A Quote by Woodrow Wilson
The natural man inevitably rebels against mathematics, a mild form of torture that could only be learned by painful processes of drill.
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I don't know about torture. I have educated myself on many things but on torture I have not known the boundary between what is torture and what isn't torture. I know the NRA tie these people (rebels, etc.) when they catch them. They tie their hands backwards. I am now being told that is torture. It is the traditional method.
But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.
An avant-garde man is like an enemy inside a city he is bent on destroying, against which he rebels; for like any system of government, an established form of expression is also a form of oppression. The avant-garde man is the opponent of an existing system.
She had won the battle against her memories. But one form of torture remained, untouched by the years, the torture of the word "why?
A snowflake is another beautifully ordered example of what simple, natural meteorological processes can produce. Stars form by gravity, collapsing into spherically ordered structures that can remain in this form only if they release tremendous heat energy into the environment.
Geology, perhaps more than any other department of natural philosophy, is a science of contemplation. It requires no experience or complicated apparatus, no minute processes upon the unknown processes of matter. It demands only an enquiring mind and senses alive to the facts almost everywhere presented in nature. And as it may be acquired without much difficulty, so it may be improved without much painful exertion.
If it is true that only misfortune can awaken a man's soul, it is a bitter truth, one that is hard to hear and accept, and it is only natural that many people deny it and say it is better for a man to live on in a trance than to wake up to torture.
If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
He that rebels against reason is a real rebel, but he that in defence of reason rebels against tyranny has a better title to Defender of the Faith, than George the Third.
The presentation of mathematics in schools should be psychological and not systematic. The teacher, so to speak, should be a diplomat. He must take account of the psychic processes in the boy in order to grip his interest, and he will succeed only if he presents things in a form intuitively comprehensible. A more abstract presentation is only possible in the upper classes.
We're all afraid of suffering or agony or torture. It's only natural in some ways. It's only human, let's say. I don't know how natural it is. It probably is conditioning.
It is natural to man to indulge in the illusion of hope. We are apt to shut our eyes against a painful truth, till she transforms us into beasts.
The most painful thing about mathematics is how far away you are from being able to use it after you have learned it.
There's no Hell mentioned in the Old Testament. The punishment of the dead is not specified there. It's only with gentle Jesus, meek and mild, that the idea of eternal torture for minor transgressions is introduced.
In more than half the nations of our world, torture certifies that the form of government is tyranny. Only tyranny, no matter how camouflaged, needs and employs torturers. Torture has no ideology.
Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.
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