Roger Penrose: The Road to Reality


In the development of mathematical ideas, one important initial driving force has always been to find mathematical structures that accurately mirror the behaviour of the physical world. But it is normally not possible to examine the physical world itself in such precise detail that appropriately clear-cut mathematical notions can be abstracted directly from it. Instead, progress is made because mathematical notions tend to have a "momentum" of their own that appears to spring almost entirely from within the subject itself. Mathematical ideas develop, and various kinds of problem seem to arise naturally.

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How do I really feel about the possibility that all my actions, and those of my friends, are ultimately governed by mathematical principles (...)? I can live with that. I would, indeed, prefer to have these actions controlled by something residing in some (...) aspect of Plato`s fabulous mathematical world than to have them be subject to the kind of simplistic base motives, such as pleasure-seeking, personal greed, or aggressive violence, that many would argue to be the implications of a strictly scientific standpoint.

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It is always the case, with mathematics, that a little direct experience of thinking over things on your own can provide a much deeper understanding than merely reading about them.

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