What’s special or interesting about a musical piece that can be played cyclically? Such a piece is easy to compose by editing the two ends to align, even without reference to whatever is in the middle of the piece.
In the Bach example, if you go up an octave on every loop, you can’t play forever anyway (within human hearing).
It’s not that hard to do (somewhat harder if you want to keep your Bach-style harmonies intact), and I don’t think anyone claimed it was that hard, simply that it induces an interesting self-referential cycle. There’s something rather amusing (at least to me) about a piece of music that can be played an infinite number of times without repeating a musical phrase more than the few times it occurs in a single cycle.
As for the quick rise out of the human range of hearing, it’s just a small side effect that prevents musicians from getting caught in an infinite loop.
So GEB’s entire point here is that some infinite sequences of similar-but-different objects have self-referential formulations?
Just like these are equivalent:
a(n+1)=a(n)+2; a(0)=0
vs:
a(n)=2n for all n
Each element has the structure of “an even integer”, but the first form is self referential while the second one isn’t.
I fail to see a deep meaning in this, or any similarity with consciousness. Can someone enlighten me? Did I merely take the book’s example out of context?
Nope, you’ve got the right idea about his example. It occurs early on in the book, while he’s trying to explain simple concepts to readers through non-technical analogy; sort of the way he explained complement spaces to readers by first asking which word contains the sequence “ADAC” in order (headache), and then asked what word contains the sequence “HEHE” in order; nothing particularly special about that either, but it teaches the reader a useful trick without presenting it mathematically.
If I recall correctly, he focuses on the fact that the piece may be played in a cyclical fashion, allowing an infinite loop of sorts.
What’s special or interesting about a musical piece that can be played cyclically? Such a piece is easy to compose by editing the two ends to align, even without reference to whatever is in the middle of the piece.
In the Bach example, if you go up an octave on every loop, you can’t play forever anyway (within human hearing).
It’s not that hard to do (somewhat harder if you want to keep your Bach-style harmonies intact), and I don’t think anyone claimed it was that hard, simply that it induces an interesting self-referential cycle. There’s something rather amusing (at least to me) about a piece of music that can be played an infinite number of times without repeating a musical phrase more than the few times it occurs in a single cycle.
As for the quick rise out of the human range of hearing, it’s just a small side effect that prevents musicians from getting caught in an infinite loop.
So GEB’s entire point here is that some infinite sequences of similar-but-different objects have self-referential formulations?
Just like these are equivalent: a(n+1)=a(n)+2; a(0)=0 vs: a(n)=2n for all n
Each element has the structure of “an even integer”, but the first form is self referential while the second one isn’t.
I fail to see a deep meaning in this, or any similarity with consciousness. Can someone enlighten me? Did I merely take the book’s example out of context?
Nope, you’ve got the right idea about his example. It occurs early on in the book, while he’s trying to explain simple concepts to readers through non-technical analogy; sort of the way he explained complement spaces to readers by first asking which word contains the sequence “ADAC” in order (headache), and then asked what word contains the sequence “HEHE” in order; nothing particularly special about that either, but it teaches the reader a useful trick without presenting it mathematically.