The Triumph of Gödel, Escher, Bach 04-05-2011

I wanted to write about this about one month ago when I finally finished Gödel, Escher, Bach but it never materialized. Part of the delay can be attributed to a ridiculously busy schedule. But a significant part can also be chalked up to my ongoing struggle to consume and process all of the information in those 742 pages that I had finally finished (which assumes, of course, that one does ever really finish something like GEB and that it's not something that evolves as time passes). I started reading this masterpiece near the beginning of the Fall semester of my final year as an undergraduate and finally finished near the end of the Spring semester. It is only fitting that I spent a healthy portion of my Senior year reading Professor Douglas Hofstadter's magnum opus. GEB encompasses so much knowledge and wisdom across such a wide variety of fields that it seems to be the quintessential work to tie together a scientific education, particularly for a Computer Scientist.

A great many people have asked me, "what is it about?" So I would like to think that I have had ample practice at giving an elevator pitch about GEB. The truth is, though, that I still have trouble succinctly describing the book. I'll try now, watch:

Gödel, Escher, Bach draws on themes from the work of the three eponymous artists/thinkers to attempt to explain how cognition, thought and consciousness come into being within the mind. Its central premise posits that "emergent phenomena" in human brains arise from the interactions between different levels in the brain's representational hierarchy. It utilizes extensive word play, illustrations, reflective dialogues and other structures to describe the fundamentals behind concepts such as meaning, intelligence and logic. Along the way to building its main arguments, the book also takes time to point out parallels between key concepts in a number of fields and areas, including everything from Number Theory to Artificial Intelligence to Zen Buddhism.

See? That is the best that I can muster on the fly and it proceeds to simultaneously understate and overshoot what GEB is all about. Gödel, Escher, Bach is one of those seminal pieces of work which so thoroughly, elegantly and beautifully dissects its subject matter that the reader is left shaking his head wondering what just happened. Blindsided by insight. Enlightenment in its purest form. It's so hard to concisely, completely summarize GEB because it escapes the very premise of summarization. Choosing one concept from the book as more worthy than any other concept for inclusion in some sort of abstract ignores its massive, sprawling structure. It's a self-contained wealth of knowledge that weaves its content into a giant, wondrous web that alters the very way that the reader perceives and thinks.

I cannot hope to reduce Hofstadter's work down to a series of talking points. Nor can I dream of being able to successfully navigate the entire book to discuss it as a singular topic. Reductionism and Holism both fail. GEB is the kind of book that analogizes analogies between topics with analogies within different components of itself in order to illustrate how analogies are interpreted in the first place!

As I said, I'm still attempting to digest what I gathered from GEB and, quite frankly, a great deal of it went straight over my head. Brilliance is what it is. But I do know that it has had a palpable effect on how I view the world around me. I've always had a fondness for symmetries and recursions and complex structures in the daily mundane (as a child, I invented a game wherein I count the number of syllables of something that I am reading or hearing and map this number onto the physical structures of objects in my immediate vicinity). Hofstadter shows how they permeate and touch everything all the time, from small neurons and molecular structures and ants and musical notes and number theoretical statements up to thought processes and genetic code and colonies and musical structure and Mathematics itself.

Dialogues like the "Crab Canon" and "A Mu Offering" and "Little Harmonic Labyrinth" and "The Magnificrab, Indeed" use complex and fascinating word play and semantic structure to illustrate the mysteries that are unraveled in the adjacent chapters, mysteries such as where free will does or does not come from and how to escape never-ending chains of self-reference and self-representation to view something as a whole. Thoughts and ideas from great thinkers like Turing and Babbage and J.R. Lucas and Lewis Carroll are brought in to provide new perspectives to what Hofstadter constructs before the reader's eyes. The art of Escher is used to vividly portray self-reference in its most exotic forms, including the mind-boggling 1956 lithograph entitled "Print Gallery" wherein dozens of tangled, overlapping, interleaving layers of reality collide. The Mathematical work of Gödel provides a large layer of abstraction over the widest and most broad of topics and concepts that are presented, simultaneously grounding lofty and abstract ideas and elevating concrete details to new heights. The music of Bach is broken down in excruciating detail to present new structures and ideas, while Hofstadter simultaneously replicates many of these musical forms within GEB itself (he admits on page 28, and again at the end of the book, that each dialogue is modeled after a different piece by Bach!).

The beauty of GEB is that it can be perceived and observed in infinitely conceivable ways. It is both a sum of its parts and an emergent piece of complexity. It is both a weaving of separate analyzable threads and an inseparable "Eternal Golden Braid". It is about Music, Art, Mathematics, Science, Philosophy, Abstraction, Form, Aesthetics, ... and it is about none of these things. It transcends normal story telling and non-fictional consideration. It simultaneously invites and compels the reader to enter its crazy world where the only thing more pervasive than the disorder is the order. And it is beautiful.

Gracious! There is a world of difference between your piece and mine. Perhaps this is a place where words fail to convey what the spirit can feel. Indeed, I would venture to say that there exists no set of rules which delineate what it is that makes a piece beautiful, nor could there ever exist such a set of rules. The sense of Beauty is the exclusive domain of Conscious Minds, minds which through the experience of living have gained a depth that transcends explanation by any mere set of rules.

- Crab, "The Magnificrab, Indeed", Page 555

In the midst of discussing relations between Number Theory and Musical form to make a point about the Church-Turing Thesis, Hofstadter (or should I say, the Crab) stops to make a point about Beauty and its inherent subjectivity... and then continues right along with its normal route. GEB is filled with moments like this: deep, theoretically intense conversations are interluded by short but amazingly poignant tangents. It comes swiftly, and departs just as it arrived. It shocks the reader's mind and freezes it in its synaptic steps to compel just a single moment to consider what is happening.

But it's not all free form wonder. Hofstadter can tie it all back together as a solid, such as when he finally describes his theory of Consciousness:

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. In other words, a self-reinforcing "resonance" between different levels -- quite like the Henkin sentence which, by merely asserting its own provability, actually becomes provable. The self comes into being at the moment it has the power to reflect itself.

- Douglas R. Hofstadter, "Strange Loops, Or Tangled Hierarchies", Page 709

Notice how in the process of giving such a hypothesis, GEB reveals its very self! The theory of the Crux of Consciousness is a almost a pure abstraction of Escher's never-ending staircase in "Ascending and Descending" or one of Bach's endlessly rising canons which re-join with their selves or the inherent battle between consistency and completeness in Gödel's Incompleteness Theorem!

And these amazingly apt parallels are abound in GEB:

I was talking one day with two systems programmers for the computer I was using. They mentioned that the operating system seemed to be able to handle up to about thirty-five users with great comfort, but at about thirty-five users or so, the response time all of a sudden shot up, getting so slow that you might as well log off and go home and wait until later. Jokingly I said, "Well, that's simple to fix -- just find the place in the operating system where the number '35' is stored, and change it to '60'!" Everyone laughed. The point is, of course, that there is no such place. Where, then, does the critical number -- 35 users -- come from? The answer is: It is a visible consequence of the overall system organization -- an "epiphenomenon".

Similarly, you might ask about a sprinter, "Where is the '9.3' stored, that makes him be able to run 100 yards in 9.3 seconds?" Obviously, it is not stored anywhere. His time is a result of how he is built, what his reaction time is, a million factors all interacting when he runs. The time is quite reproducible, but it is not stored in his body anywhere. It is spread around among all the cells of his body and only manifests itself in the act of the sprint itself.

Epiphenomena abound. In the game of "Go", there is the feature that "two eyes live". It is not built into the rules, but it is a consequence of the rules. In the human brain, there is gullibility. How gullible are you? Is your gullibility located in some "gullibility center" in your brain? Could a neurosurgeon reach in and perform some delicate operation to lower your gullibility, otherwise leaving you alone? If you believe this, you are pretty gullible, and should perhaps consider such an operation.

- Douglas R. Hofstadter, "Levels of Description, and Computer Systems", Page 308

These quotations are great, but they are cherry-picked because they have the ability to stand on their own. There is a plethora of material which is too tightly woven to be extracted in the form of pure text quotations, to be separated from its neighboring paragraphs, chapters and dialogues, and still maintain meaning and context. If I really wanted to get across true representations of GEB, I would be forced to quote the entire book!

And if it seems like I am prattling on like an excited, spastic fanboy whom barely understands what he read, it is probably because that is a valid observation. GEB was by far the deepest, densest, most informative, most marvelous work that I have ever encountered. To feign a mastery of its content would do everyone a disservice. I will have to come back again and again to converge on fully absorbing its lessons. Converge, but never reach. And I'm okay with that. I want to come back and discover more with each excursion. I learned so much and yet barely scratched the surface. And that's why I find it so amazing.

So, can I adequately explain Gödel, Escher, Bach: an Eternal Golden Braid? Not a chance. I haven't the ability. But why would I even try when Hofstadter can do so far more elegantly?

Things are going on on many levels in the Musical Offering. There are tricks with notes and letters; there are ingenious variations on the King's Theme; there are original kinds of canons; there are extraordinarily complex fugues; there is beauty and 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 and 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, and Bach are woven into an Eternal Golden Braid.

- Douglas R. Hofstadter, "Strange Loops, Or Tangled Hierarchies", Page 719