For starters, anybody who considers Escher's work to be artistic is already fighting a losing battle.
I disagree. I consider Escher's work to be artistic. The reasons I do so are the usual reasons something is considered artistic: because I like most of it, and also because some of it makes me think. Not deep, world-shattering thoughts, but thoughts nonetheless.
It's perfectly reasonable for you to not like his work, but that doesn't automatically disqualify it as "art" (And yes, I do realise this vague definition allows virtually anything to be defined as art).
Second, claiming that the primary source of greatness in any artistic work can be reduced to a mathematical formula is idiotic.
Agreed -- even if you believe that a brain can be represented deterministically and mathematically, it seems unlikely that any such representation would be a "reduction", in the sense of simplifying the original. And as art is judged by the brain, or at least a significant part of it, that claim seems ridiculous to me also.
However, I do not recall reading any such claim in Godel, Escher, Bach. He may have suggested that Escher used mathematicals concepts to aid him in conceiving and producing his artistic creations, but that is by no means the same claim.
Third, using a flawed understanding of art and music as a basis to claim that a mathematician's work is representative of some holy truth is doomed to failure.
That's another strawman argument, as far as I can tell.
I'm not sure what "holy truth" you are referring to. Hofstader's point in that book was that he believed AI -- real artifical consciousness and creativity, not just some watered-down "expert system" -- is possible within the deterministic framework of a sufficiently complex computer or similar device. He used ideas drawn from the work of Bach, Escher, and mostly relevantly Godel to help explain this. It's an interesting conclusion, but a debatable one.
It's also a very straightforward conclusion, but many people seem to have missed it.
Unfortunately, people seem to have gotten bogged down in the final third of the book and hence been confused about his goal. He is not trying to show some underlying fundamental connection in the universe between mathematics, art and music. He is not trying to show that life in an enormous braid. He is trying to explain his theory of consciousness.
His intended goal has been overshadowed by the remarkable quality of his writing. Using concepts from many different fields to explain things and provide interesting examples, and interspersing it with cleverly written dialogues makes for excellent reading. By working so hard to make his ideas approachable to the layman, he seems to have disguised his ideas beyond reach of many people. It's a pity, but the book is a good read regardless.
I might be wrong about your understanding of the book, but it seems to me that your criticisms of it are based on a misunderstanding of it.
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