A Quote by Samuel Johnson
The mathematicians are well acquainted with the difference between pure science, which has only to do with ideas, and the application of its laws to the use of life, in which they are constrained to submit to the imperfections of matter and the influence of accidents.
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In geometry I find certain imperfections which I hold to be the reason why this science, apart from transition into analytics, can as yet make no advance from that state in which it came to us from Euclid.
As belonging to these imperfections, I consider the obscurity in the fundamental concepts of the geometrical magnitudes and in the manner and method of representing the measuring of these magnitudes, and finally the momentous gap in the theory of parallels, to fill which all efforts of mathematicians have so far been in vain.
Relations between pure and applied mathematicians are based on trust and understanding.
Namely, pure mathematicians do not trust applied mathematicians, and applied mathematicians do not understand pure mathematicians.
The laws of thought are natural laws with which we have no power to interfere, and which are of course not to be in any way confused with the artificial laws of a country, which are invented by men and can be altered by them. Every science is occupied in detecting and describing the natural laws which are inflexibly observed by the objects treated in the Science.
While, on the one hand, the end of scientific investigation is the discovery of laws, on the other, science will have reached its highest goal when it shall have reduced ultimate laws to one or two, the necessity of which lies outside the sphere of our cognition. These ultimate laws-in the domain of physical science at least-will be the dynamical laws of the relations of matter to number, space, and time. The ultimate data will be number, matter, space, and time themselves. When these relations shall be known, all physical phenomena will be a branch of pure mathematics.
He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics. The fact which interests us most is the life of the naturalist. The purest science is still biographical.
The notion that "applied" knowledge is somehow less worthy than "pure" knowledge, was natural to a society in which all useful work was performed by slaves and serfs, and in which industry was controlled by the models set by custom rather than by intelligence. Science, or the highest knowing, was then identified with pure theorizing, apart from all application in the uses of life; and knowledge relating to useful arts suffered the stigma attaching to the classes who engaged in them.
The law given from Sinai was a civil and municipal as well as a moral and religious code; it contained many statutes . . . of universal application-laws essential to the existence of men in society, and most of which have been enacted by every nation which ever professed any code of laws.
Nature is constrained by the cause of her laws which dwell inborn in her. Variant: Nature is constrained by the order of her own law which lives and works within her.
I'm interested in such things as the difference between how we perceive the world and what the world turns out to be. The difference is between the stories we tell others and the stories we tell ourselves. There is a wonderful Russian saying, which I use as the epigraph of one of my novels, which goes, He lies like an eyewitness. Which is very sly, clever and true.
Long intervals frequently elapse between the discovery of new principles in science and their practical application... Those intellectual qualifications, which give birth to new principles or to new methods, are of quite a different order from those which are necessary for their practical application.
The world of strict naturalism in which clever mathematical laws all by themselves bring the universe and life into existence, is pure [science] fiction. Theories and laws do not bring matter/energy into existence. The view that they nevertheless somehow have the capacity seems a rather desperate refuge...from the alternative possibility...Trying to avoid the clear evidence for the existence of a divine intelligence behind nature, atheist scientists are forced to ascribe creative powers to less and less credible candidates like mass/energy and the laws of nature.
There is no such thing as applied science, only the application of pure science.
It is certain that the only hope of retroductive reasoning ever reaching the truth is that there may be some natural tendency toward an agreement between the ideas which suggest themselves to the human mind and those which are concerned in the laws of nature.
One cannot ignore half of life for the purposes of science, and then claim that the results of science give a full and adequate picture of the meaning of life. All discussions of 'life' which begin with a description of man's place on a speck of matter in space, in an endless evolutionary scale, are bound to be half-measures, because they leave out most of the experiences which are important to use as human beings.
When it comes to the application to life of existing laws and morals, woman, because of her willing receptiveness, her elasticity and adaptability combined with her power of tenacious retention, has exerted an influence, the value of which is too vast to be measured.
There is a fundamental difference between religion, which is based on authority, [and] science, which is based on observation and reason. Science will win because it works.
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