Godel, Escher, Bach: A strange, Strange Loop of a book

Douglas Hofstadter’s Pullitzer-winning 1979 novel-tangled-up-in-a-science-book is a strange, illuminating and utterly brilliant work of art which also happens to be extremely difficult to read. (Is that a paradox?)

Godel, Escher, Bach: An Eternal Golden Braid is  sprawling, ambitious, and very atypical as far as books go. It tells so many stories, argues in so many different directions, and touches upon such monumental topics in such an inventive way that it’s hard not to simply be impressed with the author’s creativity and ability to weave it all together into a (semi-)coherent yarn. Clocking in at over 740 pages (about one third of it being fairly dense “mathy-computery” talk), it takes some perseverance to get through.

The book is curious in its form, in that each chapter begins with a Dialogue, usually between two characters—the Tortoise and Achilles (who Hofstadter has borrowed from Lewis Carroll). The intention of the Dialogues is (in addition to breaking up the “computery” language chapters) to be able to introduce the content or subject matter of the chapters in two voices. We are always introduced to a concept or idea through the lighthearted conversations of Tortoise, Achilles, and some of their friends, before diving in more deeply with more technical, traditional scientific language. I found myself reading briskly through the dense sections (probably skimming and scanning more than I’d like to admit) to get to the next Dialogue more quickly.

On its surface, this book weaves the mathematics and logic of Kurt Godel with the artwork of MC Escher and the music of JS Bach, explaining the implications of Godel’s Theorem and the Strange Loops which result. Through the course of explaining the work of Godel, we are introduced to Escher, a Dutch artist whose paradoxical prints tease the mind, forcing us to question what we mean by reality. Hofstadter shows that many of Escher’s works visually display the properties of Godel’s theorems, and he incorporates a number of Escher prints directly in his narrative, at one point even having his characters travel into Convex and Concave to steal the lamp from the two lizard guards:

MC Escher - Convex and Concave

Tortoise and Achilles pop into this Escher print to start one of their adventures.


But deeper, beneath and beyond the triad of historical figures, Hofstadter covers much ground in his sprawling fictional non-fiction hybrid, explaining the language of machines (computer programs), the language of life (ATCG base pairs) and DNA, and the use and potential for Artificial Intelligence to play chess, appear human, and ultimately to ‘think.’  But what Hofstadter eventually comes back to, hundreds of pages later, is the importance of the Strange Loop. He writes in the final chapter, in the section Strange Loops as the Crux of Consciouness (p. 709):

“My belief is that the explanations of ’emergent’ phenomena in our brains—for instance, ideas, hopes, images, analogies, and finally consciousness and free will—are based on a kind of Strange Loop, an interaction between levels in which the top level reaches back down towards the bottom level and influences it, while at the same time being itself determined by the bottom level.”

But what exactly is a Strange Loop? As one example, Hofstadter uses the example of ribosomes and proteins, which are encoded in DNA, again from the final chapter (p. 707):

“Godel’s Theorem doesn’t ban our reproducing our own level of intelligence via programs any more than it bans reproducing our own level of intelligence via transmission of hereditary information in DNA, followed by education. Indeed, we have seen, in Chapter XVI, how a remarkable Godelian mechanism—the Strange Loop of proteins and DNA—is precisely what allows transmission of intelligence!”

That is, we need DNA to store the information which codes for proteins, and we need ribosomes to help make proteins, but we also need to have some proteins present for ribosomes to be made (p. 528):

“How do you get around the vicious circle? Which comes first—the ribosome or the protein? Which makes which? Of course there is no answer because one always traces things back to previous members of the same class—just as with the chicken-and-the-egg question—until everything vanishes over the horizon of time.” 

An example of a Strange Loop is displayed visually in MC Escher’s Drawing Hands:

Drawing Hands

Which one started drawing first? Similar to the chicken and the egg, it’s difficult to discern.

It’s incredibly interesting how Hofstadter is able to have his characters interact within Escher’s works of art, in the grooves of vinyl records, and on rides at Coney Island, all while illustrating, on some level, principles of mathematics, art, music, reality, logic, or Artificial Intelligence, just to name a few.

With all that it touches upon, a central theme of sorts can be described. If this book were said to have one purpose, it would be to tackle the issue of Godel’s Incompleteness Theorem, for which the philosopher and logician was most well-known. My rudimentary understanding of Godel’s Theorem is that it implies we can never truly prove everything within a system, for we are always dependent upon some higher level of rules which structures our reasoning and logic within that system. Therefore, we will always be left with some statements which are unprovable within a particular system.

Near the end of the book, Godel explains how Escher has “given a pictorial parable for Godel’s Incompleteness Theorem” in the mind-bending Print Gallery, which Escher considered to be one of his best works.

Print Gallery

Hofstadter calls this Escher work a “pictorial parable for Godel’s Incompleteness Theorem.” Why? Look to the center of the painting, is there any way logical way to complete it?


Could you use this book in a classroom?

I don’t think Godel, Escher, Bach is for everybody, but at the same time, I think that everybody could get something from it. (Again, a paradox? I don’t know anymore.) What I mean is, while the core of the book will likely only appeal to the computery/mathy/techie types, an art teacher could get countless ideas from it, a music teacher would make connections to the use of Bach’s canons and fugues, while a high school English teacher could have an excellent few classes discussing some of the Dialogues between the Tortoise and Achilles. Interestingly enough, according to Wikipedia, “For Summer 2007, the Massachusetts Institute of Technology created an online course for high school students[6] built around the book.” So apparently, yes, it can and has been used in the classroom.

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