Kurt, Maurits and Johann

Tackling Douglas Hofstadter’s “Gödel, Escher, Bach” in earnest

This book comprises a (probably unique) adventure through phenomena of self-reference, formal systems, and their limits in mathematics, art and music, in the pursuit of conveying the author’s point of view of how unique human consciousness arises from fundamental biological processes.

That’s a mouthful! And is all in likeliness less than a complete summary, due to the sheer scope of this book. It dates from 1979, and has made such an impact on the appreciation of so many fields that it has its own Wikipedia page

Indeed, this is how the Wikipedia page describes the work:

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“…By exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Escher, and composer Johann Sebastian Bach, the book expounds concepts fundamental to mathematics, symmetry, and intelligence. Through short stories, illustrations, and analysis, the book discusses how systems can acquire meaningful context despite being made of”meaningless” elements. It also discusses self-reference and formal rules, isomorphism, what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of “meaning” itself.

In response to confusion over the book’s theme, Hofstadter emphasized that Gödel, Escher, Bach is not about the relationships of mathematics, art, and music, but rather about how cognition emerges from hidden neurological mechanisms. One point in the book presents an analogy about how individual neurons in the brain coordinate to create a unified sense of a coherent mind by comparing it to the social organization displayed in a colony of ants.

Gödel, Escher, Bach won the Pulitzer Prize for General Nonfiction and the National Book Award for Science Hardcover. …”

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Maybe an expansive, interdisciplinary work such as this may have more than one theme. I was first attracted to this book as a college student, hoping to read a well-researched viewpoint on the relationships of mathematics, art and music. The list of chapters promised substantial wordplay and showed a love for the music of J S Bach, even before beginning to read. And I had always warmed to the impossible pseudo-reality of Escher’s art.

But in that first attempt at the book, and I think one other I started since, I became bogged down in the descriptions of formal systems and number theory and found it difficult to relate Gödel’s incompleteness theorem to the other strands of thought in the book in anything other than a superficial manner.

This holiday season has given me the opportunity to tackle the work in earnest, once more. I have the soul of a musician, not a mathematician, and I don’t think I’m fully grasping the author’s explanations toward his vision of how the limits of mathematical theorem induction relate to how human cognition ‘escapes’ the bounds of the rule-based ‘formal system’ of human neuronal biology. Nonetheless, this is the most I’ve ever grasped of this book, aided in no small part by the appreciation I’ve developed for the music of J S Bach in the years since.

Perhaps the most important takeaway - and one of the main reasons I picked up this volume again - is the author’s view of whether “Artificial Intelligence” can emerge from a rules-based, but sufficiently complex system. That mechanical system may not necessarily be the neurons of a carbon-based life form. Although this book substantially predates many developments in computing and statistical learning (especially the emergence of GPTs and LLMs), it seems to elaborate many worthwhile principles for understanding modern developments. (Given the length of time that has passed, I wonder what the author’s opinion might be of potential outcomes and limits of the current ‘AI’ wave?)

It is indeed an enormous read whose key concepts could likely be conveyed in much less text. I wonder, though, whether it would make the same impact on the reader’s mind and memory without the vivid metaphors and imagery (and the almost exhaustingly clever wordplay). If you’re not a fan of understanding more of the underpinnings of mathematical systems, of canons, fugues and hidden patterns in music, or of visual deception in art, then you would likely not find enough entertainment in this book to make it to the core of Hofstadter’s message.

Progress at the time of writing

Approximately 480 of 720 pages read. I’ll update this blog post with further progress and comments - hopefully I will finish in the next couple of weeks.

2025-01-07: another several chapters; approximately 600 pages completed