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

18:46Cole Smead: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.

19:03Tom Griffiths: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 SmeadCap.com. At our firm, we are stock market investors. We advise investors who play the long game with a discipline that has proven success over long periods of time. Learn more about our funds at SmeadCap.com. Past performance is not indicative of future results. Investing involves risks, including loss of principle. Please refer to the prospectus for important information about the investment company, including objectives, risks, charges, and expenses.

19:39Tom Griffiths:Read and consider it carefully before investing. Smead funds distributed by Smead funds distributors, LLC, not affiliated. So let's pivot next to Alan Turing and the Turing machine. And I'm going to 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 an act. 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 did.

20:17Tom Griffiths:I tried to take as little math classes 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? Yeah.

20:31Cole Smead: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.

21:03Cole Smead: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 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, right? And then they sort of maybe look back and forth and then they're sort of thinking about what the next step is. But that basic operation, right, 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.

21:39Cole Smead: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, it's 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.

22:19Cole Smead:And that's it. That's enough to be able to then characterize all the things that mathematicians do.

22:26Tom Griffiths: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?

23:00Cole Smead: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 talk about that. 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. 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.

23:34Cole Smead: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. Sure. Right? So you can't build a computer that's going to tell you whether a computer can solve a problem. Sure. Which, you know, mostly, there are certainly cases where we might like to be able to do something like that.

24:13Cole Smead:But most of the time, that's not a practical constraint on the things that we use computers for.

24:17Tom Griffiths: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?

24:33Cole Smead: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 had imagined an infinitely long tape with, you know, numbers that can be written on it.

24:49Tom Griffiths:Yeah.

24:49Cole Smead: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. Sure. Although Turing actually built tape-based computers during World War II when he was doing code breaking that, you know, resembled his ideas about a Turing machine.

25:06Tom Griffiths:Sure. Sure.

25:07Cole Smead:Well, Neumann was trying to think about how do you turn this into a sort of practical device that you can use for solving problems? Like, so now we're going to build something, which is, you know, an electrical computer that's going to be representing information inside that computer in terms of using magnets and other kinds of like, you know, 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?

25:45Cole Smead:So it sort of has this distinction between 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, well, 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 uh plugs that were going into an array of sockets in order to like rewire the machine to solve every different problem that's solving um and there was actually a a team of women who was responsible for this um for this first computer that was sort of did this with these plugs and so on.

26:34Cole Smead: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 it was. Von Neumann wrote the report, but he might have, you know, in doing so undermined his collaborators who helped to 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.

27:09Cole Smead: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. 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.

27:21Tom Griffiths:Well, and effectively what we just discussed is, I mean, that's the, what we, you know, as a kid, you know, with a floppy disk drive or a hard disk drive. I mean, that's in effect what that did over time structurally to compute. Yeah, no, that's right.

27:34Cole Smead:So, you know, it's laying the foundation for what we now think of as a computer.

27:38Tom Griffiths:Sure. You mentioned Bruner earlier. I was just caught by this. I love the picture you used for this. Bruner called some disjunctive categories. He called these intellectual nightmares, quote, 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 two here where this is what he shows. And this is what you'd walk away as you're trying to study categories and learning to be, this is an intellectual nightmare.

28:16Cole Smead: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 a 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. here. 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?

28:58Cole Smead:How do I store things in memory? And Bruner's trying to figure out, how do I rigorously study the mind and sort of overcome the constraints of behaviorism? And it's a 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 and 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 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.

29:39And so the key idea that he has is then,

29:47Cole Smead: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 you know uh the square is part of the concept if it has a black shape or and it has three things on the border right that would be relatively easy to learn sure it's really hard to learn things that are disjunctive concepts so things that have an or so learning it's in the concept if it has a black shape or it has three lines on the border it's very counterintuitive for people and most of our natural concepts don't necessarily take that form.

30:30Cole Smead:It seems like there's sort of more and-like things, right? And there are or-like things that we sort of think about when we're thinking about how the world is organized.

30:39Tom Griffiths:Sure. Yeah. And I guess 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 non-linear relationships at times. Claude Shannon created the information theory. Why was this important to this story?

30:59Cole Smead:Shannon was important in translating Boole's abstract ideas about logic into something that you could use to actually build electrical circuits. So 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 and 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.

31:40Cole Smead:And so again, this was influenced by World War II. 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, right? Like, you know, how much information you need to transmit.

32:10Tom Griffiths: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? 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.

32:48Tom Griffiths: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 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. 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 gonna wear? What am I gonna 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.

33:27Tom Griffiths: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.

33:37Cole Smead:Yeah, and Shannon, you know, 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. 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. And he was also doing work on memory. So how many things can you remember? And then he was asked to give a presentation. There was an hour long presentation and he didn't have an hour long presentation.

34:20Cole Smead: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, you know uh pitches or seven different you know uh luminosities of light um uh without seeming to lose information and after that you started to lose information and you could remember about seven things uh you know um but then you know if you tried to go too much above that you would start losing information and so that was 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 Yeah.

35:02Tom Griffiths: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?

35:13Cole Smead: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. 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 to 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 it's exactly the same problem as a problem of like playing a good chess game right if you think about a chess game going back to our board game analogy right you've got a choice about what move you make is 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 a you know the 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 um and so newell simon and shaw were interested in creating machines that were able to solve this problem and they tried to do that using strategies that human mathematicians use right so just like turing was inspired by thinking about what is going on inside the head of a mathematician sure um uh newell simon and shaw looked at um these kinds of strategies or heuristics that human mathematicians use that are things like if you know that you can get to the solution from some other place then work towards that place right like if you know if i could prove this then i can prove this then it's sufficient to just prove that first thing or if you know uh 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 know you could take away from the endpoint.

37:26Cole Smead: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.

37:38Tom Griffiths: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?

37:49Cole Smead: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 characterize human languages. Sure. And Chomsky wanted something which was different from that. He wanted to have a way of characterizing, you know, if you had a single language, could you come up with something like a mathematical system that would allow you to characterize all of the sentences that were grammatical statements in that language, right?

38:28Cole Smead:So trying to create a formal system, right, that gives you a way of producing all the sentences that are in that language and nothing else. okay 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 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 yeah that then could capture the structure that sentences have in order to get even close to the structure of English.

39:11Tom Griffiths:Sure. Explain what's a finite state language versus something that's not a finite state language.

39:17Cole Smead: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 there's 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.

39:57Cole Smead: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. Sure. 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, right, 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 behaviorists that was nice because it suggested that you could learn language just by learning associations between words sure so you could learn that after dog then you're more likely to produce the word runs right sure 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.

40:58Cole Smead: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 board game like that.

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41:45Tom Griffiths: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.

41:59Cole Smead:So the challenge that Chomsky ran into, so he showed that English was not a finite state language, that there are sort of structures in English which are richer than the kinds of things that you can capture using those simple board games.

42:12Tom Griffiths:Okay.

42:13Cole Smead: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. 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.

42:49Cole Smead: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. so logic is the math of how you go from things that you know to be true to things that you uh know or you know 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 uh 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?

43:52Cole Smead:And can you give it the same kind of precision that we give to deductive inference?

43:55Tom Griffiths:Sure. Hume argued it was habits though, didn't he?

43:59Cole Smead:Yeah. So David Hume, the Scottish philosopher, said that we're not going to find something that's like deductive inference, right? 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.

44:28Tom Griffiths: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?

44:39Cole Smead:Well, so I think what Hume is missing there is that something can be a habit, but it can still be systematic. Sure.

44:46Tom Griffiths: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.

44:56Cole Smead: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 you know 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.

45:39Cole Smead: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.

45:57Tom Griffiths:Sure. Eleanor Roche worked on family resemblance. I really liked this idea because it gets to the idea of like 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?

46:14Cole Smead: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 brunner's experiments is something like a rule that tells you oh if it has this property and this property then it's you know then it's something that belongs to that category and what rush realized is that uh in fact real categories are nothing like that right so um I can ask you, like, is a chair a piece of furniture? What would you say? I'd say, yeah. Yeah. Is a telephone a piece of furniture? And I would say, no.

46:55Cole Smead:Is a rug a piece of furniture?

46:58Tom Griffiths:I'd probably say, yeah.

47:00Cole Smead:Okay, so that probably, right, 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 we're absolutely certain that they're not, but other things where it's just somewhere in between and we're not really sure. Well, yeah, it's your point.

47:22Tom Griffiths: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.

47:30Cole Smead:I think that's going to get you in trouble though because there's plenty of things in Ikea. I know, I'm teasing. so um but but that uh that that idea is that um you know that the categories have fuzzy edges right yeah and that maybe rather than rules we decide based on the experiences that we have where we're like oh well you know 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 trying to taste trace these you know connections between things and trying to make judgments based on that sure um why did amos

48:10Tom Griffiths:tversky reject multi-dimensional scaling that's a very technical question so so but but now you're

48:18Cole Smead:according to your book yeah now now you have the problem of um uh saying what um what categories are, right? Now we've got rid of logic. I mean, it's no 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 like 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, you know, the different attributes of things. And so, you know, chair is one point in that space, and then rug is another point in that space, and telephone is another point in that space.

48:58Cole Smead:and so you end up with something where you have um uh 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 about explaining how you can have that fuzziness okay um and so that was one idea is that we could think about similarity in terms of um spaces right that the distance between two things in a space reflects how similar they are. And then Tversky, who's famous for his work with Daniel Kahneman on decision-making. If you think about the work that he did in decision-making, it was really about challenging the axioms, the mathematical rules that characterized rationality.

49:42Cole Smead: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. 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.

50:19Cole Smead: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. They sort of say a camel is like a horse more than a horse is like a camel.

50:35Tom Griffiths:Well, I think you mentioned he says that similarity judgments violate the triangle inequality. Yeah.

50:41Cole Smead: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, right, 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 like the worst case scenario is the one where you have like a flat line, but for any kind of triangle, it's going to be less than that. Yeah. 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. Okay. Right. And the moon is also similar to a soccer ball, but a light bulb is not that similar to a soccer ball.

51:28Tom Griffiths:Yeah. Right.

51:31Cole Smead:And so that's a violation of the triangle inequality.

51:33Tom Griffiths:Sure. Teach us about Frank Rosenblatt's perceptron because this is a big part of the story when he comes to this.

51:40Cole Smead:So we're now at this point where now we're thinking, okay, maybe thoughts are like, you know, 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.

52:15Cole Smead: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 Rosenblatt 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.

52:58Cole Smead: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.

53:20Tom Griffiths:The perceptron had linear boundaries. Why was this so problematic to Marvin Minsky?

53:24Cole Smead: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 just 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 like logical ands and logical ors with functions that can be characterized by a linear boundary.

54:05Cole Smead:but there are other kinds of things that are hard to characterize by linear boundary like um 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 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. Sure. And that's not something you could characterize by a linear boundary.

54:42Cole Smead:Yeah. And so that meant that what you could learn with that very simple kind of perceptron was fundamentally limited.

54:50Tom Griffiths:Sure. Beth Loftus, Alan Collins, and Ross Quillian worked on the idea of spreading activation. Teach us what their work did.

54:59Cole Smead:this was really a way that you know even after perceptrons have 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 know you might be you know there are different concepts that you have and again we can think about those nodes as getting activated and those nodes is 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.

55:43Cole Smead:And so they could show that by doing that, you could explain why, you know, when people, you know, hear the word hockey, they're more likely to think of the word fight or something like that. Or Canada or something like that.

55:56Tom Griffiths:Yeah.

55:57Cole Smead:You can form these associations between things that then sort of propagate through the mind. And it's the same idea that 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.

56:20Tom Griffiths:Sure. Jeff Hinton worked on unsupervised learning. What do we get from his work?

56:24Cole Smead: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. Sure. And Jeff Hinton was, first of all, I should mention, I told you that the Boole family was going to come back. Right. So he was actually the great, great grandson of George Boole.

56:57Tom Griffiths:Sure.

56:57Cole Smead:And so he was very interested in mathematics, but also interested in psychology and philosophy, as you might expect, based on his heritage.

57:04Tom Griffiths:Yeah. Yeah.

57:05Cole Smead:And he worked with David Rummelhart, 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.

57:40Cole Smead: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. 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 backpropagation algorithm. And that algorithm allows you to train neural networks that have multiple layers of weights.

58:14Tom Griffiths:Sure. You also mentioned the big news that obviously came out of Hinton's lab in 2009 and then again in 2012.

58:22Cole Smead:Yeah. So Hinton, you know, 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 the 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 Jeff Hinton was still working on neural networks through this time.

58:54Cole Smead: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, and figuring out sort of tricks that you could use for actually making gradient descent work in these deep networks.

59:35Cole Smead:And so, you know, 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 Rosakhovsky and Jia Dang, was used to train a very large, deep neural network by the sort of standards of the time using the graphics processing units on Confuture. 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 that thought we weren't going to be able to solve.

1:00:31Tom Griffiths: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're searching for funds with a proven track record, give the Smead funds a look or better yet, reach out at SmeadCap.com. And don't forget to mention your fan of the podcast. Past performance is not indicative of future results.

1:01:05Tom Griffiths:Investing involves risks, including loss of principle. 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?

1:01:37Cole Smead:So I talked a little bit about our sort of modern AI moment, right? 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, you know, 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 like, if you think about large language models, like, you know, chat GPT 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, right?

1:02:20Cole Smead:So like 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, you know, they end up. And so there's a real question of like, yeah, what's that gap about, right? Like how can we characterize what's going on there? And so probability theory gives us a tool for talking about that because Bayesian probability in particular says, so you mentioned in Cardano. Cardano was interested in characterizing the outcomes of gambling games. And that's one traditional way of thinking about probability. It's called frequentist probability, where you think about, like, 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 - Sure.

1:03:06Cole Smead:And you can think about it from paths, too.

1:03:08Tom Griffiths:What path do you go down and how many coin flips, et cetera.

1:03:10Cole Smead:But it's about the relative frequencies of different kinds of events, really. That's 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, right? Like how strongly we believe that a hypothesis is true. So if I say, you know, oh, you know, I think there's a 30 % chance that, you know, this is a fair coin or something like that, if someone's flipping a coin, right? That's something you can't really, there's no frequentist analog of that, right?

1:03:48Cole Smead: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. 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.

1:04:10Tom Griffiths:Sure.

1:04:10Cole Smead: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.

1:04:24Tom Griffiths:Sure. When I think of that also in a card game, like as a card comes out, you have more information. Therefore, your confidence changes based on the information. That's right.

1:04:32Cole Smead:You should be updating your beliefs.

1:04:33Tom Griffiths:Yeah. Let's see. So what am I like? I think I have three more questions here. I love Peter Wasson's card experiment because for the person studying the mind, 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.

1:05:06Cole Smead: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. 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 have 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 you know like you know k a seven four whatever they are right um uh and then uh the rule is if it has an even number on one side, then it has a vowel on the other side.

1:06:00Cole Smead:Sure. Right. Then you ask people 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, you know, 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.

1:06:35Cole Smead: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, you know, 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?

1:07:16Cole Smead: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.

1:07:26Tom Griffiths:Sure. Let's see, I'm going to put something else up here and I'm going to talk about, you know, something you have late in the book. You know, 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 or big differences, if that matters. So if we could put up slide three, 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, i.e. corrections by the verbal community.

1:07:58Tom Griffiths:Study of the actual observability of a speaker to distinguish sentences from non-sentences, detect ambiguities, etc. 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 he's really saying if you think of how we do 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.

1:08:44Tom Griffiths:And the child doesn't have really much, if any, data or store of information to go and execute on. And yet, 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?

1:09:16Cole Smead: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 the way that neural networks work, they're really good at just learning anything. 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. The same ones that we use for learning language you can use to learn things about vision and so on. And so that means that they're sort of like these general purpose learning machines.

1:09:49Cole Smead: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 like 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, right? We know that just that end point, like we only have this much data, right? And so all of the rest of that needs to be what we call inducted bias. And so the humans are bringing to the learning problem some set of sort of, yeah, innate and expectations, but also other kinds of experiences, right?

1:10:23Cole Smead: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 a 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.

1:10:58Cole Smead: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. 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, 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?

1:11:36Cole Smead: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. 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. 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.

1:12:03Tom Griffiths:Yeah, and I mentioned you before, it reminds me of like a new intern to an industry, right? It's got jagged intelligence or information. It can be refined over time, but you 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. 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.

1:12:42Tom Griffiths: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 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 innate ability.

1:13:37Tom Griffiths: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 who knows how you define divine, but there's something more incredible or awesome that is fairly unexplainable and to your point, tough to replicate and compute.

1:14:00Cole Smead:Yeah, I mean, I think that's an interesting way of framing it in terms of like the, it kind of goes back past Chomsky, back to Plato. 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. And we're remembering things that are like stored in our souls that come from the experience that we had in some platonic realm, right? And comes through. And so I think Chomsky would think about this in much more materialistic terms, right?

1:14:38Cole Smead:That he really thinks that it is biology, right? It's, you know, 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. Yeah. And then that's the way that he thinks about forming 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 know, 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 language as having that same kind of, you know, relationship to biology.

1:15:18Cole Smead:And at some points it's called his approach, one of biolinguistics. linguistics.

1:15:22Tom Griffiths: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 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.

1:15:59Tom Griffiths: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 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 there's m 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.

1:16:31Tom Griffiths: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 to 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, not just a quantitative one. It's not that the child has less data.

1:17:02Tom Griffiths: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 AI would argue that it's not generative like 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?

1:17:42Okay.

1:17:42Cole Smead: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 superintelligence. 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.

1:18:12Cole Smead: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 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 sure 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, right?

1:19:10Cole Smead: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. 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.

1:19:40Cole Smead:And so those are sort of a humanistic perspective, right? But it's one which is emphasizing 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, right? Increasingly different from us rather than more like us.

1:20:12Tom Griffiths:Well, and I think there's another paradox that I'm just witnessing as I use this. So, for example, when I look at most people's use of AI from just a consumer perspective, let's just say, not from maybe an enterprise perspective, most people are using AI as glorified search, okay? Okay, versus as you go out and look and say, okay, say people in technology or with a higher intellectual capacitor, 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 possibly, based on time, have maybe the same intellect when they start using it.

1:21:00Tom Griffiths: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. Yep. 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 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.

1:21:41Cole Smead: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, right? 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 the sort of more abstract question of what things to focus on, right? That metacognitive skill that might be used for managing our own minds or for managing other people's time before 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.

1:22:18Tom Griffiths:Sure, all right, that's a great idea. Where can people follow you going forward, Tom?

1:22:23Cole Smead: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

1:22:34Tom Griffiths:you don't have like a burner handle on X that you're out there sharing ideas on or anything like that

1:22:39Cole Smead:no we have a handle for my lab as well which

1:22:43Tom Griffiths:people can find online 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 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.

1:23:22Tom Griffiths:For our tribe, if you have a great book that you'd like to recommend, email podcast at smeedcap.com. That's podcast at smeedcap.com. You can also send your suggestions to us on X. Our handle is at smeedcap. Thank you for joining us for A Book With Legs podcast. We look forward to the next episode. Thank you for listening to A Book with Legs, a podcast brought to you by Smead Capital Management. The material provided in this podcast is for informational use only and should not be construed as investment advice. You can learn more about Smead Capital Management and its products at SmeadCap.com or by calling your financial advisor.