#76 – John Hopfield: Physics View of the Mind and Neurobiology

The following is a conversation with John Hopfield, professor at Princeton, whose life's work weaved beautifully to biology, chemistry, neuroscience and physics. Most crucially, he saw the messy world of biology through the piercing eyes of a physicist. He's perhaps best known for his work on associative neural networks, now known as Hopfield networks. They were one of the early ideas that catalyzed the development of the modern field of deep learning. As his 2019 Franklin Medal in Physics award states. He applied concepts of theoretical physics to provide new insights on important biological questions in a variety of areas, including genetics and neuroscience, with significant impact on machine learning. And as John says in his 2018 article titled now what? His accomplishments have often come about by asking that very question, now what? And often responding by a major change of direction. This is the Artificial Intelligence Podcast.

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What difference between biological neural networks and artificial neural networks is most captivating and profound to you.

At the higher philosophical level?

Let's not get technical just yet.

One of the things that very much intrigues me is the fact that neurons have all kinds of components properties to them in evolutionary biology. If you have some little quirk in how A molecule works or how a cell works and it can be made use of, evolution will sharpen it up and make it into a useful feature rather than a glitch. And so you expect in neurobiology for evolution to have captured all kinds of possibilities of getting neurons, of how you get neurons to do things for you. And that aspect has been completely suppressed in artificial neural networks.

So the glitches become features in them, in the biological neural network.

They can. Look, let me take one of the things that I used to do research on. If you take things which oscillate, have rhythms which are sort of close to each other, under some circumstances these things will have a phase transition and suddenly the rhythm will, everybody will fall into step. There was a marvelous physical example of that in the Millennium Bridge across the Thames river, built about 2001. And pedestrians walking across, pedestrians don't walk synchronized, they don't walk in lockstep, but they all walk at about the same frequency. And the bridge could sway at that frequency. And the slight sway made pedestrians tend a little bit to lock into step. And after a while the bridge was oscillating back and forth and the pedestrians were walking in step to it. And you could see it in the movies made out of the bridge. And the engineers made a simple minded mistake. They assumed when you walk, it's step, step, step and it's back and forth motion. But when you walk, it's also right foot, left foot, side to side motion. It's a side to side motion for which the bridge was strong enough, but it wasn't, it wasn't stiff enough. And as a result, you would feel the motion and you'd fall into stiff with it. And people were very uncomfortable with it. They closed the bridge for two years, really fully built, stiffening for it. Now nerves, look, nerve cells produce action potentials. You have a bunch of cells which are loosely coupled together, producing action potentials at the same rate. There'll be some circumstances under which these things can lock together, other circumstances which they won't. While they fire together, you can be sure that other cells are going to notice it. So you can make a computational feature out of this. In an evolving brain, most artificial neural networks don't even have action potentials, let alone have the possibility for synchronizing them.

And you mentioned the evolutionary process. So there, the evolutionary process that builds on top of biological systems leverages that, the weird mess of it somehow. So how do you make sense of that ability to leverage all the different kinds of complexities in the biological brain?

Well, look at the biological molecule level. You'd have a piece of DNA which encode for a particular protein. You could duplicate that piece of DNA and now one part of it encode for that protein, but the other one could itself change a little bit and thus start coding for a molecule which is slightly different. Now, that molecule was slightly different, had a function which helped. Any old chemical reaction was important to the cell. It would go ahead and let that try and evolution would slowly improve that function. And so you have the possibility of duplicating and then having things drift apart. One of them retain the old function, the other one do something new for you. And there's evolutionary pressure to improve. Look, there is in computers too, but improvement has to do with closing some companies and opening some others. The evolutionary process looks a little different.

Yeah. Similar time scale, perhaps much shorter in timescale. Companies close. Yeah. Go bankrupt and are born. Yeah, Shorter, but not much shorter. Some, some companies last a century, couples. But yeah, you're right. I mean, if you think of companies as a single organism that builds and you own that. Yeah. That's a fascinating dual correspondence there between.

Biological and companies have difficulty having a new product competing with an old product.

Yeah.

And when IBM built its first PC, you probably read the book, they made a little isolated internal unit to make the PC. And for the first time in IBM's history, they didn't insist that you build it out of IBM components, but they understood that they could get into this market, which is a very different thing, by completely changing their culture. And biology finds other markets in a more adaptive way.

Yeah, it's better at it.

It's better at that kind of integration.

So maybe you've already said it, but what to use the most beautiful aspect or mechanism of the human, Is it.

The adaptive, the ability to adapt as.

You'Ve described, or is there some other little quirk that you particularly like?

Adaptation is everything, when you get down to it. But the difference, there are differences between adaptation, where your learning goes on only over generations, over evolutionary time. Your learning goes on at the time scale of one individual who must learn from the environment during that individual's lifetime. And biology has both kinds of learning in it. And the thing which makes neurobiology hard is that it's a mathematical system, as it were, built on this other kind of evolutionary system.

What do you mean by mathematical system? Where is the math and the biology?

When you talk to a computer scientist about neural networks, it's all math. The fact that biology actually came about from evolution and the fact that biology is about a system which you can build in three dimensions. If you look at computer chips. Computer chips are basically two dimensional structures, maybe 2.1 dimensions, but they really have difficulty doing three dimensional wiring. Biology is the neocortex is actually also sheet like and it sits on top of the white matter, which is about 10 times the volume of the gray matter and contains all what you might call the wires. But there's a huge, the, the effect, the effect of computer structure on what is easy and what is hard is immense.

So.

And biology does. It makes some things easy that are very difficult to understand how to do computationally. On the other hand, it can't do simple floating point arithmetic. So it's awfully stupid.

Yeah. And you're saying this kind of three dimensional complicated structure makes. It's still math. It's still doing math. The kind of math is doing enables you to solve problems of a very different kind.

That's right. That's right.

So you mentioned two kinds of adaptation. The evolutionary adaptation at the end, the adaptation or learning at the scale of a single human life, which do you. Which is particularly beautiful to you and interesting from a research and from just a human perspective and which is more powerful.

I find things most interesting that I begin to see how to get into the edges of them and tease them apart a little bit and see how they work. And since I can't see the evolutionary process going on, I am in awe of it, but I find it just a black hole as far as trying to understand what to do. And so in a certain sense I'm in awe of it, but I couldn't be interested in working on it.

The human life's time scale is however.

A thing you can tease apart and study.

Yeah, you can do. There's developmental neurobiology, which understands how the connections and the structure evolves from a combination of what the genetics is like. And the real, the fact that you're building a system in three dimensions.

In just days and months, those early, early days of a human life are really interesting.

They are. And of course there are times of immense cell multiplication. There are also times of the greatest cell death in the brain. This is during infancy.

It's turnover.

So what is not effective, what is not wired well enough to use at the moment? Throw it out.

It's a mysterious process. From, let me ask, from what field do you think the biggest breakthroughs in understanding the mind will come in the next decades? Is it neuroscience, Computer science, Neurobiology, Psychology, Physics, Maybe math, maybe literature?

Well, of course I See the world always through a lens of physics. I grew up in physics and the way I pick problems is very characteristic of physics and of an intellectual background, which is not psychology, which is not chemistry, and so on and so on.

Both of your parents are physicists?

Both of our parents were physicists. And the real thing I got out of that was a feeling that the world is an understandable place. And if you do enough experiments and think about what they mean and structure things so you can do the mathematics of the relevant to the experiments, you ought to be able to understand how, how things work.

But that was, that was a few years ago. Did you change your mind at all? Through many decades of trying to understand the mind, of studying in different kinds of way, not even the mind, just biological systems, you still have hope that physics that you can understand.

There's a question of what do you mean by understanding? Of course, when I taught freshman physics, I used to say I wanted to get physics to understand the subject, to understand Newton's laws. I didn't want them simply to memorize a set of examples to which they knew the equations to write down to generate the answers. I had this nebulous idea of understanding so that if you looked at a situation, you could say, oh, I expect the bull to make that trajectory, or I expect some intuitive notion of understanding. And I don't know how to express that very well, and I've never known how to express it well. And you run smack up against it when you do these. Look at these simple neural nets, feed forward neural nets, which do amazing things and yet, you know, contain nothing of the essence of what I would have felt was understanding. Understanding is more than just an enormous lookup table.

Let's linger on that how sure you are of that. What if the table gets really big? So, I mean, asked another way, these feed forward neural networks, do you think they'll ever understand?

Could answer that in two ways. I think if you look at real systems, feedback is an essential aspect of how these real systems compute. On the other hand, if I have a mathematical system with feedback, I know I can unlayer this and do it. But I have an exponential expansion in the amount of stuff I have to build if I can solve the problem that way.

So feedback is essential, so we can talk even about recurrent neural recurrence. But do you think all the pieces are there to achieve understanding through these simple mechanisms? Like back to our original question, what is the fundamental. Is there a fundamental difference in artificial neural networks and biological. Or is it just a bunch of Surface stuff.

Suppose you ask a neurosurgeon, when is somebody dead?

Yeah.

They'll probably go back to saying, well, I can look at the brain rhythms and tell you this is a brain which is never going to function again. This other one is one which, if we treat it well, is still recoverable. And then just do that by some electrodes looking at simple electrical patterns which don't look in any detail at all at what individual neurons are doing. These rhythms are utterly absent from anything which goes on at Google.

Yeah, but the rhythms.

But the rhythms.

What so. Well, that's like comparing. Okay, I'll tell you. It's like you're comparing the. The greatest classical musician in the world to a child first learning to play. The question I'm at, but they're still both playing the piano. I'm asking, is there. Will it ever go on a Google. Do you have a hope? Because you were one of the seminal figures in both launching both disciplines, both sides of the. Of the river.

I think it's going to go on generation after generation the way it has where what you might call the AI computer science community says, let's take the following. This is our model of neurobiology at the moment. Let's pretend it's good enough and do everything we can with it. And it does interesting things. And after the while it sort of grinds into the sand and you say, ah, something else is needed for neurobiology and some other grand thing comes in and enables you to go a lot further. What will go into the sand again? There can be generations of this evolution, I don't know how many of them. And each one is going to get you further into what a brain does and in some sense pass the Turing test. Longer and more broad aspects. And how many of these are there are going to have to be before you say, I've made something, I've made a human. I don't know.

But your senses, it might be a couple.

My senses, it might be a couple more.

Yeah.

And going back to my brain waves, as it were.

Yes.

From the AI point of view, they would say, ah, maybe these are an EPH phenomenon and not important at all. The first car I had a real wreck of a 1936 Dodge go above 45 miles an hour on the wheels with Jimmy.

Yeah.

Good, good speedometer, that. Now, nobody designed the car that way. The car is malfunctioning to have that. But in biology, if it were useful to know when are you going more than 45 miles an hour? You just capture that and you wouldn't worry about where it came from.

Yeah.

It's going to be a long time before that kind of thing, which can take place in large complex networks of things, is actually used in the computation. Look, the. How many transistors are there in your laptop these days?

Actually, I don't, I don't know the number. It's.

It's on the scale of 10 to the 10. I can't remember the number either.

Yeah.

And all the transistors are somewhat similar and most physical systems with that many parts, all of which are similar, have collective properties.

Yes.

Sound waves in air, earthquakes. What have you of collective properties. Weather. There are no collective properties used in artificial neural networks in AI.

Yeah, it's very.

If biology uses them, it's going to take us to more generations of things for people to actually dig in and see how they are used and what they mean.

See, you're, you're very right. We might have to return several times to neurobiology and try to make our transistors more messy.

Yeah, yeah. At the same time the simple ones will concert, will conquer big aspects and I think one of the most biggest surprises to me was how well learning systems which are manifestly non biological, how important they can be actually, how important and how useful they can be in AI.

So if we can just take a stroll to some of your work. That is incredibly surprising that it works as well as it does. That launched a lot of the recent work with neural networks. If we go to what are now called hopfield networks, can you tell me what is associative memory in the mind for the human side? Let's explore memory for a bit.

Okay. What you mean by associative memory is. Ah, you have a memory of each of your friends. Your friend has all kinds of properties from what they look like to what their voice sounds like, to where they went to college, where you met them. You can go on and on what science papers they've written. If I start Talking about a 5 foot 10 wiry cognitive scientist who's got a very bad back, it doesn't take very long for you to say, oh, he's talking about Geoff Hinton. I never mentioned the name or anything thing very particular. But somehow a few facts that are associated with this with a particular person enables you to get hold of the rest of the facts, or not the rest of them, another subset of them. And there's this ability to link things together, link experiences together, which it goes under the general name of associative memory. And a large Part of intelligent behavior is actually just large associative memories at work, as far as I can see.

What do you think is the mechanism of how it works in the mind? Is it a mystery to you still? Do you have inklings of how this essential thing for cognition works?

What I made 35 years ago was of course a crude physics model to show the kind to actually enable you to understand my old sense of understanding as a physicist. Because you could say, ah, I understand why this goes to stable states. It's like things going down downhill, right? And that gives you something with which to think in physical terms rather than only in mathematical terms.

So you've created these associative artificial networks.

That's right. Now, if you look at what I did, I didn't at all describe a system which gracefully learns. I described a system in which you could understand how learning could link things together, how very crudely it might learn. One of the things which intrigues me as I reinvestigate that system now to some extent is, look, I see you. I'll see you every second for the next hour or what have you. Each look at you is a little bit different. I don't store all those second by second images. I don't store 3,000 images. I somehow compact this information. So I now have a view of you which can. Which I can use. It doesn't slavishly remember anything in particular, but it compacts the information into useful chunks which are somehow. It's these chunks which are not just activities of neurons, bigger things than that which are the real entities, which are. Which are useful, which are useful to you.

Useful. Useful to you to describe, to compress this information.

And you have to compress it in such a way that if the information comes in just like this again, I don't bother to bother to rewrite it, or efforts to rewrite it simply do not yield anything because those things are already written. And that needs to be. Not look this up, have written it. Have I started somewhere already? It's got to be something which is much more automatic in the machine hardware, right?

So in the human mind, how complicated is that process, do you think? So you. You've created. Feels weird to be sitting with John Hopfield, calling him Hodfield Networks, but it.

Is weird.

Yeah, but nevertheless, that's what everyone calls him. So here we are. So that's a simplification. That's what a physicist would do. You and Richard Feynman sat down and talked about associative memory. Now, if you as a If you look at the mind, you can't quite simplify it so perfectly. Do you think?

Let me backtrack just a little bit.

Yeah.

Biology is about dynamical systems. Computers are dynamical systems. You can ask if you want the model biology, if you want to model neurobiology, what is the time scale? There's a dynamical system in which of a fairly fast time scale in which you could say the synapses don't change much during this computation. So I'll think of the synapses fixed and just do the dynamics of the activity. Or you can say the synapses are changing fast enough that I have to have the synaptic dynamics working at the same time as the system dynamics in order to understand the biology most artificial. If you look at the feed forward artificial neural nets, they're all done as learnings. First of all, I spend some time learning, not performing, then I turn off learning and I perform.

Right.

That's not biology. And so as I look more deeply at neurobiology, even at associative memory, I've got to face the fact that the dynamics of a synapse change is going on all the time. And I can't just get by by saying I'll do the dynamics of activity with fixed synapses.

So the dynamics of the synapses is actually fundamental to the whole system.

Yeah, yeah. And there's not, there's nothing necessarily separating the time scales when timescales can be separated. It's neat from the physicist or the mathematician's point of view, but it's not necessarily true in neurobiology.

So you're kind of dancing beautifully between showing a lot of respect to physics and then also saying that physics cannot quite reach the complexity of biology. So where do you land? Or do you continuously dance between the two?

I continuously dance between them because my whole notion of understanding is that you can describe to somebody else how something works in ways which are honest and believable and still not describe all the nuts and bolts in detail. Whether I can describe weather, has 10 to the 32 molecules colliding in the atmosphere, I can simulate whether that way I have a big enough machine, I'll simulate it accurately. It's no good for understanding. If I just want to understand things. I want to understand things in terms of wind patterns, hurricanes, pressure differentials and so on. All things as they're collective. And the physicists in me always hopes that biology will have some things which can be said about it which are both true and for which you don't need all the molecular details of the molecules colliding. That's what I mean from the roots of physics by understanding.

So what did again, sorry, but Hopfield networks help you understand what insight did give us about memory, about learning?

They didn't give insights about learning. They gave insights about how things having learned could be expressed. How having learned. A picture of you reminds me of your name. That would. But it didn't describe a reasonable way of actually doing the learning error only said if you had previously learned the connections of this kind of pattern would now be able to behave in a physical way. Which is if I put the part of the pattern in here, the other pattern part of the pattern will complete over here. I could understand that physics, if the right learning stuff had already been put in and you could understand why then putting in a picture of somebody else would generate something else over here. But it did not have a reasonable description of the learning process.

But even so, forget learning. I mean that's just a powerful concept that sort of forming representations that are useful to be robust, you know, for error correction kind of thing. So this is kind of what the biology does we're talking about.

Yeah, and what bipaper did was simply enable you. There are lots, there are lots of ways of being robust. If you think of it of a dynamical system, think of a system where a path is going on in time and if you think of a computer, there's a computational path which is going on in a huge dimensional space of ones and zeros. And an error correcting system is a system which if you get a little bit off that trajectory will push you back onto that trajectory again. So you get to the same answer in spite of the fact that there were things so that the computation wasn't being ideally done all the way along the line. And there are lots of models for error correction. But one of the models for error correction is to say there's a valley that you're following flowing down and if you push a little bit off the valley, it's just like water being pushed a little bit by a rock. It gets back and follows the course of the river. And that basically the analog in the physical system which enables you to say oh yes, error free computation and an associative memory are very much like things that I could understand from the point of view of a physical system. The physical system can be under some circumstances an accurate metaphor. It's not the only metaphor. There are error correction schemes which don't have a value and energy behind them, but those are Error correction schemes which a mathematician may be able to understand, but I don't.

So there's the physical metaphor that seems to work here.

That's right, that's right.

So.

So these kinds of networks actually led to a lot of the work that is going on now in neural networks, artificial neural networks. So the follow on work with restricted Boltzmann machines and deep belief nets followed on from these ideas of the Hopfield network. So what do you think about this continued progress of that work towards now revigorated and exploration of feed forward neural networks and recurrent neural networks and convolutional neural networks and kinds of networks that are helping solve image recognition, natural language processing, all that kind of stuff.

It always intrigued me that one of the most long lived of the learning systems is the Boltzmann machine, which is intrinsically a feedback network and with the brilliance of Hinden and Sinowski to understand how to do learning in that. And it's still a useful way to understand learning and understand. And the learning that you understand in that has something to do with the way that feed forward systems work. But it's not always exactly simple to express that intuition. But it always amuses me to see Hinton going back to the will yet again on a form of the Boltzmann machine, because really that which has feedback and interesting probabilities in it is a lovely encapsulation of something computational.

Something computational.

Something both computational and physical computational. And they very much related to feed forward networks physical in that Boltzmann machine learning is really learning a set of parameters for a physics Hamiltonian or energy function.

What do you think about learning in this whole domain? Do you think the aforementioned guy, Jeff Hinton, all the work there with back propagation, all the kind of learning that goes on in these networks, how do you, if we compare it to learning in the brain? For example, is there echoes of the same kind of power that back propagation reveals about these kinds of recurrent networks? Or is it something fundamentally different going on in the brain?

I don't think the brain is as deep as the deepest networks go, the deepest computer science networks. And I do wonder whether part of that depth of the computer science networks is necessitated by, by the fact that the only learning that's easily done on the machine is feed forward. And so there is the question of to what extent has the biology which has some feed forward and some feedback been captured by something which has got many more neurons, much more depth than neurons, you know.

So part of you wonders if the feedback is actually more essential than the Number of neurons or the depth, the. The dynamics of the feedback.

The dynamics of the feedback. Look, if you don't have. If you don't have feedback, it's a little bit like building a big computer and having. Running it through one clock cycle and then you can't do anything. Do you put. You'd reload something coming in. How do you use the fact that there are multiple clock cycles? How do I use the fact that you can close your eyes, stop listening to me and think about a chessboard for two minutes without any input whatsoever?

Yeah, that memory thing, that's fundamentally a feedback kind of mechanism. You're going back to something.

Yes.

It'S hard. It's hard. It's hard to understand, it's hard to introspect, let alone consciousness. Oh, because that's all.

Let alone consciousness.

Yes, yes, because that's tied up in there too. You can't just put that on another shelf.

Every once in a while. I got interested in consciousness and then I go and I done that for years and ask one of my betters, as it were, their view on consciousness. It's been interesting collecting them.

What. What is consciousness? Let's. Let's try to take a brief step into that room.

Well, I asked Marvin Minsky if you want consciousness, and Marvin said, consciousness is basically overrated. It may be an epiphenomenon after all. All the things your brain does, which are, which are actually hard computations you do non consciously. And there's so much evidence that even the things, the simple things you do, you can make decisions, you can make committed decisions about them. The neurobiologist can say he's now committed, he's going to move the hand left before you know it.

So his view that consciousness is not. That's just a little icing on the cake. The real cake is in the subconscious.

Yeah, yeah, Subconscious. Non conscious.

Non conscious, that's the better word.

Sorry. It's only that Freud captured the other word.

Yeah, it's.

That's a confusing word, subconscious.

Nicholas Chater wrote an interesting book. I think the title of it is the Mind is Flat. Flat, and in a neural net sense might be flat as something which is a very broad neural net without very many layers in depth, whereas a deep brain would be many layers and not so broad in the same sense that if you push Minsky hard enough, he would probably have said, consciousness is your effort to explain to yourself that which you have already done.

Yeah.

It's the weaving of the narrative around the things that already been computed for you that's right.

And so much of what we do for our memories of events. For example, if there's some traumatic event you witness, you will have a few facts about it, correctly done. If somebody asks you about it, you will weave a narrative which is actually much more rich in detail than that, based on some anchor points you have of correct things and pulling together general knowledge on the other. But you will have a narrative. And once you generate that narrative, you are very likely to repeat that narrative and claim that all the things you have in it are actually the correct things. There was a marvelous example of that in the Watergate impeachment era of John Dean. John Dean, you're too young to know, had been the personal lawyer of Nixon. And so John Dean was involved in the COVID up. And John Dean ultimately realized the only way to keep himself out of jail for a long time was actually to tell some of the truths about Nixon. And John Dean was a tremendous witness. He would remember these conversations in great detail and very convincing detail. And long afterward, some of the tapes, the secret tapes as it were, from which Dean was recalling these conversations were published. And one found out that John Dean had a good but not exceptional memory. What he had was an ability to paint vividly and in some sense accurately the tone of what was going on.

By the way, that's a beautiful description of consciousness. Do you in like where, where do you stand in your today? So perhaps it changes day to day, but where do you stand on the importance of consciousness in our whole big mess of cognition? Is it just a little narrative maker or is it actually fundamental to intelligence?

That's a very hard one. When I asked Francis Crick about consciousness, he launched forward in a long monologue about Mendel and the peas. Yeah. And how Mendel knew that there was something and how biologists understood that there was something in inheritance which was just very, very different. And the fact that inherited traits didn't just wash out into a gray, but were this or this and propagated, that was absolutely fundamental to biology. And it took generations of biologists to understand that there was genetics. And it took another generation or two to understand that genetics came from DNA. But very shortly after Mendel thinking biologists did realize that there was a deep problem about inheritance. And Francis would have liked to have said, and that's why I'm working on consciousness. But of course he didn't have any smoking gun in the sense of Mendel. And that's the weakness of his position. If you read his book on which he wrote with Koch, I think yeah.

Kristoff Koch.

Yeah. I find it unconvincing for the smoking gun reason. So I've gone on collecting views without actually having taken a very strong one myself, because I haven't seen the entry point. Not seeing the smoking gun. From the point of view of physics, I don't see the entry point. Whereas in neurobiology, once I understood the idea of a collective, an evolution of dynamics, which could be described as a collective phenomenon, I thought, ah, there's a point where what I know about physics is so different from any neurobiologist that I have something I might be able to contribute.

And right now there's no way to grasp at consciousness from a physics perspective.

From my point of view, that's correct. And of course, people, physicists, like everybody else, think very muddily about things. You ask the closely related question about free will, do you believe you have free will? Physicists will give an offhand answer and then backtrack, backtrack, backtrack, where they realize that the answer they gave must fundamentally contradict the laws of physics.

Answering questions of free will and consciousness naturally lead to contradictions from a physics perspective, because it eventually ends up with quantum mechanics. And then you get into that whole mess of trying to understand how much from a physics perspective, how much is determined already predetermined, how much is already deterministic about our universe. There's lots of different.

And if you don't push quite that far, you can say essentially all of neurobiology which is relevant can be captured by classical equations of motion.

Right?

Because in my view of the mysteries of the brain are not the mysteries of quantum mechanics, but the mysteries of what can happen when you have a dynamical system driven system with 10 to the 14 parts. That that complexity is something which is the physical complex systems is at least as badly understood as the physics of phase coherence in quantum mechanics.

Can we go there for a second? You've talked about attractor networks and just maybe you could say, what are attractor networks and more broadly, what are interesting network dynamics that emerge in these or other complex systems.

You have to be willing to think in a huge number of dimensions, because in a huge number of dimensions, the behavior of a system can be thought of as just the motion of the point over time in this huge number of dimensions.

Right?

And an attractor network is simply a network where there is a line and other lines converge on it in time. That's the essence of an attractor network.

That's how you in a highly dimensional.

Space and the Easiest way to get that is to do it in a high dimensional space where some of the dimensions provide the dissipation which makes which I have a physical system. Trajectories can't contract everywhere. They have to contract in some places and expand in others. There's a fundamental classical theorem of statistical mechanics which goes under the name of Liouville's theorem, which says you can't contract everywhere. If you contract somewhere, you expand somewhere else. In interesting physical systems, you've got driven systems where you have a small subsystem, which is the interesting part, and the rest of the contraction and expansion. The physicists would say it's entropy flow in this other part of the system system. But basically attractor networks are dynamics funneling down. So you can't be any. So that if you start somewhere in the dynamical system, you will soon find yourself on a pretty well determined pathway which goes somewhere. If you start somewhere else, you'll wind up on a different pathway. But you don't have just all possible things. You have some defined pathways which are allowed and under which you will converge. That's the way you make a stable computer and that's the way you make a stable behavior.

So in general, looking at the physics of the emergent stability in these networks, what are some interesting characteristics that, what are some interesting insights from studying the dynamics of such high dimensional systems?

Most dynamical systems, most driven dynamical systems by driven, they're coupled somehow to an energy source. And so their dynamics keeps going because it's coupling to the energy source. Most of them, it's very difficult to understand at all what the dynamical behavior is going to be.

You have to run it.

You have to run it. There's a subset of systems which has what is actually known to the mathematicians as a Lyapunov function. And those systems, you can understand convergent dynamics by saying you're going downhill on something or other. And that's what I found without ever knowing what Lyapunov functions were. In the simple model I made in the early 80s was an energy function. So you could understand how you could get this channeling onto pathways without having to follow the dynamics in infinite detail. You started rolling a ball at the top of a mountain, it's going to wind up at the bottom of a valley. You know that's true without actually watching the ball fall, roll down.

There are certain properties of the system that when you can know that that's right.

And not all systems behave that way. Most don't probably most don't but it provides you with the metaphor for thinking about systems which are stable and who do have these attractors behave. Even if you can't find a Lyapunov function behind them or an energy function behind them. It gives you a metaphor for thought.

Speaking of thought, if I had a glint in my eye with excitement and said, you know, I'm really excited about this something called deep learning and neural networks and I would like to create an intelligent system and came to you as an advisor, what would you recommend? Is it a hopeless pursuit to use neural networks to achieve thought? Is it? What kind of mechanisms should we explore? What kind of ideas should we explore?

Well, you look at the simple networks, we have one past networks, they don't support multiple hypotheses very well. As I have tried to work with very simple systems which do something which you might consider to be thinking. Thought has to do with the ability to do mental exploration before you take a physical action.

Almost like we were mentioning playing chess, visualizing, simulating inside your head different outcomes.

Yeah, yeah. And now you could do that in a feed forward network because you've pre calculated all kinds of things. But I think the way neurobiology does it hasn't pre calculated everything. It actually has parts of a dynamical system in which you're doing exploration in a way which is.

There'S a creative.

Element, like there's an, there's a creative element. And in a simple minded neural net you have a constellation of instances from which you've learned. And if you are within that space, if a new question is a question within this space, you can actually rely on that system pretty well to come up with a good suggestion for what to do. If on the other hand, the query comes from outside the space, you have no way of knowing how the system is going to behave. There are no limitations on what could happen. And so the artificial neural network is always very much. I have a population of examples. The test set must be drawn from this equivalent population. The test set has examples which are from a population which is completely different. There's no way that you could expect to get the answer right.

Yeah. And so what they call outside the distribution.

That's right, that's right. And so if you see a ball rolling across the street at dusk, if that wasn't in your training set, the idea that a child may be coming close behind, that is not going to.

Occur to the neural net and it is to our. There's something in the neurobiology that allows that.

Yeah, there's something in the way of what it means to be outside of the population of the training set. The population of the training set isn't just sort of this set of examples. There's more to it than that. It gets back to my question of what is it to understand something.

Yeah. You know, in a small tangent you've talked about the value of thinking of deductive reasoning in science versus large data collection. So sort of thinking about the problem. I suppose it's the physics side of you, of going back to first principles and thinking. But what do you think is the value of deductive reasoning in the scientific process?

Well, look, there are obviously scientific questions in which the root of the answer to it comes through the analysis of one hell of a lot of data.

Right. Cosmology, that kind of stuff.

And that's never been the kind of problem in which I've had any particular insight. Though I must say, if you look at cosmology is one of those. If you look at the actual things that Jim Peebles one of this year's Nobel Prize visit in physics funds from the local physics department, the kinds of things he's done, he's never crunched large data. Never, never, never. He's used the encapsulation of the work of others in this regard.

But it ultimately boiled down to thinking through the problem. Like what are the principles under which a particular phenomena operates?

Yeah, yeah. And look, physics is always going to look for ways in which you can describe the system in a way which rises above the. Rises above the details. And to the hard dyed the wool biologist, biology works because of the details in physics. To the physicists we want an explanation which is right in spite of the details. And there will be questions which we cannot answer as physicists because the answer cannot be found that way.

There's not sure if you're familiar with the entire field of brain computer interfaces that's become more and more intensely research and develop recently, Especially with companies like Neuralink with Elon Musk.

Yeah, I know. There have always been the interest both in things like getting the eyes to be able to control things or getting the thought patterns to be able to move what had been a connected limb which is now connected through a computer.

That's right. So in the case of neuralink, they're doing a thousand plus connections where they're able to do two way activate and read spikes, neural spikes. Do you have hope for that kind of computer brain interaction in the near or maybe even far future of being able to expand the ability of the mind of cognition or understand the mind.

As interesting watching things go. When I first became interested in neurobiology, most of the practitioners thought you would be able to understand neurobiology by techniques which allowed you to record only one cell at a time.

One cell, yeah.

People like David Hubel very strongly reflected that point of view. And that's been taken over by a generation, a couple of generations later by a set of people who says not until we can record from 10 to the 4, 10 to the 5 at a time will we actually be able to understand how the brain actually works. And in a general sense, I think that's right. You have to begin to be able to look for the collective modes of collective operation of things. It doesn't rely on this action potential or that cell. It relies on the collective properties of this set of cells connected with this kind of pattern and so on. And you're not going to succeed in seeing what those collective activities are without recording many cells at once.

The question is how many at once?

What's the threshold?

And that's the, that's the.

Yeah. And, and look, it's being pursued hard in the motor cortex. The motor cortex does something which is complex and yet the problem you're trying to address is very, is fairly simple. Now neurobiology does it in ways that are different from the way an engineer would do it. An engineer would put in six highly accurate stepping motors controlling a limb rather than 100,000 muscle fibers, each of which has to be individually controlled. And so understanding how to do things in a way which is much more forgiving and much more neural, I think would benefit the engineering world. The engineering world. Touch. Let's put in a pressure sensor or two rather than an array of gazillion pressure sensors, none of which are accurate, all of which are perpetually recalibrating themselves.

So you're saying your hope is, your advice for the engineers of the future is to embrace the large chaos of a messy air prone system like those of the biological systems. Like that's probably the way to solve some of these.

I think you'll be able to make better computation slash robotics that way than by trying to force things into, into a. Robotics for joint motors are powerful and stepping motors are accurate.

But then the physicists.

The physicist and you will be lost forever in such systems because there's no simple fundamentals to explore in systems that are so large and well, you say.

That and yet there's a lot of physics. The Navier Stokes equations, the equations of nonlinear hydrodynamics, huge amount of physics in them. All the Physics of atoms and molecules has been lost, but it's been replaced by this other set of equations, which is just as true as the equations at the bottom. Now, those equations are going to be harder to find in neurobiology, but the physicist in me says there are probably some equations of that sort.

They're out there.

They're out there. And if physics is going to contribute anything, it may contribute to trying to find out what those equations are and how to capture them from the biology.

Would you say that's one of the main open problems of our age, is to discover those equations?

Yeah. If you look at there's molecules and there's psychological behavior, and these two are somehow related. They're layers of detail, they're layers of collectiveness. And to capture that in some vague way, Several stages on the way up to see how these things can actually be linked together.

So it seems in our universe there's a lot of. A lot of elegant equations that can describe the fundamental way that things behave, which is a surprise. I mean, it's compressible into equations. It's simple and beautiful, but there isn't. It's still an open question whether that link is equally between molecules and the brain is equally compressible into elegant equations. But your sense some. Well, you're both a physicist and a dreamer. You have a sense that.

Yeah, but I can only dream physics dreams.

Physics dreams.

There is an interesting book called Einstein's Dreams, which alternates between chapters on his life and descriptions of the way time might have been, but isn't as the linking between these being, of course, ideas that Einstein might have had to think about the essence of time as he was thinking about time.

So, speaking of the essence of time and neurobiology, you're one human, famous, impactful human, but just one human with a brain, living the human condition, but you're ultimately mortal, just like all of us. Has studying the mind as a mechanism changed the way you think about your own mortality?

It has, really. Because particularly as you get older and the body comes apart in various ways, I became much more aware of the fact that what is somebody is contained in the brain and not in the body that you worry about burying. And it is to a certain extent true that for people who write things down, equations, dreams, notepads, diaries, fractions of their thought does continue to live after they're dead and gone, after their body is dead and gone. And there's a sea change in that going on in my lifetime between when my father died, when, except for the things which were Actually written by hymns that were. Very few facts about him will have ever been recorded. And the number of facts which are recorded about each and every one of us forever now, as far as I can see in the digital world. And so the whole question of what is death may be different for people a generation ago and a generation further ahead.

Maybe we have become immortal under some definitions.

Yeah, yeah.

Last easy question. What is the meaning of life? Looking back, you've studied the mind, us weird descendants of apes. What's the meaning of our existence on this little Earth?

Oh, that word meaning is as slippery as the word understand.

Interconnected somehow, perhaps is there. It's slippery. But is there something that you, despite being slippery, can hold long enough to express?

Well, I've been amazed at how hard it is to define the things in a living system in the sense that one hydrogen atom is pretty much like another, but one bacterium is not so much like another bacterium, even of the same nominal species. In fact, the whole notion of what is a species gets a little bit fuzzy and do species exist in the absence of certain classes of environments? And pretty soon one winds up with the biology which. The whole thing is living. But whether there's actually any element of it which by itself would be said to be living becomes a little bit vague in my mind.

So in a sense, the idea of meaning is something that's possessed by an individual, like a conscious creature. And you're saying that it's all interconnected in some kind of way, that there might not even be an individual. We're all kind of this complicated mess of biological systems at all different levels where. Where the human starts and when the human ends is unclear.

Yeah, yeah. And we're in neurobiology, where the. Oh, you say the neocortex does the thinking, but there's lots of things that are done in the spinal cord. And so we say, what is the essence of thought? It's just going to be neocortex. Can't be. Can't be.

Yeah. Maybe to understand and to build thought, you have to build the universe along with the neocortex. It's all interlinked through the spinal cord. John, it's a huge honor talking today. Thank you so much for your time. I really appreciate it.

Well, thank you for the challenge of talking with you. And it'll be interesting to see whether you can win five minutes out of this just coherent sense to anyone or another.

Beautiful.

Thanks for listening to this conversation with John Hopfield and thank you to our presenting sponsor, Cash App. Download it, use code Lex podcast. You'll get $10 and $10 will go to first, an organization that inspires and educates young minds to become science and technology innovators of tomorrow. If you enjoy this podcast, subscribe on YouTube, give it five stars on Apple Podcasts, support on Patreon, or simply connect with me on Twitter lexfriedman. And now let me leave you with some words of wisdom from John Hopfield in his article titled now what? Choosing Problems is the Primary Determinant of what one accomplishes in Science. I have generally had a relatively short attention span in science problems. Thus I have always been on the lookout for more interesting questions, either as my present ones get worked out or as they get classified by me as intractable given my particular talents. He then goes on to say, what I have done in science relies entirely on experimental and theoretical studies by experts. I have a great respect for them, especially for those who are willing to attempt communication with someone who is not an expert in the field. I would only add that experts are good at answering questions. If you are brash enough, ask your own. Don't worry too much about how you found them. Thank you for listening and hope to see you next time.