I think about this quote a lot. When I thrill to the excitement of solving a new problem with friends, when I share a much-loved problem with students, and when I find new surprises in well-worn places. This has been a good week.
TORTOISE: And there is something very dramatic about the few moments of silent suspense hanging between prelude and fugue-that moment where the theme of the fugue is about to ring out, in single tones, and then to join with itself in ever-increasingly complex levels of weird, exquisite harmony.
ACHILLES: I know just what you mean. There are so many preludes and fugues which I haven’t yet gotten to know, and for me that fleeting interlude of silence is very exciting; it’s a time when I try to second-guess old Bach. For example, I always wonder what the fugue’s tempo will be: allegro or adagio? Will it be in 6/8 or 4/4? Will it have three voices or five-or four? And then, the first voice starts…. Such an exquisite moment.
CRAB: Ah, yes, well do I remember those long-gone days of my youth, the days when I thrilled to each new prelude and fugue, filled with the excitement of their novelty and beauty and the many unexpected surprises which they conceal.
ACHILLES: And now? Is that thrill all gone?
CRAB: It’s been supplanted by familiarity, as thrills always will be. But in that familiarity there is also a kind of depth, which has its own compensations. For instance, I find that there are always new surprises which I hadn’t noticed before.
ACHILLES: Occurrences of the theme which you had overlooked?
CRAB: Perhaps-especially when it is inverted and hidden among several other voices, or where it seems to come rushing up from the depths, out of nowhere. But there are also amazing modulations which it is marvelous to listen to over and over again, and wonder how old Bach dreamt them up.
ACHILLES: I am very glad to hear that there is something to look forward to, after I have been through the first flush of infatuation with the Well-Tempered Clavier-although it also makes me sad that this stage could not last forever and ever.
CRAB: Oh, you needn’t fear that your infatuation will totally die. One of the nice things about that sort of youthful thrill is that it can always be resuscitated, just when you thought it was finally dead. It just takes the right kind of triggering from the outside.
ACHILLES: Oh, really? Such as what?
CRAB: Such as hearing it through the ears, so to speak, of someone to whom it is a totally new experience-someone such as you, Achilles. Somehow the excitement transmits itself, and I can feel thrilled again.
– Gödel, Escher, Bach: An eternal golden braid by Douglas Hofstadter
(Thanks to Dawson and VSA 2008 for helping me to fall in love with this passage.)
(Note: we solved it “by hand” first – then @CmonMattTHINK shared his solution on Mathematica after we were finished celebrating.)