Douglas Hofstadter, Author of the Legendary Gödel, Escher, Bach (GEB), Has a New Book — and He’s Coming to China Next Week

His second book is called Surfaces and Essences.

On April 17 and 18, the well-known American scholar and writer Douglas Richard Hofstadter will be in China for two events, promoting the forthcoming Chinese edition of his book Surfaces and Essences: Analogy as the Fuel and Fire of Thinking.

Both events take up a question that has been argued over endlessly in recent years — human creativity versus artificial intelligence. What exactly makes human thought unique? How should we meet the challenges of the AI era? And so on. The April 17 event is at Tsinghua University, open to the public and free, though you have to register. Besides Hofstadter, the guests include Peng Kaiping, dean of Tsinghua University’s School of Social Sciences; Chen Jin, director of Tsinghua’s Research Center for Technological Innovation; Liu Jian, head of the Department of Earth and Atmospheric Sciences library at Indiana University; Han Yan, chair of Cheers Publishing; and David Moser, a foreign faculty member at Capital Normal University. The April 18 event is a closed-door discussion for 50 invited guests, but it will be livestreamed on the Dushuren app. Where the April 17 list leans academic, the April 18 lineup comes mostly from industry: Cheng Mingxia, assistant dean of the Tencent Research Institute; Wang Xiaochuan, CEO of Sogou; Duan Yongchao, founding partner of the think tank Weicao Zhiku; Master Xiandu, director of the Artificial Intelligence and Information Technology Center at Longquan Temple; Zhang Jiang, a professor in the School of Systems Science at Beijing Normal University; and Han Yan.

Hofstadter, now 73, was born in New York in 1945; his father was the Nobel Prize–winning physicist Robert Hofstadter. He began his academic career in 1975, after earning a PhD in physics from the University of Oregon. He has spent nearly all of his teaching and research life at Indiana University, where he is now College of Arts and Sciences Distinguished Professor of Cognitive Science and directs the Center for Research on Concepts and Cognition. His books include Gödel, Escher, Bach and Surfaces and Essences.

You cannot mention Hofstadter without mentioning his world-famous “legendary book,” Gödel, Escher, Bach: An Eternal Golden Braid (GEB for short). This 1,000-page work of popular science sets out the mathematical logic of Gödel, the prints of the engraver Escher and the music of Bach together, and out of the three gives an absorbing introduction to mathematical logic, computability theory, artificial intelligence, linguistics, genetics, music and the theory of painting. One reviewer called it “intricately conceived, deep in meaning, broad in vision and rich in philosophical flavor.”

Gödel, Escher, Bach caused a considerable stir when it appeared in 1979, and drew a great deal of praise. Martin Gardner, the famous Scientific American columnist, wrote: “Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event.” John Holland, the first American to earn a doctorate in computer science (then still called “communication science”), recalled: “Pretty much everyone I knew reacted with intense awe.”

The Atlantic reported that Hofstadter seemed destined to become an indelible part of that cultural moment. Gödel, Escher, Bach was not only a hugely influential book; it was a book entirely about the future. People called it the bible of artificial intelligence — the field where computer science, cognitive science, neuroscience and psychology meet. Hofstadter’s descriptions of computer programs were accurate and also inventive, and his picture of “the secret software structures in our brains” sent a whole generation of young people off to explore artificial intelligence.

At 35, Hofstadter won America’s two most famous book prizes — the Pulitzer and the National Book Award — for Gödel, Escher, Bach, his first book, and became a tenured professor at Indiana University. He was riding high. But this was also the moment when the field of artificial intelligence was shrinking, its focus drifting toward practical systems and away from basic research. He disliked that intensely, and “cast a skeptical eye over many widely praised AI projects and over the direction of the field as a whole.” When the chess player Garry Kasparov lost to the supercomputer Deep Blue, for instance, he said: “That was a historic turning point, but it had nothing to do with computers getting smarter.” What he cared about was always the nature of human thought, which pushed him further and further to the margins of what people call artificial intelligence. “I don’t want to get mixed up in ‘high-end’ projects that look like they’re studying intelligence but have nothing to do with intelligence at all. I don’t know why more and more people are obsessed with that kind of thing,” he said.

According to a 2013 story in The Atlantic, Hofstadter had not been to a single artificial intelligence conference in 30 years. “There’s no communication between me and these people,” he said of his AI peers. “I don’t want to talk to people who refuse to budge. You know, I call them my peers, but they’re barely my peers at all — we can’t even talk to each other.” And: “I don’t like going to conferences and running into people who are pigheaded and wrong, or who don’t understand what I’m thinking about. I only enjoy talking with people whose thinking is closer to mine.”

So there is something to look forward to in his coming to China for an AI conference. It is also worth noting that Gödel, Escher, Bach reached China back in the 1980s in an abridged translation, included in the hugely influential “Toward the Future” series under the title 《GEB：一条永恒的金带》 (GEB: An Eternal Golden Band). It opened many young readers’ eyes and shaped a generation — though because it was abridged, that version ran to just over 200 pages, about a fifth of the original. Not until 1997 did the Commercial Press bring out a complete translation. The work reportedly took more than ten years, and Hofstadter himself took part in it.

Surfaces and Essences, due out this year, will be Hofstadter’s second book formally published in China. The English edition appeared in 2013, written with Emmanuel Sander. As they see it, analogy is the fuel and fire of human thought, something our mental life needs every day. “Look at your own conversations and you will be surprised, again and again, to find that this is exactly the process of making analogies,” Hofstadter said. Because a conversation is only this: someone says something that reminds you of something else; you say something that reminds someone else of yet another thing, back and forth, without end.

Finally, so that you can get to know Hofstadter better, the publisher Cheers Publishing has allowed us to run an excerpt from his new book, Surfaces and Essences. We hope you get something out of it.

Chapter 8: An Earth-Shattering Analogy (Excerpt)

What Mechanism of Thought Lay Hidden Behind Einstein’s Brain?

What happened in the secret recesses of Einstein’s mind that led him, after two years of thought and with no experimental evidence at the time, to arrive at this most bewildering idea?

To begin with, we have every reason to believe Einstein thought that a beam of light leaving a flashlight carries not only energy but also mass (both of which are “subtracted” from the flashlight). This means that anomalous mass, on leaving the flashlight, does not vanish into nothing; it changes from one form into another. Before the two beams of light are produced, the anomalous mass sits in the chemical bonds of the flashlight’s battery. Once the beams are released, it sits in the electromagnetic waves that make up the beams. (If someone were to weigh a mirror-lined box with light trapped and bouncing back and forth inside it, they would find the box a tiny bit heavier than before it captured the light.)

The fluidity of anomalous mass — the fact that it can slide from one form into another — could hardly have failed to remind Einstein of the fluidity of energy, since energy too can slide from one form into another. He would have found it all the easier to see a connection between the two because his own formula had already exposed an unexpected link between mass and energy. But even though one particular kind of anomalous mass could slide readily into another kind of anomalous mass, it seemed self-evident that normal mass could not change at all. As noted above, no one had ever seen a boulder or any other solid object (liquids or gases would do as examples too) suddenly dissolve into a beam of light, or spring magically out of one. Tangible things are made of touchable material; they belong to a different category altogether from intangible energy and its “anomalous mass.” That apparent distinction seemed to demand a strict, impassable barrier inside the concept of mass, splitting it into two subspecies that could never be converted into each other.

Like every physicist of his day, Einstein was thoroughly versed in the solid, well-established fact of the conservation of energy: energy can change form, but it can neither be created nor destroyed. Countless experiments had shown that heat (thermal energy) can be turned into the motion of macroscopic objects (kinetic energy) — the piston in a cylinder, for instance. The reverse is also true: friction can heat an object. A battery’s chemical energy can turn into electromagnetic energy, and so on. The science and technology of the day rested on this basic principle.

Einstein believed firmly in the conservation of energy. Now he suddenly found himself facing another, similar conservation principle: the conservation of anomalous mass. That is, anomalous mass, like energy, seemed able to slide from one form to another while its total quantity neither grew nor shrank. If a crystal absorbs radiation, for example, a tiny portion of electromagnetic anomalous mass (that is, a beam of light) suddenly disappears. At the same moment, a tiny portion of thermal anomalous mass suddenly appears. Likewise, in radiation the reverse conversion takes place. So we can imagine that in Einstein’s mind, the analogy between the conservation of energy and the conservation of anomalous mass began to forge a tight analogical link between the concept of energy and the concept of anomalous mass.

So far we have not mentioned another very important kind of energy — potential energy. The term was coined by the French physicist Pierre Simon de Laplace in 1799. Potential energy may be the strangest and most counterintuitive form of energy, because it depends entirely on the relative positions of objects. Strange or not, it plays a key role in the conservation of energy. A ball rolling down a hill, for example, gains kinetic energy and loses potential energy (potential energy being proportional to its height). The reverse holds too: if the ball rolls uphill, it loses speed, and hence kinetic energy, while gaining potential energy. Take a spring as another example of the key role potential energy plays in energy conservation. In its neutral state, neither stretched nor compressed, a spring has no potential energy; stretched or compressed, it acquires some. As long as we hold it stretched and keep it from springing back to neutral, it holds on to that potential energy. The instant we let go, the potential energy turns into kinetic energy. At every moment in this process, the total amount of energy stays constant.

So energy, like mass, seems to come in two very different variants. On one hand there are the dynamic forms of energy tied to motion — heat (molecular vibration), waves, rotation, motion through space and so on. On the other there is static potential energy. This kind seems very different, because it has nothing to do with motion and everything to do with position. Remember the parable about money we told earlier? We can liken the first kind of wealth to flowing energy, because it is always tied to something in motion; and the second kind of wealth to potential energy, because its existence involves no action at all — we might call it frozen energy.

Splitting the concept of energy into two categories, flowing and frozen, naturally leads us to split the concept of mass into two as well — anomalous and normal (remember, this division was forced on us by Einstein’s own formula). The analogy is so clear it is almost begging to be drawn. But obvious as it is, it runs into a problem, because in Einstein’s day it had been common knowledge for a century that the two kinds of energy, dynamic and static, can be fully converted into each other (otherwise the conservation of energy would not hold). Whereas we have insisted all along that the two kinds of mass, anomalous and normal, cannot be converted into each other. If they could, an iron atom, a pearl or a pebble could suddenly vanish without a trace, so long as it left behind an equal amount of anomalous mass — heat, sound or light. But this never happens, or so any sane person would naturally assume. In short, where mass is concerned there seems to have to be an airtight barrier between the two categories, and where energy is concerned there should be no barrier at all. And so our budding mass–energy analogy collapses. What a pity!

But this is exactly where Einstein’s “intuition for the unity of the universe” comes into play. As Banesh Hoffmann put it, insisting on an airtight barrier between anomalous and normal mass “requires positing two different kinds of mass, and there is no sufficient reason to posit two when one will do. The distinction lacks elegance and is hard to justify logically.” If we take Hoffmann at his word, in 1907 Einstein must have said to himself, in essence: “My firm belief in the unity of nature leads me to conclude that an ordinary piece of matter with normal mass should be able to convert into a certain quantity of anomalous mass, and the other way around, even though nothing of the kind has ever been seen by anyone, anywhere.” The powerful inspiration Einstein drew from his own aesthetic of simplicity closely resembles Jane’s epiphany. Faced with the threat of having her property seized, she broke through an invisible barrier around money and hit on a previously unimaginable way to turn frozen assets into liquid funds.

But what drove Einstein to break through the seemingly unbreakable barrier inside the concept of mass? Which metaphorical “enforcement officer” came knocking on a fine day and put enough intellectual pressure on him? The aesthetically grounded hope for a unified universe was not enough on its own, because, as noted above, it was self-evident that the two kinds of mass could not be converted into each other. Clocks and stones never evaporate into beams of light, sound waves or anything else. They just sit there, unmoved. All of this was perfectly clear. So what exactly made Einstein see things differently?

Let us recall once more how Banesh Hoffmann summed up Einstein’s state of mind about mass in 1907. If we restate his passage in the terms this chapter has been using, Einstein’s basic line of reasoning ran like this: “Normal mass should perhaps possess energy, because it is essentially the same thing as anomalous mass. And the latter, according to the formula I derived two years ago, possesses energy. So the analogy forces me to generalize. I therefore conclude: every kind of mass possesses energy.” The analogy plainly lies in the phrase “it is essentially the same thing as X.” But we still have to ask: given that normal mass and anomalous mass were known to differ enormously, why was Einstein so confident in this analogy — confident enough to imagine, with no experimental evidence whatsoever, that locked inside every seemingly ordinary piece of matter lay an enormous reserve of energy, in fact an almost unimaginably enormous reserve of energy?

Einstein’s crucial clue was very likely potential energy, because, as noted earlier, potential energy calls normal mass to mind. Other forms of energy involve motion; potential energy does not. Likewise, anomalous mass involves motion, while normal mass does not.

So far the analogy between potential energy and normal mass was strong. But in Einstein’s mind its force was weakened by the fact that all forms of energy, potential energy included, can be converted into one another. For mass, the notion of mutual convertibility applied only to one side of the divide, specifically excluding normal, “frozen” mass. This was a deeply troubling asymmetry. And for that very reason it was also the most challenging part. Why must there be an impassable barrier separating anomalous mass from normal mass, when no comparable barrier stood in the way within energy itself? This was precisely the critical question that led to the critical breakthrough.

To propose that normal, “frozen” mass could also take part in the same fluid-like process of overall mass conservation was clearly a blindfolded leap into the dark. There was no reason for the leap other than a deep aesthetic yearning for unity, backed by a suggestive analogy: that potential energy takes part in the overall conservation of energy. But however suggestive the analogy, this was still a reckless leap, because it forced you to accept an outlandish idea — that an object could vanish into thin air, leaving no trace whatever. That was an unprecedented, unheard-of event.

What is more, and this makes the idea still more surreal, Einstein understood perfectly well that because of the enormous constant c² in his formula, itself a squared quantity, even the most negligible amount of normal mass converting into anomalous mass would produce an unimaginably vast burst of energy, seemingly out of nowhere. (Though in fact this energy had been there all along, simply hidden inside seemingly ordinary matter, invisible to us — much like chemical potential energy lying dormant inside chemical bonds.) Releasing such a vast store of energy could be used to develop enormous new energy sources, to say nothing of superweapons. If this conversion ever became a reality, the world would be utterly transformed.

In short, this new reading of the formula E = mc² amounted to a bold step into the boundless territory of science fiction. Yet there was nothing more to the formula than a single intuitive analogy grounded in aesthetics — and still, what Einstein committed to paper in 1907 was truly a leap, one that opened the door to a revolutionary new vista. Here a tangible object with normal mass could turn into another, intangible form of mass, and so release the vast hidden energy locked inside it in the form of potential energy. 1907 was the year the metaphorical Leaning Tower began to tilt, and it was the tilt that first drew the world’s attention. From that moment on, the phrase “Einstein’s theory of relativity,” which would soon become a household term, began to be bound up in the public imagination with the formula E = mc².

Yet in 1907 there was not a shred of experimental evidence to support Einstein’s extension of the formula’s original meaning. Only many years later, in 1928, did a British physicist — through a subtle combination of relativity and quantum mechanics — propose the idea of antiparticles theoretically (the positron, for example, as the antiparticle of the electron). A few years after that, the sudden and complete mutual annihilation of two stable pieces of matter — specifically an electron and a positron — was observed experimentally for the first time. The process produced only two photons (the elegant and indispensable word “photon” was finally coined by Gilbert Lewis in 1926), each flying off in the opposite direction at the predetermined speed of light, oscillating and carrying a precise amount of electromagnetic energy. That quantity, divided by c², turned out to equal exactly the normal mass of the two particles that had just been destroyed. In other words, the experiment showed that ordinary matter possessing normal mass (here the electron and the positron, which can be thought of as “nano-pebbles” annihilating each other) really could suddenly vanish and cease to exist, so long as it was replaced at the same instant by a burst of radiant energy carrying exactly the same amount of anomalous mass. And so, twenty-five years later, Einstein’s risky leap, built entirely on analogy and grounded in aesthetics, finally got its experimental proof.

We find it illuminating, as Banesh Hoffmann does, that the dramatic conclusion Einstein reached in 1907 — that mass always contains energy — was only the flip side of the discovery he had made in 1905, that energy always contains mass. It is as if, having written the formula down, he first read it in only one direction (“m = E/c²,” read as: “an inconceivably tiny quantity of mass is possessed by a standard amount of energy”), and then, two years later, finally saw that it could be read in the other direction as well (“E = mc²,” read as: “an inconceivably vast quantity of energy lies hidden within a standard amount of mass”). Which shows that even the boldest thinkers sometimes need a great deal of time, intense concentration and an inner conflict driven by analogy before they can achieve what, in hindsight, turns out to be the most elementary reversal of a concept.

Cover image: Douglas Hofstadter. Source: Indiana University