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.
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.