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Crab: I improvise quite a bit. In fact, sometimes I think about devoting my full time to |
music. There is so much to learn about it For instance, when I listen to playbacks of |
myself, I find that there is a lot there that I wasn't aware of when improvising it. I |
really have no idea how my mind does it all. Perhaps being a good improviser is |
incompatible with knowing how one does it. |
Author: If true, that would be an interesting and fundamental limitation on thought |
processes. |
Crab: Quite Godelian, Tell me -does your Six-Part Rice rear Dialogue attempt to copy in |
fonn the Bach piece it's based on? |
Author: In many ways, yes. For instance, in the Bach, there’s a section where the texture |
thins out to three voices only. I imitate that in the |
Dialogue, by having only three characters interact for a while. Achilles: That's a nice |
touch. |
Author: Thank you. |
Crab: And how do you represent the King's Theme in your Dialogue? |
Author: It is represented by the Crab's Theme, as I shall now demonstrate. Mr. Crab, |
could you sing your Theme f or my readers, as well as f or us assembled musicians? |
Crab: Compose Ever Greater Artificial Brains (By And By). |
Babbage: Well, I’ll be-an EXQUISITE Theme! I'm pleased you tacked on that last little |
parenthetical note; it is a mordant Author: He Simply HAD to, you know. |
Crab: I simply HAD to. He knows. |
Babbage: You simply HAD to-I know. In any case, it is a mordant commentary on the |
impatience and arrogance of modern man, who seems to imagine that the implications |
of such a right royal Theme could be worked out on the spot. Whereas, in my opinion, |
to do justice to that Theme might take a full hundred years-if not longer. But I vow |
that after taking my leave of this century, I shall do my best to realize it in full; and I |
shall offer to your Crabness the fruit of my labors in the next. I might add, rather |
immodestly, that the course through which I shall arrive at it will be the most |
entangled and perplexed which probably ever will occupy the human mind. |
Crab: I am most delighted to anticipate the form of your proposed Offering, Mr. |
Babbage. |
Turing: I might add that Mr. Crab's Theme is one of MY favorite Themes, as well. I've |
worked on it many times. And that Theme is exploited over and over in the final |
Dialogue? |
Author: Exactly. There are other Themes which enter as well, of course. Turing: Now we |
understand something of the form of your book-but what about its content? What does |
that involve, if you can summarize it? |
Author: Combining Escher, Godel, And Bach, Beyond All Belief. Achilles: I would like |
to know how to combine those three. They seem an |
unlikely threesome, at first thought. My favorite artist, Mr. T’s favorite composer, and- |
Crab: My favorite logician! |
Tortoise: A harmonious triad. I'd say. |
Babbage: A major triad. I’d say. |
Turing: A minor triad. I’d say. |
Author: I guess it all depends on how you look at it. But major or minor, I’d be most |
pleased to tell you how I braid the three together, Achilles. #f course, this project is |
not the kind of thing that one does in just one sitting-it might take a couple of dozen |
sessions. I’d begin by- telling you the story of the Musical Offering , stressing the |
Endlessly Rising Canon, and |
Achilles: #h, wonderful! I was listening with fascination to you and Mr. Crab talk about |
the Musical #ffering and its story. From the way you two talk about it, I get the |
impression that the .Musical Offering contains a host of formal structural tricks. |
Author: After describing the Endlessly Rising Canon, I'd go on to describe formal |
systems and recursion, getting in some comments about figures and grounds, too. |
Then we’d come to self-reference and self-replication, and wind up with a discussion |
of hierarchical systems and the Crab’s Theme. |
Achilles: That sounds most promising. Can we begin tonight? |
Author: Why not? |
Babbage: But before we begin, wouldn’t it be nice if the six of us-all of us by chance avid |
amateur musicians-sat down together and accomplished the original purpose of the |
evening: to make music? |
Turing: Now we are exactly the right number to play the Six-Part Ricercar from the |
Musical Offering. What do you say to that? |
Crab: I could get along veiy well with such a program. |
Author: Well put, Mr. C. And as soon as we’re finished. I'll begin my Braid, Achilles. I |
think you'll enjoy it. |
Achilles: Wonderful! It sounds as if there are many levels to it, but I’m finally getting |
used to that kind of thing, having known Mr. T for so long. There's just one request I |
would like to make: could we also play the Endlessly Rising Canon? It's my favorite |
canon. |