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How is it that mathematical ideas can be communicated in this way? I imagine that whenever the mind perceives a mathematical idea, it makes contact w… - Roger Penrose
" "How is it that mathematical ideas can be communicated in this way? I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts. ... When one 'sees' a mathematical truth, one's consciousness breaks through into this world of ideas, and makes direct contact with it ('accessible via the intellect'). I have described this 'seeing' in relation to Gödel's theorem, but it is the essence of mathematical understanding. When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through this process of 'seeing'. (Indeed, often this act of perception is accompanied by words like 'Oh, I see'!) Since each can make contact with Plato's world directly, they can more readily communicate with each other than one might have expected. The mental images that each one has, when making this Platonic contact, might be rather different in each case, but communication is possible because each is directly in contact with the same externally existing Platonic world!
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About Roger Penrose
Sir Roger Penrose (born 8 August 1931) is an English mathematical physicist and Professor of Mathematics at the Mathematical Institute, University of Oxford, famous for his work in mathematical physics, cosmology, general relativity, and his musings on the nature of consciousness.
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R. Penrose
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Sir Roger Penrose
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Additional quotes by Roger Penrose
...the entire physical world is depicted as being governed according to mathematical laws. We shall be seeing in later chapters that there is powerful (but incomplete) evidence in support of this contention. On this view, everything in the physical universe is indeed governed in completely precise detail by mathematical principles — perhaps by equations, such as those we shall be learning about in chapters to follow, or perhaps by some future mathematical notions fundamentally different from those which we would today label by the term ‘equations’. If this is right, then even our own physical actions would be entirely subject to such ultimate mathematical control, where ‘control’ might still allow for some random behaviour governed by strict probabilistic principles.
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One is left with the uneasy feeling that even if supersymmetry is actually false, as a feature of nature, and that accordingly no supersymmetry partners are ever found by the LHC or by any later more powerful accelerator, then the conclusion that some supersymmetry proponents might come to would not be that supersymmetry is false for the actual particles of nature, but merely that the level of supersymmetry breaking must be greater even that the level reached at that moment, and that a new even more powerful machine would be required to observe it!
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