This discussion is about the implementation of computing in matter. That was the topic of John von Neumann’s last book, The Computer and the Brain. He died before he finished it, so it was published posthumously in 1958. I don’t know when I first learned about it, perhaps sometime in the mid-1970s. Though I knew about von Neumann and his role in early computing, it dismissed the book itself, figuring that we’d learned so much about the brain since then, and the nature of computers had changed so much, that it must be obsolete.
I was wrong. When I finally read the book, probably in the early to mid-1980s I was stunned. This was a profound book and free of mathematics beyond some simple back-of-the-envelope calculations. For one thing von Neumann talked of both analog and digital computation; that contrast was central. When I first started reading about computers in the mid-to-late 1960s that contrast was at the beginning of every article or book. But once personal computers appeared and proliferated in the late 1970s and 1980s, analog computing was all but forgotten.
It was good to see it back. For one thing, I had been strongly influenced by the work of William Powers, whose 1973 book, Behavior: The Control of Perception, offered an elegant analog model of the brain. That was central to the work of my teacher and mentor, David Hays, who had been one of the founders of computational linguistics. In 1974 and 1975 he worked out a scheme in which cognitive networks were grounded in Powers’s analog model. This was years before anyone else was working on the problem, before Steven Harnad coined the term, “symbol grounding” in his 1990 paper on the problem in Physica D.
Now, with the success of artificial neural networks, there’s another aspect of physical implementation we’ve got to deal with, distributed representation. You’re looking at an apple. Where is that apple represented in your brain? There might be some one neuron or a tightly clustered group of neurons that represent that apple. That’s a local representation. But the representation might be distributed across a loosely linked population of neurons. That’s a distributed representation. We now know that that’s how the brain works, though I assume there’s some laggards still stuck in the previous century where local representation was widely favored. And that’s how artificial neural nets work. The concept of apple isn’t localized in one or a small group of weights, it’s smeared over a population of weights. The same for the concepts of truth, beauty, and justice, or, for that matter, neuron.
Consequently von Neumann’s 1958 discussion must now be extended to distributed representation. It is for that purpose that I asked Claude to convene a conversation between Charles Babbage, who conceived of an elaborate mechanical computer in the 19th century, von Neumann himself, and Geoffrey Hinton, one of the so-called godfathers of artificial intelligence – a bit of journalistic and pop culture slight-of-hand that obscures a long and complex history. Moreover, since these three gentleman did not co-exist in time, though there’s a bit of overlap between von Neumann and Hinton, I decided that I might also have Claude transport them to Mars for the occasion. Anything is possible in virtual reality.
Or is it?
Image by ChatGPT.
A sun-facing room on Mars. Three chairs arranged loosely, angled toward a broad window. Through it, the Martian plain stretches red and absolutely still, and the sun — recognizable but wrong, too small, too distant — hangs in a pale pink sky. Three men stir and look about them, bewildered but unhurt.
I. Awakening
Charles Babbage
I am not dead — I can confirm that much. My pulse is steady and my faculties appear intact. But this room is not any room I have entered by ordinary means. That light through the window — is that the sun? The colour is right but the disc is too small by half. And that plain outside... brick red, entirely without vegetation or track or any sign of habitation. Gentlemen, I should very much like an explanation.
John von Neumann
I was in Princeton not five minutes ago. I notice the gravity is reduced — perhaps sixty percent of normal. The sky has the ferric oxide colouration one would predict. The solar disc subtends roughly two-thirds the angle it does from Earth. I believe I know where we are, and I find the hypothesis almost too extraordinary to voice.
Geoffrey Hinton
Mars. We're on Mars. I was at a conference in Toronto. But that sky, the dust, the sun at that distance — I'd stake my reputation on it. He exhales slowly. I've recently left a position at Google partly so I could speak freely about alarming possibilities. I did not anticipate that the alarming possibilities would include this. May I ask what year it is, from each of your perspectives?
Charles Babbage
The year of Our Lord 1862. I am Charles Babbage, formerly Lucasian Professor of Mathematics at Cambridge, Fellow of the Royal Society. I have spent the better part of forty years attempting to build mechanical calculating engines, with results that have been — a pause — mixed, as regards the support of Her Majesty's government.
John von Neumann
John von Neumann. The year is 1955. I work at the Institute for Advanced Study in Princeton, and consult for various government and military bodies. Mr. Babbage — I know your name extremely well. Better, I suspect, than you know mine.
Geoffrey Hinton
Geoffrey Hinton. For me it is 2024. And I know both of you — Mr. Babbage, you designed the Difference Engine and the Analytical Engine. Dr. von Neumann, you are among the most formidable mathematicians of the twentieth century and you gave your name to the architecture that every conventional computer on Earth is built upon. You are, in a real sense, my ancestors. The field I work in — machine learning, artificial intelligence — descends directly from the problems both of you were grappling with.
Charles Babbage
A long pause, during which he stares at Hinton with an expression mixing hunger, pride, and something close to grief. The Analytical Engine. Did anyone build it?
Geoffrey Hinton
Not in your lifetime. The government never provided the funds. But the ideas were entirely right — and they were eventually built, first in relay and vacuum tube and then in silicon, by people who in some cases had read your work and in other cases had arrived at the same conclusions independently. You were approximately a century early.
Charles Babbage
Very quietly. A century. I had hoped twenty years would suffice. I petitioned the Chancellor. Three times.
II. The mill and the store
John von Neumann
Mr. Babbage, allow me to tell you what your Analytical Engine set in motion — because it bears directly on the work that has occupied all three of us. You made a distinction, in your design, between what you called the Mill and the Store. The Mill performs the operations — addition, subtraction, multiplication. The Store holds the numbers awaiting operation and the results of operations completed. That separation of active calculation from passive memory was the foundational insight.
Charles Babbage
It seemed to me the only sensible arrangement. The columns of number-wheels in the Store are passive — they merely hold values. The Mill acts upon them. To mix the two functions in the same mechanism would create hopeless confusion.
John von Neumann
And yet it is precisely that separation which I have spent the last years of my life questioning — not as an engineering choice, which was entirely sound, but as a principle of intelligence itself. My colleagues and I formalized your Mill-and-Store distinction into what is now called the stored-program architecture. The processor executes instructions sequentially; the memory holds both data and those instructions passively until called upon. It is a serial machine, one operation following another, orchestrated by a central clock. The computers being built in my era all follow this pattern.
Geoffrey Hinton
And in my era they still do, at bottom. But you've just described the tension at the heart of everything, Dr. von Neumann. Serial, precise, with a strict wall between computation and memory — that is the von Neumann architecture. And it is, in a sense, the architecture that human intelligence refuses to use.
Charles Babbage
You are saying the brain does not separate Mill from Store?
Geoffrey Hinton
Exactly. In the brain, every neuron is simultaneously a memory element and a processing element. It holds information in the strength of its connections to other neurons, and it also fires — it computes — based on what it receives. There is no central Mill. There is no passive Store. Computation and memory are fused at every node in the network, and the whole thing operates in parallel, millions of neurons active at once.
John von Neumann
This is precisely what troubles me — and I am glad to find the trouble is still alive in your era, Mr. Hinton, because it means I was not merely chasing a phantom. I have been writing a manuscript, unfinished I'm afraid, called "The Computer and the Brain." My central puzzle is this: where, in a neuron, is the Mill? A neuron receives signals, sums them, and if the sum exceeds a threshold, it fires. That threshold operation is a computation. But the synaptic weights — the strengths of the incoming connections — those are also the memory. The neuron is its own Mill and its own Store simultaneously. I have been calling such things active elements, to distinguish them from the passive memory elements of our conventional machines. But I confess I have not yet worked out the full implications.
Geoffrey Hinton
With genuine feeling. Dr. von Neumann, the full implications are what I have spent my career working out. And you had named the essential thing: active elements. That is exactly what the nodes of a neural network are. Each one holds a weight — that is its memory — and each one applies a non-linear function to its inputs — that is its computation. Fused. Inseparable. Replicated millions or billions of times, connected in layers, and trained by adjusting all those weights simultaneously until the network's outputs match the desired answers.



