Books: Gödel, Escher, Bach: An Eternal Golden Braid (Douglas Hofstader)

By Serdar Yegulalp on 2011-02-14 15:48:40 No comments

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Brain, n. That with which we think we think.

I first heard that joke when I was, I believe, ten years old. I first read Douglas Hofstader’s Gödel, Escher Bach: An Eternal Golden Braid when I was about ten years old, too—and while I understood precious little of the book at the time, I definitely laughed at that joke. I was closer to the spirit of the book than I realized.

Nearly thirty years have passed. Since then I have read GEB cover-to-cover no less than five or maybe six times, each reading about five years apart. Very little, if anything, has been published since that approaches the creativity, the insight or the sheer joy of intellectual adventure radiated by this book. A professor of a friend of mine gave all his departing students a photocopied list of reading recommendations; GEB was at the top of the list in the category “SUPER INCREDIBLY MIND-BLOWING BOOKS”. It was #1 in a category of one.

“This is a book about how we think,” the professor’s blurb for GEB read, and that is as succinct a summary as I can devise on my own as well. It is an attempt to explain how thought, or maybe better to say sentience, is no one thing but a whole aggregate of things that interrelate. Any one of them alone is not thinking; but in the same way, all of them together do not constitute thinking either. It is the dance they execute when they are together that is thinking, and even that, too, falls apart when you look at it too closely. The serpent eats its tail, and thus the circle of the earth is borne.

No conventional discussion would do for a subject this sprawling. GEB is no conventional discussion. The book dances through a whole panopoly of loosely- and tightly-woven topics—Zen Buddhism, AI programming, recursive behaviors, pattern recognition, mathematical themas. Through all of them is asked, in any number of forms, the same question: What exactly is the “mind”? What is this thing that calls itself “I”, and how does it work? Hofstader felt the answer lurked near the concept he eventually called the “strange loop”, a thing which feeds back into itself, a self-contained paradox. He chased strange loops in various incarnations throughout his whole career, but GEB was his first great Hunting of that particular Snark. The analogy to Lewis Carroll is entirely deliberate, since the book’s subtitle is “A metaphorical fugue on minds and machines in the spirit of Lewis Carroll”.

The book opens with a meditation on its three titular figures. Bach, the man who more than almost anyone else was responsible for Western classical music (and maybe Western music, period) as we know it; Escher, the visual artist whose works revolved around optical illusions and paradox; and Gödel, the mathematician who examined how math could be used to examine the behavior of math itself. The works left by all three men parallel each other in the ways they examine how patterns can be created and recognized—and one concept the book revisits often is the idea that the ability to recognize patterns, however blatant or rarefied, is a hallmark of intelligence.

Good, but what constitutes a pattern in the first place? Hofstader dives into that problem in the first chapter, where he posits a simple math game (the “MU”-game; a reference to Zen Buddhism that is evoked more than once), where the player has to derive one pattern from another. We eventually learn it’s not possible to do this by the rules laid down, but why it’s not possible is a far more involved matter. From there Hofstader branches off into how patterns are evoked and recognized, how decisions about meaning are made, how things are said to be distinct from one another, how things can be assigned levels of interpretation or consistency, and so on. “How do we know?” gives rise in turn to “How do we know we know?”, and from there “How do we know that we know that we know?” Once the snake starts swallowing, there’s no stopping it.

What’s wonderful—in the best sense of the term: full of wonder—is how Hofstader presents his material. The even-numbered chapters are the meat of the book, where he explains his concepts with the vigor and humor of scientific popularizers like Asimov or Sagan. The odd-numbered chapters are the salad and soup and dessert: they’re dialogues between a number of characters gleaned from myth and legend—namely, Achilles and the Tortoise, who find themselves in one situation after another that are used to embody or exemplify the concepts described in the preceding and following chapters. Hofstader’s taste for spirited fantasy comes through best here: at one point when obliquely illustrating the concept of the “stack” in programming, his heroes find themselves walking down the spiral groove of a record in its jacket. It’s tempting to read the book as a kind of novel—an even-brainier cousin to Umberto Eco or Georges Perec, perhaps, where the “factual” parts are no less imaginative than the “fictional” ones.

GEB has to be approached on its own terms to get the best results, since every piece of it supports some other piece, if only indirectly. You won’t get much of anywhere just taking what you like and dumping the rest. As a kid, I remembered getting so frustrated with the odd-numbered chapters that I just stuck with the dialogues, and discovered later on that I had picked up at least two-thirds of what the book had been talking about anyway. Later on, as an adult, I rediscovered the book and smashed through the whole thing, even- and odd-numbered chapters alike. I bought copies for friends as gifts. When I ran into a slightly battered version of the original edition for $1 at a local Goodwill store, I bought it and send it to a friend who’d professed an interest in AI. He was stumped by GEB, but in a good way: he was made aware of how the whole concept of what is thinking or awareness in the first place is a far knottier predicate to AI than it seemed.

The book was written during the 1970s, and reflects that in more than a few ways, but not badly. For one, its original manuscript was composed on a primitive computer typesetting system that could be thought of as a precursor to today’s desktop publishing software. Some of that was out of necessity, since Hofstader felt that was the most direct way to compose the invented numerical systems or synthetic computer languages used as teaching examples. But the sheer hassle that Hofstader endured (described in his introduction to the new edition of the book) is a testament to his patience with what today we would consider intolerably primitive technology. What little else has dated in the book is mostly situational, in much the same way that 2001 is most dated by its Pan Am and Bell Tel logos. Hofstader even apologizes retroactively, in the book’s 20th-anniversary edition, for the reflexive use of male pronouns in gender-indeterminate situations.

The most conspicuously dated part of the book, for those with a high degree of computer literacy, is the role of LISP—the computer language devised in part for furthering AI research. Entire machine architectures dedicated to running LISP were coming to the fore shortly after the book’s publication. They were legendary for having powerful development environments that could put to shame other systems a decade or more down the road. But they were costly, and they lost out to the cheaper, more commodity UNIX-driven C/C++ systems that were proliferating in both academic and professional settings. Today you can’t find a Lisp-M anywhere except in a museum, and the language itself has been marginalized as a curiosity.

One thing which has evolved, but which the book still reflects on quite intelligently, is the very role of AI in human life. We have, I think, grown a little more temperate about our expectations for AI. Most of our discussions about AI appear to have drifted away from the concept of making a machine as smart as a man, and more towards what I could call the Google approach: using machines to aggregate human intelligence and making it into a consumable commodity. Instead of trying to build smarts from scratch, we take what we already have and systematize it. Let the humans do what the humans do best, and let the machines do what the machines do best.

But at the same time, our concepts about “what the machines do best” have evolved, too. We no longer flinch as much at the concept of a computer beating a human in chess if only because we have come to understand how a game like chess can be reduced to set of mathematical problems. Computing power and storage have exploded to the point where a finitely-bounded problem like a chess game can be “solved”. (Less so with go, for which no good computer player has yet emerged and which contains a problem space many orders of magnitude beyond chess.) But none of this dilutes the excitement we feel when two human beings sit down and match wits with each other over a chessboard. Few people, except for the most die-hard of chess fans and AI buffs, are excited about two chess programs duking it out. The fact that competing human players are not computers makes the game all the more exciting; that they are, if only in a very specific way, seemingly transcending human limitations through the game is what fascinates us. The same goes for teaching a computer to win at Jeopardy!, which sounds more to me like the folks at IBM have done a good job of creating a reverse search engine and less like they have created anything truly smart. Teaching computers to win at games is trivial; teaching a computer to invent a game, or to learn how to play any game—that would be remarkable, and frightening.

I suspect it is in the nature of sentient beings to question, and worry about, the nature and value of our sentience. If you want a definition, then, there it is: a sentient being, then, is one that asks “What am I?”, and produces books like Gödel, Escher, Bach in an attempt to answer that question. But it takes another sentient being to understand that this question has been asked in the first place—and yet another to verify the relationship between those two, and so on, something Hofstader himself is painfully aware of. The snake has swallowed its tail once again. Hofstader’s insights in that sense are somewhat Buddhist: nothing exists by itself but instead as part of a matrix of relationships between things which are themselves only aggregates. To even talk about such a thing is to open the lid of a box with no bottom.

What makes the book such a delight, and so endlessly absorbing through any number of re-readings, is how Hofstader asks and answers all the questions engendered by his premise in a way that seems as effortless as play. We may never get answers, but books like this demonstrate how the very asking of the questions is what is most crucial. Questions of any size are almost never asked in a fashion this inventive, this amusing and this perennially rediscoverable.

Tags: Buddhism Douglas Hofstader Lewis Carroll Zen artificial intelligence books computers mathematics nonfiction psychology review science