Reviews

Gödel, Escher, Bach: an Eternal Golden Braid (1979)

Douglas R. Hofstadter (writer).

Read in 2020.

I read the 20th-anniversary edition.

Most centrally, metamathematical logic, especially a series of pedagogical and interdisciplinary analogies illustrating Kurt Gödel’s incompleteness theorems and applying them speculatively to other fields, chief among these being phonograph record players (equivalently, cassette tapes), genetic material and epigenesis in microbiology, computer programming, metacognition in human psychology, and the apparent intersection of programming and psychology in cybernetics and artificial intelligence research.

The book is about 300,000 words long and covers other topics, as well as branches of its main topics, in some detail, orbiting its central idea. The Author—a mere fictional character named Douglas Hofstadter—puts it this way on the last page:

After describing the Endlessly Rising Canon, I’d go on to describe formal systems and recursion, getting in some comments about figures and grounds, too. Then we’d come to self-reference and self-replication, and wind up with hierarchical systems and the Crab’s Theme.

The music of J. S. Bach and the pictures of M. C. Escher recur throughout, mined for further analogies, but were absent from an unpublished early version. Lewis Carroll’s “What the Tortoise Said to Achilles” (1895) is quoted in full and provides the model for similar dialogues between and around all the chapters of the book. “Jabberwocky” (1871) is quoted in no less than three languages, illustrating the problems of translation between languages as a degenerate case of isomorphism. In a preface added in 1999, Hofstadter tries again to formulate what it’s all about:

In a word, GEB is a very personal attempt to say how it is that animate beings can come out of inanimate matter. What is a self, and how can a self come out of stuff that is as selfless as a stone or a puddle? What is an “I”, and why are such things found (at least so far) only in association with, as poet Russell Edson once wonderfully phrased it, “teetering bulbs of dread and dream” — that is, only in association with certain kinds of gooey lumps encased in hard protective shells mounted atop mobile pedestals that roam the world on pairs of slightly fuzzy, jointed stilts?

Along the way: Cantor’s diagonal; arguments over introspection typified by perspectives on the nature of Ramanujan’s brilliant and sometimes flawed leaps of logic as something possibly akin to savant syndrome; holism vs. reductionism and dualism and essentialism (not mentioned as such but as “soulism”) and a related criticism in which an anti-science version of the Church-Turing thesis is jokingly ascribed to Theodore Roszak; Tesler’s theorem and its reinterpretation by Hofstadter; one brief mention of Comenius’s dream of a language in which falsehood cannot be expressed; a meta-analogy of analogies as chords where notes are concepts; a notion of conceptual “slippage”; determinism as exemplified by Dean Wooldridge’s story of a wasp’s seemingly-intelligent behaviour being reset and thus revealed as automatic in Mechanical Man: The Physical Basis of Intelligent Life (1968); Bertrand Russell and Alfred North Whitehead’s grand project, David Hilbert’s challenge for or against it, and Saccheri’s similar, earlier project of fixing what was not broken in Euclid (the fifth postulate, variable for useful non-Euclidean geometries); Goldbach’s conjecture, Fermat’s last theorem and computability; heuristics; teleology; the work of Alfred Tarski; the vague but more novel concept of a “strange loop” wherein “a formal system acquires a self”, explained using the image of a version of chess where the pieces on the board function simultaneously as pieces in the game and as settings indicating the rules of the same, so that the rules vary while something is nonetheless held “inviolate” on a higher level, without infinite regress; extraterrestrial intelligence; Bongard problems; rationality; the Epimenides paradox; Lisp and the history of computing; J. R. Lucas’s refutation of computationalism with Lovelace and Samuel’s less careful arguments against AI; etc.; etc.

Given the number of different topics, perhaps the book can be more easily distinguished by what is absent. There are many references to Frederick the Great, but no discussion of economics or power, except a mention of Watergate as it pertains to the heterarchy of the US constitution and, in the preface, a curious admission that the Yom Kippur war made “a very deep impression”, though it is completely absent from the work. Again in the preface, the author admits to a deep sexist bias. There is a one-page biography of Alan Turing, but only a suggestion that he may have committed suicide, not a word on his homosexuality or the oppressive treatment he suffered for it. This sexism is not what the preface laments.

One critic apparently honed in on references to John Cage as highly significant. Relating this story in the preface, Hofstadter refutes the interpretation, but who can blame the errant critic? Zen Buddhism features quite heavily, but is poorly characterized as zany and “one of the principal religions in Japan”; vague and inaccurate. Although Bach, Escher and Magritte all feature—while Beethoven, Shakespeare and many others are mentioned more briefly—and lend a welcome humanistic touch to the work and a sort of break from the hard-edged science, they are not discussed with “thickness” as they would be by a scholar; they are symbols and diversions, side shows to Hofstadter’s thesis, which never quite crystallizes.

The writing is idiosyncratic, sometimes to a fault. For instance, the author introduces Adriaan de Groot’s 1940s work on chunking in chess, which is perfectly cogent and relevant, but then he overextends the concept to stand in for all gestalts and scale separation, instead of introducing a more direct analogy from his own field (physics, e.g. thermodynamics), which would have been simpler and more relevant to his discussions of chaos, levels of description and hardware-software separation. Instead, he’s got an anthropomorphic anteater that thinks it’s befriended an ant hill at a high level; no wonder some critics missed his point.

Similarly, the author uses the term “epiphenomenon” in place of “emergence” (as in emergent effects) for no apparent reason. He refers to the Collatz conjecture not by its name but as “wondrousness”. He introduces “quining” as if it were an arbitrary term, mentioning that Quine is a person only much earlier (in the annotated table of contents) and much later. Some such problems may have grown over time. The Chinese room argument was only invented in 1980, so while Hofstadter frequently approaches it and could have formulated it himself, I can’t fault him for not doing so. He lampshades his own weird reluctance to give credit on page 722, apropos of Minsky.

Hofstadter’s idiosyncrasies extend to multiple discussions—outside the preface—of how he wrote the book. He talks about Jauch’s reuse of Galileo’s characters in his dialogues, and then discusses at some length the process of writing his own by spinning off of Carroll spinning off of Zeno. He inserts not one but three versions of his book within his book: Copper, Silver, Gold: an Indestructible Metallic Alloy recurs as a kind of The Grasshopper Lies Heavy; Giraffes, Elephants, Baboons: An Equatorial Grasslands Bestiary is a throwaway joke; and finally Gödel, Escher, Bach: an Eternal Golden Braid, ontologically dubious but purportedly identical to the book in which it appears. Seeking to explain why he even included Escher, he argues not from a perceived pedagogical value but from an abstruse personal conviction of what he calls “intrinsic rightness”:

It’s just that time and again, while writing about my notion of strange loops, I would catch fleeting glimpses of this or that Escher print flashing almost subliminally before my mind’s eye, and finally one day I realized that these images were so connected in my own mind with the ideas that I was writing about that for me to deprive my readers of the connection that I myself felt so strongly would be nothing less than perverse.

This is the thinking of a conspiracy theorist. In the preface, Hofstadter relates reading about diverse matters by flashlight while voluntarily homeless on a cross-country trip, discouraged by the way his life in general was going. Indeed, more broadly, the author focuses too much on coincidence, correspondence and correlation, even superficial links at the level of language in his own presentation, such as calling Charles Babbage “Ba. Ch.”. Hofstadter is not a conspiracy theorist, but it is evident that he mined microbiological sources for material in service to his thesis, as much as for impartial research. He succeeded. The result is as striking as a plausible conspiracy theory would be. He admits to its flaw: “probably little useful to molecular biologists (to whom it is likely quite obvious)”.

It is rare and delightful to see a mind organized this way come down on the side of science, in opposition to superstition, anthropocentrism and even “bio-chauvinism”. The obsessive writing technique, however ill conceived, is at least careful. Hofstadter says he was enabled by early word processing software (TV-Edit), and that is telling: Word processors would make a lot of worse writing in this style too easy. The book certainly did not need to be so long or so dilute to convey passion. The Selfish Gene (1976) was not and provides a much better answer to the question of “how it is that animate beings can come out of inanimate matter”. Thankfully, GEB’s introduction is excellent, almost a microcosm of the work.

The main stylistic mistake lies in the dialogues. The only very good dialogue is “Contracrostipunctus”. Many others are tedious, particularly as fiction. The allegories and form-content fusions are dubious, the puns are tasteless, the characters and their environments so thin and reflective that Hofstadter seems to be constantly harping on flippant metafiction as another overarching analogy for Gödel’s incompleteness. Carroll at least enjoyed the benefits of close collaboration with illustrator John Tenniel. I imagine the medium of comics would have worked better than dialogues for GEB, at least for the purposes of accessible diversion and superior opportunities for playing with form and content.

In the 1999 preface, the author rejects a proposed CD-ROM version of the book. Such a version would have been forgotten by 2019, but the book does seem to be in the wrong medium. The wealth of interconnected topics, references to sound, and Hofstadter’s tendency to pose questions and have the reader actually work on problems (“translate (if you have not already done so) Peano’s fourth postulate into TNT-notation, and then derive that string as a theorem”), suggest that the book would have benefited from hypertext annotations instead of long asides.

As for the intellectual content, pried loose from the form, the author is good enough to offer concrete predictions on the future of AI, and good enough to admit in 1999 that at least one of these, on chess, was dead wrong. It’s wrong in the clichéd anthropocentric manner of popular science fiction. AI research has continued to diverge from Hofstadter’s expectaction. I read the book when GPT3 came out and the Artificial Chemist was found to accelerate some real and physical scientific work by orders of magnitude, all without a blip of introspection or self-awareness, and arguably without connection even to the idea of “critical mass”.

Some of the more peripheral subject matter, including the chapters surveying microbiology and the state of AI research, are so outdated that you can skim them in favour of more recent sources, but don’t skip them. As of 2020, the majority of the book remains readable, mainly because of Hofstadter’s attention to detail. Most of the time, he is careful to present the material in the right order for a general intellectual audience, and there is joy in his long trains of thought meeting. After 40 years, having influenced the world view of two generations of thinkers and thus the world, the book’s central ideas seem quite toothless. Even so, this methodical sprawl still has its charm.

References here: Gödel, Escher, Bach: an Eternal Golden Braid (1979), “Understand” (1991), “Elementary, Dear Data” (1988).

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