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Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Pascal, Fermat, Wallis, and Barrow. It was Newton's good luck to come at a time when everything was ripe for the discovery, and his ability enabled him to construct almost at once a complete calculus.
In every living being there exists a capacity for endless diversity of form; each possesses the power of adapting its organization to the variations of the external world, and it is this power, called into activity by cosmic changes, which has enabled the simple zoophytes of the primitive world to climb to higher and higher stages of organization, and has brought endless variety into nature.
It is evident, therefore, that one of the most fundamental problems of psychology is that of investigating the laws of mental growth. When these laws are known, the door of the future will in a measure be opened; determination of the child's present status will enable us to forecast what manner of adult he will become.
Just as the spectroscope opened up a new astronomy by enabling the astronomer to determine some of the constituents of which distant stars are composed, so the seismograph, recording the unfelt motion of distant earthquakes, enables us to see into the earth and determine its nature with as great a certainty, up to a certain point, as if we could drive a tunnel through it and take samples of the matter passed through.
Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates. Indeed, the beauty and elegance of the physical laws themselves are only apparent when expressed in the appropriate mathematical framework.
One should not understand this compulsion to construct concepts, species, forms, purposes, laws ('a world of identical cases') as if they enabled us to fix the real world; but as a compulsion to arrange a world for ourselves in which our existence is made possible:—we thereby create a world which is calculable, simplified, comprehensible, etc., for us.
The attainment of knowledge is the high and exclusive attribute of man, among the numberless myriads of animated beings, inhabitants of the terrestrial globe. On him alone is bestowed, by the bounty of the Creator of the universe, the power and the capacity of acquiring knowledge. Knowledge is the attribute of his nature which at once enables him to improve his condition upon earth, and to prepare him for the enjoyment of a happier existence hereafter.
The theory of the method of knowing which is advanced in these pages may be termed pragmatic. ... Only that which has been organized into our disposition so as to enable us to adapt the environment to our needs and adapt our aims and desires to the situation in which we live is really knowledge.
To render aid to the worthless is sheer waste. Rain does not freshen the Dead Sea, but only enables it to dissolve more salt.
We are in the presence of a recruiting drive systematically and deliberately undertaken by American business, by American universities, and to a lesser extent, American government, often initiated by talent scouts specially sent over here to buy British brains and preempt them for service of the U.S.A. ... I look forward earnestly to the day when some reform of the American system of school education enables them to produce their own scientists so that, in an aimiable free trade of talent, there may be adequate interchange between our country and theirs, and not a one-way traffic.
We know enough to be sure that the scientific achievements of the next fifty years will be far greater, more rapid, and more surprising, than those we have already experienced. Wireless telephones and television, following naturally upon the their present path of development, would enable their owner to connect up to any room similarly equipped and hear and take part in the conversation as well as if he put his head in through the window.
When we look back beyond one hundred years over the long trails of history, we see immediately why the age we live in differs from all other ages in human annals. It remained stationary in India and in China for thousands of years. But now it is moving very fast. A priest from Thebes would probably have felt more at home at the council of Trent, two thousand years after Thebes had vanished, than Sir Isaac Newton at a modern undergraduate physical society, or George Stephenson in the Institute of Electrical Engineers. The changes have have been so sudden and so gigantic, that no period in history can be compared with the last century. The past no longer enables us even dimly to measure the future.
[Magic] enables man to carry out with confidence his important tasks, to maintain his poise and his mental integrity in fits of anger, in the throes of hate, of unrequited love, of despair and anxiety. The function of magic is to ritualize man's optimism, to enhance his faith in the victory of hope over fear. Magic expresses the greater value for man of confidence over doubt, of steadfastness over vacillation, of optimism over pessimism.