Continuing on the series: "Mathematics, the language of nature". Imagine an image of some object, say a black vase in front of a white background. Assume now that the image of the object is sharply depicted, so that its boundaries, its contours, define perfectly the area od space which is the object itself. But then also the complementary portion of space, the object's surroundings, are completely and perfectly defined, aren't they? Well... not necessarily. Many too many sets in mathematics (take them as "the object") are completely and perfectly definable, but "what remains out of the set" is... impossible to define this way. And vice versa. Many thimes you know the "rest of the world except the object", and still you can't say what exactly is the object. And this strange behavior is directly connected to the icompleteness theorem. A *theorem* and not any "it looks as if", and I insist on enhancing the meaning of that. A theorem of a science through which the science speaks of the science itself, and says exactly where it just can do any better, even if many would wish it perfect and complete at the same time. Only mathematics has done this up to now. Only mathematics is humble enough to not just "guess" but to *know* the own limitations.
The queen of sciences is a very sincere girl, it seems. You will find absolutely no diva that demands and pretends. You will find only a serving queen, one that helps all other sciences and never claims to be so special. That's why I like her!
And this subject was what I was trying to get here. Something that suggests this kind of incompleteness. Any comments would be very welcome.
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