Recognise Quotes (12 quotes)
A mathematician will recognise Cauchy, Gauss, Jacobi or Helmholtz after reading a few pages, just as musicians recognise, from the first few bars, Mozart, Beethoven or Schubert.
In view of such harmony in the cosmos which I, with my limited human mind, am able to recognise, there are yet people who say there is no God. But what makes me really angry is that they quote me for support of such views.
Order and regularity are more readily and clearly recognised when exhibited to the eye in a picture than they are when presented to the mind in any other manner.
Our ultimate task is to find interpretative procedures that will uncover each bias and discredit its claims to universality. When this is done the eighteenth century can be formally closed and a new era that has been here a long time can be officially recognised. The individual human being, stripped of his humanity, is of no use as a conceptual base from which to make a picture of human society. No human exists except steeped in the culture of his time and place. The falsely abstracted individual has been sadly misleading to Western political thought. But now we can start again at a point where major streams of thought converge, at the other end, at the making of culture. Cultural analysis sees the whole tapestry as a whole, the picture and the weaving process, before attending to the individual threads.
Scientists have been only too willing to show their haughty disregard for philosophy. It is also true that in going against the practices of oneâ€™s own time and in ignoring the fashion prevailing in the schools and in books, one runs the risk of being very poorly received. But, after all, each philosopher works in his own way, and each brings to his philosophical speculations the imprint of his other studies and the turn of mind which they have given him. The theologian, the jurist, the mathematician, the physicist, and the philologist can each be recognised at a glance by the way in which he wears the mantle of philosophy.
The actual evolution of mathematical theories proceeds by a process of induction strictly analogous to the method of induction employed in building up the physical sciences; observation, comparison, classification, trial, and generalisation are essential in both cases. Not only are special results, obtained independently of one another, frequently seen to be really included in some generalisation, but branches of the subject which have been developed quite independently of one another are sometimes found to have connections which enable them to be synthesised in one single body of doctrine. The essential nature of mathematical thought manifests itself in the discernment of fundamental identity in the mathematical aspects of what are superficially very different domains. A striking example of this species of immanent identity of mathematical form was exhibited by the discovery of that distinguished mathematician â€¦ Major MacMahon, that all possible Latin squares are capable of enumeration by the consideration of certain differential operators. Here we have a case in which an enumeration, which appears to be not amenable to direct treatment, can actually be carried out in a simple manner when the underlying identity of the operation is recognised with that involved in certain operations due to differential operators, the calculus of which belongs superficially to a wholly different region of thought from that relating to Latin squares.
The first principle for the student to recognise, and one to which in after life he will often have to recur, is that his work lies not in the fluctuating balance of menâ€™s opinion, but with the unchangeable facts of nature.
The â€śconflictâ€ť between the fundamental realities of Religion and the established facts of Science, is seen to be unreal as soon as Religion and Science each recognises the true borders of its dominion.
Theory always tends to become abstract as it emerges successfully from the chaos of facts by the processes of differentiation and elimination, whereby the essentials and their connections become recognised, whilst minor effects are seen to be secondary or unessential, and are ignored temporarily, to be explained by additional means.
There is a story which shows his ready wit, dating from the meeting of the British Association in Canada before the war. Tizard and a colleague inadvertently crossed over into the United States, near Niagara. When challenged by a policeman, and not having their passports with them, they produced their British Association membership cards. When the policeman told them that â€śThe American Government doesn't recognise British Science,â€ť the lightning reply came from Tizard, â€śOh, that's all right, neither does the British Government.â€ť
These were errors in thinking which caused me two years of hard work before at last, in 1915, I recognised them as such. â€¦ The final results appear almost simple; any intelligent undergraduate can understand them without much trouble. But the years of searching in the dark for a truth that one feels, but cannot express; the intense desire and the alternations of confidence and misgiving, until one breaks through to clarity and understanding, are only known to him who has himself experienced them.
We have no other means of recognising a work of art than our feeling for it.