Since it first came out in 1979, Douglas Hofstadter’s Pulitzer Prize-winning book “Gödel, Escher, Bach: An Eternal Golden Braid” has widened the eyes of multiple generations of nerdy kids, and I was certainly no exception. The book draws all sorts of parallels between music, art, math, and computer science, ultimately shaping them into a bold thesis about how consciousness arises from self-reference and recursion. It’s also a very playful book, full of puzzles, puns, and imagined dialogues between Achilles and a tortoise which weave in and out of the main chapters, illustrating the concepts therein.
One of those dialogues, titled “Crab Canon,” seems puzzling when you begin reading it – sprinkled with seeming non-sequitors, the word choice a bit awkward and off-kilter. Then shortly after the halfway point, when you start to see recent lines repeated, in reverse order, you realize: the whole dialogue is a line-level palindrome. The first line is the same as the last, the second line is the same as the second-to-last, and so on. But because Hofstadter chooses his sentences carefully, they often have different meanings when they reoccur in the reverse order. So, for example, the following bit of dialogue in the first half…
Tortoise: Tell me, what's it like to be your age? Is it true that one has no worries at all?
Achilles: To be precise, one has no frets.
Tortoise: Oh, well, it's all the same to me.
Achilles: Fiddle. It makes a big difference, you know.
Tortoise: Say, don't you play the guitar?
… becomes this bit of dialogue in the second half:
Achilles: Say, don't you play the guitar?
Tortoise: Fiddle. It makes a big difference, you know.
Achilles: Oh, well, it's all the same to me.
Tortoise: To be precise, one has no frets.
Achilles: Tell me, what's it like to be your age? Is it true that one has no worries at all?
Hofstadter does “cheat” a bit, by allowing himself to vary punctuation (for example, “He often plays, the fool” reoccurs later in a new context as “He often plays the fool”). Nevertheless, it’s an impressive execution of a clever conceit.
