A crab canon for Douglas Hofstadter

(published at 3 Quarks Daily)

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.

Thumbing through Gödel, Escher, Bach again recently, I came across the Crab Canon and was struck with the desire to attempt a similar feat myself: a line-level palindrome that tells a linear story, that is, a story in which a series of non-repeating events occur.

It’s maddeningly difficult trying to come up with lines that make sense, that in fact make a different sense, in both directions. And because all of the lines interlock — each relying simultaneously on the line preceding it, the line following it, and its mirror-image line — changing any one line in the poem tends to set off a ripple effect of necessary changes to all the other lines as well.

I eventually figured out a few crucial tricks, like relying on ambiguous pronouns (“they,” “their”) and using images that carry a different meaning depending on what’s already happened. Below is the final result – my own canon, in homage to the book that dazzled my teenaged self years ago:

SEASIDE CANON, for Douglas Hofstadter

by Julia Galef

The ocean was still.
In an empty sky, two gulls turned lazy arcs, and
their keening cries echoed
off the cliff and disappeared into the sea.
When the child, scrambling up the rocks, slipped
out of her parents’ reach,
they called to her. She was already
so high, but those distant peaks above —
they called to her.  She was already
out of her parents’ reach
when the child, scrambling up the rocks, slipped
off the cliff and disappeared into the sea.
Their keening cries echoed
in an empty sky. Two gulls turned lazy arcs, and
the ocean was still.


11 Responses to A crab canon for Douglas Hofstadter

  1. Andrew T says:

    Impressive! I wonder if it would’ve been easier or harder to do with dialogue?

    • Julia Galef says:

      Thanks, Andrew! I think one thing that makes this approach harder is that I wanted my sentences (at least some of them) to span multiple lines. That means when you reverse the order of the lines, some of the sentences get chopped up and shuffled. Whereas in Hofstadter’s original canon, all the sentences in a character’s comment remain together.

  2. Matt says:

    That was beautiful, thank you.

  3. Brian Engler says:

    Apparently there is no end to your talent, Julia. Very, very well done!

  4. Julia Galef says:


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  6. Rick Toews says:

    Cleverly crafted. I imagine that was fun to put together. And I remember that book. I believe that’s where I first learned of Escher’s drawings, of which Waterfall is probably my favorite.

  7. Adam says:

    A half-remembered dream
    is always a ghost born of
    those long-broken bonds;
    sentiments of
    one who once felt
    for us.
    for us,
    one who once felt
    sentiments of
    those long-broken bonds
    is always a ghost, born of
    a half-remembered dream.

  8. Len says:

    My daughter wrote this one for a Grade 11 school assignment:

    My Disoriented Life

    We are locked in a cycle of cynicism
    I do not believe that
    We can change for the better
    You might not agree, but I know
    My friends are all selfish
    I refuse to believe that
    They genuinely care for each other
    Because I know
    My friends are only concerned about themselves
    It’s not true that
    We are all good at heart
    My family and friends,
    Are not my priority
    My own prosperity and wealth
    Is essential to my happiness
    Taking care of others
    Means that I cannot live my life in peace
    I know that being selfish
    Is not a bad thing and
    Will make me successful and that
    Working hard
    is overrated
    “Money makes the world go round”
    is the truth
    People do really care about me
    Only when it is convenient for them
    It is not true that people care.
    But if we reverse this, then we can see the truth in these pessimistic lies.
    (Read it all backwards)

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  10. lingaraj Patnaik says:

    Internet put to correct use, to further culture: poetry, philosophy, art all in search of beauty. Enough of technology and civilization. Lingaraj.

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