Review of Gödel, Escher, Bach by Tony Longshanks LeTigre

Review of Douglas Hofstadter’s Gödel, Escher, Bach: An Eternal Golden Braid

by Tony Longshanks LeTigre

When I lived in San Francisco, there was a hackerspace in the Mission district that became my entire world for two wild years. It was like being beamed aboard an experimental anarchist spacecraft full of creative technology & the coolest, weirdest people imaginable, forever immersed in fascinating projects & conversations. All at once, I realized that hackers were the people I’d been searching & subconsciously waiting for my whole life. Everything was free in both senses. There was a laser cutter, a kitchen, a darkroom for photography, a woodshop; there were 3D printers, fabrics & sewing materials, tables & bins & shelves stacked with gadgets & computer parts & soldering materials; there were two classrooms, & best of all in my view, a beautiful little library where I spent many happy hours. I got to know hacker history & culture & what hackers like to read. I read The Jargon File & delved into the dazzling vortex of The Illuminatus! Trilogy. And I heard many raves for a book called Gödel, Escher, Bach.

By the time I finally got around to reading GEB (as we henceforth abbreviate it), I had left San Francisco & life had changed; but Douglas Hofstadter’s “metaphorical fugue on minds & machines” will always remind me of that hackerspace in the Mission district where I spent some unforgettable days.

When I did finally tackle GEB, I became enamored of it at once. It’s a nearly-800-page, uniquely designed, profound meditation on human intelligence, self-awareness, neurology, & the effort to create machine minds (computer, robot, etc) possessed of similar intelligence. It was written when cybernetics, to use the old term, was morphing into the field of AI (Artificial Intelligence) as we know it today, & the culture at large was deeply stirred by questions such as: What exactly distinguishes human intelligence from that of other animals or programmable machines? Can that elusive quality of intelligence & creativity be mechanized? Can we program a computer to learn, to create original work, to be as smart as—or smarter than—ourselves? And should we?


Some were excited, others were disturbed, by such questions. In exploring them, Hofstadter reveals how little we understand the workings of our own brains, particularly at the fundamental level of neurology. He steers a cautious course between the enthusiasts & the adversaries of AI; between pioneer technologists already working to create machine intelligence & reactionary technophobes who oppose the endeavor; those who say it can’t be done, that intelligence is unique to the human brain; that it shouldn’t be done, or that it might be dangerous; as well as those overoptimistic others who see it as a simpler & more achievable task than it really is.


This book took me deeper into the mathematical & computer scientific conundrums I was already investigating, with a warmer & more personal tone than elsewhere. The book evinces a playful, philosophical exuberance I’ve come to regard as the quintessential “hacker” quality. (Hackers as I knew them, on their own turf & by their own definition: not malevolent media miscaricatures, but autonomous wizards & inventors of genius.) Hofstadter was a math / physics / logic grad student & tenderfoot teacher, exploring the world & not yet sure of his path, when he entered the consciousness of the reading public with GEB back in 1979. It was a propitious introduction, immediately establishing its author as an international bestseller; all the more remarkable in that GEB is a highly intellectual work replete with abstruse concepts aimed at a general audience: something that isn’t supposed to work, but does, or at least can.

A many-voiced Fugue & a hole in the Fortress of Logic

Since the core meaning or message of the book has been oft misconstrued, much to Hofstadter’s chagrin over the years (“I sometimes feel as if I had shouted a deeply cherished message out into an empty chasm & nobody heard me”), let us be sure we have the right idea starting off. Here in the author’s own slightly abbreviated words, from his preface to the 20th anniversary edition (from 1999, the version that I read), is the book’s intention:

In a word, GEB is a very personal attempt to say how it is that animate beings can come out of inanimate matter. [It] approaches these questions by slowly building up an analogy that likens inanimate molecules to meaningless symbols, & further likens selves (or “I’s”—whatever it is that distinguishes animate from inanimate matter) to special, vortex-like & meaningful patterns that arise only in particular types of systems of meaningless symbols. It is these strange, twisty patterns that the book spends so much time on, because they are quite filled with mystery. I call such patterns “strange loops,” although I also use the phrase “tangled hierarchies” to describe basically the same idea. GEB was inspired by my long-held conviction that the “strange loop” notion holds the key to unraveling the mystery that we call “being” or “consciousness.”


Among the many artists, engineers & innovators past & present to appear in this opus, three stand out & lend their names to the book’s title. Each in their respective fields & novel ways experimented with form, toyed with paradox & left riddles for posterity: J. S. Bach, the classical composer, whose musical offerings inspired the book’s design on multiple scales; M. C. Escher, the graphic artist whose mathematics-related prints & drawings dwell upon the strange loops & conceptual tangles that Hofstadter finds so compelling; & Kurt Gödel, the Austrian mathematician whose 1931 paper Über formal unentscheidbare Sätze der “Principia Mathematica” und verwandter Systeme knocked an ineluctable hole in the rigorous fortress of logic that Georg Cantor, Bertrand Russell, et al. had built to keep out the chaos & contradiction of the real world.


Apropos of the book’s titular trio the author tells us:


Things are going on on many levels in [J. S. Bach’s] Musical Offering. There are tricks with notes & letters; there are ingenious variations on the King’s Theme; there are original kinds of canons; there are extraordinarily complex fugues; there is beauty & extreme depth of emotion; even an exultation in the many-leveledness of the work comes through. The Musical Offering is a fugue of fugues, a Tangled Hierarchy like those of Escher & Gödel, an intellectual construction which reminds me, in ways I cannot express, of the beautiful many-voiced fugue of the human mind. And that is why in my book the three strands of Gödel, Escher, & Bach are woven into an Eternal Golden Braid.


But it isn’t just three biographies woven together; GEB is more ambitious & more amorphous than that. We enter a web full of puzzlement & paradox, recursions & level-crossing feedback circuits, symbolic, canons & fugues, “quined” phrased & Zen koans, ribosomes & Möbius strips.The book’s uniqueness is manifest in both both form & content, which are equally fluid—indeed, form & content become the same thing in some parts of this unique book. This happens when Hofstadter or his characters defines a term or introduces an idea, & the text or dialogue itself goes wonky (repeats itself, becomes disjointed or nonsensical, starts to run backward or talk about itself) in imitation of the idea being discussed.


Eerie Intelligence & Contagious Enthusiasm

A nonfiction book that “breaks the fourth wall”—characters commenting on the dialogue in which they appear, or expressing awareness of themselves as figments of an author’s imagination—is unusual, to say the least; but categories like “fiction” & “nonfiction” dissolve in the metanarrative swirl of GEB. Each chapter of lectural discourse is followed by a quaint dialogue featuring Lewis Carroll-esque figures, chiefly Achilles & the Tortoise, who have all sorts of surreal adventures in a secondary universe that echoes the main discussion in a phantasmagoric & whimsical way. Thus the book is actually two texts, a nonfiction narrative & a fictional metanarrative, woven together in counterpoint. These interpolated dialogues seem lighthearted, even jejune at times, but are carefully crafted as meaningful analogues to the ideas discussed concurrently in the main chapters. They are also modeled upon compositions by Bach & have Bach-like titles as well—“Canon by Intervallic Augmentation,” “Sonata for Unaccompanied Achilles,” “Prelude… Ant Fugue,” “Little Harmonic Labyrinth,” etc.—so that in a way they represent pieces of music “translated” into creative writing. Music is a source of great fascination for Hofstadter; he sees it as a mysterious language of the emotions whose meaning defies analysis, & spends quite a bit of time discussing it among the larger & related mysteries.


GEB is not only a book about intelligence; it possesses an eerie quality of quasi-intelligence itself, as if the book were a sentient entity that in some way reads you even as you read it. The only other works in my reading experience so far that have had this “eerie intelligence” quality are the aforementioned Illuminatus! Trilogy & Joyce’s Finnegans Wake.


In the case of GEB, this effect is partly due to the way Hofstadter engages the reader to an interactive relationship with the text, not just passively absorbing but participating, working out problems. Questions, riddles are posed throughout; problems & exercises offered; games & illustrations designed to bring the concepts alive. Instead of merely decanting knowledge & explaining esoteric concepts from on high, he discusses them with us as equals, breathing life into the cold corridors of logic, sharing his contagious enthusiasm for subjects that might normally appear distant & daunting. It’s like a series of interactive lectures by an excursive but inspired teacher who doesn’t confine himself to one subject, or even one broad area of interest like “science,” but draws freely from diverse wells of knowledge including philosophy, literature, classical & modern music, spirituality, cellular biology, pure & applied mathematics, logic & formal systems, fine art, computer science & information systems, linguistics, entymology, translation, cryptography, & more.


This generous, sharing, humanistic approach to knowledge & learning, the belief that there should be no walls of separation in the realm of ideas, that information & technology should be free & intellectual resources held in common, is endemic to hacker culture as well, with the open-source & free software movements, which hold that source code for computer programs & operating systems should be freely available to all users, & rather than being proprietary & secretive.

Isomorphisms & DNA


One section deals with genomics & the operations of DNA at the cellular level, depicting the complex procedure by which DNA is “translated” into messenger RNA, how the genetic code is used in protein synthesis, etc—this being the genesis of living beings like ourselves. Hofstadter invents a neat way for readers to grasp the way things work in this molecular microverse of nucleotides, amino acids, ribosomes, etc: a pen-&-paper exercise that one person can do alone. Here & in other spots in GEB, it’s easy to get the feeling that we, humans, are not so different from computers after all, that maybe we are in fact machines of a sort ourselves: A viewpoint opposite that of the person who sees “machine” & “human” as rigidly separate categories & sees AI as an abomination for trying to merge them.

Regarding the origin of DNA & how this incredibly intricate microscopic process ever got started in a seemingly random universe, Hofstadter offers no speculation, merely acknowledging it as “ truly a baffling thing.” Thus he stops short of wading into the “evolution vs. intelligent design” debate which in my view rests on a false dichotomy anyway, between two things that are not necessarily mutually exclusive. (He does call his book religious, though, & ends the preface with a Latin inscription that translates roughly, “Rest in peace, as a faithful presentation of my worship.”) We get a sense of how much of the DNA code has been unraveled so far by science, & how far we have still to go. There are undoubtedly higher levels of meaning coded into a DNA strand, Hofstadter tells us, that still await our discovery. Will we ever completely solve the mystery, allowing us theoretically to “read” a strand of DNA & from it predict exactly the characteristics of a human being? Does DNA have other things to tell us relating to the mystery of intelligence? Might it possibly be the missing link that could allow us to answer the deep questions posed by GEB, the key that would empower us to imbue machines (& who knows what else) with creative intelligence?


Isomorphisms play a large role in this book. An isomorphism is a detailed correspondence between two different systems that are mapped together to show point-to-point agreement between their constituent elements. Meaning arises when such a match is made; thus are isomorphisms related to intelligence. Isomorphism is also related to analogy, the use of analogical thinking being another feature of human intelligence as we understand it so far. Isomorphisms & analogies permeate the text, from its overall structure as a “metaphorical fugue,” to the comparison of an ant colony “superorganism” with a human brain (in which individual ants represent neurons), to the “self-engulfing televisions” that function as a visual analogy for the phenomenon of infinite recursion in computer programming.


The most dramatic isomorphism of all, represented by what the author calls the “Central Dogmap” of the book, links not just two, but three different systems integral to GEB. It is presented as an original discovery of interest to science at many levels as well as to the general public. Since Hofstadter builds up to its slowly & only reveals it more than 500 pages in, I won’t spoil the surprise for new readers. Suffice to say it seems a remarkable synchronicity pertaining to the book’s centermost themes, but that its implications are still (in my view) somewhat unclear. When the reader gets to this point it may help to know that GEB‘s simpler working title was Gödel’s Theorem & the Human Brain.


Hofstadter often seems prescient, as in this passage wherein he describes Google Earth several decades before it existed:

One can imagine an atlas with arbitrary amounts of detail, going down to single blocks, houses, rooms, etc. It is like looking through a telescope with lenses of different power; each lens has its own uses. It is important that one can make use of all the different scales; often detail is irrelevant & even distracting. The nested structure of a frame gives you a way of ‘zooming in’ & looking at small details from as close up as you wish: you just zoom in on the proper subframe, & then one of its subframes, etc., until you have the desired amount of detail.


Dr. Techie & Mr. Luddite?

In the preface, Hofstadter states that despite the book’s critical & commercial success, both in the US & abroad, he still feels as though the essential message of the book has gone unheard, or been heard wrongly. Some of the neglected meaning, misinterpretation, confusion, etc. must be blamd on inattentive or indolent readers; some of it ban be attributed to the text itself, its sheer size & scope, tangential style & myriad overlapping analogies, its sophisticated jargon & subject matters; & also a fair amount of ambiguity & apparent paradox that I sense, consciously or otherwise, at the book’s heart, stemming presumably from ambivalence in the mind of its author.

Toward Zen, for example. He claims in the preface to find Zen philosophy (or antiphilosophy) “not only confusing & silly, but on a very deep level utterly inimical to my core beliefs.” Yet Zen is one strand woven prominently into the rich tapestry of GEB, featured in both main text & dialogues, & Hofstadter obviously finds it sufficiently interesting to merit study in some depth, as his knowledge of Zen koans shows. Perhaps his hacker-mathematician mind simply can’t resist the allure of riddles, even riddles that are inherently (or intentionally) unsolvable. There’s a delightful passage that describes a computer program designed by one of Hofstadter’s colleagues to generate original creative writing with a Zen Buddhist flavor, with most amusing results. The example quoted made me ROTFL.


Another most amusing passage is the author’s takedown of one J. R. Lucas, who had served up a haughty & ignorant denial of the possibility of machine intelligence, based on the arrogant assumption of human uniqueness & supremacy (in all the universe, apparently).

Most puzzling is the author’s relation to AI, computers, & technology in general. Any reader of GEB could certainly come away with the impression that he’s a high-tech guy with a strong interest in computer programming who is personally involved in contemporary AI research. Yet Hofstadter asserts in the preface that he’s “the furthest thing in the world from a technophile,” & he’s been described as “almost a Luddite, actually” by another GEB fans. (Maybe he would object to my characterization of him as a hacker, a word he never uses to self-describe.) I definitely felt he was arguing very much in favor of AI as I first read through the book, yet others have interpreted his stance as anti-AI. This is due in part to the section where Hofstadter offers his own intuitive answers  to a series of AI-related questions that comes off rather discouraging  & pessimistic about the future. (One of his predictions, as he gamely admits in the preface, concerning the ability of computer programs to beat world champions at chess, was proved wrong in 1997 when the IBM supercomputer Deep Blue defeated Garry Kasparov in a six-game match.) Happily, he clarifies his stance on AI in the new edition intro, stating that he is not opposed to AI, only to those who underestimate & thereby disrespect the miraculous complexity of their own intelligence & belittle the magnitude of our attempt to replicate it.

It’s not a review without some criticism…

GEB could be more compact. Some of its discussions could be shortened, where they err on the side of “too thorough” or “borderline redundant.” Not all readers will share the author’s zest for abstract subjects or exert the effort to do the exercises & solve the problems he sets them. I confess I skimmed the section on formal logic that gets heavily involved with strings of symbols in the PQ & TNT systems. Some have found the book overly tangential & have failed to discern the connection of the myriad “items of related interest” to its main theme. And as already mentioned, some have found the main theme itself elusive or incoherent.

As fascinating as I find art like that of Magritte & Escher, & paradoxes like those of Xeno & Epimenides, I don’t fully comprehend their connection to sentient intelligence. They seem more like intriguing anomalies than germane components of the book’s stated thesis. Perhaps I am unable to grasp the analogies offered at their most abstract level. In some ways the book strikes me as a giant knotted ball of curious & fascinating quandaries than a cogent, unified thesis. Reading it may feel more like wandering in a gargantuan labyrinth with no apparent terminus than a well-defined journey to a clearly established destination.

The book’s experimental form & ebullient tone might annoy hoity-toity types who prefer a more buttoned-up, formal, “objective” style, but why should we care what such prigs think?


Having stated the foregoing objections, let me now add that none of them are serious. I was not bothered by the length of the book or its digressiveness, for its digressions were invariably fascinating. I read all 800 pages of it in a rapt state & scarcely noticed the world outside while under its spell.


A more serious objection is voiced by Alan Hodges on p. 679 of his splendid biography of one of the founders of computer science Alan Turing: The Enigma (to which Hofstadter contributed an introduction):


The appearance of [GEB] in 1979 … put my work in a Tangled Loop, for central to [Hofstadter’s] book is its exploration of a topic I have brushed aside—the significance of Gödel incompleteness & Turing undecidability for the concept of Mind. I do not myself believe that these results, concerning as they do infinite, static, undisturbed logical systems, have any direct consequence for our finite, dynamic, interacting brains. Far more significant, in my view, is the limitation of human intelligence by virtue of its social embodiment—& this is a problem relegated to a marginal place in Hofstadter’s work as in so many other accounts, though I have placed it at the centre of my own. … Why, as Alan Turing might have put it, should machine intelligence be any less constrained by worldly reality? Indeed, there seems every reason to suppose that the clever machine will accommodate itself to the crazy demands of the political system in which it is embodied. In the academic sanctuary it is too easy to concentrate on infinitely more theoretical considerations.


An Eternal Golden Book

Now approaching its 40th birthday, GEB is a book revered by many, as attested by the rhapsodic reactions I’ve gotten just from carrying it around with me in public. It seems tantamount to a sacred text for the secular humanist set—philosophers, hackers, & all manner of bright inventive young-souled things. It belongs in a select class with other gems of the 1970s that sought to reconcile the seeming antipodes of science/technology & nature/spirituality, such as Zen & the Art of Motorcycle Maintenance (Gary Pirsig) & The Tao of Physics (Fritjof Capra).

If another edition comes out to mark the new anniversary, one wonders how much has changed in the interim with respect to AI & related endeavors Has progress been stymied & science suspended in the wake of climate change & those who would deny it? It seems to this author that the optimistic momentum re: AI, like that of space exploration, has evaporated over the past few decades, though I will admit I haven’t followed the subject closely. Having just read GEB for the first time, I feel it to be fresh & relevant, filled with questions that remain key & mostl open. Woe to any future society in which that is no longer the case.

You will undoubtedly feel smarter for having read it, & have many new things to think about. You will become familiar with terms & concepts like heuristics, algorithms, recursion, aperiodic crystals, what a “stack” is in programming terms, how to “quine” a phrase, analog vs. digital methods, etc. if you weren’t already. Anyone intelligent enough to be interested in intelligence should consider it required reading. You’ll wish it was 800 pages longer.