Analogy As The Core Of Cognition

Stanford University Thank you for your help with the seating. Um we very much appreciate it. With a lecturer of the fame and stature of Douglas Hofstadter we get a fantastic turnout and it’s a marvelous. Don’t worry if someone who was coming to meet you here hasn’t arrived. They will at least hear the lecture out in the lobby. So there’s a chance to get some small part of the action out there and um we’re just very happy you all came. This is a presidential lecture sponsored by the president and administered by the Stanford Humanities Center.

And we’re very happy to have been able to invite Douglas Hofstadter and even more happy that he has accepted. Uh Do take a look at the presidential lecture website which is accessible through the Stanford Humanities Center website shc.stanford.edu. Glen Worthy who’s here tonight has invested a lot of time and attention in presenting Doug’s work in the most complete and analytic possible way. It’s a it’s a real publication on Hofstadter and worthy of attention. Should you need to learn more about the Humanities Center, that’s also the place to go shc.stanford.edu .edu. That would include learning more if you’ve become deeply curious about the publications and materials that are out front and would like to see more about us, you can do it on that website.

Also, the tradition at the presidential lectures is not to have Q&A this evening, but to have a real discussion seminar tomorrow afternoon at 4:00. That seminar will be at the Humanities Center and the directions, if you don’t know how to get there, are on that same website shc.stanford.edu. So, I’m happy to turn now to an introducer who truly needs no introduction, Donald Kennedy, the former president of Stanford University, the editor of Science, a reasonably well-known magazine, and of course a scholar of great distinction in biology and environmental studies.

So, I will now, with no further ado, turn to Donald Kennedy. Uh this is a fantastic turnout, and I hope Doug knows uh how much of a tribute it is to the influence he’s had on the thinking of a large number of people, not only on this campus, but everywhere. It’s a great privilege to introduce him. Uh his family and mine were neighbors on San Juan Hill Hill for a time. Doug left his house before I got into Hoover House, but we had met on several occasions and actually became colleagues for a while at a time during which I had persuaded him to do some teaching in the human biology program to the benefit of our students.

And I saw a great deal of Lorie as she moved from bio major at Stanford to science writer, and I’m glad that she and and some members of her family could could be here. In Doug’s human bio period, he was working on Gödel, Escher, Bach, hereafter GEB. When the book came out, I not only thought it was a stirring accomplishment, I experienced that voyeuristic feeling of having some association, however transient and tenuous with a great literary triumph. Nowadays, I get the occasional additional dose of that by getting David Kennedy’s misdelivered mail, but fortunately, Doug also keeps me uh going with more achievements of his own.

And indeed, so much has been said of Doug and the power and luster of his intellect in that splendid piece by uh Glenn Worthy. Uh there’s not much that can be added to it, but there’s a question. And the question is, what kind of linguist, mathematician, cognitive scientist hybrid does it take to think up ambigrams, the carinian, metamagical, and so on? Answer: a charismatic imagination and an extraordinary gift for exploring how we think by substitution and analogy as he explores in fluid concepts and creative analogies, a work product that has grown out of a group he has relabeled as the fluid analogies research group, FARG, one O short of North Dakota.

The catalog, more formal than playful like Doug, lists him as director of Indiana University’s Center for Research on Concepts and Cognition. My friend Bill Kaufmann was one of those whom Doug asked about publishers and other practical matters in the early days of pre-GEB. Bill’s company W.H. Freeman had merged for a while with Scientific American of the Piel Flanagan era. Longtime admirers of Martin Gardner’s wonderful Lewis Carrollian mathematical games column in that magazine were devastated about Gardner’s announced retirement. But when Doug was announced as his replacement in 1981, everyone who knew him said, simply, “How perfect.”

His incorrigible playfulness with language and anagrams led him to redo the title to Metamagical Themas. He didn’t disappoint us in a tenure that lasted 2 and 1/2 years. Doug and I talked earlier today about the shared experience of being edited by Dennis Flanagan at Scientific American, one of the truly persistent, ego-restructuring, and capable editors of all time. I hope he won’t mind my telling a bridging story that has some personal meaning for me. Doug is deeply interested in language, how we use it, and what it tells us about how we think.

He had an early experience at the University of Oregon while doing a PhD in physics that had followed a good experience with math at a Stanford as a Stanford undergraduate and a disappointing one in a math graduate program at Berkeley. And at Oregon he at Oregon he happened to develop to develop a sidelong sideways interest in in the question how gender is used in language. E.g., how how is it that many of us in that day were saying men when we meant everybody. Now now we say guys when we mean everybody, and that’s just and that’s just as dumb a mistake. So, anyway, his his interest in linguistic sexism, for some reason, linked him to a talk I had given in the very early ’80s at, of all things, a senior athletes dinner at Stanford.

I used some data about women’s times in events like swimming and the marathon and how rapidly the performance gap between women and men had narrowed. As an example, I compared the Stanford women’s 400-meter freestyle relay time in 1981 with the best men’s college time of my undergraduate years and discovered that the women were 10 whole seconds faster than the fastest men. 10 10 seconds is a long time if you count it out, and that’s what I did at the senior athletes dinner. It was It was quite a good talk, actually. And and Doug Doug put a a snippet of that in uh uh in his his column in Scientific American, and I was I was totally thrilled. It was a far more interesting take on that subject than the snippet in Sports Illustrated at about the same time.

That suggests a lot about the exceptional range of connections that Doug is prepared to trace and analyze. The essence of his work has been to understand cognition, how we construct our knowledge of our world. The notion of some core essential to the way in which uh we link the features and structures of uh uh of thinking and language uh is brought out uh in G B G E B in in uh uh the features and structures of three very different creative and intellectual accomplishments.

And that speaks to the use he makes of computers and artificial intelligence notions or the problem of translation which has interested him or perhaps as a way to explore for some underlying formal structure. In the preface to the 25th anniversary edition of GEB, he chided some critics who had seen it as a book about three men. That’s a little like saying Moby Dick is a book about whaling. GEB is about how animacy arises and in subsequent work Doug has explored a variety of connections or braids with that theme between cognition and language, between what is written in one language and then translated into another, between what is left life and what remains.

Not only does he navigate those boundaries, he does so with a kind of loving respect that is perhaps best captured by the fact that he and his children, Danny and Monica, now teenagers, maintain an Italian only household conversation rule as a custom of honoring Doug’s beloved late wife Carol, a fellow explorer of the translation universe. At a time when the university, this one, is on a crash course to embrace and support interdisciplinary work, it is especially wonderful to hear from someone who has been there and who has set out new benchmarks for thinking that loops around cognitive science, machine intelligence, art, literature, perhaps eventually neurobiology.

You get a picture of his agility and playfulness from some of the titles of his presentations. The architecture of Jumbo, that one’s about machine learning. The slippable alphabet, hinge points of thought, speech stuff and thought stuff. His biography will break the spell check feature on your computer. Finally, my favorite from his recent uh uh passion for for uh translation. Uh you’ll need to absorb this slowly. Ma mignonne cutie pie pretty dear fairest friend pitting human against computers in poetry translation and guess who wins. Just think of what we could learn by examining Doug’s brain with functional magnetic resonance imaging. Absolutely non-invasive for those of you who aren’t kept to this.

Uh while he’s pursuing a a thought experiment about the relationship between art and and music. Phrenology would be never be the same afterward. I will close by noting that not only has he done some remarkably novel and and intellectually challenging work in the world. He has also always been a gracious and kindly and humanistic guide for those who want to explore it. I’m happy to introduce Doug Hofstadter, Stanford BS in mathematics, class of 1965. The College of Arts and Sciences Professor of Cognitive Science at Indiana University. As well as the director of the program I just described earlier on under a different name.

In his own biography, he thanks Indiana University, in some respects Stanford’s institutional parent for {quote} the fresh winds of freedom generously afforded him by his truly open-minded university. His presidential lecture in the humanities and arts is entitled Analogy as the core of cognition. Please join me in welcoming Doug back to Stanford.

I guess I’m a little bit on the spot here. Uh after an introduction like that, it was uh I have to say also Don didn’t mention that uh we used to do a little running together. He used to go up to the dish from the Hoover house and I remember well, I shouldn’t say we used to. That suggests more than once. I I joined him one time. I was a pretty good runner. Uh in fact, uh I still run and I just ran this this evening, but uh but it was hard to keep up with Don. In fact, I don’t know if I did. And uh do you still run, Don? Well, I guess that’s what happens to us all. Uh anyway, uh we’ve had a lot of experiences together of various sorts and uh he certainly did outdid himself in that wonderful wonderfully kind and uh broad introduction.

Um what when I was here as uh at as an undergraduate uh in the early ’60s, I was very interested in in understanding what the mind was. I think I had always been interested in what minds did and what creativity was and uh I had the experience of learning to program in the early ’60s before Well, Stanford one computer. It was a Burroughs 220 located in the basement of Encina. How many people here remember that? About one person.

Well, anyway, I programmed that Burroughs 220 and then I went on to other programming, but the point is that I got interested in in how language worked and uh and in certain rules for language and I don’t want to go into that very much. My model for uh producing sentences was was amusing, and it had a lot of amusing things, but it what it really inspired me to do was to think about what cognition is. It It certainly was not a model of cognition, but it was an amusing attempt, and um and over the years then I devoted uh a great deal of my life to thinking about what cognition is, and I guess tonight I’m going to be telling you uh some of the important conclusions that I’ve come to, and I don’t know if I can convince anybody, but I will do my best.

I have I will begin with a sort of a complaint, and uh Everything is in Everything is in focus. Good, that’s great. Uh by the way, I don’t use PowerPoint, for better or for worse. I don’t know what that means, but So, you’ll have to put up with my handwriting and and with sloppiness and things like that. Um and so uh in in cognitive science, the cognitive science conferences and journals and so forth, they always have they divide cognition up into all sorts of different pieces, and one of the pieces is always called analogical reasoning, and uh and uh it’s usually put together with problem solving. And uh it’s sort of one little teeny part of of thinking, and I sort of decided that I would put it this way, that uh analogical reasoning, they sort of is is the Delaware of cognition. So, I kind of feel that that shunts it off a little bit. It doesn’t make it very central.

Now, you might think that Indiana would be a better name for an analogical reasoning, but I’m going to be a little bit more uh daring than that. I’m I and it doesn’t mean California either, or Texas, or Alaska. First of all, we’re going to get rid of the word reasoning. I don’t want reasoning. An analogy has nothing to do with reasoning, or it does a little bit, but not much. I mean, it’s just a misnomer, and it’s a misconception of what analogy is, and that’s what I really want you to understand. And I suppose that’s sort of the bottom line of this talk. If we are going to make any connection between analogy and and a geographical situation, we’re going to liken it to the interstate freeway system. And it links everything together. Analogy is the interstate freeway system of cognition. It is not one little tiny zone somewhere off in the side. It’s So, that’s that’s a kind of a a way of that I think about it. I mean, I don’t really usually think about it that way. I made that up yesterday, so but it gives you the flavor.

Uh so, one of my rules, which I’m sure I will disobey tonight, is don’t cover your transparencies. Uh let everybody see everything, but I may not do that. Uh we’ll see if I’m if I I’m true to my own principles. So, uh as it says here, I think of categorization I mean, the story about analogy making, of course, has to be a little bit more than just analogy making. So, I I want to sort of show you how things fit together. Categorization is the name of the cognition game, but analogy is the mechanism that creates or that allows categorization to happen. By categorization, I mean, uh deciding what something is, what the essence of something is.

Uh now, one could sort of summarize this in a corny little analogy. Again, analogy is the motor of the car of thought, and then we then can even write it down as this little thing, analogy is to thinking as a motor is to a car. A is to B as C is to D. And this sort of reduces it down to the old standard, you know, A is to B as C is to D, proportional analogy looks like a fraction. And um that’s very nice. It’s the kind of thing, you know, like uh shoe is to foot as glove is to hand. And And these kinds of things that maybe they put on IQ tests and SATs and things like that. Uh but that’s not how I think of analogy, either. I mean, that’s That’s That’s That’s again putting it into a little tiny box and saying that all of analogy is A is to B as C is to D. And it And it again it misses the point.

Uh So, I don’t know. I can’t define anything and I kind of hate definitions, but I will at least sort of give you a sense. Analogy making is the perception of common essence between two things. And then a couple of footnotes to sort of hedge. Um I mean, things don’t have essences, but what I mean I I’m not a, you know, I’m not talking about some kind of abstract glowing philosophical essence. I’m talking about the essence that you perceive at the particular time in the frame of mind that you happen to be in. And uh and by when I say things, it’s tempting to think that the analogies are between the things in the external world, but I really want to say that analogies happen inside your head, so that they’re they’re they’re connections between two mental representations. They’re connections between things inside your head. Uh which we project to the outside world and we say these things outside out there are analogous and that’s very reasonable to do, but I wanted to emphasize how they go on inside the head and they are between mental representations.

Now, uh I’m going to give you a couple of analogies, some of my favorite analogies. Uh they’re they’re all, you know, analogies I could give you forever, but uh I’m going to give you a few that I think are are very interesting and kind of provocative. So, I’ll begin with uh when I was a kid, I was 8 years old as I recall when I found out about uh exponents. And I was in love with math, and I was fascinated with any new mathematical concept, and I made tables of not integers to various powers. I I filled uh notebooks with these kinds of things. So, uh one day I was walking through the house and I saw a paper uh that my dad was reading, and he was a physicist, and it had math notation galore, and I couldn’t make head or tail of it. But what I did notice was that there was uh there there little things that said, you know, like X sub 1, X sub 2, and stuff like that. And I thought, “Ooh, look at that. These little subscripts.” So, here’s my Here’s my little transparency. Uh the red You You can get the idea that I saw that I My guess was, “What in the world What operation on numbers does this subscripting thing do if the superscripting thing, you know, puts it to a power? What does it subscripting do?” I was really interested. And my dad told me, he said, “Oh, that doesn’t do anything. It’s just the way of naming variables.”

And I was so so disappointed, completely completely flattened. Okay. Fast forward 40 years. Fast forward 40 years. Um now I’m a father of a 1-year-old daughter named Monica, and Monica is sitting in our playroom pushing the button of the Dustbuster. Having time of her life. And then what does she see? She sees another button. And she pushes it, and nothing happens. And I’m watching her. And I go over there. I’m I’m sitting, you know, on the floor, and I get up, and I go over next to Monica, and I push the button, and I open it up, and I show her, “This is just where the garbage is, you know.” And Monica is, of course, completely destroyed.

And at that moment, you have to understand, I hadn’t thought about this thing with my dad for probably 40 years. At that moment, the whole thing of the exponents and the subscripts comes rushing to my to my head. And uh and I want you to I just want to, you know, kind of spell out this analogy. It’s a pretty complicated one. I mean uh Somebody said to me, I guess it was Don today, he said, “Oh, people make the mistake of reading out loud their transparencies.” So, I don’t know. I I I don’t know if I can avoid reading this out loud though, cuz it’s kind of fun. But I I’ve already told it to you, so maybe I won’t. I mean, I I think it’s interesting though that if you if you I mean, you know, here is me and all my love of mathematics and the subscripts. And and this is an interesting line here because I’m making an analogy. Part of this analogy is an analogy. I make an analogy between superscripts and subscripts. And I think, “Ah, there’s something there.” And then I get flattened uh by my father. Okay. And so, here’s Monica, and she comes along and she makes an analogy between one button and another. And she’s hoping, and then she gets flattened by her father. Uh who happens to be me, but that’s just a just a coincidence. But anyway, there you go. I mean, it’s it’s a pretty a pretty complicated analogy. Uh

Now, uh the next one That one’s That one is is uh what you might call uh a reminding event. And uh a lot of analogies are reminding events. And I And I want to say something immediately, which is that a lot of people think analogies are there to serve purposes. They’re not there to serve purposes at all. They just happen. That’s all. There’s no purpose. There’s no purpose at all. They just happen. Uh sure, they they’re in a certain sense, they’re serving evolution, but that’s about the only purpose that there is, you think. Um and uh I want to give you a an analogy that occurred to me a few months ago. Uh Uh I I was reading a book that my mother had loaned me by Jonathan Raban called I don’t remember exactly, something about Voyage to America or Discovering America, something. Anyway, he’s he’s traveling across his first chapter, he’s traveling across the Atlantic Ocean. I was in an airplane. I was flying back from California to Indiana, and I we we’re flying on our first leg, we’re going to Denver. And uh which is uh perhaps a United hub, I don’t know. Anyway, we were we were going to Denver, and um Uh so, I was reading this first chapter in which he Jonathan Raban goes from England from Liverpool to somewhere in Canada, and uh he was in a boat called the Atlantic Conveyor, and um the they he was very impressed by the size of this boat and thought that surely nothing could rock it, but the captain told him, “No, it’s it’s a you know, it’s it’s a boat is very vulnerable.” And uh and then what do you know, but they discovered a hurricane uh that was, you know, in their pathway, or it was actually coming up the Atlantic, and it was and it was going to be right in their way. And so, well, I mean, not very complicated thinking, but here’s what they did. There’s the Atlantic Conveyor, and there’s Hurricane Helene, and uh I I’ve drawn this a little bit off because I don’t know if they went quite that far south, but I didn’t want to put in time and everything. You get the basic idea here. I mean, the hurricane went up, and uh they went to the south, they deviated a little bit, and missed it, and and then went up and then turned back up. Okay, so, I’ve just read this thing. Well, I’ve just, you know, I’m thinking about the Atlantic Ocean and this big hurricane, which was curiously enough called a Whirly Girl by the captain. And I’m thinking about this, you know, but I mean I it’s just part of the first chapter. It’s not a major part of the first chapter. It’s just something that happens. The first chapter is all about this trip across the Atlantic and so forth and so on. And then I get out at Denver. And uh I’m walking down the corridor and uh as one does in airports and uh and uh here here’s a here’s a picture of me and this is this is a woman with a suitcase. Uh and she’s crossing the corridor. And uh and and I was swerved a little bit to the left and all of a sudden bang I said, “Hey, I’m the boat. She’s the hurricane or if you wish the whirly girl.” And and this corridor is the Atlantic Ocean. And uh and you know, 2 seconds is is is 2 days or whatever it may be. Uh and now I have to explain to you also this event inside my head happens so quickly and so fleetingly that I would not have even noticed it if I weren’t kind of an inveterate observer of my own thinking. I mean I caught it, you know, it would have disappeared in a flash and it to have no to leave no effect on the world at all. But here it is leaving an effect on all of you now.

My point is analogies happen all the time for no purpose. They’re fleeting. They just they’re they’re transient. They just appear and go away. Okay? It just your mind is filled with them. Uh now to get you know, the poster that was made used these two photographs which were taken at uh uh my parents’ ranch uh back in the ’80s I believe. Now various people may have thought various things about them and I’m just going to tell you what what is here. The upper one is in the summer and there’s this lovely oak tree that I know very very well she’s casting its shadow under the you know noonday sun more or less. The lower one is in the winter and there is no sun at all. It’s a cloudy day. What is that pat pattern that dark thing under? That is a snow shadow if you wish. That is the absence of snow. Uh the snow has fallen but it didn’t go through the tree. Uh it got caught by the tree and so no snow was on the ground and that dark patch is the absence of snow. And it’s a kind of a generalization of a shadow. I you know to me it was just a sort of a trivial uh connection but I it joined in many other kinds of shadows that I’ve thought about over the course of my life.

I mean I know that in eastern Oregon and maybe other places there is what they call a rain shadow uh which is uh to the east of the Cascade Mountains for some hundred or two hundred or some miles there’s a desert. In other words the Cascade Mountains basically stop the clouds from moving and and uh and so there’s no rain to the east of the Cascades and that’s called a rain shadow. Um and uh and there are uh all sorts of other kinds of shadows that I’m not going to go into. Shadow is a very common metaphor people being in the shadow of their parents or the in the shadow of World War II and so forth and so on. Um but I wanted to just make a curious little uh analogy that may be uh a new insight into the world uh which is that uh well firstly this idea that we’re expanding the word shadow. We’re expanding the word shadow. That in itself is is part of what I wanted to tell you that by seeing new instances of shadow we’re expanding our sense of what the word shadow means. This happens to be maybe my personal sense as opposed to a public sense but it mean it’s no less valid. But I wanted to say that um we could look at the picture of snow and maybe deduce something about light. We know that snow is made out of flakes and we might just guess that because there’s an analogy between light and snow, maybe light is made out of flakes. It’s kind of a crazy idea, but we’ll call it the light flake hypothesis. I suppose it’s it is a fairly light and flaky hypothesis.

But uh Hofstadter 2005. Maybe we’ll come back to that. Uh another shadow. This is one of my favorites. Uh and we’ll we’ll stop shadows at that point. Um I was talking with a friend who’s who’s Italian and his brother uh is a professor at some university in northern Norway and I said, “Oh my god, it must be awfully cold up there.” And he said, “No, actually it’s pretty warm.” And I said, “How can that be?” And he said, “Well, you know, the Gulf Stream the Gulf Stream uh is warm.” And I said, “Yeah, but uh you know, it’s very far north.” He said, “Yeah, but it goes north.” And and I said, “But uh he’s he says that the interesting thing is that it where it’s cold is southern Norway.” And I said, “How is that?” He said, “Because the Gulf Stream is blocked by England.” And so I I had this picture in my mind. There’s I don’t know if you can see the Gulf Stream which is supposed to be red here and uh and it gets blocked by England. And so the shadow of England is on the coast of southern Norway and and the Gulf Stream hits the up upper part of Norway. So we have a shadow thrown by England uh of the of the of the Gulf Stream. So it’s again uh a wonderful abstraction of shadow. This is the kind of thing that analogy does to our concepts.

Now, so here is uh just you know, this simple idea that uh repeated analogies expand concepts. Um, I’ve taken as an the concept of number here and I’m not going to go into it in any detail. I just simply want to say that anybody who’s done any math knows that we begin with the positive integers. We learn to count, then we learn about things like a half and a quarter and so forth and eventually we learn about zero and the negative numbers and then after many and all of these are analogies. These are all all generalizations that are made through analogy. And as we as we progress and go further and further, we get more and more abstract and so I’ve indicated some things here e and pi and e to the i pi and aleph sub omega, different kinds of infinities and I could include matrices in there and and on and on. And so we have all sorts of numbers and and and they could keep on going. Uh, concepts expand over our lifetime and they expand for each one of us and they expand for our culture.

Uh, one of the uh, key points that I want to make here though is that although concepts expand by seeing new instances, sometimes we have a concept that has only got one instance. But even there, it starts to spread and leak. So let’s talk about that a little bit. The the basic idea here is there is no fundamental difference between a single memory trace and a category by which I mean a concept. No difference category concept, same thing. Okay, that’s a very important idea of this talk and and I’m just going to give you uh, thing I call pluralization. So I’ll read these out loud because I think that they’re amusing.

So there may be two or three young Einsteins among us tonight. Okay, what is a young Einstein? That’s a pluralization of Einstein. Clearly, Milton Babbitt is no Mozart. If you happen to know know Milton Babbitt is. If if another Chopin was born in Lompoc, what would happen? Uh it’s the next Catcher in the Rye or the Soviet Union’s Vietnam, the Paris of the Middle East, which was once the name of Beirut. Uh some place can be Actually, I once heard Jerusalem being described as a Mecca for tourists. A bunch of treacherous quislings. Uh notice I’ve gone to the lower case here. Uh Mecca with lower case, even though it it comes from originally one thing, it’s it gets pluralized. And Quisling was a Norwegian uh foreign minister or prime minister or something who who I think collaborated with the Nazis. I don’t remember the details. But it became a lower case word for basically a traitor. Uh and um and then Galileo I I don’t know the the details of this, but I I I have to assume that it was Galileo who actually used the word luna in the plural and with a lower case m. Uh in other words, talking about what he saw, uh he he he equated our moon with those things, those dots that he saw through his telescope, and called those moons. That was an a magnificent leap that pluralized something that nobody had ever ever considered to be other than one unique thing in the world. So, pluralization is a way in which a single entity becomes uh a wide category. And there really is no difference between a single entity and a category. Okay.

Uh so, I guess I’m just saying this again. There’s a no fundamental difference between seeing something as a category category member and seeing something as analogous to something else. In one case, something evokes a concept which has one instance, and another case, something that evokes a concept which has many instances and which has blurred together. Uh now, we come to another very special thing about human minds. Our minds are constructed Oh, this is no not new to anybody. That that with a an unlimited quality for chunking. By that, what I mean is that primordial concepts in some interrelationship become uh a larger unit, a larger conceptual unit like, you know, a family or something like that. And then, a family can get incorporated into something larger. And And we build our concepts by taking several concepts, putting them together, putting a membrane around them, and then, sort of miraculously, the internal components sort of disappear. And we’re left with just this new concept, which is kind of like a black box. We don’t think it’s so much about the the these things become semi-visible. They’re sort of lurking in the background.

But, if it’s structured at many levels of a hierarchy, the concepts inside the concepts inside the concepts are certainly just about invisible, and it really takes some unpacking to to get there. So, um as we build up concepts, they get hierarchically larger and larger and larger and more and more complex. And I wanted to just give you one example that I thought was really very interesting. And I haven’t even touched scratched the surface of this one, but I but take a look at it anyway. Take a look at this. This is the notion of a hub for an airlines.

I I mean, it’s just an an attempt to show you how we begin with concepts that we acquire when we’re very, very young. And I’ve put here things like ball goes to roll, roll to wheel, wheel gives you spokes and hub, and gives you the notion of centrality. I’m not saying these these arrows are not necessarily analogy arrows. These arrows sort of represent the idea that this thing is sort of part of that concept. It’s sort of gotten incorporated, a glommed into that concept. They’re not precisely I’m not I don’t have time to spell it out, but I want you to see this as a series of of higher concepts that are glomming together lower ones. These are the lower ones at the top. Excuse for that reversal of directions, but it Anyway, so bike is a vehicle, a bike has wheels, car is a vehicle, a bus is a vehicle, vehicle another type of vehicle is a plane, then that a plane can lead you to an airliner, a bus is kind of like an airliner, airliner leads you to the most more abstract notion of an airline. Then we have names, which we learn when we’re very small. Names suggest that there are things that come in different types, then we learn about brands, then we learn about companies, and and airline is a particular type of company.

Moving, then we have the idea of a trip, and then a trip can be broken up into legs, and legs can be sort of formalized into routes. And that’s attached to airline. It’s also attached to a network, time, appointment, timetable, chart, network, and then this notion is abstract notion of network goes to node, and then we have to get gets, and that’s something pretty primordial. Get, and then when we’re very small, we also learn about buy. Please buy me, you know, money we learn about, and then later we learn about economizing and saving money, and then we learn about sort of downsizing and how companies have to downsize. By the way, notice I didn’t even put I forgot the whole notion of city and the whole notion of airport. I didn’t even put that here. I mean, just imagine all the concepts here that are that are all required to go into the concept of hub. And yet, when we say, you know, Denver is United hub, do you think about all this stuff? It’s you don’t think at all. I mean it’s it’s you you you know this as a chunked concept.

And uh so that’s a very important part of how we think. Uh so I another point is that there is no fundamental difference though between thinking with very very basic concepts and thinking with these very large concepts because the very large concepts become as familiar and we don’t see inside them. We don’t deal with all the stuff that’s inside them. Uh so some of the primordial concepts are these uh and some of the more sophisticated concepts are a soap opera, hub, sleazeball, wilderness protection legislation or scientific break even for laser fusion. Um complicated things. But if you’re familiar with them, they’re just a very ordinary. They’re they’re as familiar as the back of your hand.

I thought I’d illustrate some rather complex concepts just for my amusement and yours to show you how amazing our human conceptual system is. Um so uh indulge me with my reading this slide out loud. I’ll go down vertically. So we have the solar system, the concept of a slam dunk, a beltway, plagiarism, Jazzercise, laissez-faire economics, ethnic cleansing, the domino theory of condense of communism the next line, Bose-Einstein condensation or Bose-Einstein the Wikipedia. Now I want you to think to yourself how many levels of structure to explain the Wikipedia would you have to you know if you were to try to explain that to somebody from 2,000 years ago, what would you have to tell them in order to get across the idea of the Wikipedia? Uh I mean you have to explain computers and networks and the web and an encyclopedia and publishing and who knows what all. Uh Okay. dot bubble, spam. This is another It’s hard enough to understand what a Republican and a Democrat are. That’s a very complex concept. Gas war, the Final Four, Y2K, the genetic code, quantum cryptography, a baby boomer, chick flick, WASP, the Fed. I have no idea what the Fed is. I have no concept. A gravitino, I also have no concept of that. I know it’s supposed to be sort of some sort of super symmetric partner to the graviton.

Uh, pork belly futures, that’s a great one. Phishing with a cat with a ph. Radar trap, affirmative action, grocery store checkout stand, presidential lecture, and wacky walk. These are concepts that we deal with very easily, very fluently, and they are so far removed from the concept network that an ant might have, or that a mouse might have, or that a dog might have, or that a four-year-old might have, or that even a 12-year-old might have. So, you have to think how many levels there are.

Now, we’re talking about concepts at many, many levels. Uh, primordial words, simple words, some compound words, phrases, proverbs. I’m going to come to this. I’m going to sort of illustrate these. Uh, and then and then a lot of our concepts are totally unlabeled. Like, for example, my concept, whatever it was, of what happened to me when my dad told me they don’t do anything. They’re they’re just names of variables. That was stored in my brain, and it was waiting there to be triggered by some event in the future. What was the event? Monica on the floor with the Dustbuster. I mean, and and uh, you know, that was a concept. It didn’t have a name. There’s no name for Doug being disillusioned by his father about subscripts not being analogous to superscripts in mathematics. I mean that was a thing in my brain. It was a node. It was there in some sense or I don’t know if node is the right word, but it was there. It was It was retrievable under the right circumstances. It shared essence. I hope you will agree with me there. It shared essence with Monica’s disillusionment.

Now, then so we have a lot of different kinds of things. I’m going to talk about these other things, me toos in particular and scientific leaps. I want to go through this a little bit talking about how analogy making retrieves one thing at each of these levels. I’m not going to go through them all. But I just want to, you know, name some primordial concepts. I won’t read these out loud, but notice by the way in this list that I am not favoring nouns. I want you to understand that when I talk about categories, I do not think that categories are always visual things like you know, overhead projector or shoe or you know, even audience. Categories can be things like as I said, please. Please. What that means is there are certain circumstances where that word is evoked. The circumstance evokes that mental concept. It’s a please circumstance. There are certain circumstances. If I said please to you now, it wouldn’t make any sense. Makes no sense at all. But if I, you know, if I’m a little 3-year-old and I want something and I say please, it makes sense. There are certain certain circumstances where it is appropriate. And I’m trying to point out here that words of all sorts, whether they’re adverbs or prepositions or pronouns or verbs or nouns, they are all categories and they’re all equally good and most of them are not visual. Most of them a lot of them are not sensory whatsoever.

And theories of of categorization mostly are involved with visual categories, visual objects. It’s so mistaken. That is not where the action is. And one of my colleagues who I respect very greatly said that he thought that categorization at this kind of level was very very straightforward. It’s just a matter of feature detectors. And I think, “Oh my goodness, what we are not on from the same planet.” I don’t think categorization at that level is anything to do with feature detectors. Um I mean maybe they play a little role, but it’s not it’s really That’s another thing. That’s for tomorrow. That’s not for today. Okay, simple concepts. Be you know, those are primordial. Here are some, you know, they’re getting a little more sophisticated. Chair, I remember there was an exhibit of chairs at the San Francisco International Airport some years ago. Wonderful exhibit of crazy chairs. And then I got books of chairs. You can buy books of thousands of different kinds of chairs and the variety is is mind-boggling. The same for the letter A. And tell me the tell me the um the the features of a mess. If we’re talking about visual categories, what are the features of a mess? I would like to know which neurons, which feature detectors in my brain fire when I see a mess. Uh What what about the feature detectors for the word probably or for probably situations? And how about for probably which we say sometimes and other times we don’t. What are the probably situations as opposed to the probably situations? And it’s a subtle distinction. Come on. I mean well

My point is here. With a word like well, I don’t know what part of speech that is. It might be an interjection or a I think it’s something like an interjection. Maybe it’s an adverb. It’s a little blurry what it is. But that’s not my point. Uh my point is that these words that have nothing to do with visual categories, visual objects, these are evoked by circumstances. There are well situations and you know how to use them. And if you saw a well in an essay written by a foreigner and or in an email written by a foreigner, you’d say, “Ah, they don’t know how to use it right.” Or they would put some other word in there. They should have put in well. You know, you know where the word well goes if you’re a native speaker of English because there are well dot dot dot situations. And the same for high, kind of, but anyway, no kidding, and so forth and so on.

Um compound words. Uh getting a little bit more complicated. Again, I’m not going to read you this list, but just giving you a sense of compound words that are typical that we use all the time. Uh some of them have two components, some of them three, four, five, six. It’s a little blurry. It doesn’t matter. Uh they get bigger and bigger and bigger and they sort of know no limit. Uh phrases. Uh so uh let me just give you a few phrases that I happen to think of today at random. We all know these and I’m not going to read them out loud. There but for the grace of God go I. Pretty please with sugar on top. I think that’s a nice one. Been there, done that. Uh well, I can’t help but read well, excuse me. Uh Put your money where your mouth is. Uh blah blah blah blah blah. That’s for sure. And those these are evoked by situations. These are categories. These are categories. And I want you to understand that all these things are mental categories.

Um And how do we judge whether the category make the situation that we’re facing is a member of this category? Guess. Analogy. Proverbs. Okay, so I’ve listed a few proverbs random. What’s sauce for the goose is sauce for the gander. I don’t say that one very often, but I do say speak of the devil all the time. Damned if I do and damned if I don’t. I say that all the time. Go directly to jail. Do not pass go. Do not collect $200. I don’t I called that a proverb, but you know, it’s maybe it’s not exactly a proverb. Uh maybe I miscategorized that. Maybe I made a bad analogy here. Uh it’s all Greek to me. Back to square one. We’ll cross that bridge when we come to it and so forth and so on.

Okay, uh I got some of these ideas. In fact, I was deeply influenced by an article that I read in around 1975 by Joe Becker, who’s here tonight, called the phrasal lexicon. And Joe pointed out that what we have in our head is far, far richer than a set of words when we talk about our mental lexicon. And I I can’t possibly do justice to his delightful and stimulating article. I mean, very very inspiring article. Um and one of his principles was that the article should apply to itself. And he took a lot of the idioms that he used throughout the article and talked about them and listed them in his lists. I’ve always uh followed that example. Um but proverbs, this is something that Roger Schank pointed out. Proverbs are situation labels. We use them to We we In fact, sometimes proverbs are boiled down into just a single word like sour grapes. I know that sounds like two words, but I see it with a hyphen. Um uh sour grapes. You know, somebody somebody’s didn’t get a job that they said they wanted and then they said, “Oh, it probably wasn’t wouldn’t have been interesting to live in, you know, in Edmonton, Alberta.” Or whatever that Is it Alberta? Yeah. I wouldn’t want to live in Edmonton. Sour grapes, you know, it’s sort of one one word.

Uh now, I’m going to go down to the really one word level, and I want to talk about the analogies that I had to make when I went to Italy to the uh well, it’s a a research institute in Trento. Uh I spent a year there. It was a very austere place, a very nice place, but rather austere. And there were people at many levels, bureaucrats, scientists, students, uh people walking the corridors. And I never quite knew who people were. They would say hello to me, and I couldn’t quite figure. And so, the question that I had to face at you know, from the very beginning uh was what do you say to these people when you run into them in the corridor? And you don’t even know quite who they are. You recognize them, and you sort of know who they are. You have spoken to them, and you know definitely who they are. You know their name, or you know them pretty well. They’re kind of a friend. You’ve eaten lunch with them once, or you’ve you are a friend.

And uh naively being American, I would say ciao. Uh that was wrong. You don’t say ciao to people that you are not on familiar terms with. I mean, ciao is something that you can say to somebody that you say tu tu, but you don’t say ciao to, you know, to the director of the institute. Uh you that just doesn’t it just doesn’t work. You say buongiorno, or you say salve. And salve is sort of intermediary. And um I I learned this. And uh but but I nonetheless was not a native speaker. And every time at every moment as I was walking down the corridors, I had to be doing these on-the-spot categorizations. Is this a a ciao person, a salve person, or a buongiorno person? And you know, and uh sometimes I would mix them up, and I would get them confused. I would blend them. Um but it was it was, you know, gradually it kind of got clearer, and I got and I was following the what I saw other people doing. I was making analogies. Um and I met not only analogies to what other people did, but analogies between, you know, people I this person is like that person to me. And so I said, “Okay, if I say saluted that person, I’ll say saluted this person.”

Um so words, individual words, are the locus of a fight. Every time you try to figure out what word to use, there’s a subterranean fight going on, mostly hidden. And I want to just give you a little example of this. Um Uh my friends Kelly and Dick were visiting my house and um uh they kept on referring to my office. And I kept on thinking, “What does my office have to do with my house? It’s over, you know, across campus.” And then I realized, of course, they were talking about my study. Um and so uh we talked about this. I said, “Why do you always call it my office when I call it my study?” And they said, “I don’t know. It’s your seems like your office.” I said, “It doesn’t seem like my office. Uh it seems like my study. And my office is across campus.” And and so then we talked a little more and they said, “Well, you know, in our house, on our top floor, where we do our work, where we have our books and our computers, uh that’s where our office. Uh we have a home office. That’s where we do our work. And you have on your top floor, which is not your third floor, but your second floor, you have computers, you have books, and you do your work there. And it maps perfectly. So, to them it was totally obvious that this was my office. And to me it was totally obvious that it was my study because I took my dad as my prime as my prototype. He on the upper floor of our house up on Moraga, he had a study in which he had his Friden calculator and his books and his things. And and it was just like what I did. And his office was down on campus. And so to me it was a I guess you’d say a no-brainer.

Uh and it was very interesting to see that both behind both of our visions there were analogies. And it showed that word choice is guided by analogy. And I’m going to skip a couple of transparencies here. And uh uh I can see I have so many things here I’m not going to be able to really go through them all. But uh I want you to see this picture which illustrates what goes on in word choice. I I have not labeled the x-axis. But the x-axis in these bar graphs is sort of um it’s it’s a one-dimensional reduction of what you might call semantic space. Semantic space is a multi-dimensional space of concepts. And I’ve reduced it down to one dimension. I’ve pretended that there’s just concepts along one dimension. And so here I’m facing a situation which might evoke, you know, a word like dog. And so dog is the is the big winner. It’s very activated. And and maybe uh fox is a little bit activated. I don’t know. I’m just making this up. And maybe cat is a little bit activated and so forth. And so there we have it. And and it there it’s a big dog is so it towers above the others enough that it’s a big winner and there’s no visible or audible, I should say, competition. But a lot of the time when we speak there is audible competition. And I want to talk about the audible competition that we hear when we are making when we are speaking.

And so uh I’m going to talk about word blends. Uh here’s just a few. And maybe these I will read to you because I think they’re all nice examples. I have collection of literally hundreds and hundreds, maybe thousands, of word blends. I I just picked a few at random today. Uh and these are these are ones that I just listened to. I picked them up. Uh uh this was me at the Somebody calls on the phone, “Is Danny there?” That’s my son. I don’t know. I’ll go sec. They’ll end of see and check. Trivial. Everyday ordinary thing. It reveals competition. It reveals subterranean competition. Okay. Uh don’t leave your car there, I say to somebody. You you might get a ticket. May or might. Now, this is the kind of thing nobody would hear. I mean, I pay attention to these things. It’s sort of my profession. And so, I do hear them. But, most people just don’t hear these things.

Uh Danny, my son, I love this one. I can’t keep all these things in my bread at the same time. I thought that was wonderful. Brain and head. Um Uh he also said, “Hey, wait up. I’ll gum with you.” That was to his sister. She was about to go to the grocery store. “Hey, wait up. I’ll gum with you.” Gum is come and go. Just a nice blend of two different ideas. And uh my administrative assistant, Helga, said, “Every morning I took a capsy ride.” Beautiful. Beautiful. And the mayor of Bloomington was on the radio and he talked He was talking about how how it we have to be vigilant in uh in uh in uh putting in bike paths and other kinds of things in the town. And I thought that was a wonderful blend because it’s it’s it’s vigilant and it’s diligent. And it also has a little bit of village in it. And uh this is a fascinating kind of thing. Now, I don’t want you to think that blends are always that obvious. I want you to understand that blends can be extremely extremely subtle. Uh here’s some uh examples uh just two uh but uh I these were in the course that I was giving last semester called something like analogy and words and concepts. And uh I was talking to the class and at one point I just I mean I must have made 500 errors per class session, you know. I mean, today who knows how many errors I’ve made. They’re not discrete things cuz they come sort of in different levels of strength. But maybe major blend maybe major errors today I’ve made 50 and maybe I don’t maybe I’ve made 200. I don’t know. But anyway, every day there I was making 500 and I noticed about three because you can’t spend all your time monitoring yourself. But I did notice at one point I said as it says here I was having trouble finding finding. The F was a little too lengthy. And I said did anybody hear that? Nobody even heard it. And I said, well, okay, but it was a little long and you want to know why? And they I mean I guess they were captive audience. So So, anyway, I said, I know there was competition in my head and I happen to know what it was. At least part of it. I don’t know the whole story, but at least I know one of the words was find and the other was figure out. And I couldn’t quite decide. Now how much else was going on inside inside my head I don’t know. Inside inside. Okay. It was it was poised on the banister. It was poised on the banister. It was posed and it was poised. It was just a slightly wrong vowel. Slight distortion of the vowel. Now you see these kinds of things these kinds of things every word that I’m saying probably has a slight error in it. And that’s my point. Every word has a subterranean fight going on inside it. You don’t know you don’t hear it even I don’t hear it. I’m not privy to what’s going on underneath the surface. But sometimes I can feel it and sometimes you can hear little hesitations. It may It be a hesitation before the word starts. It may be the lengthening of a consonant, may be the distortion of a vowel. It may be a funny intonation. All of those are revelatory of the fight between words, the analogies that are struggling to take over and to beat the other ones out. Um phrase blends. I hope I’m coming to an end. Uh phrase blends. Uh I won’t read these out loud, but I think uh well, maybe I These are funny. Cuz I mean And phrase blends are not always funny. I’m not, you know, one of these people who collect errors because it’s funny and you publish it, you know, they say kids say the darndest things or whatever. That’s not my reason I think errors are wonderfully funny at times, but I don’t collect them for that purpose. I collect them because I’m interested in understanding what goes on in the minds of human beings. So, here’s uh in an email. This is typed. This is not spoken. This is typed. I have it still. You know, I hope the package got there in one shape. Okay. Uh from a native speaker. Okay. Uh native speakers talking two of them talking in a restaurant. Neither of them noticed this comment. I mean, it just went by. Nobody heard anything. Uh he was a real easy-go-lucky guy. Easy going and happy-go-lucky. This one I said, I should count my lucky stars. I said it on the phone and then I said, “What? Is that right?” Something Count my lucky stars. Count my blessings, thank my lucky stars. Okay? I mean, just these kinds of things are a dime a dozen. And that was a dime a dozen situation, by the way. Categorized I put my finger right on the essence there. Uh this one I I typed in an email when I was very tired and I wanted to hit the sack. And I said, “I’m worried that my editor is going to hit the stack.” And I thought that was a marvelous blend of hit the ceiling, blow his stack, and my own feeling that I wanted to hit the sack. Okay. And then my dean at one time at Indiana University was trying to lure a person to be in cognitive science, and he made this marvelous, marvelous statement that will pull no stops unturned to get him. I mean, this This is amazing.

Um All right. So, I’ve already said this, but I just say it again because I want you to see it in writing. Every effortless category assignment is actually a seething subterranean battle of analogies. When the battle is a landslide, there’s no evidence. When the battle is close, there’s evidence galore.

Okay. So, uh we’re coming really to the end here. Thought is the highest level of abstraction seeking, I’m sorry, the highest level of abstraction. Putting one’s finger on the essence of a situation, and then bouncing back and forth between the actual situation and the essence that one found in one’s memories. In one’s memory. I’m going to give you an example that I think is quite charming, and it’s actually something I found out about last year. I spent uh a long time in the year 2005 working on in a talk called Well, it wasn’t called, but it was about Einstein’s analogy making. I wanted to do something for the Annus Mirabilis 2005 and what the 100th anniversary, and I had the great pleasure of giving this talk in physics departments in a few places about the analogies that Einstein made not only in 1905, but in other years. And um what I was really astounded was I had never known how Einstein created the concept of that we now know as the photon. And it was what he thought of as his most revolutionary uh ever idea.

And I want to give you a sense of how he did it, and I can’t, obviously, give you much of a sense of it, but let me at least just give you a slight sense. So, we begin with something that was known this is the basically what’s called the black body spectrum. What it basically says is if you have radiation bouncing around inside a cavity at a certain temperature, there’s different amounts of different energies and there’s sort of a most amount at a certain peak energy you know, that’s the sort of the the wavelength the wave that wavelength or that frequency is sort of the most predominant and then there’s less and less on either side of it. Longer wavelengths are less, shorter wavelengths are less.

And now there was another situation that was the situation that people didn’t understand. People did understand the situation of thanks to Maxwell and Boltzmann of an ideal gas, an ideal gas inside a cavity where people knew that actually they didn’t really know for sure, but they thought that the behavior of an ideal gas was due to molecules bouncing around inside and if they assumed that it was molecules, they could make some mathematical calculations and figure out what the curve should be and they figured out the formula for a bell-shaped curve that looked like that that said that for all the different kinetic energies that you have and you can replace kinetic energy if you don’t like that word with velocity. So, for all the different velocities or speeds that the molecules could have, you know, at low speeds there weren’t very many, high speeds there weren’t very many, but at some intermediate speed there were a lot and and this was the distribution and and it looked kind of like that.

Now, not this was around for anybody to see, you have to understand, but nobody thought about it. Nobody connected these two ideas until Einstein. And Einstein said this looks similar to me. And so, I think that, you know, maybe it’s possible these things this thing over here the ideal gas we think as as being made of of corpuscles, particles, molecules. And so maybe it’s possible that light is also made of particles. And he did a lot of elegant mathematical calculation to to check this out. And he calculated the entropy of these systems and I won’t go into any of the details. Basically, a bell-shaped curve and a bell-shaped curve, the analogy between those two, like the analogy between my two shadows, the light shadow and the snow shadow, I decided that light may be made of flakes. Einstein decided 100 years before me that I that light might be made out of particles. And and that was the what nowadays we call the light quantum hypothesis. And that was the most revolutionary discovery Einstein ever made. It came directly out of a simple connection between two bell-shaped curves, essentially.

All right. Well, I guess I am coming to the end and all I need to say is on my last transparency. So, if strokes of genius are made of analogies and personal insights and political decisions and dinner table conversations and me too comments, which I didn’t cover unfortunately, and random remindings and instantaneous categorization and blends of all sorts are all made of analogies, might not all of cognition also be made of analogies? That’s the cognition core hypothesis. Remember, you heard it first here.

Thank you. For more, please visit us at stanford.edu.