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...when we wish to demonstrate a general theorem, we must give the rule as applied to a particular case; but if we wish to demonstrate a particular case, we must begin with the general rule. For we always find the thing obscure which we wish to prove, and that clear which we use for the proof; for, when a thing is put forward to be proved, we first fill ourselves with the imagination that it is therefore obscure, and on the contrary that what is to prove it, is clear, and so we understand it easily. 40

 

Blaise Pascal

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Rules for Demonstrations. I. Not to undertake to demonstrate any thing that is so evident of itself that nothing can be given that is clearer to prove it. II. To prove all propositions at all obscure, and to employ in their proof only very evident maxims or propositions already admitted or demonstrated. III. To always mentally substitute definitions in the place of things defined, in order not to be misled by the ambiguity of terms which have been restricted by definitions.

 

Blaise Pascal

 

The Fourth Gospel is admitted by all Greek scholars to be, in parts, extraordinarily obscure. No honest writer of history is obscure, as a rule, except through carelessness or ignorance — ignorance, it may be, of the art of writing, or of the subject he is writing about, or of the persons he is addressing, or of the words he is using, but, in any case, ignorance of something. But an honest writer of poetry or prophecy may be consciously obscure because a message, so to speak, has come into his mind in a certain form, and he feels this likely to prove the best form — ultimately, when his readers have thought about it.

 

Edwin Abbot

 

A happy man or woman is a better thing to find than a five-pound note. He or she is a radiating focus of goodwill; and their entrance into a room is as though another candle had been lighted. We need not care whether they could prove the forty-seventh proposition; they do a better thing than that, they practically demonstrate the great Theorem of the Liveableness of Life.

 

Robert Louis Stevenson

 

Changing a rod into a serpent and the serpent back into a rod may be clever magic, but how does such a demonstration prove that Moses spoke to God? If the only thing necessary to prove the truth of an extraordinary claim were to demonstrate an ability to bewilder, there would be no more mysteries to solve.
If a person claims that he can bring the dead back to life, and in proof of that power pulls a rabbit out of a hat, that is hardly a demonstration of the truth of his claim; it is merely an example of his ability in the art of deception. If he claims that he can fly without wings and without the use of mechanical help of any kind, and in proof of his ability pulls another rabbit out of another hat, that is not proof of his ability to fly, but of his ability to lie, and he will without much hesitation be condemned as a faker. The demonstration of one thing has absolutely no bearing in proving the truth of the other, when there is no relationship between them.

 

Joseph Lewis

 

If you write a lot of programs, and you're used to squeezing them all the time, you find that it's easy to write a program that's simple. A lot of it is having a clear sense of what you want to say — writing the proof by choosing what to prove, and being clear about that. In programming, a lot of simplicity comes from knowing what matters and what doesn't matter.

 

Ward Cunningham