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All of modern physics is governed by that magnificent and thoroughly confusing discipline called quantum mechanics ... It has survived all tests and there is no reason to believe that there is any flaw in it.... We all know how to use it and how to apply it to problems; and so we have learned to live with the fact that nobody can understand it.
An applied mathematician loves the theorem. A pure mathematician loves the proof.
But most of us, however strict we may be, are apt to apply the epithet “beautiful” to objects that do not provoke that peculiar emotion produced by works of art.
By their very nature chemical controls are self-defeating, for they have been devised and applied without taking into account the complex biological systems against which they have been blindly hurled.
For it is a good remedy sometimes to apply nothing at all.
Fortunately science, like that nature to which it belongs, is neither limited by time nor by space. It belongs to the world, and is of no country and of no age. The more we know, the more we feel our ignorance; the more we feel how much remains unknown; and in philosophy, the sentiment of the Macedonian hero can never apply,– there are always new worlds to conquer.
If a mixture of different kinds of electrified atoms is moving along in one stream, then when electric and magnetic forces are applied to the stream simultaneously, the different kinds of atoms are sorted out, and the original stream is divided up into a number of smaller streams separated from each other. The particles in any one of the smaller streams are all of the same kind.
In the 1860s, Pasteur not only applied his germ theory to create “Pasteurization,” rescuing France’s wine and vinegar industries, but also found both the cause and cure of silkworm disease, saving growers millions of dollars. When Napoleon asked the scientist why he had not legitimately profited by his findings, Pasteur replied: “In France scientists would consider they lowered themselves by doing so.”
It is a remarkable illustration of the ranging power of the human intellect that a principle first detected in connection with the clumsy puffing of the early steam engines should be found to apply to the whole world, and possibly, even to the whole cosmic universe.
Let us now discuss the extent of the mathematical quality in Nature. According to the mechanistic scheme of physics or to its relativistic modification, one needs for the complete description of the universe not merely a complete system of equations of motion, but also a complete set of initial conditions, and it is only to the former of these that mathematical theories apply. The latter are considered to be not amenable to theoretical treatment and to be determinable only from observation.
Mere knowledge is comparatively worthless unless digested into practical wisdom and common sense as applied to the affairs of life.
My task was to show the psychologists that it is possible to apply physiological knowledge to the phenomena of psychical life.
Now when naturalists observe a close agreement in numerous small details of habits, tastes, and dispositions between two or more domestic races, or between nearly-allied natural forms, they use this fact as an argument that they are descended from a common progenitor who was thus endowed; and consequently that all should be classed under the same species. The same argument may be applied with much force to the races of man.
Prayer is not an old woman’s idle amusement. Properly understood and applied, it is the most potent instrument of action.
Relativity applies to physics, not ethics.
Rules can seldom be safely applied without a clear understanding of the principles on which they rest.
Science by itself produces a very badly deformed man who becomes rounded out into a useful creative being only with great difficulty and large expenditure of time. … It is a much smaller matter to both teach and learn pure science than it is to intelligently apply this science to the solution of problems as they arise in daily life.
Science is not gadgetry. The desirable adjuncts of modern living, although in many instances made possible by science, certainly do not constitute science. Basic scientific knowledge often (but not always) is a prerequisite to such developments, but technology primarily deserves the credit for having the financial courage, the ingenuity, and the driving energy to see to it that so-called ‘pure knowledge’ is in fact brought to the practical service of man. And it should also be recognized that those who have the urge to apply knowledge usefully have themselves often made significant contribution to pure knowledge and have even more often served as a stimulation to the activities of a pure researcher.
The Big Idea that had been developed in the seventeenth century ... is now known as the scientific method. It says that the way to proceed when investigating how the world works is to first carry out experiments and/or make observations of the natural world. Then, develop hypotheses to explain these observations, and (crucially) use the hypothesis to make predictions about the future outcome of future experiments and/or observations. After comparing the results of those new observations with the predictions of the hypotheses, discard those hypotheses which make false predictions, and retain (at least, for the time being) any hypothesis that makes accurate predictions, elevating it to the status of a theory. Note that a theory can never be proved right. The best that can be said is that it has passed all the tests applied so far.
The essence of knowledge is, having it, to apply it.
The man who classifies facts of any kind whatever, who sees their mutual relation and describes their sequence, is applying the scientific method and is a man of science.
The mathematically formulated laws of quantum theory show clearly that our ordinary intuitive concepts cannot be unambiguously applied to the smallest particles. All the words or concepts we use to describe ordinary physical objects, such as position, velocity, color, size, and so on, become indefinite and problematic if we try to use them of elementary particles.
The only way in which to treat the elements of an exact and rigorous science is to apply to them all the rigor and exactness possible.
The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. … Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.
The truly wise ask what the thing is in itself and in relation to other things, and do not trouble themselves about the use of it,—in other words, about the way in which it may be applied to the necessities of existence and what is already known. This will soon be discovered by minds of a very different order—minds that feel the joy of living, and are keen, adroit, and practical.
The usual designation of the magnitude scale to my name does less than justice to the great part that Dr. Gutenberg played in extending the scale to apply to earthquakes in all parts of the world.
There are no better terms available to describe the difference between the approach of the natural and the social sciences than to call the former ‘objective’ and the latter ‘subjective.’ ... While for the natural scientist the contrast between objective facts and subjective opinions is a simple one, the distinction cannot as readily be applied to the object of the social sciences. The reason for this is that the object, the ‘facts’ of the social sciences are also opinions—not opinions of the student of the social phenomena, of course, but opinions of those whose actions produce the object of the social scientist.
There is common misapprehension that the magnitude scale is itself some kind of instrument or apparatus. Visitors will ask to “see the scale,” and are disconcerted by being referred to tables and charts used for applying the scale to readings taken from the seismograms.
There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that... or: There is capitalism in so far as... The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills. [p.222]
There is no arithmetician like him who hath learned to number his days, and to apply his heart unto wisdom.
These duplicates in those parts of the body, without which a man might have very well subsisted, though not so well as with them, are a plain demonstration of an all-wise Contriver, as those more numerous copyings which are found among the vessels of the same body are evident demonstrations that they could not be the work of chance. This argument receives additional strength if we apply it to every animal and insect within our knowledge, as well as to those numberless living creatures that are objects too minute for a human eye: and if we consider how the several species in this whole world of life resemble one another in very many particulars, so far as is convenient for their respective states of existence, it is much more probable that a hundred millions of dice should be casually thrown a hundred millions of times in the same number than that the body of any single animal should be produced by the fortuitous concourse of matter.
This is the reason why all attempts to obtain a deeper knowledge of the foundations of physics seem doomed to me unless the basic concepts are in accordance with general relativity from the beginning. This situation makes it difficult to use our empirical knowledge, however comprehensive, in looking for the fundamental concepts and relations of physics, and it forces us to apply free speculation to a much greater extent than is presently assumed by most physicists.
This quality of genius is, sometimes, difficult to be distinguished from talent, because high genius includes talent. It is talent, and something more. The usual distinction between genius and talent is, that one represents creative thought, the other practical skill: one invents, the other applies. But the truth is, that high genius applies its own inventions better than talent alone can do. A man who has mastered the higher mathematics, does not, on that account, lose his knowledge of arithmetic. Hannibal, Napoleon, Shakespeare, Newton, Scott, Burke, Arkwright, were they not men of talent as well as men of genius?
Wallace’s error on human intellect arose from the in adequacy of his rigid selectionism, not from a failure to apply it. And his argument repays our study today, since its flaw persists as the weak link in many of the most ‘modern’ evolutionary speculations of our current literature. For Wallace’s rigid selectionism is much closer than Darwin’s pluralism to the attitude embodied in our favored theory today, which, ironically in this context, goes by the name of ‘Neo-Darwinism.’
We live in a capitalist economy, and I have no particular objection to honorable self-interest. We cannot hope to make the needed, drastic improvement in primary and secondary education without a dramatic restructuring of salaries. In my opinion, you cannot pay a good teacher enough money to recompense the value of talent applied to the education of young children. I teach an hour or two a day to tolerably well-behaved near-adults–and I come home exhausted. By what possible argument are my services worth more in salary than those of a secondary-school teacher with six classes a day, little prestige, less support, massive problems of discipline, and a fundamental role in shaping minds. (In comparison, I only tinker with intellects already largely formed.)
What made von Liebig and his students “different” from other chemists was their effort to apply their fundamental discoveries to the development of specific chemical processes and products.
When wireless is perfectly applied the whole earth will be converted into a huge brain, which in fact it is, all things being particles of a real and rhythmic whole. We shall be able to communicate with one another instantly, irrespective of distance. Not
[Charles Kettering] is unique in that he combines in one individual the interest in pure science with the practical ability to apply knowledge in useful devices.