Mathematics have a triple aim. They must furnish an instrument for the study of nature. But that is not all: they have a philosophic aim and, I dare maintain, an esthetic aim. They must aid the philosopher to fathom the notions of number, of space, of time. And above all, their adepts find therein delights analogous to those given by painting and music. They admire the delicate harmony of numbers and forms; they marvel when a new discovery opens to them an unexpected perspective; and has not the joy they thus feel the esthetic character, even though the senses take no part therein? Only a privileged few are called to enjoy it fully, it is true, but is not this the case for all the noblest arts? This is why I do not hesitate to say that mathematics deserve to be cultivated for their own sake, and the theories inapplicable to physics as well as the others. Even if the physical aim and the esthetic aim were not united, we ought not to sacrifice either.
Henri PoincaréRelated topics
above aid aim case character dare delicate discovery esthetic fathom few find furnish given harmony instrument joy marvel mathematics music nature number numbers ought painting perspective philosopher physical physics sacrifice sake say space study take thus time triple unexpected well others artsRelated quotes
You are not traditionally beautiful; and you know it. We women do. But what most people mean by beauty is really a kind of aesthetic acceptability, not so much character as a lack of it, a set of features and lineaments that hide their history, that suggest history itself does not exist. But the template by which we recognize the features and forms in the human body that cause the heart to halt, threatening to spill us over into the silence of death-that is drawn on another part of the soul entirely...But all sing, chant, hymn the history of the body, if only because we all know how people regard bodies that deviate from the lauded and totally abnormal norm named beauty. Most of us would rather not recognize such desires in ourselves and thus avoid all contemplation of what the possession of such features means about the lives, the bodies, the histories of others, preferring instead to go on merely accepting the acceptable. But that is not who I am.
Samuel R. Delany
I have always been strong for a large increase of labour representation in the House of Commons... Now, I dare say the day may come-it may come sooner than some think-when the Liberal party will be transformed or superseded by some new party; but before the working population of this country have their destinies in their own hands, as they will assuredly do within a measurable distance of time, there is enough ground to be cleared which only the Liberal party is capable of clearing. The ideal of the Liberal party is that view of things which believes that the welfare of all is bound up with injustice being done to none. Above all, according to the ideal of the Liberal party-that party from which I beseech you, not for my sake, but for your own, not to sever yourselves-the ideal of the Liberal party is this-that in the mass of the toilers on land all the fountains of national life abide and the strongest and most irresistible currents flow.
John Morley, 1st Viscount Morley of Blackburn
My most dear lord, King and husband, / The hour of my death now drawing on, the tender love I owe you forceth me, my case being such, to commend myself to you, and to put you in remembrance with a few words of the health and safeguard of your soul which you ought to prefer before all worldly matters, and before the care and pampering of your body, for the which you have cast me into many calamities and yourself into many troubles. For my part, I pardon you everything, and I wish to devoutly pray God that He will pardon you also. For the rest, I commend unto you our daughter Mary, beseeching you to be a good father unto her, as I have heretofore desired. I entreat you also, on behalf of my maids, to give them marriage portions, which is not much, they being but three. For all my other servants I solicit the wages due them, and a year more, lest they be unprovided for. Lastly, I make this vow, that mine eyes desire you above all things. / Katharine the Quene.
Catherine of Aragon
In the "Alexandrian" explanation described above, the multiple from which evolution emerges is both secondary and sinful from its origin: it represents in fact (an idea that smacks of Manicheanism and the Hindu metaphysical systems) broken and pulverized unity. Starting from a very much more modern and completely different point of view, let us assert, as our original postulate, that, the multiple (that is, non-being, if taken in the pure state) being the only rational form of a creatable (creabile) nothingness, the creative act is comprehensible only as a gradual process of arrangement and unification, which amounts to accepting that to create is to unite. And, indeed, there is nothing to prevent our holding that union creates. To the objection that union presupposes already existing elements, I shall answer that physics has just shown us (in the case of mass) that experientially (and for all the protests of "common sense") the moving object exists only as the product of its motion.
Pierre Teilhard de Chardin
What, then, is the animal? First of all, a system of plant-souls. The unity of those plant-souls, which unity nature itself produces, is the soul of the animal. Its world is therefore partly that of the plants - its nourishment, for instance, it receives partly through synthesis from vegetable, and through analysis from animal nature - and partly that of the animals, whereof we shall speak directly. Each product of nature is an organically in-itself completed totality in space, like the plant. Hence, the unknown x which we are looking for must also be such a whole or totality, and in so far it must also have a principle of organization, a sphere and central point of this organization; in short, the same which we have called the soul of the plant, which thus remains common to both. ... The animal is a system of plant-souls, and the plant is a separated, isolated part of an animal. Both reciprocally affect each other.
Johann Gottlieb Fichte
