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Gödel, Escher, Bach: An Eternal Golden Braid.

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When I first read an earlier version of this book 30 years ago, it was easy enough to conclude that the book was only a story about the "structure of meaning" as it is manifest at the intersection somewhere in the more creative stratosphere, of various independent modalities of understanding way above the ordinary thinker's head. At the time, I thought the book was only about the ever so clear threads connecting the paradoxical drawings of M.C. Escher, to the complex Fugues of Bach, and the self-referential and intricately intertwined logic of Godel's Incompleteness Theorem. That is to say, it was part of the tapestry of "hidden dimensions" that appeared so obviously common to them all. And while as far as my understanding then went, little did I realize at the time that there was much more to the story, a much deeper purpose and underlying meaning to this, Hofstadter's literary and scientific Masterpiece.

Only in retrospect (and after reading two of his other books) is one able to see that this larger, much more deeply embedded story is about how meaning itself -- and with it, consciousness -- and how they both came into being. The story then is ultimately about how meaning, through inanimate symbols, and symbolic forms and processes, came to the present level of understanding: how symbols emerged -- inexorably and unforced -- from the ether of randomness and meaningless inanimate objects, ensnared by structure and form, into symbols that came alive with meaning. Or said differently, how once lifeless "random things," a part of the inanimate hardware of the world, eventually became an unavoidable imperative of the "software" of life.

It is a complex, curious, but always exciting and deeply scientific as well as philosophical story that necessarily keeps deepening as it unfolds. And in this regard, it must be said that it is one that could only have been told by a deeply compassionate, contemporary and patient mind such as that possessed by this author. That he was able to pull it off at all is an incredible feat in itself. That he could have done so with so much grace, style and lightness is a tribute to his own humanity and can only be a pure reflection of his deep and abiding abilities as both teacher and Scientist.

The Story within a story
As is the case with meaning itself, GEB is a story within a story, or rather several meta-stories within meta-stories, or artificial meta-narratives within artificial meta-narratives. This of course points to one of the trickiest parts of this exposition (one with so many tricky parts): how to "sneak in" the fact that so much of what we have come to accept as "meaning" is implied from a self-referential background that "compels meaning as we understand it," to spew forth as one of its imperatives. The background that does the "compelling" is of course opaque, but despite its opaqueness, is nevertheless made up of the crucially dependent dimensions of structure, form, order and hierarchy.

But "connecting the dots" between symbol and form is only one of the many tricky parts of this story. Another is an epistemological one: how to always know, and then be able to keep track of where we are in the process of going back and forth between the "content of meaning," (which we also use to tell our stories) to "its form, structure, order and hierarchy (which is always implied in the background and in the context o those stories)." Not the least of these is how to then organize all of this in an orderly fashion to tell such a complex story, simply.

With his ever-childishly creative spirit, coupled with deep wisdom, and an exquisite understanding of both the mechanics and the concepts of meaning, Hofstadter decides to use as his template for storytelling the devices which Lewis Carroll put to good effect in his "Alice in Wonderland:" He used fictional dialogues between invented characters. Hofstadter goes him one better and includes, in addition to fictional characters, also, artificial systems and forms, formal and informal games and artificial hierarchies, cultures and collectivities, all with a carefully built in trapdoor: a sometimes devious underlying didactic purpose that better drives home the larger points about the role recursive and self-referential systems play in the "meaning of meaning," writ large.

The role of Strange Loops

The "work horse" of this deeply conceptual analysis, as well as the most non-obvious continuous thread throughout the storytelling is a concept that Hofstadter has coined as a "strange loop." A strange loop is a kind of self-referential "mental free-radical," a pre-symbolic mime, as it were, of reasoning about reasoning, or thinking about thinking, that keeps popping up everywhere seemingly without purpose, but in the end one that proves to be the glue holding the whole edifice of meaning together. Most of Hofstadter's dialogues and examples are designed to explicate simply, and to otherwise put the mind at ease about the underlying meaning of the complexity implicit in the form, content and meaning of self-referential and complex hierarchical systems. Put simply, the strange loop is the inanimate link between random pre-symbolic mental forms, and the nested hierarchy of symbols that eventually emerge from the background of structural dimensionality, fully formed and "given life" by imbuing them with content we eventually come to recognize as meaning.

This is, of course, where Godel, Escher and Bach come back into the picture: For only at the interfaces where "form" meets "symbol" do we began to see these "strange loops" reappearing. For instance they "show up" at the point where Escher's paintings fold back in on themselves; where Bach appears to be able to invent fugues and other musical forms hitherto thought not to (and in principle do not) exist; and where ordinary symbolic logic begins to breakdown in the nested formal systems invented by Godel and explicated in the proof of his famous Theorem.

One could argue that there is a less onerous way to have arrived at the same conclusions, but no one can argue that it would have been quite as much fun.

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