Roger Penrose, "The Emperor's New Mind" 에서

 

Roger Penrose, The Emperor's New Mind (1989)

[Chapter] 10 Where lies the physics of mind?

Mathematical truth is not something that we ascertain merely by use of an algorithm. I believe, also, that our consciousness is a crucial ingredient in our comprehension of mathematical truth. We must 'see' the truth of a mathematical argument to be convinced of its validity. This 'seeing' is the very essence of consciousness. It must be present whenever we directly perceive mathematical truth. When we convince ourselves of the validity of Godel's theorem we not only 'see' it, but by so doing we reveal the very non-algorithmic nature of the 'seeing' process itself. (p 418)

Rigorous argument is usually the last step! Before that, one has to make many guesses, and for these, aesthetic convictions are enormously important -- always constrained by logical argument and known facts. It is these judgements that I consider to be the hallmark of conscious thinking. My guess is that even with the sudden flash of insight, apparently produced ready-made by the unconscious mind, it is consciousness that is the arbiter, and the idea would be quickly rejected and forgotten if it did not 'ring true.' (p 422)

One of the major points that Hadamard makes in his study of creative thinking is an impressive refutation of the thesis, so often still expressed, that verbalization is necessary for thought. (p 423)

Hadamard himself writes: I insist that words are totally absent from my mind when I really think ... and I fully agree with Schopenhauer when he writes, "thoughts die the moment they are embodied by words." (p 424)

[The strange role of time in conscious perception] Even the impressions of memories of one's own time-consuming experiences seem somehow to be so 'compressed' that one can virtually 're-live' them in an instant of recollection! (p 445)

Yet science seems to have driven us to accept that we are all merely small parts of a world governed in full detail (even if perhaps ultimately just probabilistically) by very precise mathematical laws. Our brains themselves, which seem to control all our actions, are also ruled by these same precise laws. (p 447)

Perhaps I am actually living backwards in time, with my streams of consciousness heading into the past .... Does the distinction between that and the normally experienced time-progression actually 'mean' something, so that the one is 'wrong' and the other 'right'? For answers to such questions to be resolvable in principle, a theory of consciousness would be needed. (p 448)

[덧붙임]

The view that mathematical concepts could exist in such a timeless, ethereal sense was put forward in ancient times by ... Plato [mathematical Platonism]. (p 97)

Recall that according to the Platonic viewpoint, mathematical ideas have an existence of their own, and inhabit an ideal Platonic world, which is accessible via intellect only. (p 428)

There must ... be some deep underlying reason for the accord between mathematics and physics, i.e. betweenPlato's world and the physical world. (p 430)

Recall my proposal that consciousness, in essence, is the 'seeing' of a necessary truth; and that it may represent some kind of actual contact with Plato's world of ideal mathematical concepts. (p 446)