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Quoting CraigS
"Absolutely .. me too !
Why/how does mathematics do this ? Is it because it describes the reality which conceived it in the first place ?"
The quick answer is we do not know. Hofstadter addresses this in his book. Paul Davies has tried to answer this as well.
Craig you will find Hofstadter's book perplexing at first. It is way above my abilities to fully comprehend but then I have only been trying for about twenty years.
Godel's Incompleteness Theorem stunned the mathematical world out of their smugness.
Escher by his brilliant drawings showed the same sort of paradoxes. Locally logical but globally paradoxical.
Bach did the same with music as his seemingly continuous descending and ascending scales fooled your senses completely. I dont have perfect pitch so I wonder if people with this skill woud be fooled.
In my humble opinion a way around these paradoxes is that at the fundamental level of QM there is only probability governed by interactions. There is no possibilty of feed back in QM so Chaos theory does not have any effect.
Once we get into the realm of the macroscopic we have feedback that causes complexity beyond the inherent qualities of the system. Is there is a boundary?
The problem is of course order out of chaos and chaos out of order so defying any so called logic!
It is difficult to get these concepts across in a few sentences. Hofstadter needed a very thick book and it is still incomprehensible to me!
Bert
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