We can now return to the distinction between language and symbolism. A symbol is language and yet not language. A mathematical or logical or any other kind of symbol is invented to serve a purpose purely scientific; it is supposed to have no emotional expressiveness whatever. But when once a particular symbolism has been taken into use and mastered, it reacquires the emotional expressiveness of language proper. Every mathematician knows this. At the same time, the emotions which mathematicians find expressed in their symbols are not emotions in general, they are the peculiar emotions belonging to mathematical thinking.
R. G. CollingwoodRelated topics
emotional find general kind language mathematician now once proper purpose return serve symbolism take thinking use whatever yet expressivenessRelated quotes
Fresh beauty opens one's eyes wherever it is really seen, but the very abundance and completeness of the common beauty that besets our steps prevents its being absorbed and appreciated. It is a good thing, therefore, to make short excursions now and then to the bottom of the sea among dulse and coral, or up among the clouds on mountain-tops, or in balloons, or even to creep like worms into dark holes and caverns underground, not only to learn something of what is going on in those out-of-the-way places, but to see better what the sun sees on our return to common every-day beauty.
John Muir
The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not; he must take care not to be the slave of his symbols, but always to have before his mind the realities which they merely serve to express. For these and other reasons it seems to me of the highest importance that a mathematician should be trained in no narrow school; a wide course of reading in the first few years of his mathematical study cannot fail to influence for good the character of the whole of his subsequent work.
James Whitbread Lee Glaisher
In the original discovery of a proposition of practical utility, by deduction from general principles and from experimental data, a complex algebraical investigation is often not merely useful, but indispensable; but in expounding such a proposition as a part of practical science, and applying it to practical purposes, simplicity is of the importance:-and... the more thoroughly a scientific man has studied higher mathematics, the more fully does he become aware of this truth-and... the better qualified does he become to free the exposition and application of principles from mathematical intricacy.
William John Macquorn Rankine
Art is simultaneously particular and general. This is a real dichotomy. The great thing about proportion, one aspect of art, is that it is both extremes at once. The level of quality of a work can usually be established by the extent of the polarity between its generality and particularity. Or, to state the idea a little too simply, the better the work, the more diverse its aspects. The nature of the general aspects and the particular ones changes from artist to artist and especially from time to time, since the changes are due to broad changes in philosophy. This change is the essential change in art, determining its purpose and appearance.
Donald Judd
If you want to be served you must draw the distinction between those who want to serve you and those who don't, and if the electors of South Lancashire and of the country generally are contented to allow this method of expenditure to go on, this Continental system of feeding the desires of classes and portions of the community at the expense of the whole-it is idle for you to satisfy yourselves with vague and general promises. ... If that is to be the system on which public finance is to be administered you must be prepared to resign all hopes of remission of taxation, even in good years, and in bad years you must look for a steady augmentation of the income-tax.
William Ewart Gladstone