Tuesday, April 24, 2012

Out of contest




Today's Gerard 't Hooft's paper. The incipit reads:


In modern science, real numbers play such a fundamental role that it is difficult to imagine a world without real numbers. Nevertheless, one may suspect that real numbers are nothing but a human invention. By chance, humanity discovered over 2000 years ago that our world can be understood very accurately if we phraze its laws and its symmetries by manipulating real numbers, not only using addition and multiplication, but also subtraction and division, and later of course also the extremely rich mathematical machinery beyond that, manipulations that do not work so well for integers alone, or even more limited quantities such as Boolean variables.

Now imagine that, in contrast to these appearances, the real world, at its most fundamental level, were not based on real numbers at all. We here consider systems where only the integers describe what happens at a deeper level. Can one understand why our world appears to be based on real numbers?


Isn't this enough to continue reading?

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