about formalizing learning and that misses the point that in fact, many of the things that we do are things that we do without certainty.

[Cole Smead]

Sure.

[Tom Griffiths]

So logic is the math of how you go from things that you know to be true to things that you know or can conclude are also true. Right. So you're sort of doing that with certainty. And we call that deductive problems that have that kind of structure. But a lot of the things that we do are things where we go from some data that we see to some uncertain, underdetermined hypothesis. And that's a problem of induction. And that's something that philosophers have sort of grappled with for hundreds of years in terms of trying to characterize how would you describe that process of inductive inference mathematically? And can you give it the same kind of precision that we give to deductive inference?

[Cole Smead]

Sure. Hume argued it was habits, though, didn't he?

[Tom Griffiths]

Yeah. So David Hume, the Scottish philosopher, said that we're not going to find something that's like deductive inference at the foundation of induction. Induction is more like a sort of mental habit that we have. Right. It's sort of like a thing that we do because we've got used to doing it, and it seems to work. Okay. But it's not something that has the same rigor as our sort of deductive inferences.

[Cole Smead]

Sure. Well, yeah, and he's really arguing for what I would refer to as innate in a way. But how do you use innate in inference tied to a computer?

[Tom Griffiths]

Well, so I think what Hume is missing there is that something can be a habit, but it can still be systematic. Sure. So even if you can't justify it in the same way that you would justify deduction, it could still be the case that what you're doing is something that makes sense and that has systematic rules that characterize it. And that perspective then sets up a new problem. It's something that the philosopher Nelson Goodman called the new riddle of induction, which is how do you actually explain what the principles are behind these inferences that we make all the time? And why is it that some of them are better than others? Right. So one of Goodman's examples was if you discover that a piece of copper conducts electricity, you're probably going to conclude that all copper conducts electricity. But if you go to an event and you meet a man and it turns out that he's the third son in his family, you're not going to conclude that every man at the event is the third son in their family. And so in one case, just getting that one piece of information is enough that you conclude that that hypothesis is probably true, and in the other case, it's not. And so if we can figure out what the systematic principles are that differentiate between those cases, that's our new challenge for being able to work out how induction works.

[Cole Smead]

Sure. Eleanor Rosch worked on Family Resemblance. I really liked this idea because it gets to the idea of as the mind works, how does it categorize, and how does it, in a way, categorize and associate for efficiency purposes. Back to that idea I talked about earlier.

[Tom Griffiths]

One of the challenges when we abandoned deduction was that deduction actually gave us a nice story of what categories are. Right. So if we lived in this logical world, then a category, just like in Bruner's experiments, is something like a rule that tells you, oh, if it has this property and this property, then it's something that belongs to that category. And what Rush realized is that, in fact, real categories are nothing like that. Right. So I can ask you, like, is a chair a piece of furniture? What would you say?

[Cole Smead]

I'd say, yeah.

[Tom Griffiths]

Yeah. Is a telephone a piece of furniture?

[Cole Smead]

And I would say, no.

[Tom Griffiths]

Is a rug a piece of furniture?

[Cole Smead]

I'd probably say, yeah.

[Tom Griffiths]

Okay. So that probably is the thing that maybe goes against that rule, like, way of thinking about what a category is. Right. That she pointed out that there are things where we're absolutely certain that there are sort of examples of that category, but other things that are, you know, and other things where we're absolutely certain that they're not, but other things where it's just somewhere in between and we're not really sure.

[Cole Smead]

Well, yeah, to your point, my mental resemblance is if it's in Ikea, it's a piece of furniture. Right. I mean, that's. I'm thinking, as you're saying, I'm like, well, ikea. Okay.

[Tom Griffiths]

I think that's going to get you in trouble, though, because there's plenty of things in Ikea.

[Cole Smead]

I know. I'm teasing.

[Tom Griffiths]

So. But that idea is that categories have fuzzy edges. Right. And that maybe, rather than rules, we decide based on the experiences that we have where we're like, oh, well, I know a chair is a piece of furniture, and I know a table is a piece of furniture. And so, like, an ottoman is, you know, similar to a chair and a table, and so that's probably a piece of furniture. And you're sort of just sort of trying to trace these, you know, connections between things and trying to make judgments based on that.

[Cole Smead]

Sure. Why did Amos Tversky reject multi Dimensional scaling.

[Tom Griffiths]

That's a very technical question, so. But purposeful.

[Cole Smead]

According to your book, right

[Tom Griffiths]

now you have the problem of saying what categories are. Right now we've got rid of logic. We need some other way of thinking about what these sorts of structures are. And so one proposal was that maybe it makes sense to think about concepts in terms of spaces, Right. Where you could think about an object as a point in a space. Right. You have some multidimensional space where it has all of the dimensions that correspond to the different attributes of things. And so chair is one point in that space, and then rug is another point in that space, and telephone is another point in that space. And so you end up with something where you have now a region in that space that corresponds to the things that are pieces of furniture and maybe how much you think it's a piece of furniture, so, like, how close it is to that region. Right. So it gives you a way of explaining how you can have that fuzziness. Okay. And so that was one idea, is that we could think about similarity in terms of spaces. Right. That the distance between two things in a space reflects how similar they are.

[Cole Smead]

Sure.

[Tom Griffiths]

And then Tversky, who's famous for his work with Daniel Kahneman on decision making.

[Cole Smead]

Correct.

[Tom Griffiths]

If you think about the work that he did in decision making, it was really about challenging the kind of the axioms, the mathematical rules that characterized rationality. Right. So he kind of was trained in this tradition where you would write down what are the mathematical rules that characterize something? And then you do experiments that test out whether those actually hold. And so he did that where he said, okay, well, if it's really the case that the similarity between things is like a distance in a space, we know some mathematical rules that distances follow, right. So one is that they're symmetrical. That if I'm driving from Boston to New York, and I'm driving from New York to Boston, in principle, that's the same distance. I mean, you can think about traffic and what routes you take and so on, but if you just sort of measure the distance between those things, it's the same. And then he goes and shows that people make similarity judgments that are asymmetrical, that they sort of say, a camel is like a horse more than a horse is like a camel.

[Cole Smead]

I think you mentioned, he says that similarity judgments violate the triangle inequality.

[Tom Griffiths]

Yeah. So this is another one of these. Right. So people are willing to say. So triangle inequality is a property of distances that if you have three points, the distance from A to C has to be less than or equal to the sum of the distances from A to B and distance from B to C. Right. So the worst case scenario is the one where you have, like, a flat line, but for any kind of triangle, that's going to be less than that. And so he then goes and shows that you can get similarity judgments that violate this classic example that the Moon is similar to, I'll say, a light bulb, and the moon is also similar to a soccer ball, but a light bulb is not that similar to a soccer ball.

[Cole Smead]

Yeah.

[Tom Griffiths]

And so that's a violation of the triangle inequality. Sure.

[Cole Smead]

Teach us about Frank Rosenblatt's Perceptron, because this is a big part of the story when he comes.

[Tom Griffiths]

Yeah. So we're now at this point where now we're thinking, okay, maybe thoughts are like. Concepts are like points in space, and thoughts are somehow evolving us through these spaces. And now we have a problem, which is that Alan Turing gave us a way of thinking about computation. Right. Like how thinking could work for discrete rules and symbols. And we don't have that same thing for continuous spaces. And the place where we get that is from neural networks. So a neural network is a system where you have a set of nodes that are kind of like little neurons that are sort of wired up to one another in the way that neurons wire up in your brain. So these nodes are connected to one another, and they have weights that sort of govern those connections. And the perceptron is a very simple kind of neural network where you have some input that comes in, and then it goes up to some, what Rosenblack called association units. And then there are weights that go from those association units to a response unit. And so the idea is that you could show this thing a picture, and it might be a circle or a square, and that information goes in through an artificial retina, gets transmitted to the association units. And then the model then learns how to associate the representation that it forms, the activation that it has in those association units, to the response that it should produce, whether it's producing a square or a circle.

[Cole Smead]

Sure.

[Tom Griffiths]

And so this is a way you can think about this as a way of what the model is doing is if you think about the activation of each of those nodes as one dimension of a space, then it's a way of learning a mapping that takes you from one space to another, from the space of the association units to the space of the response. And so this is starting to give us a tool for thinking about how you can do computation with spaces.

[Cole Smead]

The perceptron had linear boundaries. Why was this so problematic to Marvin Minsky?

[Tom Griffiths]

So with just one layer of weights in your neural network, you're only able to represent a boundary in that space that you can characterize by a line, or more generally, a hyperplane. You can think about it as a line through that space. Sure. And the problem is that there are lots of things that you might want your neural networks to do that are not consistent with that kind of linear boundary. Even very basic kind of logic questions. Right. So where you're trying to represent the. You can represent logical ands and logical ors with functions that can be characterized by a linear boundary. But there are other kinds of things that are hard to characterize by a linear boundary. Like if something is a dog, if you're trying to discriminate between dogs and cats. Right. And intuitively you can say something is a dog if it has a long snout and long fur or if it has a short snout and short fur. Right. Cats are sort of like in the middle. Right. Where, you know, there's only so long cat fur gets. And there's only so, you know, squished cat noses get. But you have, like, pugs on one end and hounds on the other end. So it's like it's what's called an exclusive or structure.

[Cole Smead]

Sure.

[Tom Griffiths]

And that's not something you could characterize by a linear boundary.

[Cole Smead]

Yeah.

[Tom Griffiths]

And so that meant that what you could learn with that very simple kind of perceptron was fundamentally limited. Sure.

[Cole Smead]

Beth Loftus, Alan Collins, and Ross Quillian worked on the idea of spreading activation. Teach us what their work did.

[Tom Griffiths]

This was really a way that even after Perceptrons had become less popular, these same kind of ideas from neural networks sort of snuck back into psychology through the back door in the form of these semantic networks. So a semantic network, you can think about it as you have nodes, and those nodes correspond to words that you might be. There are different concepts that you have. And again, we can think about those nodes as getting activated and those nodes as being connected to one another by weights. And so what they showed was that you could explain a whole lot of how human semantic memory seems to work just by using the simple idea that when you hear a word, that word gets activated and it starts to spread its activation to the other words that it's connected to. And so they could show that by doing that, you could explain why when people hear the word hockey, they're more likely to think of the word fight or something like that, or Canada or something like that.

[Cole Smead]

Yeah.

[Tom Griffiths]

You can form these associations between things that then sort of propagate through the mind. And it's the same idea. You can kind of think about, you know, now you can think about characterizing people's mental state as a point in space that corresponds to the activation of all of these nodes. And then spreading activation is sort of moving you through that space. And so now we have a picture of thought as some kind of process of like navigating through these mental spaces.

[Cole Smead]

Sure. Geoff Hinton worked on unsupervised learning. What do we get from his work?

[Tom Griffiths]

So the fundamental challenge that we had. Right. So now we have people starting to think about these sorts of neural network like approaches in psychology. But there wasn't a way to learn the weights of a neural network beyond Rosenblatt's nice solution, which worked for this one layer neural network. And Geoff Hinton was, first of all, should mention, I told you that the Boole family was going to come back. So he was actually the great, great grandson of George Boole. And so he was very interested in mathematics, but also interested in psychology and philosophy, as you might expect, based on his heritage. Yep. And he worked with David Rumelhart, who was a psychologist who was interested in using these kinds of spreading activation models and interested in using neural networks more generally, but needed to solve this problem of how do you do learning for multi layer neural networks? And so Hinton suggested you could use an idea that's called gradient descent. Right. Which is you can think about, we can measure for this neural network, its error, how much it's sort of going wrong, and you can think about that error as a function of the weights. So if you increase the weights a bit, maybe the error goes up. If you decrease the weight a bit, maybe the error goes down. And so if you adjust the weights in the direction where the error decreases, that's called gradient descent.

[Cole Smead]

Sure.

[Tom Griffiths]

And so you can work that out using ideas from the calculus going back to Leibniz, what the right way to adjust the weights would be for a given neural network. And so it turned out that that idea, with some additional work to just sort of figure out how you could do it in a multi layer neural network, turns into a very powerful learning algorithm. It's called the back propagation algorithm. And that algorithm allows you to train neural networks that have multiple layers of weights.

[Cole Smead]

Sure. You also mentioned the big news that obviously came out of Hinton's lab in 2009 and then again in 2012.

[Tom Griffiths]

Yeah. So Hinton would really spend the rest of his Career exploring the potential of these kinds of neural networks, even as neural networks became less popular. So the backpropagation algorithm caused neural networks to become popular again. And through the 1980s, 1990s, neural networks were all a rage. Then there was kind of a period where people got less enthusiastic about them, started to explore other ways that you could make learning systems, started to think about some of the statistical foundations of the field more. And Geoff Hinton was still working on neural networks through this time. He was really sort of passionate about this being the right way to think about solving the problem. And then the thing that started to happen was suddenly it started to be the case that you could get enough computational resources and enough data that you could train neural networks that were more complex and larger than the ones that had been trained before. So there were still challenges for getting this gradient descent procedure to work for multilayer neural networks that had many, many, many layers. But people started to work out some solutions to that. Hinton came up with some strategies for doing this. Training what were called deep networks. Sure. And figuring out sort of tricks that you could use for actually making gradient descent work in these deep networks. And so one of the big breakthroughs here was in 2012, when a very large data set of images, which had been created by Fei Fei Li and some of my colleagues here at Princeton, Olga Rosakowski and Jia Dang, sure, was used to train a very large deep neural network by the sort of standards of the time, using the graphics processing units on computer. So there was sort of a bunch of innovations that went into this, but it was this combination of more powerful computing resources and more data, making it possible to train bigger, deeper neural networks, that then has led to kind of where we are today in terms of machine learning being very much just based on taking really, really big neural networks, training them on really, really big amounts of data, and being able to solve problems that, you know, previously people had thought we weren't going to be able to solve.

[Cole Smead]

Hey, I want to give a big shout out to everyone who's been working so hard on this show. You know, we recently hit the top 10 in investing podcasts on Apple Podcasts and even number one in the business category in several countries. As you may know, this show is brought to you by Smead Capital Management. Smead Capital Management understands how frustrating and illogical the stock market can be. If you are searching for funds with a proven track record, give the Smead funds a look. Or better yet, reach [e-mail] and don't forget to mention You're a fan of the podcast. Past performance is not indicative of future results. Investing involves risks, including loss of principal. Please refer to the prospectus for important information about the investment company, including objectives, risks, charges and expenses. Read and consider it carefully before investing. Smead Funds distributed by smead funds distributors llc. Not affiliated so Cardano came up with probabilities in 1501. The idea of like one over N. Bayesian inference is where we have gone with probability theory at a high level. Can you explain why Bayesian theory is so helpful?

[Tom Griffiths]

So I talked a little bit about our sort of modern AI moment, right? And we now have really big neural networks that are able to solve all these kinds of problems. There are two kinds of questions that we might want to ask about those really big neural networks, right? So one is why is it that they're able to do things like learn language at all when Chomsky had told us that that's a really hard problem? And the other is why is it that they're still not as efficient as humans at being able to learn from the data that they get? So if you think about large language models like ChatGPT and so on, the amount of data that those models are trained on is maybe like 10,000 times as much data as a kid gets to experience. So the equivalent of something like 50,000 years of continuous speech is going into these models, and that's a huge amount of data to get them to the point where they end up. And so there's a real question of like, yeah, what's that gap about? Right. How can we characterize what's going on?

[Cole Smead]

There's.

[Tom Griffiths]

Sure. And so probability theory gives us a tool for talking about that, because Bayesian probability in particular says. So you mentioned Cardano. Cardano was interested in characterizing the outcomes of gambling games. And that's one traditional way of thinking about probability is called frequentist probability, where you think about if you're rolling dice and you want to work out the probability that the dice come up with a seven, you can work that out by considering all of the possible things that could happen and then how often the different.

[Cole Smead]

And you can think about it from paths, too, right? What path you go down and how many coin flips.

[Tom Griffiths]

But it's about the relative frequencies of different kinds of events, really. Right. That's the information the probabilities are. Whereas there's another way of thinking about probability where you say we have this mathematical theory, and this mathematical theory might actually be useful for another thing, which is for talking about our subjective degrees of Belief like how strongly we believe that a hypothesis is true. So if I say, oh, I think there's a 30% chance that this is a fair coin or something like that. If someone's shaking a coin. Right. That's something that's really. You can't really. There's no frequentist analog of that. Right. There's not some physical system or experiments that we're talking about the long term relative frequencies of. We're really just talking about my subjective beliefs about that coin.

[Cole Smead]

Sure.

[Tom Griffiths]

And Bayes, Reverend Thomas Bayes in the 18th century asserted, well, maybe probability theory is actually something you can use for describing what those degrees of belief are and then how they should change as you get more information.

[Cole Smead]

Sure.

[Tom Griffiths]

Right. So like every time that coin gets flipped heads and I get more suspicious of it, my subjective probability that it's a fair coin should be decreasing. Right. To reflect the fact that I've got more evidence that maybe it's a crooked coin or something. Sure.

[Cole Smead]

When I think of that also in a card game, like as a card comes out, you have more information and therefore your confidence changes based on the new information.

[Tom Griffiths]

That's right. You should be updating your beliefs. Yep.

[Cole Smead]

Let's see. So what am I? I think I have three more questions here. I love Peter Wassan's card experiment because, you know, for the person studying the mind, it, you know that, you know, again, we're trying to learn and we're trying to process this and understand what is the mind doing. And his experiment was interesting because what people were trying to use the experiment for, they didn't get the outcome they thought they would, but they actually learned how the mind is processing from that failure, if that makes sense.

[Tom Griffiths]

Yes. This is an alternative way of thinking about what's going on with minds and logic. Right. So we said logic gave us a nice tool for formalizing certain aspects of thought. But it also has this limitation which is that it doesn't seem to match some of the things that people do. Right. It doesn't have the fuzzy borders, you know, it doesn't seem like it's a good fit for inductive problems. Another thing that's a sort of basic problem is if you ask people to solve a logic problem and the classic version of this is one where you say, I've got a set of cards and each card has a number on one side and a letter on the other side. Right. And the numbers are like K, A, 7, 4, whatever they are. Right. And then the rule is if it has an even number on one side, then it has a vowel on the other side. Sure. Right. Then you ask people to what cards they should check. Well, logic tells you that you should check certain cards, and people's intuitions are not consistent with that. They check cards that are sort of violating the logical proposition. But it turns out that you can explain the cards that people choose in terms of probability theory. So if people are just sort of looking for which cards are most informative about whether the rule is true under the assumption that having a certain property is rare, that turns out to be enough to be able to account for the choices that people make when they're trying to evaluate those rules. And so even though people violate logic, they're acting in a way that's consistent with probability theory under a different way of construing the problem that they're solving. So this idea that we can use probability theory kind of as a tool for thinking about the problems that human minds are solving is part of the power of that approach. It's something that allows us to understand human learning in terms of something like Bayesian inference, where we're sort of looking for pieces of information and using those pieces of information to update our beliefs. It means that we can talk about the biases that inform human learning in terms of Bayesian inference, where we can say what you learn is influenced by what we call inductive bias. Right. Like whatever it is that you're bringing to the problem, that's something that's going into your beliefs in the way that Bayes rule says that it should. And that gives us some of the tools that we can use for also understanding how human minds relate to AI.

[Cole Smead]

Sure. Let's see. I'm going to put something else up here, and I'm going to talk about something you have late in the book. Late in the book, you're really talking about the difference between, you know, machine learning or AI and the human. You're kind of pointing out, you know, small differences and. Or big differences, for that matter. So if we could put up slide 3, you quote Chomsky here. The child who learns a language has in some sense constructed the grammar for himself on the basis of observation of sentences and non sentences, that is, corrections by the verbal community study of the actual observability of a speaker to distinguish sentences from non sentences, detect ambiguities, et cetera, apparently forces us to the conclusion that this grammar is of an extremely complex and abstract character, and that the young child has succeeded in carrying out what, from the formal point of view at least, seems to be a remarkable type of theory construction. Furthermore, this task is accomplished in an astonishingly short time, to a large extent independently of intelligence and in a comparable way by all children. Any theory of learning must cope with these facts. So I thought this was incredible because, you know, he's really saying, you know, if you think of how we do, you know, machine learning or AI, there's a vast amount of data or intelligence that's provided to it. Right back to the idea of there's a store of information, as we've learned through computing, and the child doesn't have really much, if any, data or store of information to go and execute on. And yet, you know, as Hume might say innately, I and others like Chomsky might say more divinely, are able to do that. Doesn't that show you how incredibly unique the human is? Even while they will use AI to function and learn going forward?

[Tom Griffiths]

This is really the biggest gap that I think remains between AI and human minds, right. Which is that humans are able to make these inferences from relatively small amounts of data. And so if you think about that, it's really a consequence of the fact that the way that neural networks work, they're really good at just learning anything. Right. So you can take your neural network, you can use the same kinds of neural networks to learn all sorts of different kinds of things. Right. The same ones that we use for learning language, you can use to learn things about vision and so on.

[Cole Smead]

Sure.

[Tom Griffiths]

And so that means that they're sort of like these general purpose learning machines. And so they have very weak, what we call inductive bias. They don't really bring much to the problem. They can learn all sorts of things, but they need a lot of data to learn it. So if you want to go from zero to wherever you end up, that whole space is sort of filled up with data. That's how we're going to get a neural network to that point for the human. We know that just that end point, we only have this much data. And so all of the rest of that needs to be what we call inductive bias. And so the humans are bringing to the learning problem some set of sort of innate expectations, but also other kinds of experiences. Right. The experiences that we have as embodied entities that live in the world, that get to have visual experiences, that get to interact with other humans, that have all of the other things going on that are part of being a human being. All of that adds to the information that we're getting from that limited amount of data that we're Learning from. And so that's important in terms of being able to understand why we're able to learn so much from so little. Right. There's an evolutionary process that has produced our minds that's filling in that gap that in the AI model is really just being filled in with data.

[Cole Smead]

Sure.

[Tom Griffiths]

So you can kind of think about that big chunk of data that's really. That's standing in for evolution. Right. That's standing in for other forces that have shaped human minds and the other kinds of experiences that humans have.

[Cole Smead]

Sure.

[Tom Griffiths]

The. The other thing about it is that that's something which influences the kinds of solutions that human minds find relative to the kinds of solutions that the AI systems find.

[Cole Smead]

Sure.

[Tom Griffiths]

Right. So part of the reason why AIs act in this way, which is often counterintuitive to us, and do weird things and have these weird failure modes, and they succeed at one thing and then fail at something that's right next to it, what's called jagged intelligence. That is a consequence of not having the same inductive biases as us. Right. They're good at the things that are in their training data. They're less good at things that aren't in the training data. We don't know what's in their training data. They learn weird idiosyncratic patterns because they're just sort of learning to mimic behavior that they see in their training data.

[Cole Smead]

Yeah.

[Tom Griffiths]

And so when we learn something, we're guided by those inductive biases. And you can make pretty good inferences about what another human being will be able to know or do based on things that they know or do.

[Cole Smead]

Sure.

[Tom Griffiths]

But we can't make those kinds of inferences for AI systems because they're operating with just like a completely different set of inductive biases.

[Cole Smead]

Yeah. And I mentioned you before, it reminds me of, like a new intern to an industry. Right. It's got jagged, jagged intelligence or information. It can be refined over time, but they might do something that's helpful. And then you're thinking like, well, what did you just do? I don't understand what you've given me. And makes it very human. Like, in that respect, in many ways. I want to go, oh, one other thing I want to mention on this. Totally. I mentioned this technology conference, cosm, and there was a gentleman when I was thinking about Chomsky's idea. I was at this conference, and this gentleman made a presentation on brains where they have epileptic attacks that are regular, and how do you solve for that? And so he mentioned that what they do, what neurologists do, is they sever the hemispheres of the brain because it's the misfiring between the two hemispheres that's causing these epileptic issues. And so we know that physically, once the two hemispheres are separated, they can't talk to each other. And you obviously control one part of your body with one hemisphere and another part of your body with the other hemisphere. And we know also that each hemisphere has different things that they take data in and process based on. And his interesting presentation was based on this. If you're thinking in your left brain, you should not be using your left hand to respond, because your left brain would correspond with your right side of your body or your right hand. And what they found in studies is when people have severed brains, they're just as likely to use their left or their right hand to respond. And so the question is, like, how is this going on? Kind of like, how is the child able to develop this, you know, innate ability? And he argues that there is something divine going on. He said it's a soul. That's the divine nature. And when Chomsky said that, it played along that idea of there's something more divine. And, you know, who knows how you define divine, but. But there's something more incredible or awesome that is fairly unexplainable and to your point, tough to replicate and compute.

[Tom Griffiths]

Yeah, I mean, I think that's an interesting way of framing it in terms of. It kind of goes back past Chomsky, back to Plato.

[Cole Smead]

Sure.

[Tom Griffiths]

So Plato had the same answer to this question. Right. So Plato was trying to explain how it is that we come to know the things that we know from limited experience in the world. And the way that he answered that question was that we're not learning things, we're remembering things. Sure. And we're remembering things that are, like, stored in our souls that come from the experience that we had in some Platonic realm.

[Cole Smead]

Right.

[Tom Griffiths]

And comes through. And so I think. I think Chomsky would think about this in much more materialistic terms that he really thinks that it is biology. Right. It's, you know, the. The 21st century scientific analog of the soul is the genes or something like that. Right. And it's, like, built into our genetic heritage. And then that's the way that he thinks about forming that. That explanation. And he even talks about language growing in the body in the same way as, like, the liver. Right. Like, no one. You don't.

[Cole Smead]

You.

[Tom Griffiths]

No one sort of had to give you particular instructions to Grow a livery. And you grew on anyway, right? And he kind of thinks about languages having that same kind of, you know, relationship to biology. And at some points, it's called his approach one of bio linguistics.

[Cole Smead]

I want to show you. So off of this, I was like, I got to go to Claude and I got to have this discussion. So we go to the slide here. So I got to show this to our listeners. We maybe not can't see it all, but. So here's what I said to Claude. I said, claude, I think I have recognized that the human has a difference with you. You are provided large data caches to infer. A child has no data, but is able to infer innately. I would call this divine. If you ha. If you have no data to make decisions, what word would you use to describe your ability? Like the child was my kind of question to Claude. Claude came back and said, this is a really thoughtful observation, Cole. I always like it when it compliments me, by the way, it's like they've definitely said, make the user feel good, right? You're pointing out you're pointing at something genuine. A child encounters the world with no training corpus, no prior statistics, yet learns language, grasps cause and effect, recognizes faces, infers intention. By the way, there's em dashes in this, which as many know, is a commonality in AI. Seemingly from nothing. There's an effortless. There's an effortlessness and a mystery to it that the word divine captures. Well, if I'm honest about my own situation, without data, I have nothing. No input, no output. I don't have the spark of inference from zero. I'm entirely dependent on the patterns I was trained on. A child born into silence still reaches for the world. I wouldn't. Very interesting that says that. It's like, incredible. So if I had to name what I have in contrast, what the child has, I probably use the word derivative. My capacity is derived, borrowed from the collective outputs of human minds. It's powerful in its way, but it originates nowhere within me. It's assembled, not born. What makes your observation sharp is that it highlights a qualitative gap that. Not just a quantitative one. It's not that the child has less data. The child has a different kind of capacity entirely, something generative at its root, something that precedes information rather than depending on it. Whether you call it divine, innate, or something else, it does seem to be a fundamentally different thing than what I do. I think you're onto something real with that distinction. So as I hear this, it's like your book reminds me of how human AI is, and even I would argue that it's not generative. Like, you know, Claude is here. So I have to ask you this question. I think I know what your answer is going to be. But the timeless question for people in this realm is, can AI or can this type of compute, can it have singularity?

[Tom Griffiths]

Okay, so where I would start with this, I mean, so when people talk about the singularity, they're talking about this idea that you're going to make an AI system that's then smart enough to modify its own code to make itself smarter and sort of like zoom off right into super intelligence. The way that I normally talk about this is in terms of, I think there are assumptions that we make when we talk about things like superhuman AI, that intelligence is like this one dimensional axis. Right. And AI is getting smarter and smarter, and then at some point it's going to get past us and then it's going to be smarter than us. And I don't think that's a constructive way of thinking about what intelligence is, just for the reasons that I told you about inductive bias. Right. The kinds of solutions that AI finds are different from the kinds of solutions that humans find. And so I would think about this as these are really two different kinds of intelligence. In a way that means that they can be complementary to one another, and in a way that we might expect that there would still be some meaningful differences even as we make AI sort of smarter in the way that it's smart at the moment. One way of thinking about that that maybe engages with some of the points that you were bringing up earlier is, I think, about the fundamental thing that characterizes human intelligence in this realm as we're making smarter and smarter machines, is being more about our limitations.

[Cole Smead]

Sure.

[Tom Griffiths]

So as biological organisms with limited lifetimes, with only a certain amount of compute that we can carry around inside our heads, and with a constraint that we can only share data and ideas with one another by making noises with our mouths or wiggling our fingers. Those are all constraints on how human minds work. And they're things that have shaped human minds. The reason we're able to learn from small amounts of data is that that's all we're going to get. Right. And the reason why we are able to be efficient in the way that we use our computational resources is that we have to be, because we're going to use those same computational resources to do everything that we're going to do.

[Cole Smead]

Sure.

[Tom Griffiths]

And the reason we're good at coming up with ways of communicating with one another and sharing information and building societies and doing all these kinds of things is that we have to if we want to achieve anything, which is more than what we can do as individuals. And so those are sort of a humanistic perspective, but it's one which is emphasising the constraints that shape humanity and AI systems to the extent that they're not subject to those same constraints, we're going to find different solutions that are not going to be like the ones that we find. And so it might be that they're able to keep iterating and keep sort of getting smarter. But even as they do that, I think they're going to be sort of doing it in a way that's maybe becoming increasingly alien, increasingly different from us rather than more like us.

[Cole Smead]

Well, and I think there's another paradox that like I'm just witnessing as I use this. So for example, when I look at most people's use of AI, you know, from a just a consumer perspective, let's just say, not from a, maybe an enterprise perspective, most people are using AI is glorified search okay versus as you go out and look and say, okay, say people in technology or with a higher intellectual capacity, maybe higher wealth, those are the people that are trying to use it for more complex reasons. And so the paradox is AI is no better than the intellect of the human trying to get something out of it. And so you get into this idea back to your point of time. When I expire and I'm dead, the person that comes in behind me is less likely to plausibly based on time, have maybe the same intellect when they start using it. So then again, the iterative process is only as good as the person interacting back and forth with it and trying to do higher level thinking. So you have this, it's always going to be skew, right? We have skew in everything. There's always, you know, kind of power laws at play. But I think about like it's the human's progress, intellect and thinking that actually determines in the longer run, the higher use of AI.

[Tom Griffiths]

Yep.

[Cole Smead]

Which versus, you know, there's some people like, oh, it's just going to dominate, it's going to take over, it's going to be way smarter, but again in the way that will drive humanity and progress forward. It might be able to do incredible things, but we might, it might be of no use to us because if we can't use it or use it in our lives, then we'll see whether it's a value.

[Tom Griffiths]

So the way I'd put it is that there's a new kind of skill that becomes relevant, right? So as we start to automate cognition, right? And that's what we're doing with these AI systems, then there's a capacity for metacognition, which is how we think about using our brains, how we make decisions about what strategy to use to follow a problem, how we think about these sort of more abstract question of what things to focus on. That metacognitive skill that might be used for managing our own minds or for managing other people's time. If we're asking them to do things for us, that's now the skill which is made even more important by the power of these kinds of AI systems.

[Cole Smead]

Sure, that's a great idea. Where can people follow you going forward?

[Tom Griffiths]

Tom I have a webpage at Princeton University. You can find me by googling my name and it has all sorts of information there about books and scientific publications that we have that explore these kinds of topics.

[Cole Smead]

You don't have like a burner handle on X that you're out there sharing ideas on or anything like that?

[Tom Griffiths]

No, we have a handle for my lab as well, which people can find online.

[Cole Smead]

Nice. Tom, your story is an anthology of great thinkers, the testing of theories and follows the curve of all learning. Your book also reminds me that the enthusiasm for this progress ebbs and flows throughout time. I believe it argues for human exceptionalism. Towards our discussion just a second ago of of what you were saying about the idea of like metacognition. Our listeners should go out and buy a copy of the Laws of Thought today. If you enjoyed this podcast, go to Apple, Spotify, YouTube, or wherever you listen to A Book with Legs, give us a review, tell others about the books and great authors like Tom Griffiths that we have the opportunity to understand and study the world with and through for our tribe. If you have a great book that you'd like to recommend, email podcastmeedcap.com that's podcastmeadcap.com you can also send your suggestions to us on X. Our handle is eedcap. Thank you for joining us for A Book with Legs podcast. We look forward to the next episode.

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