Douglas R. Hofstadter published his monumental work “Gödel, Escher, Bach: an Eternal Golden Braid” (hereinafter “GEB”) in 1979 when he was still in his 30s. It won the Pulitzer Prize. It took me almost a year-and-a half to read it. Like many before, I’m not going to pretend to fully understand it, therefore I will leave it to Prof. Hofstadter to explain it from his Preface to the 20th Anniversary Edition:

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.

While the theoretical math is beyond my ability, there are some absolute gems of thought in this that make accepting concepts such as the Ineffable or “Turtles All The Way Down” much easier. GEB approaches difficult conceptual topics slowly and methodically in its chapters which are then usually followed by entertaining dialogues to help grasp the concepts. At around 750 pages, I want to cover only a couple of the ideas that were most important to me, or otherwise end up writing a book about a book.

The first is M.C. Escher’s 1952 wood engraving “Dragon” (https://en.wikipedia.org/wiki/Dragon_%28M._C._Escher%29#/media/File:Escher_Dragon.jpg). A wood engraving is a three-dimensional device for producing a two-dimensional image. The Dragon is depicted as trying to bite its own tail by having both its head and tail protrude from three-dimensional boxes. But this is rendered in two dimensions. As Hofstadter says, “The dragon tries very hard to fight his two-dimensionality. He defies the two-dimensionality of the paper on which he thinks he is drawn, by sticking his head through it; and yet all the while, we outside the drawing can see the pathetic futility of it all, for the dragon and the holes and the folds are all merely two-dimensional simulations of those concepts, and not one of them is real.” The Dragon also has no concept of the three-dimensional wood block. How hard do we fight our four-dimensionality? What glimpses do we have of other dimensions that we try to prove, yet are not “real?” Of what do we have no knowledge or concept? It is fitting that this is the Year of the Wood Dragon.

Secondly, after all one has been through in reading this book, the final chapter “Strange Loops, Or Tangled Hierarchies” and final dialogue “Six-Part Ricercar” are absolutely mind blowing. I’m going to try to simplify (poorly). First, take Escher’s 1948 lithograph “Drawing Hands” (https://en.wikipedia.org/wiki/Drawing_Hands#/media/File:DrawingHands.jpg). The left hand is drawing the right hand which is drawing the left hand. A strange loop. But it is also an illusion. Who drew the hands? Escher. But you don’t see him; he’s at the Inviolate Level (invisible). The hands have no concept of Escher. If you saw a photograph of him drawing the lithograph you would be up another level and Escher would have no concept of you. There is always an inviolate level, even when its affects are plain as day at the lower level. That level is ineffable to the subject. We can go either up or down to find an inviolate level. We can only go so big, or so small or so far back in time until we meet our limits. For example, even if we are aware of its presence, we can only have limited understanding of the Existential Third Man (https://dispatchestk.com/2022/02/01/communique-to-the-public-from-the-fifth-philosophical-council-of-keeferton/). The issue of levels is also important when I hear people talking about changing reality at the classical level by utilizing quantum physics (QED), without addressing the principle of decoherence. Levels matter. The “Six-Part Ricercar” takes you on a wild trip of self-reference, strange loops, and wondering what is real. Does Free Will truly exist? See “The Great Divorce” C.S. Lewis, ch. 14. All of this leaves us with a question of what about this level of reality can we truly understand, or is it ineffable? Hofstadter seems to make a strong case that it is infinitely regressive and turtles all the way down.

An aside: Today, many look to Hofstadter and GEB for insights into Artificial Intelligence (AI). It is true that portions of GEB are consumed with AI and those discussions are very interesting, especially considering he was writing in the 1970s! What they do in my view, however, is point us back to the strange loops and inviolable levels discussed above. I found the second to last chapter “Artificial Intelligence: Prospects” with its speculations to be interesting but, in the end, of little value.

GEB is incredible. The fact that a human being in his 30s in the 1970s could put this work together astounds me. At times I marveled that a person could not only grasp the concepts being put forth, but then weave them into brilliant, coherent, and logical stories. It was a flash of brilliance, super-human effort, or a combination of the two. Perhaps, it was a strange loop.