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It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards, that certain mathematical statements are irrefutable facts. What is unfortunate about this is that a proof, in spite of the fact that it is perfectly correct, does not in any way have to be enlightening. Thus, mathematicians, and mathematics students, are faced with two problems: the generation of proofs, and the generation of internal enlightenment. To understand a theorem requires enlightenment. If one has enlightenment, one knows in one's soul why a particular theorem must be true. ↗
Its hard to stay up. Its been a long long day And you've got the sandman at your door. But hang on, leave the TV on and lets do it anyway. Its ok. You can always sleep through work tomorrow. Ok? Hey, Hey, Tomorrow's just your future yesterday. Tell the clock on the wall, "Forget the wake up call." Cause the night's not nearly through. Wipe the sleep from your eyes. Give yourself a surprise. Let your worries wait another day. And if you stay too late at the bar, At least you made it out this far. So make up your mind and say, "Let's do it anyway!" Its Ok You can always sleep through work tomorrow, ok? Hey, Hey, Tomorrow's just your future yesterday. Life's too short to worry about the things that you can live without And I regret to say, the morning light is hours away. The world can be such a fright, But it belongs to us tonight. What's the point of going to bed? You look so lovely when your eyes are red. Tomorrow's just your future yesterday. ↗
The calculative exactness of practical life which the money economy has brought about corresponds to the ideal of natural science: to transform the world by mathematical formulas. Only money economy has filled the days of so many people with weighing, calculating, with numerical determinations, with a reduction of qualitative values to quantitative ones. ↗
The language of mathematics differs from that of everyday life, because it is essentially a rationally planned language. The languages of size have no place for private sentiment, either of the individual or of the nation. They are international languages like the binomial nomenclature of natural history. In dealing with the immense complexity of his social life man has not yet begun to apply inventiveness to the rational planning of ordinary language when describing different kinds of institutions and human behavior. The language of everyday life is clogged with sentiment, and the science of human nature has not advanced so far that we can describe individual sentiment in a clear way. So constructive thought about human society is hampered by the same conservatism as embarrassed the earlier naturalists. Nowadays people do not differ about what sort of animal is meant by Cimex or Pediculus, because these words are used only by people who use them in one way. They still can and often do mean a lot of different things when they say that a mattress is infested with bugs or lice. The study of a man's social life has not yet brought forth a Linnaeus. So an argument about the 'withering away of the State' may disclose a difference about the use of the dictionary when no real difference about the use of the policeman is involved. Curiously enough, people who are most sensible about the need for planning other social amenities in a reasonable way are often slow to see the need for creating a rational and international language. ↗
