John Hopfield's Physics of Mind: Glitches Become Features

Lex Fridman opens at the philosophical level: what is most captivating about biological versus artificial neural networks? Hopfield's answer is evolutionary opportunism. If a molecule or a neuron has a quirk, evolution will often sharpen it into a useful feature rather than treat it as a glitch. You should therefore expect brains to have captured every available trick for getting neurons to do work. Artificial networks, he says, have suppressed that aspect almost completely.

He illustrates with a physical phase transition. Oscillators whose rhythms are close can, under some conditions, suddenly fall into step. The Millennium Bridge over the Thames, opened around 2001, was a public demonstration. Pedestrians do not start in lockstep, but they walk at about the same frequency; the bridge could sway at that frequency, and the slight motion pulled walkers into synchrony. Engineers had thought of walking as a back-and-forth, heel-toe problem. They had not taken the side-to-side, right-foot left-foot motion seriously enough. The bridge was strong enough laterally but not stiff enough, people felt the sway and fell into step, and the span closed for two years of stiffening.

Nerve cells generate action potentials. Put a loosely coupled group of cells firing at similar rates together and, under some conditions, they will lock; under others they will not. Once they fire together, Hopfield says, you can be sure other cells will notice. An evolving brain can turn that into a computational feature. Most artificial networks do not even have action potentials, let alone a route to synchronizing them. What looks like a defect in a living system can be made into a feature.

At the molecular level the same logic appears as gene duplication. A stretch of DNA that encodes a protein can be copied; one copy keeps doing the old job while the other mutates into a slightly different molecule. If that new molecule happens to help a reaction the cell cares about, evolution starts improving it. You get a general ability: duplicate, let the copies drift apart, keep the old function, try a new one.

Fridman maps the pattern onto companies. Hopfield agrees, with a shorter but not wildly shorter timescale: firms go bankrupt and are born, and some last a century. Large organizations have trouble letting a new product compete with an old one. When IBM built its first PC, it created an isolated internal unit and, for the first time, did not insist on IBM components, because entering a different market required changing the culture. Biology, Hopfield adds, finds new markets in a more adaptive way and is better at that kind of integration.

Asked for the most beautiful mechanism of the human mind, he barely hesitates: adaptation is everything. But there are two adaptations. One runs over generations, on evolutionary time; the other runs inside a single lifetime, as an individual learns from the environment. Biology has both, and that is what makes neurobiology hard. It is a mathematical-looking system built on top of an evolutionary one. Computer scientists talking about neural nets can stay in math. Biology actually came from evolution, and it is built in three dimensions.

Computer chips, Hopfield says, are basically two-dimensional, maybe 2.1, and they have real difficulty doing three-dimensional wiring. Biology is not built that way. Neocortex is sheet-like, sitting on white matter about ten times the volume of the gray matter, packed with what you might call the wires. Structure decides what is easy and what is almost impossible. Biology makes some things easy that are computationally hard to see how to do at all. In the other direction, it cannot do simple floating-point arithmetic, which would be an awfully stupid use of that hardware.

Of the two adaptations, he is drawn to the one he can get his hands on. He cannot see the evolutionary process happening; he is in awe of it, but it is a black hole for research, and he has no interest in working on it. The human-life timescale can be teased apart. Developmental neurobiology watches connections and structure grow from genetics plus the fact of building in three dimensions, in days and months. Infancy is both a time of immense cell multiplication and of the craziest cell death in the brain. What is not effective, not wired well enough to use, gets thrown out. It is a screening process, not a one-shot design.

Where will the next decades of progress on the mind come from? Hopfield always sees the world through a physics lens. Both of his parents were physicists, and what he took from that was a feeling that the world is an understandable place: do enough experiments, think about what they mean, structure the mathematics, and you should be able to see how things work. Teaching freshman physics, he did not want students to memorize examples and then write down the matching equation. He wanted them to *understand* Newton's laws, to look at a situation and say they expected the ball to take that trajectory. He has a nebulous idea of that 'understanding' and has never known how to express it well.

That vague standard of understanding, he says, runs smack into simple feed-forward nets. They do amazing things and contain nothing of the essence of what he would have called understanding. Understanding is more than an enormous lookup table. Fridman presses: what if the table gets really big? Hopfield answers in two directions. In real systems, feedback is essential to how computation happens. A mathematical system with feedback can be unrolled, but you pay an exponential expansion in what you have to build. Feedback is not a nicety. It is the difference between computing and looking things up.

Ask a neurosurgeon when someone is gone, and the answer will likely come from brain rhythms: this brain could never function again, that one might still be recoverable if treated well. The judgment is made from electrodes looking at simple electrical patterns, not from the details of individual neurons. Those rhythms, Hopfield notes, are already absent from anything that goes on at Google. Fridman compares a world-class pianist with a child first learning. Hopfield's retort is that they are still both playing the piano. The question is whether the Google side will ever play.

He thinks the two communities will keep cycling, generation after generation. AI and computer science take the current model of neurobiology, pretend it is good enough, and do everything they can with it. Interesting things happen, then the work grinds into the sand, and someone says something else is needed from neurobiology. A larger idea arrives, progress runs farther, then it hits sand again. He does not know how many generations it will take before anyone can say they have made a human. His sense is it might be a couple more, each one getting further into what a brain does and passing Turing-style tests on longer and broader tasks.

From the AI point of view, brain waves might be dismissed as epiphenomena. His first car, a 1936 Dodge, would shimmy the wheels above 45 miles an hour: a malfunction, not a design. In biology, if knowing you were going faster than 45 were useful, evolution would just capture the shimmy and not worry about where it came from. It will be a long time, he says, before that kind of accident in a large complex network is actually used for computation. A laptop has on the order of 10^10 similar transistors, and physical systems with that many similar parts almost inevitably have collective properties: sound in air, earthquakes, weather. In today's AI, no collective properties are used. If biology uses them, it will take more generations of stubborn people to dig in and see how.

One of Hopfield's biggest surprises is how useful learning systems can be even when they have no biological relationship at all. Fridman steers him to the associative nets now called Hopfield networks. Associative memory, on the human side, is ordinary and powerful. You have a memory of each friend: looks, voice, college, where you met, which papers they wrote. Start describing a five-foot-ten wiry cognitive scientist with a very bad back, and it does not take long to realize you are talking about Geoff Hinton. Nobody said the name. A few facts bound to a person let you take hold of the rest, or at least another subset. A large part of intelligent behavior, as Hopfield sees it, is just large associative memories at work.

What he made about 35 years earlier was a crude physics model, crude on purpose, so that his physicist's sense of understanding could stand up. You could say, ah, I understand why this goes to stable states: it is like things going downhill. That gives you something to think with in physical terms, not only in mathematical symbols. He did not describe a system that gracefully learns. He described a system in which you could see how learning, once in place, could link things together.

Revisiting the system, he is intrigued by compression. Seeing the same face every second for an hour, you do not store 3,000 images. You compact the views into chunks larger than single-neuron activities, so that if similar information comes in again, rewriting it yields nothing because it is already written. Biology, unlike the usual machine setup, does not first spend a period learning, then turn learning off and perform. Synapses change on a timescale that can overlap activity dynamics. To look more deeply at associative memory in neurobiology, he says, you have to face synaptic change going on all the time. Separating those timescales is neat for physicists and mathematicians. It is not necessarily true in brains.

He dances between physics and biology because his whole notion of understanding is that you can describe how something works in ways that are honest and believable without all the nuts and bolts. You could in principle simulate 10^32 molecules colliding in the atmosphere and still understand nothing. What he wants are wind patterns, hurricanes, pressure differentials: statements that remain true without the molecular collisions. The physicist in him always hopes biology will have some of those statements.

Pressed for what the networks taught about memory and learning, Hopfield is careful. They did not give insights about learning. They gave insights about how things, having been learned, could be expressed: how a picture of you reminds him of your name. If the right connections were already in place, putting part of a pattern in would complete the rest, and that completion you can understand as physics. Put in a picture of somebody else and something else appears. The paper did not describe a reasonable process of actually doing the learning.

Even setting learning aside, the useful idea is robustness. Think of a computation as a path through a huge space of ones and zeros. An error-correcting system pushes you back onto that trajectory if you drift, so you reach the same answer even if the computation was not done ideally all along. One model of that correction is a river valley: water pushed aside by a rock still follows the course. Associative memory and error-free computation, in this metaphor, are things a physical system can make intelligible. There are correction schemes with no valley and no energy behind them. A mathematician may understand those. He does not.

Restricted Boltzmann machines and deep belief nets followed from these ideas. What has always intrigued him is how long-lived the Boltzmann machine remains. It is intrinsically a feedback network; the brilliance of Hinton and Terry Sejnowski was understanding how to do learning in it. The learning is, physically, learning a set of parameters for a Hamiltonian or energy function. It still amuses him that Hinton keeps going back to yet another form of the Boltzmann machine, because something with feedback and interesting probabilities is a lovely encapsulation of a thing that is both computational and physical.

He does not think the brain is as deep as the deepest computer-science networks. He wonders whether some of that depth is forced by the fact that the learning easily done on a machine is feed-forward. Biology has some feed-forward and some feedback; the open question is how much of that mix can be approximated by many more neurons stacked much deeper. He suspects the dynamics of feedback may matter more than neuron count or depth. Without feedback, it is a bit like building a big computer, running it for one clock cycle, and then being unable to do anything until you reload an input. How do you use the fact that you can close your eyes, stop listening, and think about a chessboard for two minutes with no input at all? That memory thing is fundamentally a feedback mechanism.

Feedback, he admits, will not stay on a shelf away from consciousness, which is hard to introspect and harder to study. Over the years, when the topic interests him, he asks people he considers his betters and collects views. Marvin Minsky told him consciousness is basically overrated, possibly an epiphenomenon. The hard computations are not done consciously. There is ample evidence that you can be committed to moving a hand left before you know it; neurobiology can see the commitment first. On that view, consciousness is icing. The cake is non-conscious, a word Hopfield prefers to Freud's 'subconscious.'

He mentions Nick Chater's book *The Mind Is Flat*, reading 'flat' in a neural-net sense as very broad, without many layers of depth. Push Minsky hard enough and he would have said consciousness is your effort to explain to yourself what you have already done: a narrative woven around things already computed. Memories of events work that way. Witness a traumatic scene and you will have a few facts right. Asked about it, you weave a much richer story from those anchors plus general knowledge, then repeat the story and claim the invented details are true.

John Dean, Nixon's personal lawyer during Watergate, is his exhibit. Dean realized that telling some truths about the cover-up was the way to keep himself out of jail for a long time. He was a tremendous witness, recalling conversations in great detail, very convincingly. When secret tapes of those conversations later became public, Dean turned out to have a good but not exceptional memory. What he had was the ability to paint, vividly and in some sense accurately, the tone of what was going on. Fridman calls that a beautiful description of consciousness. Hopfield does not object.

Asked where he stands, he is still collecting views. He once asked Francis Crick about consciousness and got a long monologue about Mendel and peas: inherited traits do not wash out into gray; they are this or that and they propagate. Biologists took generations to see that genetics existed, and another generation or two to see that it came from DNA, but thinking biologists knew after Mendel that inheritance was a deep problem. That is why Crick was working on consciousness. Hopfield's objection is that Crick had no Mendel-style smoking gun, which is why the book with Christoph Koch felt unconvincing. Hopfield himself has not seen an entry point. Collective dynamics in neurobiology gave physics something to contribute; consciousness, from a physics perspective, currently does not. Free will is the neighboring trap: physicists give an offhand answer and then backtrack into contradictions with physical law. He draws a hard line. Quantum mechanics need not come in. The mystery of the brain is a driven dynamical system with on the order of 10^14 parts. The physics of that complexity, he says, is at least as badly understood as phase coherence in quantum mechanics.

An attractor network, he says, requires thinking in a huge number of dimensions. The system's behavior is the motion of a point over time in that space. An attractor is a line that other lines converge onto. Liouville's theorem from classical statistical mechanics says you cannot contract everywhere in phase space: if you contract somewhere, you expand somewhere else. Interesting driven physical systems handle this by taking a small subsystem as the interesting part and letting contraction happen there while expansion, the entropy flow, lives in the rest. Start somewhere and you soon find yourself on a fairly determined pathway; start somewhere else and you land on a different one. That is how you make a stable computer and stable behavior.

Most driven dynamical systems, coupled to an energy source so the motion keeps going, are very hard to understand without just running them. A subset has what mathematicians call a Lyapunov function. Those you can understand as going downhill on something. In the simple model he made in the early 1980s, without knowing the name, that something was an energy function. Roll a ball off a mountain and it will end in a valley; you know that without watching every bounce. Not all systems behave that way, probably most do not, but the picture is a metaphor for thinking about stable attractors even when you cannot find the energy function.

If a young person with a glint in the eye wanted to build a thinking system out of neural nets, Hopfield's first criticism is that simple networks do not support multiple hypotheses well. Thought, as he understands it, is mental exploration before physical action: visualizing chess outcomes with your eyes closed. A feed-forward net does that by precalculating. He does not think neurobiology precalculates everything; it has a dynamical system in which exploration actually runs, with a creative element. In a simple net you have a constellation of learned instances. If a new question sits inside that space, you can rely on a decent suggestion. If the query comes from outside, there are no limitations on what could happen.

In the artificial-net world, the premise is always a population of examples, and the test set must be drawn from the same population. Examples from a completely different distribution give you no reason to expect a right answer. That is out-of-distribution failure. A ball rolls across the street at dusk. If that was not in the training set, the idea that a child may be coming close behind will not occur to the net. Something in our biology lets that thought appear. The training distribution, he says, is not just the set of examples; there is more to it, and that 'more' is his old question of what it is to understand something.

On deductive reasoning versus large data, Hopfield grants that some scientific questions, cosmology among them, only yield through analyzing a hell of a lot of data. Those have never been the problems where he had insight. Jim Peebles, a Nobel physics laureate that year in a neighboring department, never crunched large data. He used encapsulations of other people's work and ultimately boiled things down to thinking through the principles under which a phenomenon operates. Physics will always look for descriptions that rise above the details. Hard-core biologists think biology works because of the details. Physicists want an explanation that is right in spite of the details, and they will leave questions they cannot answer that way.

Fridman asks about brain-computer interfaces and companies such as Neuralink, with a thousand-plus connections that can read and write spikes. Hopfield's hope is historical. When he first became interested in neurobiology, most practitioners, David Hubel among them, thought you could understand the field by recording one cell at a time. A couple of generations later, the view flipped: not until you can record from 10^4 or 10^5 cells at once will you understand how the brain works. In a general sense he thinks that is right. You have to look for collective modes that do not live in this action potential or that cell. The question is how many at once, and what the threshold is.

Motor cortex is a revealing case: the thing it does is complex, but the problem you are trying to address is relatively simple. An engineer would put six highly accurate stepper motors on a limb. Neurobiology uses on the order of a hundred thousand muscle fibers, each individually controlled. Understanding how to do a job in a much more forgiving, much more neural way would benefit engineering. Do not tile a robot with a gazillion inaccurate pressure sensors that recalibrate forever, or at least do not stop at one or two precise sensors plus a tight control loop. Embrace a messy, error-prone, self-calibrating crowd. That, he thinks, is how you make better computations and better robotics than by forcing everything onto powerful, accurate joint motors.

Would the physicist then be lost in systems too large for simple fundamentals? Hopfield refuses the premise. There is a huge amount of physics in the Navier-Stokes equations of nonlinear hydrodynamics. All the physics of atoms and molecules has been lost, replaced by another set of equations just as true as the underlying ones. Such equations will be harder to find in general biology, but the physicist in him insists they are probably out there. If physics still has something to contribute, it may be finding those equations and learning how to capture them from biology. Molecules sit at one end, psychological behavior at the other, with layers of collectiveness in between. The open problem is to catch the links several stages up, without computing from the atoms. He can only dream physics dreams, he says, and physics shapes them. He mentions Alan Lightman's *Einstein's Dreams*, with its chapters on how time might have been.

Studying the mind as a mechanism has changed how Hopfield thinks about mortality. As you get older and the body comes apart in various ways, he became much more aware that what somebody is is contained in the brain, not in the body you worry about burying. For people who write things down, equations, notepads, diaries, fractions of thought do continue to live after the body is gone. In his lifetime there has been a sea change. When his father died, except for what he had actually written, very few facts about him were ever recorded. Now a vast number of facts about each of us are kept in the digital world, as far as he can see, forever. The question of what death is may differ for a generation ago and a generation ahead. Under some definitions, we have become immortal.

The meaning of life, he says, is a word as slippery as *understand*. Living systems are astonishingly hard to define. One hydrogen atom is pretty much like another; one bacterium is not so much like another even of the same nominal species. The notion of a species gets fuzzy, and whether species exist in the absence of certain environments is itself a question. Pretty soon the whole of biology looks living, while it becomes vague whether any element by itself would be said to be living. Meaning, in that light, may be something possessed by an individual, a conscious creature, while the interconnecting mess of biological systems makes it unclear where a human starts and ends.

Neurobiology has the same blur. People say neocortex does the thinking, but lots of work is done in the spinal cord, so the essence of thought cannot simply live in neocortex. To understand thought, and to build it, you might have to build the universe along with the cortex; it is all interlinked. Fridman closes with lines from Hopfield's 2018 article *Now What?*: choosing problems is the primary determinant of what one accomplishes in science; Hopfield has generally had a short attention span and has always been on the lookout for more interesting questions as present ones get worked out or classified as intractable. Experts are good at answering questions. If you are brash enough, ask your own, without worrying too much about how you found them.