Gödel, Escher, Bach VI

I’m working my way, day by day, through the Pulitzer Prize-winning classic, "Gödel, Escher, Bach"; it’s one of the seminal books on the search for the "I" within us, and a prodigious work (pray for me). You can find earlier entries below, or collected at right.

By Dale Conour

Curiouser and curiouser becomes the learning as I drop further down the GEB rabbit hole. Hofstadter begins what will be the pattern of the entire book: ping-ponging between "Dialogues," featuring the characters of Achilles and the Tortoise and delving into his concepts through metaphor, and "Chapters," addressing the same concepts through more formal means.

Achilles and the Tortoise were first employed by ancient philosopher Zeno of Elea (he predated Socrates and Plato), who used them to illustrate his famed paradoxes, and then resurrected millennia later by Lewis Carroll to show off a paradox of his own (to come later in the book, promises Hofstadter).

Hofstadter retells Zeno’s account of a race between Achilles and the Tortoise in which the philosopher puts forth the following argument: Given a head start and constant, infinite motion, the Tortoise will always stay ahead of the fleeter Achilles if he merely vacates each point in space before Achilles arrives there. After all, Achilles must reach the point where the Tortoise just was before he can then advance to the one where the Tortoise is now.

It’s a variation of Zeno’s "dichotomy paradox" that supports his theorem that Motion is Inherently Impossible (Motion Unexists) because, in traveling from A to B, you have to go halfway first, but first halfway of that, and halfway of that, and so on, to infinity.

Since Zeno managed to get around despite his clever argument, he was really using these paradoxes to show that space and time clearly aren’t segmental, that they are continuous, and therefore, the linear concept of Motion must be a mental, not a physical construct.

Hofstadter’s variation of the race includes A and T remarking on a Zen koan in which two monks argue about a flag. "The flag is moving," says one. "The wind is moving," counters the other. A master happens by, and says they’re both wrong: "Mind is moving."

Is it possible I’m oversimplifying all this? Uh, yeah...

And of course, the author’s version of the tale also has loops. The two characters discuss Zeno’s paradox only to have Zeno show up and encourage them to have the race that they were just conversing about to "empirically" prove the theorem that he’s already used them metaphorically to prove.

And they will be racing toward a distant flag that resembles Escher’s Möbius Strip I—something they both acknowledge can’t really be there because it hasn’t come into existence yet (from their perspective).

What’s it all mean? We’ve covered plenty to chew on already. But the Chapter that follows lays out the underpinnings of a "formal system." Formal systems house theorems (like Zeno’s presumably). Do I understand how the first Dialogue and Chapter completely relate? Not completely yet. But hopefully I’ll be much closer by the next time I report on this...

Hang in there with me: We’re not only chasing the "I," we're attempting to understand a new version of "reality." Nothing like a good brain stretch.

Next time: The puzzle of MU, and the importance of jumping out of the system

Let’s stay in touch.

Comments

[Dale Conour]

There is a definite "down the rabbit hole" feeling to this book, so I can see already what you mean by "journey," Larry. I'm behind on that trip, though—need to get reading and writing!

[Larry]

GEB was a turning point for me in the late 80s. I went from teaching classical guitar at a university to working for a startup software company in the 90s, much because GEB inspired me to get back back into programming.

In one of those strange twists of fate, the software company I worked for was called Zenographics (www.zeno.com), which later merged with Marvell Semiconductor. The founder was a PhD candidate in philosophy at Johns Hopkins who named his computer graphics company after Zeno.

GEB is a fun book but understanding it may be a journey rather than something you get after reading it once. I recently bought it to reread it and it's very different for me not that the ideas have become old friends.

I'm back to teaching music but I still program on the side and I do some art too!

Enjoy your journey.