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As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. but we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. but we do not know in what grace consists, which is the object of poetry.
-Blaise Pascal
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As We Speak Of Poetical Beauty, So

Blaise Pascal
As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. but we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. but we do not know in what grace consists, which is the object of poetry.
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Beauty Healing Medicine

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Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. appearances suggest the contrary, but there are easy explanations. music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity
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It is the facts that matter, not the proofs. physics can progress without the proofs, but we can't go on without the facts ... if the facts are right, then the proofs are a matter of playing around with the algebra correctly.
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Unless we put medical freedom into the constitution, the time will come when medicine will organize into an undercover dictatorship to restrict the art of healing to one class of men and deny equal privileges to others; the constitution of the republic should make a special privilege for medical freedoms as well as religious freedom.
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Yes, i share your concern: how to program well -though a teachable topic- is hardly taught. the situation is similar to that in mathematics, where the explicit curriculum is confined to mathematical results; how to do mathematics is something the student must absorb by osmosis, so to speak. one reason for preferring symbol-manipulating, calculating arguments is that their design is much better teachable than the design of verbal/pictorial arguments. large-scale introduction of courses on such calculational methodology, however, would encounter unsurmoutable political problems.
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