By the way there is 2 parts in Godel proof of incompleteness...
The first brilliant idea THE MORE PROFOUND ONE is Godel numberings, with the PRIMES, which is a way to represent any formal system in a perfect non arbitrary way with natural numbers and speak about it in term of the properties of natural numbers...
The second part is the brillant and more spectacular construction of the famous formal sentence that is analogous to the Cretan paradox...The more well known part ...The first part being only a preparation mostly it seems to this second crucial part...
The first part is the more illuminative but underestimated one.... Guess why?
If you guess right you will begin to understand why Roger Penrose is right in spite of some illustrious logician critics that has attacked his argument rightfully it seems at first look, when he plead for the non- algorithmic nature of consciousness...
Even Godel, a mystic, has affirmed that we cannot distinguish between a robot and a living consciousness, using ONLY his result...( I was surprised that you dont used that like an objection when I speak about Godel-Penrose argument, this is on Wikipedia easy to spot) :)
Then why Penrose is and will be right about it in spite of Godel affirmation?
Try your brain (neural networks) on that ….
hint: the answer is not on Wikipedia.... :)
All that enigma is part of my own perception of the absoluteness of Primes existence and consciousness...
Atoms are almost vapour compared to the hardness reality of primes..
The human brain or a black hole has almost zero measure complexity compared to the prime numbers distribution which is of complexity almost measure one.....
And Consciousness is the only phenomenon there is ultimately....
Call it God if you are an atheist or a believer, which are only that: men of different faiths; call it also the most unknown part of yourself and of all that exist if you think and perceive it....
I am a constructivist Platonist.... :)
I am perhaps a fool... But you can guess that I think by myself at least.... My best to you.... Sorry for my arrogant rant.... But....it was not against you it was against arrogant "scientism"....
The first brilliant idea THE MORE PROFOUND ONE is Godel numberings, with the PRIMES, which is a way to represent any formal system in a perfect non arbitrary way with natural numbers and speak about it in term of the properties of natural numbers...
The second part is the brillant and more spectacular construction of the famous formal sentence that is analogous to the Cretan paradox...The more well known part ...The first part being only a preparation mostly it seems to this second crucial part...
The first part is the more illuminative but underestimated one.... Guess why?
If you guess right you will begin to understand why Roger Penrose is right in spite of some illustrious logician critics that has attacked his argument rightfully it seems at first look, when he plead for the non- algorithmic nature of consciousness...
Even Godel, a mystic, has affirmed that we cannot distinguish between a robot and a living consciousness, using ONLY his result...( I was surprised that you dont used that like an objection when I speak about Godel-Penrose argument, this is on Wikipedia easy to spot) :)
Then why Penrose is and will be right about it in spite of Godel affirmation?
Try your brain (neural networks) on that ….
hint: the answer is not on Wikipedia.... :)
All that enigma is part of my own perception of the absoluteness of Primes existence and consciousness...
Atoms are almost vapour compared to the hardness reality of primes..
The human brain or a black hole has almost zero measure complexity compared to the prime numbers distribution which is of complexity almost measure one.....
And Consciousness is the only phenomenon there is ultimately....
Call it God if you are an atheist or a believer, which are only that: men of different faiths; call it also the most unknown part of yourself and of all that exist if you think and perceive it....
I am a constructivist Platonist.... :)
I am perhaps a fool... But you can guess that I think by myself at least.... My best to you.... Sorry for my arrogant rant.... But....it was not against you it was against arrogant "scientism"....