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Home > Category Index for Science Quotations > Category Index V > Category: Value

Value Quotes (365 quotes)
Valuable Quotes


...the study of butterflies—creatures selected as the types of airiness and frivolity—instead of being despised, will some day be valued as one of the most important branches of Biological science.
From The Naturalist on the River Amazons: A record of Adventures, Habits of Animals, Sketches of Brazilian and Indian life, and Aspects of Nature under the Equator, During Eleven Years of Travel (1864), 413.
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Clarke's Law of Evolution: It has yet to be proven that intelligence has any survival value.
M. S. Thambirajah, Psychological Basis of Psychiatry (2005), 33.
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Conclusions
I. A curve has been found representing the frequency distribution of standard deviations of samples drawn from a normal population.
II. A curve has been found representing the frequency distribution of values of the means of such samples, when these values are measured from the mean of the population in terms of the standard deviation of the sample…
IV. Tables are given by which it can be judged whether a series of experiments, however short, have given a result which conforms to any required standard of accuracy or whether it is necessary to continue the investigation.
'The Probable Error of a Mean', Biometrika, 1908, 6, 25.
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Discovery always carries an honorific connotation. It is the stamp of approval on a finding of lasting value. Many laws and theories have come and gone in the history of science, but they are not spoken of as discoveries. Kepler is said to have discovered the laws of planetary motion named after him, but no the many other 'laws' which he formulated. ... Theories are especially precarious, as this century profoundly testifies. World views can and do often change. Despite these difficulties, it is still true that to count as a discovery a finding must be of at least relatively permanent value, as shown by its inclusion in the generally accepted body of scientific knowledge.
Discovery in the Physical Sciences (1969). In Rodney P. Carlisle, Scientific American Inventions and Discoveries (2004), 179.
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If the Indians hadn’t spent the $24. In 1626 Peter Minuit, first governor of New Netherland, purchased Manhattan Island from the Indians for about $24. … Assume for simplicity a uniform rate of 7% from 1626 to the present, and suppose that the Indians had put their $24 at [compound] interest at that rate …. What would be the amount now, after 280 years? 24 x (1.07)280 = more than 4,042,000,000.
The latest tax assessment available at the time of writing gives the realty for the borough of Manhattan as $3,820,754,181. This is estimated to be 78% of the actual value, making the actual value a little more than $4,898,400,000.
The amount of the Indians’ money would therefore be more than the present assessed valuation but less than the actual valuation.
In A Scrap-book of Elementary Mathematics: Notes, Recreations, Essays (1908), 47-48.
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Il y aura toujours une valeur (ou plusieurs) qui dépassera toutes les autres.
There will always be one (or more) value that will exceed all others.
Origin French in 'Les Valeurs Extrêmes des Distributions Statistiques', Annales de l'Institut Henri Poincaré (1935), 5, 115. English by Webmaster using Google Translate.
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La santé est le trésor le plus précieux et le plus facile à perdre; c'est cependant le plus mal gardé.
Health is the most valuable and most easily lost treasure; yet it is the most poorly kept.
Maxim No. 308 in Maximes, Réflexions et Pensées Diverses (1819), 242.
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Mathematical truth has validity independent of place, personality, or human authority. Mathematical relations are not established, nor can they be abrogated, by edict. The multiplication table is international and permanent, not a matter of convention nor of relying upon authority of state or church. The value of π is not amenable to human caprice. The finding of a mathematical theorem may have been a highly romantic episode in the personal life of the discoverer, but it cannot be expected of itself to reveal the race, sex, or temperament of this discoverer. With modern means of widespread communication even mathematical notation tends to be international despite all nationalistic tendencies in the use of words or of type.
Anonymous
In 'Light Thrown on the Nature of Mathematics by Certain Aspects of Its Development', Mathematics in General Education (1940), 256. This is the Report of the Committee on the Function of Mathematics in General Education of the Commission on Secondary School Curriculum, which was established by the Executive Board of the Progressive Education Association in 1932.
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A general course in mathematics should be required of all officers for its practical value, but no less for its educational value in training the mind to logical forms of thought, in developing the sense of absolute truthfulness, together with a confidence in the accomplishment of definite results by definite means.
In 'Mathematics at West Point and Annapolis', United States Bureau of Education, Bulletin 1912, No. 2, 11.
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A calculating engine is one of the most intricate forms of mechanism, a telegraph key one of the simplest. But compare their value.
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 174.
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A conflict arises when a religious community insists on the absolute truthfulness of all statements recorded in the Bible. This means an intervention on the part of religion into the sphere of science; this is where the struggle of the Church against the doctrines of Galileo and Darwin belongs. On the other hand, representatives of science have often made an attempt to arrive at fundamental judgments with respect to values and ends on the basis of scientific method, and in this way have set themselves in opposition to religion. These conflicts have all sprung from fatal errors.
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A machine has value only as it produces more than it consumes—so check your value to the community.
As given in M. P. Singh, Quote Unquote: A Handbook of Quotations (2005), 86. Webmaster has not yet found a more reliable source.
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A man who sets out to justify his existence and his activities has to distinguish two different questions. The first is whether the work which he does is worth doing; and the second is why he does it (whatever its value may be).
In A Mathematician's Apology (1940, 2012), 66.
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A man’s first duty, a young man’s at any rate, is to be ambitious … the noblest ambition is that of leaving behind one something of permanent value.
In A Mathematician's Apology (1940, 2012), 77.
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A man’s value to the community depends primarily on how far his feelings, thoughts, and actions are directed towards promoting the good of his fellows. We call him good or bad according to how he stands in this matter. It looks at first sight as if our estimate of a man depended entirely on his social qualities.
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A person who is religiously enlightened appears to me to be one who has, to the best of his ability, liberated himself from the fetters of his selfish desires and is preoccupied with thoughts, feelings, and aspirations to which he clings because of their superpersonal value. It seems to me that what is important is the force of this superpersonal content and the depth of the conviction concerning its overpowering meaningfulness, regardless of whether any attempt is made to unite this content with a divine Being, for otherwise it would not be possible to count Buddha and Spinoza as religious personalities. Accordingly, a religious person is devout in the sense that he has no doubt of the significance and loftiness of those superpersonal objects and goals which neither require nor are capable of rational foundation. They exist with the same necessity and matter-of-factness as he himself. In this sense religion is the age-old endeavor of mankind to become clearly and completely conscious of these values and goals and constantly to strengthen and extend their effect. If one conceives of religion and science according to these definitions then a conflict between them appears impossible. For science can only ascertain what is, but not what should be, and outside of its domain value judgments of all kinds remain necessary.
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A subtle thought that is in error may yet give rise to fruitful inquiry that can establish truths of great value.
In Steven D. Price, 1001 Smartest Things Ever Said (2005), 163.
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About 6 or 8 years ago My Ingenious friend Mr John Robinson having [contrived] conceived that a fire engine might be made without a Lever—by Inverting the Cylinder & placing it above the mouth of the pit proposed to me to make a model of it which was set about by having never Compleated & I [being] having at that time Ignorant little knoledge of the machine however I always thought the Machine Might be applied to [more] other as valuable purposes [than] as drawing Water.
Entry in notebook (1765). The bracketed words in square brackets were crossed out by Watt. in Eric Robinson and Douglas McKie (eds.), Partners in Science: Letters of James Watt and Joseph Black (1970), 434.
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Accountants and second-rate business school jargon are in the ascendant. Costs, which rise rapidly, and are easily ascertained and comprehensible, now weigh more heavily in the scales than the unquantifiable and unpredictable values and future material progress. Perhaps science will only regain its lost primacy as peoples and government begin to recognize that sound scientific work is the only secure basis for the construction of policies to ensure the survival of Mankind without irreversible damage to Planet Earth.
In New Scientist, March 3, 1990.
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All fossil anthropoids found hitherto have been known only from mandibular or maxillary fragments, so far as crania are concerned, and so the general appearance of the types they represented had been unknown; consequently, a condition of affairs where virtually the whole face and lower jaw, replete with teeth, together with the major portion of the brain pattern, have been preserved, constitutes a specimen of unusual value in fossil anthropoid discovery. Here, as in Homo rhodesiensis, Southern Africa has provided documents of higher primate evolution that are amongst the most complete extant. Apart from this evidential completeness, the specimen is of importance because it exhibits an extinct race of apes intermediate between living anthropoids and man ... Whether our present fossil is to be correlated with the discoveries made in India is not yet apparent; that question can only be solved by a careful comparison of the permanent molar teeth from both localities. It is obvious, meanwhile, that it represents a fossil group distinctly advanced beyond living anthropoids in those two dominantly human characters of facial and dental recession on one hand, and improved quality of the brain on the other. Unlike Pithecanthropus, it does not represent an ape-like man, a caricature of precocious hominid failure, but a creature well advanced beyond modern anthropoids in just those characters, facial and cerebral, which are to be anticipated in an extinct link between man and his simian ancestor. At the same time, it is equally evident that a creature with anthropoid brain capacity and lacking the distinctive, localised temporal expansions which appear to be concomitant with and necessary to articulate man, is no true man. It is therefore logically regarded as a man-like ape. I propose tentatively, then, that a new family of Homo-simidæ be created for the reception of the group of individuals which it represents, and that the first known species of the group be designated Australopithecus africanus, in commemoration, first, of the extreme southern and unexpected horizon of its discovery, and secondly, of the continent in which so many new and important discoveries connected with the early history of man have recently been made, thus vindicating the Darwinian claim that Africa would prove to be the cradle of mankind.
'Australopithicus africanus: The Man-Ape of South Africa', Nature, 1925, 115, 195.
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All government, in its essence, is organized exploitation, and in virtually all its existing forms it is the implacable enemy of every industrious and well-disposed man ... The typical politician is not only a rascal but also a jackass, so he greatly values the puerile notoriety and adulation that sensible men try to avoid.
…...
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All knowledge attains its ethical value and its human significance only by the human sense with which it is employed. Only a good man can be a great physician.
Inaugural address (1882), quoted in Johann Hermann Baas, Henry Ebenezer Handerson (trans.), Outlines of the History of Medicine and the Medical Profession (1889), 966.
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All of the books in the world contain no more information than is broadcast as video in a single large American city in a single year. Not all bits have equal value.
…...
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All schools, all colleges have two great functions: to confer, and to conceal valuable knowledge.
(5 Nov 1908). 'More Maxims of Mark,' Mark Twain Collected Tales, Sketches, Speeches, & Essays, 1891-1910 (1992), 941. In Mark Twain and Brian Collins (ed.), When in Doubt, Tell the Truth: and Other Quotations from Mark Twain (1996), 43.
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All sorts of dung and compost contain some matter which, when mixed with the soil, ferments therein; and by such ferment dissolves, crumbles, and divides the earth very much. This is the chief and almost only use of dung. … This proves, that its (manure) use is not to nourish, but to dissolve, i.e., divide the terrestrial matter, which affords nourishment to the Mouths of vegetable roots.
His underestimate of the value of manure.
In The Horse-Hoeing Husbandry (1733), 18.
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All that is valuable in human society depends upon the opportunity for development accorded the individual.
…...
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Always preoccupied with his profound researches, the great Newton showed in the ordinary-affairs of life an absence of mind which has become proverbial. It is related that one day, wishing to find the number of seconds necessary for the boiling of an egg, he perceived, after waiting a minute, that he held the egg in his hand, and had placed his seconds watch (an instrument of great value on account of its mathematical precision) to boil!
This absence of mind reminds one of the mathematician Ampere, who one day, as he was going to his course of lectures, noticed a little pebble on the road; he picked it up, and examined with admiration the mottled veins. All at once the lecture which he ought to be attending to returned to his mind; he drew out his watch; perceiving that the hour approached, he hastily doubled his pace, carefully placed the pebble in his pocket, and threw his watch over the parapet of the Pont des Arts.
Popular Astronomy: a General Description of the Heavens (1884), translated by J. Ellard Gore, (1907), 93.
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Among people I have met, the few whom I would term “great” all share a kind of unquestioned, fierce dedication; an utter lack of doubt about the value of their activities (or at least an internal impulse that drives through any such angst); and above all, a capacity to work (or at least to be mentally alert for unexpected insights) at every available moment of every day of their lives.
From The Lying Stones of Marrakech: Penultimate Reflections in Natural History (2000), 76.
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Anthropology has reached that point of development where the careful investigation of facts shakes our firm belief in the far-reaching theories that have been built up. The complexity of each phenomenon dawns on our minds, and makes us desirous of proceeding more cautiously. Heretofore we have seen the features common to all human thought. Now we begin to see their differences. We recognize that these are no less important than their similarities, and the value of detailed studies becomes apparent. Our aim has not changed, but our method must change. We are still searching for the laws that govern the growth of human culture, of human thought; but we recognize the fact that before we seek for what is common to all culture, we must analyze each culture by careful and exact methods, as the geologist analyzes the succession and order of deposits, as the biologist examines the forms of living matter. We see that the growth of human culture manifests itself in the growth of each special culture. Thus we have come to understand that before we can build up the theory of the growth of all human culture, we must know the growth of cultures that we find here and there among the most primitive tribes of the Arctic, of the deserts of Australia, and of the impenetrable forests of South America; and the progress of the civilization of antiquity and of our own times. We must, so far as we can, reconstruct the actual history of mankind, before we can hope to discover the laws underlying that history.
The Jesup North Pacific Expedition: Memoir of the American Museum of Natural History (1898), Vol. 1, 4.
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Anthropology is the study of human beings as creatures of society. It fastens its attention upon those physical characteristics and industrial techniques, those conventions and values, which distinguish one community from all others that belong to a different tradition.
In 'The Science of Custom', Patterns of Culture (1934, 2005), 1.
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Any experiment may be regarded as forming an individual of a 'population' of experiments which might be performed under the same conditions. A series of experiments is a sample drawn from this population.
Now any series of experiments is only of value in so far as it enables us to form a judgment as to the statistical constants of the population to which the experiments belong. In a great number of cases the question finally turns on the value of a mean, either directly, or as the mean difference between the two qualities.
If the number of experiments be very large, we may have precise information as to the value of the mean, but if our sample be small, we have two sources of uncertainty:— (I) owing to the 'error of random sampling' the mean of our series of experiments deviates more or less widely from the mean of the population, and (2) the sample is not sufficiently large to determine what is the law of distribution of individuals.
'The Probable Error of a Mean', Biometrika, 1908, 6, 1.
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Any man who is intelligent must, on considering that health is of the utmost value to human beings, have the personal understanding necessary to help himself in diseases, and be able to understand and to judge what physicians say and what they administer to his body, being versed in each of these matters to a degree reasonable for a layman.
Affections, in Hippocrates, trans. P. Potter (1988), Vol. 5, 7.
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Armed with all the powers, enjoying all the wealth they owe to science, our societies are still trying to practice and to teach systems of values already destroyed at the roots by that very science. Man knows at last that he is alone in the indifferent immensity of the universe, whence which he has emerged by chance. His duty, like his fate, is written nowhere.
In Jacques Monod and Austryn Wainhouse (trans.), Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology (1971), 171.
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Art arises in those strange complexities of action that are called human beings. It is a kind of human behavior. As such it is not magic, except as human beings are magical. Nor is it concerned in absolutes, eternities, “forms,” beyond those that may reside in the context of the human being and be subject to his vicissitudes. Art is not an inner state of consciousness, whatever that may mean. Neither is it essentially a supreme form of communication. Art is human behavior, and its values are contained in human behavior.
In Art Is Action: A Discussion of Nine Arts in a Modern World (1939), 1.
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As children we all possess a natural, uninhibited curiosity, a hunger for explanation, which seems to die slowly as we age—suppressed, I suppose, by the high value we place on conformity and by the need not to appear ignorant.
It betokens a conviction that somehow science is innately incomprehensible. It precludes reaching deeper, thereby denying the profound truth that understanding enriches experience, that explanation vastly enhances the beauty of the natural world in the eye of the beholder.
In Toward the Habit of Truth (1990).
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As to Bell’s talking telegraph, it only creates interest in scientific circles, and, as a toy it is beautiful; but … its commercial value will be limited.
Letter to William D. Baldwin, his attorney (1 Nov 1876). Telephone Investigating Committee, House of Representatives, United States 49th Congress, 1st Session, Miscellaneous Documents (1886), No. 355, 1186.
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Ask why God made the GEM so small,
And why so huge the granite?
Because God meant, mankind should set
That higher value on it.
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Astrology is a disease, not a science... It is a tree under the shadow of which all sorts of superstitions thrive. ... Only fools and charlatans lend value to it.
Letter to Marseilles, 1195. Responsa, ii. 25b. In Philip Birnbaum (ed.), Mishneh Torah: Maimonides' Code of Law and Ethics (1974), 35.
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Authority—the fact, namely, that something has already happened or been said or decided, is of great value; but it is only a pedant who demands authority for everything.
In The Maxims and Reflections of Goethe (1906), 188.
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Bad times have a scientific value. These are occasions a good learner would not miss.
In 'Considerations by the Way', The Conduct of Life (1860) collected in The Works of Ralph Waldo Emerson: Comprising His Essays, Lectures, Poems and Orations (1882), Vol. 2, 420.
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Biodiversity is our most valuable but least appreciated resource.
In 'Unmined Riches', The Diversity of Life (1992), 281.
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But having considered everything which has been said, one could by this believe that the earth and not the heavens is so moved, and there is no evidence to the contrary. Nevertheless, this seems prima facie as much, or more, against natural reason as are all or several articles of our faith. Thus, that which I have said by way of diversion (esbatement) in this manner can be valuable to refute and check those who would impugn our faith by argument.
On the Book of the Heavens and the World of Aristotle [1377], bk. II, ch. 25, sect. 10, trans. A. D. Menut and A. J. Denomy, quoted in Marshall Clagett, The Science of Mechanics in the Middle Ages (1959), 606.
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But to proceed; as in order and place, so also in matter of her Creation, Woman far excells Man. things receive their value from the matter they are made of, and the excellent skill of their maker: Pots of common clay must not contend with China-dishes, nor pewter utensils vye dignity with those of silver…. Woman was not composed of any inanimate or vile dirt, but of a more refined and purified substance, enlivened and actuated by a Rational Soul, whose operations speak it a beam, or bright ray of Divinity.
In Female Pre-eminence: Or, The Dignity and Excellency of that Sex above the Male, translation (1670).
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But weightier still are the contentment which comes from work well done, the sense of the value of science for its own sake, insatiable curiosity, and, above all, the pleasure of masterly performance and of the chase. These are the effective forces which move the scientist. The first condition for the progress of science is to bring them into play.
from his preface to Claude Bernard's 'Experimental Medicine'
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But when you come right down to it, the reason that we did this job is because it was an organic necessity. If you are a scientist you cannot stop such a thing. If you are a scientist you believe that it is good to find out how the world works; that it is good to find out what the realities are; that it is good to turn over to mankind at large the greatest possible power to control the world and to deal with it according to its lights and values.
Regarding the atomic bomb project.
From speech at Los Alamos (17 Oct 1945). Quoted in David C. Cassidy, J. Robert Oppenheimer and the American Century (2009), 214.
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By research in pure science I mean research made without any idea of application to industrial matters but solely with the view of extending our knowledge of the Laws of Nature. I will give just one example of the ‘utility’ of this kind of research, one that has been brought into great prominence by the War—I mean the use of X-rays in surgery. Now, not to speak of what is beyond money value, the saving of pain, or, it may be, the life of the wounded, and of bitter grief to those who loved them, the benefit which the state has derived from the restoration of so many to life and limb, able to render services which would otherwise have been lost, is almost incalculable. Now, how was this method discovered? It was not the result of a research in applied science starting to find an improved method of locating bullet wounds. This might have led to improved probes, but we cannot imagine it leading to the discovery of X-rays. No, this method is due to an investigation in pure science, made with the object of discovering what is the nature of Electricity. The experiments which led to this discovery seemed to be as remote from ‘humanistic interest’ —to use a much misappropriated word—as anything that could well be imagined. The apparatus consisted of glass vessels from which the last drops of air had been sucked, and which emitted a weird greenish light when stimulated by formidable looking instruments called induction coils. Near by, perhaps, were great coils of wire and iron built up into electro-magnets. I know well the impression it made on the average spectator, for I have been occupied in experiments of this kind nearly all my life, notwithstanding the advice, given in perfect good faith, by non-scientific visitors to the laboratory, to put that aside and spend my time on something useful.
In Speech made on behalf of a delegation from the Conjoint Board of Scientific Studies in 1916 to Lord Crewe, then Lord President of the Council. In George Paget Thomson, J. J. Thomson and the Cavendish Laboratory in His Day (1965), 167-8.
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Can the cultural evolution of higher ethical values gain a direction and momentum of its own and completely replace genetic evolution? I think not. The genes hold culture an a leash. The leash is very long, but inevitably values will be constrained in accordance with their effects in the human gene pool. The brain is a product of evolution. Human behaviour—like the deepest capacities for emotional response which drive and guide it—is the circuitous technique by which human genetic material has been and will be kept intact. Morality has no other demonstrable ultimate function.
In On Human Nature (1978), 167. In William Andrew Rottschaefer, The Biology and Psychology of Moral Agency (1998), 58.
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Conservation is an American value, and it is lacking from this bill.
Jim Costa
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Decades spent in contact with science and its vehicles have directed my mind and senses to areas beyond their reach. I now see scientific accomplishments as a path, not an end; a path leading to and disappearing in mystery. Science, in fact, forms many paths branching from the trunk of human progress; and on every periphery they end in the miraculous. Following these paths far enough, one must eventually conclude that science itself is a miracle—like the awareness of man arising from and then disappearing in the apparent nothingness of space. Rather than nullifying religion and proving that “God is dead,” science enhances spiritual values by revealing the magnitudes and minitudes—from cosmos to atom—through which man extends and of which he is composed.
A Letter From Lindbergh', Life (4 Jul 1969), 60B. In Eugene C. Gerhart, Quote it Completely! (1998), 409.
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Despite rapid progress in the right direction, the program of the average elementary school has been primarily devoted to teaching the fundamental subjects, the three R’s, and closely related disciplines… Artificial exercises, like drills on phonetics, multiplication tables, and formal writing movements, are used to a wasteful degree. Subjects such as arithmetic, language, and history include content that is intrinsically of little value. Nearly every subject is enlarged unwisely to satisfy the academic ideal of thoroughness… Elimination of the unessential by scientific study, then, is one step in improving the curriculum.
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Discoveries that are anticipated are seldom the most valuable. … It’s the scientist free to pilot his vessel across hidden shoals into open seas who gives the best value.
From 'Why Our Scientific Discoveries Need to Surprise Us', in The Globe and Mail (1 Oct 2011).
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Diversity, be it ever so little, has value in relieving stress.
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Each time one of the medicine men dies, it's as if a library has burned down.
{Referring to potential knowledge from indiginous peoples of the medicinal value of tropical plants, speaking as director of the plant program of the World Wildlife Fund and having spent many months living with the Tirio tribe on the Suriname-Brazil border.]
Quoted in Jamie Murphy and Andrea Dorfman, 'The Quiet Apocalypse,' Time (13 Oct 1986).
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Education is a mechanism for inducing change and for providing the means of accommodation and adjustment to change. At the same time, as an institution, education is given the responsibility for insuring the preservation and transfer and therefore, the continuity of society’s knowledge, skills, and values.
As quoted by Luther H. Evans and George E. Arnstein (eds.), in Automation and the Challenge to Education: Proceedings of a Symposium (1962).
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Even as a coin attains its full value when it is spent, so life attains its supreme value when one knows how to forfeit it with grace when the time comes.
In The Crystal Arrow: Essays on Literature, Travel, Art, Love, and the History of Medicine (1964), 436.
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Every scientist, through personal study and research, completes himself and his own humanity. ... Scientific research constitutes for you, as it does for many, the way for the personal encounter with truth, and perhaps the privileged place for the encounter itself with God, the Creator of heaven and earth. Science shines forth in all its value as a good capable of motivating our existence, as a great experience of freedom for truth, as a fundamental work of service. Through research each scientist grows as a human being and helps others to do likewise.
Address to the members of the Pontifical Academy of Sciences (13 Nov 2000). In L’Osservatore Romano (29 Nov 2000), translated in English edition, 5.
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Few people doubt that the Apollo missions to the Moon as well as the precursory Mercury and Gemini missions not only had a valuable role for the United States in its Cold War with the Soviet Union but also lifted the spirits of humankind. In addition, the returned samples of lunar surface material fueled important scientific discoveries.
In 'Is Human Spaceflight Obsolete?', Issues in Science and Technology (Summer 2004).
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Finally, I aim at giving denominations to things, as agreeable to truth as possible. I am not ignorant that words, like money, possess an ideal value, and that great danger of confusion may be apprehended from a change of names; in the mean time it cannot be denied that chemistry, like the other sciences, was formerly filled with improper names. In different branches of knowledge, we see those matters long since reformed: why then should chemistry, which examines the real nature of things, still adopt vague names, which suggest false ideas, and favour strongly of ignorance and imposition? Besides, there is little doubt but that many corrections may be made without any inconvenience.
Physical and Chemical Essays (1784), Vol. I, xxxvii.
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For between true Science, and erroneous Doctrines, Ignorance is in the middle. Naturall sense and imagination, are not subject to absurdity. Nature it selfe cannot erre: and as men abound in copiousnesses of language; so they become more wise, or more mad than ordinary. Nor is it possible without Letters for any man to become either excellently wise, or (unless his memory be hurt by disease, or ill constitution of organs) excellently foolish. For words are wise men's counters, they do but reckon by them; but they are the money of fools that value them by the authority of an Aristotle, a Cicero, or a Thomas, or any other Doctor whatsoever, if but a man.
Leviathan (1651), ed. C. B. Macpherson (1968), Part 1, Chapter 4, 106.
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For those who have seen the Earth from space, and for the hundreds and perhaps thousands more who will, the experience most certainly changes your perspective. The things that we share in our world are far more valuable than those which divide us.
As quoted, without citation, in Jeffrey O. Bennett, The Cosmic Perspective (1999), 24.
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For those [observations] that I made in Leipzig in my youth and up to my 21st year, I usually call childish and of doubtful value. Those that I took later until my 28th year [i.e., until 1574] I call juvenile and fairly serviceable. The third group, however, which I made at Uraniborg during approximately the last 21 years with the greatest care and with very accurate instruments at a more mature age, until I was fifty years of age, those I call the observations of my manhood, completely valid and absolutely certain, and this is my opinion of them.
In H. Raeder, E. and B. Stromgren (eds. and trans.), Tycho Brahe’s Description of his Instruments and Scientific Work: as given in Astronomiae Instauratae Mechanica, Wandesburgi 1598 (1946), 110.
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Former arbiters of taste must have felt (as so many apostles of ‘traditional values’ and other highminded tags for restriction and conformity do today) that maintaining the social order required a concept of unalloyed heroism. Human beings so designated as role models had to embody all virtues of the paragon–which meant, of course, that they could not be described in their truly human and ineluctably faulted form.
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Gradually, … the aspect of science as knowledge is being thrust into the background by the aspect of science as the power of manipulating nature. It is because science gives us the power of manipulating nature that it has more social importance than art. Science as the pursuit of truth is the equal, but not the superior, of art. Science as a technique, though it may have little intrinsic value, has a practical importance to which art cannot aspire.
In The Scientific Outlook (1931, 2009), xxiv.
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Guard well your spare moments. They are like uncut diamonds. Discard them and their value will never be known. Improve them and they will become the brightest gems in a useful life.
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He that knows the secrets of nature with Albertus Magnus, or the motions of the heavens with Galileo, or the cosmography of the moon with Hevelius, or the body of man with Galen, or the nature of diseases with Hippocrates, or the harmonies in melody with Orpheus, or of poesy with Homer, or of grammar with Lilly, or of whatever else with the greatest artist; he is nothing if he knows them merely for talk or idle speculation, or transient and external use. But he that knows them for value, and knows them his own, shall profit infinitely.
In Bertram Doben (ed.), Centuries of Meditations (1908), The Third Century, No. 41, 189-190.
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How many and how curious problems concern the commonest of the sea-snails creeping over the wet sea-weed! In how many points of view may its history be considered! There are its origin and development, the mystery of its generation, the phenomena of its growth, all concerning each apparently insignificant individual; there is the history of the species, the value of its distinctive marks, the features which link it with the higher and lower creatures, the reason why it takes its stand where we place it in the scale of creation, the course of its distribution, the causes of its diffusion, its antiquity or novelty, the mystery (deepest of mysteries) of its first appearance, the changes of the outline of continents and of oceans which have taken place since its advent, and their influence on its own wanderings.
On the Natural History of European Seas. In George Wilson and Archibald Geikie, Memoir of Edward Forbes F.R.S. (1861), 547-8.
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However, all scientific statements and laws have one characteristic in common: they are “true or false” (adequate or inadequate). Roughly speaking, our reaction to them is “yes” or “no.” The scientific way of thinking has a further characteristic. The concepts which it uses to build up its coherent systems are not expressing emotions. For the scientist, there is only “being,” but no wishing, no valuing, no good, no evil; no goal. As long as we remain within the realm of science proper, we can never meet with a sentence of the type: “Thou shalt not lie.” There is something like a Puritan's restraint in the scientist who seeks truth: he keeps away from everything voluntaristic or emotional.
Essays in Physics (1950), 68.
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I am glad that the life of pandas is so dull by human standards, for our efforts at conservation have little moral value if we preserve creatures only as human ornaments; I shall be impressed when we show solicitude for warty toads and slithering worms.
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I am more of a sponge than an inventor. I absorb ideas from every source. I take half-matured schemes for mechanical development and make them practical. I am a sort of middleman between the long-haired and impractical inventor and the hard-headed businessman who measures all things in terms of dollars and cents. My principal business is giving commercial value to the brilliant but misdirected ideas of others.
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I am of the decided opinion, that mathematical instruction must have for its first aim a deep penetration and complete command of abstract mathematical theory together with a clear insight into the structure of the system, and doubt not that the instruction which accomplishes this is valuable and interesting even if it neglects practical applications. If the instruction sharpens the understanding, if it arouses the scientific interest, whether mathematical or philosophical, if finally it calls into life an esthetic feeling for the beauty of a scientific edifice, the instruction will take on an ethical value as well, provided that with the interest it awakens also the impulse toward scientific activity. I contend, therefore, that even without reference to its applications mathematics in the high schools has a value equal to that of the other subjects of instruction.
In 'Ueber das Lehrziel im mathemalischen Unterricht der höheren Realanstalten', Jahresbericht der Deutschen Mathematiker Vereinigung, 2, 192. (The Annual Report of the German Mathematical Association. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 73.
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I am told that the wall paintings which we had the happiness of admiring in all their beauty and freshness [in the chapel she discovered at Abu Simbel] are already much injured. Such is the fate of every Egyptian monument, great or small. The tourist carves it over with names and dates, and in some instances with caricatures. The student of Egyptology, by taking wet paper “squeezes” sponges away every vestige of the original colour. The “Collector” buys and carries off everything of value that he can, and the Arab steals it for him. The work of destruction, meanwhile goes on apace. The Museums of Berlin, of Turin, of Florence are rich in spoils which tell their lamentable tale. When science leads the way, is it wonderful that ignorance should follow?
Quoted in Margaret S. Drower, The Early Years, in T.G.H. James, (ed.), Excavating in Egypt: The Egypt Exploration Society, 1882-1982 (1982), 10. As cited in Wendy M.K. Shaw, Possessors and Possessed: Museums, Archaeology, and the Visualization of History in the Late Ottoman Empire (2003), 37. Also quoted in Margaret S. Drower, Flinders Petrie: A Life in Archaeology (1995), 57.
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I became expert at dissecting crayfish. At one point I had a crayfish claw mounted on an apparatus in such a way that I could operate the individual nerves. I could get the several-jointed claw to reach down and pick up a pencil and wave it around. I am not sure that what I was doing had much scientific value, although I did learn which nerve fiber had to be excited to inhibit the effects of another fiber so that the claw would open. And it did get me interested in robotic instrumentation, something that I have now returned to. I am trying to build better micromanipulators for surgery and the like.
In Jeremy Bernstein, 'A.I.', The New Yorker (14 Dec 1981).
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I conclude that, while it is true that science cannot decide questions of value, that is because they cannot be intellectually decided at all, and lie outside the realm of truth and falsehood. Whatever knowledge is attainable, must be attained by scientific methods; and what science cannot discover, mankind cannot know.
Religion and Science (1935), 243.
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I do not maintain that the chief value of the study of arithmetic consists in the lessons of morality that arise from this study. I claim only that, to be impressed from day to day, that there is something that is right as an answer to the questions with which one is able to grapple, and that there is a wrong answer—that there are ways in which the right answer can be established as right, that these ways automatically reject error and slovenliness, and that the learner is able himself to manipulate these ways and to arrive at the establishment of the true as opposed to the untrue, this relentless hewing to the line and stopping at the line, must color distinctly the thought life of the pupil with more than a tinge of morality. … To be neighborly with truth, to feel one’s self somewhat facile in ways of recognizing and establishing what is right, what is correct, to find the wrong persistently and unfailingly rejected as of no value, to feel that one can apply these ways for himself, that one can think and work independently, have a real, a positive, and a purifying effect upon moral character. They are the quiet, steady undertones of the work that always appeal to the learner for the sanction of his best judgment, and these are the really significant matters in school work. It is not the noise and bluster, not even the dramatics or the polemics from the teacher’s desk, that abide longest and leave the deepest and stablest imprint upon character. It is these still, small voices that speak unmistakably for the right and against the wrong and the erroneous that really form human character. When the school subjects are arranged on the basis of the degree to which they contribute to the moral upbuilding of human character good arithmetic will be well up the list.
In Arithmetic in Public Education (1909), 18. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 69.
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I do not value any view of the universe into which man and the institutions of man enter very largely and absorb much of the attention. Man is but the place where I stand, and the prospect hence is infinite.
Journal, April 2, 1852.
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I don't really care how time is reckoned so long as there is some agreement about it, but I object to being told that I am saving daylight when my reason tells me that I am doing nothing of the kind. I even object to the implication that I am wasting something valuable if I stay in bed after the sun has risen. As an admirer of moonlight I resent the bossy insistence of those who want to reduce my time for enjoying it. At the back of the Daylight Saving scheme I detect the bony, blue-fingered hand of Puritanism, eager to push people into bed earlier, and get them up earlier, to make them healthy, wealthy and wise in spite of themselves.
In The Diary of Samuel Marchbanks (1947), 75.
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I had made considerable advance ... in calculations on my favourite numerical lunar theory, when I discovered that, under the heavy pressure of unusual matters (two transits of Venus and some eclipses) I had committed a grievous error in the first stage of giving numerical value to my theory. My spirit in the work was broken, and I have never heartily proceeded with it since.
[Concerning his calculations on the orbital motion of the Moon.]
Private note (29 Sep 1890). In George Biddell Airy and Wilfrid Airy (ed.), Autobiography of Sir George Biddell Airy (1896), 350.
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I have been branded with folly and madness for attempting what the world calls impossibilities, and even from the great engineer, the late James Watt, who said ... that I deserved hanging for bringing into use the high-pressure engine. This has so far been my reward from the public; but should this be all, I shall be satisfied by the great secret pleasure and laudable pride that I feel in my own breast from having been the instrument of bringing forward new principles and new arrangements of boundless value to my country, and however much I may be straitened in pecuniary circumstances, the great honour of being a useful subject can never be taken from me, which far exceeds riches.
From letter to Davies Gilbert, written a few months before Trevithick's last illness. Quoted in Francis Trevithick, Life of Richard Trevithick: With an Account of his Inventions (1872), Vol. 2, 395-6.
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I have decided today that the United States should proceed at once with the development of an entirely new type of space transportation system designed to help transform the space frontier of the 1970s into familiar territory, easily accessible for human endeavor in the 1980s and ’90s. This system will center on a space vehicle that can shuttle repeatedly from Earth to orbit and back. It will revolutionize transportation into near space, by routinizing it. It will take the astronomical costs out of astronautics. In short, it will go a long way toward delivering the rich benefits of practical space utilization and the valuable spin-offs from space efforts into the daily lives of Americans and all people.
Statement by President Nixon (5 Jan 1972).
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I have just received copies of “To-day” containing criticisms of my letter. I am in no way surprised to find that these criticisms are not only unfair and misleading in the extreme. They are misleading in so far that anyone reading them would be led to believe the exact opposite of the truth. It is quite possible that I, an old and trained engineer and chronic experimenter, should put an undue value upon truth; but it is common to all scientific men. As nothing but the truth is of any value to them, they naturally dislike things that are not true. ... While my training has, perhaps, warped my mind so that I put an undue value upon truth, their training has been such as to cause them to abhor exact truth and logic.
[Replying to criticism by Colonel Acklom and other religious parties attacking Maxim's earlier contribution to the controversy about the modern position of Christianity.]
In G.K. Chesterton, 'The Maxims of Maxim', Daily News (25 Feb 1905). Collected in G. K. Chesterton and Dale Ahlquist (ed.), In Defense of Sanity: The Best Essays of G.K. Chesterton (2011), 86.
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I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world... Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value.
A Mathematician's Apology (1940), 90-1.
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I have never done anything “useful.” No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world... Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value. [The things I have added to knowledge do not differ from] the creations of the other artists, great or small, who have left some kind of memorial beind them.
Concluding remarks in A Mathmatician's Apology (1940, 2012), 150-151.
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I know a good many men of great learning—that is, men born with an extraordinary eagerness and capacity to acquire knowledge. One and all, they tell me that they can't recall learning anything of any value in school. All that schoolmasters managed to accomplish with them was to test and determine the amount of knowledge that they had already acquired independently—and not infrequently the determination was made clumsily and inaccurately.
In Prejudices: third series (1922), 261.
For a longer excerpt, see H. L. Mencken's Recollections of School Algebra.
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I know nothing of the science of astrology and I consider it to be a science, if it is a science, of doubtful value, to be severely left alone by those who have any faith in Providence.
The Collected Works of Mahatma Gandhi (1976), Vol. 36, 46.
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I know well there are those who would have the Study of Nature restrained wholly to Observations; without ever proceeding further. But due Consideration, and a deeper Insight into Things, would soon have undeceived and made them sensible of their error. Assuredly, that man who should spend his whole life in amassing together stone, timber, and other materials for building, without ever at the making any use, or raising any fabrick out of them, might well be reputed very fantastic and extravagant. And a like censure would be his due, who should be perpetually heaping up of natural collections without design. building a structure of philosophy out of them, or advancing some propositions that might turn to the benefit and advantage of the world. This is in reality the true and only proper end of collections, of observations, and natural history: and they are of no manner of use or value without it.
In An Attempt Toward a Natural History of the Fossils of England (1729), xiii-xiv.
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I looked for it [heavy hydrogen, deuterium] because I thought it should exist. I didn't know it would have industrial applications or be the basic for the most powerful weapon ever known [the nuclear bomb] … I thought maybe my discovery might have the practical value of, say, neon in neon signs.
[He was awarded the 1931 Nobel Prize in Chemistry for discovering deuterium.]
Quoted in 'Moon-Struck Scientist,' New York Times (27 Apr 1961), 42.
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I should like to draw attention to the inexhaustible variety of the problems and exercises which it [mathematics] furnishes; these may be graduated to precisely the amount of attainment which may be possessed, while yet retaining an interest and value. It seems to me that no other branch of study at all compares with mathematics in this. When we propose a deduction to a beginner we give him an exercise in many cases that would have been admired in the vigorous days of Greek geometry. Although grammatical exercises are well suited to insure the great benefits connected with the study of languages, yet these exercises seem to me stiff and artificial in comparison with the problems of mathematics. It is not absurd to maintain that Euclid and Apollonius would have regarded with interest many of the elegant deductions which are invented for the use of our students in geometry; but it seems scarcely conceivable that the great masters in any other line of study could condescend to give a moment’s attention to the elementary books of the beginner.
In Conflict of Studies (1873), 10-11.
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I think I have been much of my life an irritant. But some people say that something good came out of my research, something valuable that could be regarded as a pearl, and I can assure those who worked with me it was you who made the pearls and I was merely the grain of sand, the irritant to produce the pearls.
Recalling how, when increasingly in demand to serve on committees, upon attempting to resign from one, he was told by the chairman “We want you as an irritant.” Remark at a luncheon, quoted in Obituary, 'Nicholas Kurti, C. B. E. 14 May 1908-24 November 1998', by J.H. Sanders, Biographical Memoirs of Fellows of the Royal Society (Nov 2000), 46, 309.
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I value science—none can prize it more,
It gives ten thousand motives to adore;
Be it religious, as it ought to be,
The heart humbles, and it bows the knee.
The Microcosm and Other Poems (1880), 21.
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I would much prefer to have Goddard interested in real scientific development than to have him primarily interested in more spectacular achievements [Goddard’s rocket research] of less real value.
Letter to Harry Guggenheim of the Guggenheim Foundation (May 1936). As quoted in Robert L. Weber, A Random Walk in Science (1973), 67.
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I would teach the world that science is the best way to understand the world, and that for any set of observations, there is only one correct explanation. Also, science is value-free, as it explains the world as it is. Ethical issues arise only when science is applied to technology – from medicine to industry.
Response to question “What is the one thing everyone should learn about science?” in 'Life Lessons' The Guardian (7 Apr 2005).
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I … share an excitement and a certain pride in the wonders opened up by scientific investigation …, and also a recognition of the value in scientific method of keeping the hypotheses as simple as possible—my Oxford tutor gave me a great respect for Occam’s razor.
In Letter to periodical, Chemistry and Industry (17 Feb 1997).
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If a man devotes himself to the promotion of science, he is firstly opposed, and then he is informed that his ground is already occupied. At first men will allow no value to what we tell them, and then they behave as if they knew it all themselves.
In The Maxims and Reflections of Goethe (1906), 199.
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If Bacon erred here [in valuing mathematics only for its uses], we must acknowledge that we greatly prefer his error to the opposite error of Plato. We have no patience with a philosophy which, like those Roman matrons who swallowed abortives in order to preserve their shapes, takes pains to be barren for fear of being homely.
In 'Lord Bacon', Edinburgh Review (Jul 1837). Collected in Critical and Miscellaneous Essays: Contributed to the Edinburgh Review (1857), Vol. 1, 396.
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If texts are unified by a central logic of argument, then their pictorial illustrations are integral to the ensemble, not pretty little trifles included only for aesthetic or commercial value. Primates are visual animals, and (particularly in science) illustration has a language and set of conventions all its own.
…...
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If we view mathematical speculations with reference to their use, it appears that they should be divided into two classes. To the first belong those which furnish some marked advantage either to common life or to some art, and the value of such is usually determined by the magnitude of this advantage. The other class embraces those speculations which, though offering no direct advantage, are nevertheless valuable in that they extend the boundaries of analysis and increase our resources and skill. Now since many investigations, from which great advantage may be expected, must be abandoned solely because of the imperfection of analysis, no small value should be assigned to those speculations which promise to enlarge the field of anaylsis.
In Novi Comm. Petr., Vol. 4, Preface.
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If, unwarned by my example, any man shall undertake and shall succeed in really constructing an engine embodying in itself the whole of the executive department of mathematical analysis upon different principles or by simpler mechanical means, I have no fear of leaving my reputation in his charge, for he alone will be fully able to appreciate the nature of my efforts and the value of their results.
In Passages from the Life of a Philosopher (1864), 450.
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In a democracy dissent is an act of faith. Like medicine, the test of its value is not in its taste, but its effects.
Speech to the U.S. Senate (21 Apr 1966). In Tristram Coffin, Senator Fulbright; Portrait of a Public Philosopher (1966), 12.
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In a dispassionate comparison of the relative values of human and robotic spaceflight, the only surviving motivation for continuing human spaceflight is the ideology of adventure. But only a tiny number of Earth’s six billion inhabitants are direct participants. For the rest of us, the adventure is vicarious and akin to that of watching a science fiction movie.
In 'Is Human Spaceflight Obsolete?', Issues in Science and Technology (Summer 2004). [Note: published one year after the loss of seven lives in the Space Shuttle Columbia disaster. —Webmaster]
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In an objective system … any mingling of knowledge with values is unlawful, forbidden. But [the] … “first commandment” which ensures the foundation of objective knowledge, is not itself objective. It cannot be objective: it is an ethical guideline, a rule for conduct. True knowledge is ignorant of values, but it cannot be grounded elsewhere than upon a value judgment…
In Chance and Necessity (1970), 176.
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In defining an element let us not take an external boundary, Let us say, e.g., the smallest ponderable quantity of yttrium is an assemblage of ultimate atoms almost infinitely more like each other than they are to the atoms of any other approximating element. It does not necessarily follow that the atoms shall all be absolutely alike among themselves. The atomic weight which we ascribe to yttrium, therefore, merely represents a mean value around which the actual weights of the individual atoms of the “element” range within certain limits. But if my conjecture is tenable, could we separate atom from atom, we should find them varying within narrow limits on each side of the mean.
Address to Annual General Meeting of the Chemical Society (28 Mar 1888), printed in Journal of the Chemical Society (1888), 491.
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In due time the evolution theory will have to abate its vehemence, cannot be allow’d to dominate everything else, and will have to take its place as a segment of the circle, the cluster—as but one of many theories, many thoughts, of profoundest value—and readjusting the differentiating much, yet leaving the divine secrets just as inexplicable and unreachable as before—maybe more so.
In Specimen days & Collect (1883), 326.
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In former times, … when ships buffeted by storms threw a portion of their cargo overboard, it was recognized that those whose goods were sacrificed had a claim in equity to indemnification at the expense of those whose goods were safely delivered. The value of the lost goods was paid for by agreement between all those whose merchandise had been in the same ship. This sea damage to cargo in transit was known as “havaria” and the word came naturally to be applied to the compensation money which each individual was called upon to pay. From this Latin word derives our modern word average.
In 'On the Average', Facts From Figures (1951), Chap. 4, 34.
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In Man the brain presents an ascensive step in development, higher and more strongly marked than that by which the preceding subclass was distinguished from the one below it. Not only do the cerebral hemispheres overlap the olfactory lobes and cerebellum, but they extend in advance of the one, and further back than the other. Their posterior development is so marked, that anatomists have assigned to that part the character of a third lobe; it is peculiar to the genus Homo, and equally peculiar is the 'posterior horn of the lateral ventricle,' and the 'hippocampus minor,' which characterize the hind lobe of each hemisphere. The superficial grey matter of the cerebrum, through the number and depth of the convolutions, attains its maximum of extent in Man. Peculiar mental powers are associated with this highest form of brain, and their consequences wonderfully illustrate the value of the cerebral character; according to my estimate of which, I am led to regard the genus Homo, as not merely a representative of a distinct order, but of a distinct subclass of the Mammalia, for which I propose a name of 'ARCHENCEPHALA.'
'On the Characters, Principles of Division, and Primary Groups of the Class MAMMALIA' (1857), Journal of the Proceedings of the Linnean Society of London (1858), 2, 19-20.
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In particular, and most importantly, this is the reason why the scientific worldview contains of itself no ethical values, no esthetical values, not a word about our own ultimate scope or destination, and no God, if you please. Whence came I and whither go I?
…...
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In preparing the present volume, it has been the aim of the author to do full justice to the ample material at his command, and, where possible, to make the illustrations tell the main story to anatomists. The text of such a memoir may soon lose its interest, and belong to the past, but good figures are of permanent value. [Justifying elaborate illustrations in his monographs.]
In Dinocerata: a monograph of an extinct order of gigantic mammals (1884), Preface, xvii.
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In pure mathematics we have a great structure of logically perfect deductions which constitutes an integral part of that great and enduring human heritage which is and should be largely independent of the perhaps temporary existence of any particular geographical location at any particular time. … The enduring value of mathematics, like that of the other sciences and arts, far transcends the daily flux of a changing world. In fact, the apparent stability of mathematics may well be one of the reasons for its attractiveness and for the respect accorded it.
In Fundamentals of Mathematics (1941), 463.
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In science men have discovered an activity of the very highest value in which they are no longer, as in art, dependent for progress upon the appearance of continually greater genius, for in science the successors stand upon the shoulders of their predecessors; where one man of supreme genius has invented a method, a thousand lesser men can apply it. … In art nothing worth doing can be done without genius; in science even a very moderate capacity can contribute to a supreme achievement.
Essay, 'The Place Of Science In A Liberal Education.' In Mysticism and Logic: and Other Essays (1919), 41.
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In scientific matters there was a common language and one standard of values; in moral and political problems there were many. … Furthermore, in science there is a court of last resort, experiment, which is unavailable in human affairs.
In Enrico Fermi: Physicist (1970), 149. Segrè refers to the issues regarding the consequences of mastering the release of atomic energy.
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In the discussion of the. energies involved in the deformation of nuclei, the concept of surface tension of nuclear matter has been used and its value had been estimated from simple considerations regarding nuclear forces. It must be remembered, however, that the surface tension of a charged droplet is diminished by its charge, and a rough estimate shows that the surface tension of nuclei, decreasing with increasing nuclear charge, may become zero for atomic numbers of the order of 100. It seems therefore possible that the uranium nucleus has only small stability of form, and may, after neutron capture, divide itself into two nuclei of roughly equal size (the precise ratio of sizes depending on liner structural features and perhaps partly on chance). These two nuclei will repel each other and should gain a total kinetic energy of c. 200 Mev., as calculated from nuclear radius and charge. This amount of energy may actually be expected to be available from the difference in packing fraction between uranium and the elements in the middle of the periodic system. The whole 'fission' process can thus be described in an essentially classical way, without having to consider quantum-mechanical 'tunnel effects', which would actually be extremely small, on account of the large masses involved.
[Co-author with Otto Robert Frisch]
Lise Meitner and O. R. Frisch, 'Disintegration of Uranium by Neutrons: a New Type of Nuclear Reaction', Nature (1939), 143, 239.
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In the matter of physics, the first lessons should contain nothing but what is experimental and interesting to see. A pretty experiment is in itself often more valuable than twenty formulae extracted from our minds.
…...
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In the social equation, the value of a single life is nil; in the cosmic equation, it is infinite… Not only communism, but any political movement which implicitly relies on purely utilitarian ethics, must become a victim to the same fatal error. It is a fallacy as naïve as a mathematical teaser, and yet its consequences lead straight to Goya’s Disasters, to the reign of the guillotine, the torture chambers of the Inquisition, or the cellars of the Lubianka.
In 'The Invisible Writing', Arrow in the Blue: An Autobiography (1952), Vol. 2, 357.
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In the world’s history certain inventions and discoveries occurred of peculiar value, on account of their great efficiency in facilitating all other inventions and discoveries. Of these were the art of writing and of printing, the discovery of America, and the introduction of patent laws. The date of the first … is unknown; but it certainly was as much as fifteen hundred years before the Christian era; the second—printing—came in 1436, or nearly three thousand years after the first. The others followed more rapidly—the discovery of America in 1492, and the first patent laws in 1624.
Lecture 'Discoveries, Inventions and Improvements' (22 Feb 1860) in John George Nicolay and John Hay (eds.), Complete Works of Abraham Lincoln (1894), Vol. 5, 109-10.
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In using the present in order to reveal the past, we assume that the forces in the world are essentially the same through all time; for these forces are based on the very nature of matter, and could not have changed. The ocean has always had its waves, and those waves have always acted in the same manner. Running water on the land has ever had the same power of wear and transportation and mathematical value to its force. The laws of chemistry, heat, electricity, and mechanics have been the same through time. The plan of living structures has been fundamentally one, for the whole series belongs to one system, as much almost as the parts of an animal to the one body; and the relations of life to light and heat, and to the atmosphere, have ever been the same as now.
In Manual of Geology, Treating of the Principles of the Science (1863), 7.
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Inspiration plays no less a role in science than it does in the realm of art. It is a childish notion to think that a mathematician attains any scientifically valuable results by sitting at his desk with a ruler, calculating machines or other mechanical means. The mathematical imagination of a Weierstrass is naturally quite differently oriented in meaning and result than is the imagination of an artist, and differs basically in quality. But the psychological processes do not differ. Both are frenzy (in the sense of Plato’s “mania”) and “inspiration.”
Max Weber
From a Speech (1918) presented at Munich University, published in 1919, and collected in 'Wissenschaft als Beruf', Gessammelte Aufsätze zur Wissenschaftslehre (1922), 524-525. As given in H.H. Gerth and C. Wright-Mills (translators and eds.), 'Science as a Vocation', Max Weber: Essays in Sociology (1946), 136.
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Is no one inspired by our present picture of the universe? This value of science remains unsung by singers: you are reduced to hearing not a song or poem, but an evening lecture about it. This is not yet a scientific age.
Perhaps one of the reasons for this silence is that you have to know how to read music. For instance, the scientific article may say, “The radioactive phosphorus content of the cerebrum of the rat decreases to one-half in a period of two weeks.” Now what does that mean?
It means that phosphorus that is in the brain of a rat—and also in mine, and yours—is not the same phosphorus as it was two weeks ago. It means the atoms that are in the brain are being replaced: the ones that were there before have gone away.
So what is this mind of ours: what are these atoms with consciousness? Last week’s potatoes! They now can remember what was going on in my mind a year ago—a mind which has long ago been replaced. To note that the thing I call my individuality is only a pattern or dance, that is what it means when one discovers how long it takes for the atoms of the brain to be replaced by other atoms. The atoms come into my brain, dance a dance, and then go out—there are always new atoms, but always doing the same dance, remembering what the dance was yesterday.
'What do You Care What Other People Think?' Further Adventures of a Curious Character (1988), 244.
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Isolated facts and experiments have in themselves no value, however great their number may be. They only become valuable in a theoretical or practical point of view when they make us acquainted with the law of a series of uniformly recurring phenomena, or, it may be, only give a negative result showing an incompleteness in our knowledge of such a law, till then held to be perfect.
'The Aim and Progress of Physical Science' (1869). Trans. E. Atkinson, Popular Lectures on Scientific Subjects (1873), 369.
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Isolated, so-called “pretty theorems” have even less value in the eyes of a modern mathematician than the discovery of a new “pretty flower” has to the scientific botanist, though the layman finds in these the chief charm of the respective Sciences.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1869), 19. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 92. From the original German, “Einzelne, sogenannte „hübsche Sätze“ haben an und für sich in den Augen eines modernen Mathematikers noch weniger Werth, als für den wissenschaftlichen Botaniker die Entdeckung einer neuen „hübschen Blume“, obgleich dem Laien gerade hierin der Hauptreiz der betreffenden Wissenschaft zu liegen pflegt.”
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It has become a cheap intellectual pastime to contrast the infinitesimal pettiness of man with the vastnesses of the stellar universes. Yet all such comparisons are illicit. We cannot compare existence and meaning; they are disparate. The characteristic life of a man is itself the meaning of vast stretches of existences, and without it the latter have no value or significance. There is no common measure of physical existence and conscious experience because the latter is the only measure there is of the former. The significance of being, though not its existence, is the emotion it stirs, the thought it sustains.
Philosophy and Civilization (1931), reprinted in David Sidorsky (ed.), John Dewey: The Essential Writings (1977), 7.
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It is a custom often practiced by seafaring people to throw a bottle overboard, with a paper, stating the time and place at which it is done. In the absence of other information as to currents, that afforded by these mute little navigators is of great value.
In The Physical Geography of the Sea (1855), 28.
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It is a misfortune to pass at once from observation to conclusion, and to regard both as of equal value; but it befalls many a student.
In The Maxims and Reflections of Goethe (1906), 183.
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It is also vital to a valuable education that independent critical thinking be developed in the young human being, a development that is greatly jeopardized by overburdening with too much and too varied subjects. Overburdening necessarily leads to superficiality.
From interview with Benjamin Fine, 'Einstein Stresses Critical Thinking', New York Times (5 Oct 1952), 37. [Here, “superficiality” has been inserted as a correction for a typo, “superciality”, in the original text. —Webmaster]
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It is clear that all the valuable things, material, spiritual, and moral, which we receive from society can be traced back through countless generations to certain creative individuals. The use of fire, the cultivation of edible plants, the steam engine–each was discovered by one man.
…...
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It is curious to observe how differently these great men [Plato and Bacon] estimated the value of every kind of knowledge. Take Arithmetic for example. Plato, after speaking slightly of the convenience of being able to reckon and compute in the ordinary transactions of life, passes to what he considers as a far more important advantage. The study of the properties of numbers, he tells us, habituates the mind to the contemplation of pure truth, and raises us above the material universe. He would have his disciples apply themselves to this study, not that they may be able to buy or sell, not that they may qualify themselves to be shop-keepers or travelling merchants, but that they may learn to withdraw their minds from the ever-shifting spectacle of this visible and tangible world, and to fix them on the immutable essences of things.
Bacon, on the other hand, valued this branch of knowledge only on account of its uses with reference to that visible and tangible world which Plato so much despised. He speaks with scorn of the mystical arithmetic of the later Platonists, and laments the propensity of mankind to employ, on mere matters of curiosity, powers the whole exertion of which is required for purposes of solid advantage. He advises arithmeticians to leave these trifles, and employ themselves in framing convenient expressions which may be of use in physical researches.
In 'Lord Bacon', Edinburgh Review (Jul 1837). Collected in Critical and Miscellaneous Essays: Contributed to the Edinburgh Review (1857), Vol. 1, 394.
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It is impossible to answer your question briefly; and I am not sure that I could do so, even if I wrote at some length. But I may say that the impossibility of conceiving that this grand and wondrous universe, with our conscious selves, arose through chance, seems to me the chief argument for the existence of God; but whether this is an argument of real value, I have never been able to decide.
[Replying to query about his religious views]
Letter to a Dutch student (2 Apr 1873), in Charles Darwin and Sir Francis Darwin (ed.), The Life and Letters of Charles Darwin (1896), 276.
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It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.
Quoted in Return to Mathematical Circles H. Eves (Boston 1988).
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It is not enough to teach man a specialty. Through it he may become a kind of useful machine, but not a harmoniously developed personality. It is essential that the student acquire an understanding of and a lively feeling for values. He must acquire a vivid sense of the beautiful and of the morally good. Otherwise he—with his specialized knowledge—more closely resembles a well-trained dog than a harmoniously developed person.
From interview with Benjamin Fine, 'Einstein Stresses Critical Thinking', New York Times (5 Oct 1952), 37.
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It is not only a decided preference for synthesis and a complete denial of general methods which characterizes the ancient mathematics as against our newer Science [modern mathematics]: besides this extemal formal difference there is another real, more deeply seated, contrast, which arises from the different attitudes which the two assumed relative to the use of the concept of variability. For while the ancients, on account of considerations which had been transmitted to them from the Philosophie school of the Eleatics, never employed the concept of motion, the spatial expression for variability, in their rigorous system, and made incidental use of it only in the treatment of phonoromically generated curves, modern geometry dates from the instant that Descartes left the purely algebraic treatment of equations and proceeded to investigate the variations which an algebraic expression undergoes when one of its variables assumes a continuous succession of values.
In 'Untersuchungen über die unendlich oft oszillierenden und unstetigen Functionen', Ostwald’s Klassiker der exacten Wissenschaften (1905), No. 153, 44-45. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 115. From the original German, “Nicht allein entschiedene Vorliebe für die Synthese und gänzliche Verleugnung allgemeiner Methoden charakterisiert die antike Mathematik gegenüber unserer neueren Wissenschaft; es gibt neben diesem mehr äußeren, formalen, noch einen tiefliegenden realen Gegensatz, welcher aus der verschiedenen Stellung entspringt, in welche sich beide zu der wissenschaftlichen Verwendung des Begriffes der Veränderlichkeit gesetzt haben. Denn während die Alten den Begriff der Bewegung, des räumlichen Ausdruckes der Veränderlichkeit, aus Bedenken, die aus der philosophischen Schule der Eleaten auf sie übergegangen waren, in ihrem strengen Systeme niemals und auch in der Behandlung phoronomisch erzeugter Kurven nur vorübergehend verwenden, so datiert die neuere Mathematik von dem Augenblicke, als Descartes von der rein algebraischen Behandlung der Gleichungen dazu fortschritt, die Größenveränderungen zu untersuchen, welche ein algebraischer Ausdruck erleidet, indem eine in ihm allgemein bezeichnete Größe eine stetige Folge von Werten durchläuft.”
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It is not so very important for a person to learn facts. For that he does not really need a college. He can learn them from books. The value of an education in a liberal arts college is not the learning of many facts but the training of the mind to think something that cannot be learned from textbooks.
1921, commenting on Thomas Edison’s opinion that a college education is useless, in Einstein: His Life and Times by Philipp Frank (1953).
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It is of priceless value to the human race to know that the sun will supply the needs of the earth, as to light and heat, for millions of years; that the stars are not lanterns hung out at night, but are suns like our own; and that numbers of them probably have planets revolving around them, perhaps in many cases with inhabitants adapted to the conditions existing there. In a sentence, the main purpose of the science is to learn the truth about the stellar universe; to increase human knowledge concerning our surroundings, and to widen the limits of intellectual life.
In 'The Nature of the Astronomer’s Work', North American Review (Jun 1908), 187, No. 631, 915.
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It is rather astonishing how little practical value scientific knowledge has for ordinary men, how dull and commonplace such of it as has value is, and how its value seems almost to vary inversely to its reputed utility.
In A Mathematician's Apology (1940, 2012), 117-118.
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It is the function of notions in science to be useful, to be interesting, to be verifiable and to acquire value from anyone of these qualities. Scientific notions have little to gain as science from being forced into relation with that formidable abstraction, “general truth.”
In paper delivered before the Royal College of Surgeons of England (15 Feb 1932), in 'The Commemoration of Great Men', British Medical Journal (1932), 1, 32. Collected in The Collected Papers of Wilfred Trotter, FRS (1941), 29.
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It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used.
Describing, in 1685, the value to astronomers of the hand-cranked calculating machine he had invented in 1673.
From 'Machina Arithmetica in qua non Aditio tantum Subtractio', as translated by Mark Kormes in David Eugene Smith, A Source Book in Mathematics (1929), 181.
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It seems plain and self-evident, yet it needs to be said: the isolated knowledge obtained by a group of specialists in a narrow field has in itself no value whatsoever, but only in its synthesis with all the rest of knowledge and only inasmuch as it really contributes in this synthesis toward answering the demand, ‘Who are we?’
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It seems to me that the older subjects, classics and mathematics, are strongly to be recommended on the ground of the accuracy with which we can compare the relative performance of the students. In fact the definiteness of these subjects is obvious, and is commonly admitted. There is however another advantage, which I think belongs in general to these subjects, that the examinations can be brought to bear on what is really most valuable in these subjects.
In Conflict of Studies and other Essays (1873), 6-7.
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Its [the anthropological method] power to make us understand the roots from which our civilization has sprung, that it impresses us with the relative value of all forms of culture, and thus serves as a check to an exaggerated valuation of the standpoint of our own period, which we are only too liable to consider the ultimate goal of human evolution, thus depriving ourselves of the benefits to be gained from the teachings of other cultures and hindering an objective criticism of our own work.
'The History of Anthropology', Science, 1904, 20, 524.
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I’m very intense in my work. At any given moment, I think I know the answer to some problem, and that I’m right. Since science is the only self-correcting human institution I know of, you should not be frightened to take an extreme stand, if that causes the stand to be examined more thoroughly than it might be if you are circumspect. I’ve always been positive about the value of the Hubble constant, knowing full well that it probably isn’t solved.
As quoted in John Noble Wilford, 'Sizing up the Cosmos: An Astronomers Quest', New York Times (12 Mar 1991), C10.
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Know the true value of time; snatch, seize, and enjoy every moment of it. No idleness, no delay, no procrastination; never put off till tomorrow what you can do today.
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Knowing, henceforth, the physiognomy of the disease when allowed to run its own course, you can, without risk of error, estimate the value of the different medications which have been employed. You will discover which remedies have done no harm, and which have notably curtailed the duration of the disease; and thus for the future you will have a standard by which to measure the value of the medicine which you see employed to counteract the malady in question. What you have done in respect of one disease, you will be able to do in respect of many; and by proceeding in this way you will be able, on sure data, to pass judgment on the treatment pursued by your masters.
In Armand Trousseau, as translated by P. Victor and John Rose Cormack, Lectures on Clinical Medicine: Delivered at the Hôtel-Dieu, Paris (1873), Vol. 1, 40-41.
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Knowledge is like a knife. In the hands of a well-balanced adult it is an instrument for good of inestimable value; but in the hands of a child, an idiot, a criminal, a drunkard or an insane man, it may cause havoc, misery, suffering and crime. Science and religion have this in common, that their noble aims, their power for good, have often, with wrong men, deteriorated into a boomerang to the human race.
In 'Applied Chemistry', Science (22 Oct 1915), New Series, 42, No. 1086, 548.
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Laws are important and valuable in the exact natural sciences, in the measure that those sciences are universally valid.
In Max Weber with translation by Edward Shils and Henry A. Finch (eds.), The Methodology of the Social Sciences (1949), 80.
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Machines are worshipped because they are beautiful and valued because they confer power; they are hated because they are hideous and loathed because they impose slavery.
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Man is the highest product of his own history. The discoverer finds nothing so grand or tall as himself, nothing so valuable to him. The greatest star is at the small end of the telescope, the star that is looking, not looked after nor looked at.
In Theodore Parker and Rufus Leighton (ed.), Lessons from the World of Matter and the World of Man: Selected from Notes of Unpublished Sermons (1865), 70.
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Mathematical knowledge, therefore, appears to us of value not only in so far as it serves as means to other ends, but for its own sake as well, and we behold, both in its systematic external and internal development, the most complete and purest logical mind-activity, the embodiment of the highest intellect-esthetics.
In 'Ueber Wert und angeblichen Unwert der Mathematik', Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 13, 381.
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Mathematical magic combines the beauty of mathematical structure with the entertainment value of a trick.
In 'Preface', Mathematics, Magic, and Mystery (1956), ix. Webmaster checked the actual page, in the 1956 edition, and there Gardner plainly uses the beginning words “Mathematical magic.” On page 113, Gardner credits Royal V. Heath for originating the term “Mathemagic,” used as Heath’s book title in 1933. Anywhere you see the quote incorrectly beginning with “Mathemagical mathematics…” or saying Gardner coined the term “mathemagical” obviously did not check the primary source.
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Mathematicians have long since regarded it as demeaning to work on problems related to elementary geometry in two or three dimensions, in spite of the fact that it it precisely this sort of mathematics which is of practical value.
As coauthor with and G.C. Shephard, in Handbook of Applicable Mathematics, Volume V, Combinatorics and Geometry (1985), v.
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Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.
As co-author with Herbert Robbins, in What Is Mathematics?: An Elementary Approach to Ideas and Methods (1941, 1996), x.
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Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols—necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.
In 'Science as an Instrument of Education', Popular Science Monthly (1897), 253.
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Mathematics is not only one of the most valuable inventions—or discoveries—of the human mind, but can have an aesthetic appeal equal to that of anything in art. Perhaps even more so, according to the poetess who proclaimed, “Euclid alone hath looked at beauty bare.”
From 'The Joy of Maths'. Collected in Arthur C. Clarke, Greetings, Carbon-Based Bipeds!: Collected Essays, 1934-1998, 460.
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Mathematics, among all school subjects, is especially adapted to further clearness, definite brevity and precision in expression, although it offers no exercise in flights of rhetoric. This is due in the first place to the logical rigour with which it develops thought, avoiding every departure from the shortest, most direct way, never allowing empty phrases to enter. Other subjects excel in the development of expression in other respects: translation from foreign languages into the mother tongue gives exercise in finding the proper word for the given foreign word and gives knowledge of laws of syntax, the study of poetry and prose furnish fit patterns for connected presentation and elegant form of expression, composition is to exercise the pupil in a like presentation of his own or borrowed thoughtsand their development, the natural sciences teach description of natural objects, apparatus and processes, as well as the statement of laws on the grounds of immediate sense-perception. But all these aids for exercise in the use of the mother tongue, each in its way valuable and indispensable, do not guarantee, in the same manner as mathematical training, the exclusion of words whose concepts, if not entirely wanting, are not sufficiently clear. They do not furnish in the same measure that which the mathematician demands particularly as regards precision of expression.
In Anleitung zum mathematischen Unterricht in höheren Schulen (1906), 17.
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Mathematics, like dialectics, is an organ of the inner higher sense; in its execution it is an art like eloquence. Both alike care nothing for the content, to both nothing is of value but the form. It is immaterial to mathematics whether it computes pennies or guineas, to rhetoric whether it defends truth or error.
From Wilhelm Meislers Wanderjahre (1829), Zweites Buch. Collected in Goethe’s Werke (1830), Vol. 22, 252. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 36-37. The same book has another translation on p.202: “Mathematics, like dialectics, is an organ of the higher sense, in its execution it is an art like eloquence. To both nothing but the form is of value; neither cares anything for content. Whether mathematics considers pennies or guineas, whether rhetoric defends truth or error, is perfectly immaterial to either.” From the original German, “Die Mathematik ist, wie die Dialektik, ein Organ des inneren höheren Sinnes, in der Ausübung ist sie eine Kunst wie die Beredsamkeit. Für beide hat nichts Wert als die Form; der Gehalt ist ihnen gleichgültig. Ob die Mathematik Pfennige oder oder Guineen berechne, die Rhetorik Wahres oder Falsches verteidige, ist beiden vollkommen gleich.”
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Medals are great encouragement to young men and lead them to feel their work is of value, I remember how keenly I felt this when in the 1890s. I received the Darwin Medal and the Huxley Medal. When one is old, one wants no encouragement and one goes on with one's work to the extent of one's power, because it has become habitual.
Letter to Major Greenwood (8 Dec 1933). Quoted in M. E. Magnello, 'Karl Pearson', in P. Armitage and T. Colton (eds.), The Encyclopedia of Biostatistics (1998), Vol. 4, 3314.
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Models so constructed, though of no practical value, serve a useful academic function. The oldest problem in economic education is how to exclude the incompetent. The requirement that there be an ability to master difficult models, including ones for which mathematical competence is required, is a highly useful screening device.
In Economics, Peace, and Laughter (1981), 40-41.
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Modern Physics impresses us particularly with the truth of the old doctrine which teaches that there are realities existing apart from our sense-perceptions, and that there are problems and conflicts where these realities are of greater value for us than the richest treasures of the world of experience.
In The Universe in the Light of Modern Physics (1931), 107.
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More discoveries have arisen from intense observation of very limited material than from statistics applied to large groups. The value of the latter lies mainly in testing hypotheses arising from the former. While observing one should cultivate a speculative, contemplative attitude of mind and search for clues to be followed up. Training in observation follows the same principles as training in any activity. At first one must do things consciously and laboriously, but with practice the activities gradually become automatic and unconscious and a habit is established. Effective scientific observation also requires a good background, for only by being familiar with the usual can we notice something as being unusual or unexplained.
The Art of Scientific Investigation (1950), 101.
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Most of the scientists in their twenties and thirties who went in 1939 to work on wartime problems were profoundly affected by their experience. The belief that Rutherford's boys were the best boys, that we could do anything that was do-able and could master any subject in a few days was of enormous value.
'The Effect of World War II on the Development of Knowledge in the Physical Sciences', Proceedings of the Royal Society of London, 1975, Series A, 342, 531.
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Motion with respect to the universal ocean of aether eludes us. We say, “Let V be the velocity of a body through the aether”, and form the various electromagnetic equations in which V is scattered liberally. Then we insert the observed values, and try to eliminate everything which is unknown except V. The solution goes on famously; but just as we have got rid of all the other unknowns, behold! V disappears as well, and we are left with the indisputable but irritating conclusion —
0 = 0
This is a favourite device that mathematical equations resort to, when we propound stupid questions.
From Gifford Lecture, Edinburgh, (1927), 'Relativity', collected in The Nature of the Physical World (1928), 30.
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My books have sold largely in England, have been translated into many languages, and passed through several editions in foreign countries. I have heard it said that the success of a work abroad is the best test of its enduring value. I doubt whether this is at all trustworthy; but judged by this standard my name ought to last for a few years.
The Life and Letters of Charles Darwin (1896), 81-82.
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My picture of the world is drawn in perspective and not like a model to scale. The foreground is occupied by human beings and the stars are all as small as three-penny bits. I don't really believe in astronomy, except as a complicated description of part of the course of human and possibly animal sensation. I apply my perspective not merely to space but also to time. In time the world will cool and everything will die; but that is a long time off still and its present value at compound discount is almost nothing.
From a paper read to the Apostles, a Cambridge discussion society (1925). In 'The Foundations of Mathematics' (1925), collected in Frank Plumpton Ramsey and D.H. Mellor (ed.), Philosophical Papers (1990), Epilogue, 249. Citation to the paper, in Nils-Eric Sahlin, The Philosophy of F.P. Ramsey (1990), 225.
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My profession often gets bad press for a variety of sins, both actual and imagined: arrogance, venality, insensitivity to moral issues about the use of knowledge, pandering to sources of funding with insufficient worry about attendant degradation of values. As an advocate for science, I plead ‘mildly guilty now and then’ to all these charges. Scientists are human beings subject to all the foibles and temptations of ordinary life. Some of us are moral rocks; others are reeds. I like to think (though I have no proof) that we are better, on average, than members of many other callings on a variety of issues central to the practice of good science: willingness to alter received opinion in the face of uncomfortable data, dedication to discovering and publicizing our best and most honest account of nature’s factuality, judgment of colleagues on the might of their ideas rather than the power of their positions.
…...
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Natural history is a matter of observation; it is a harvest which you gather when and where you find it growing. Birds and squirrels and flowers are not always in season, but philosophy we have always with us. It is a crop which we can grow and reap at all times and in all places and it has its own value and brings its own satisfaction.
From Under the Apple-Trees (1916), Preface.
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Natural knowledge has not forgone emotion. It has simply taken for itself new ground of emotion, under impulsion from and in sacrifice to that one of its 'values', Truth.
Man on His Nature (1940), 404.
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Nature, the parent of all things, designed the human backbone to be like a keel or foundation. It is because we have a backbone that we can walk upright and stand erect. But this was not the only purpose for which Nature provided it; here, as elsewhere, she displayed great skill in turning the construction of a single member to a variety of different uses.
It Provides a Path for the Spinal Marrow, Yet is Flexible.
Firstly, she bored a hole through the posterior region of the bodies of all the vertebrae, thus fashioning a suitable pathway for the spinal marrow which would descend through them.
Secondly, she did not make the backbone out of one single bone with no joints. Such a unified construction would have afforded greater stability and a safer seat for the spinal marrow since, not having joints, the column could not have suffered dislocations, displacements, or distortions. If the Creator of the world had paid such attention to resistance to injury and had subordinated the value and importance of all other aims in the fabric of parts of the body to this one, he would certainly have made a single backbone with no joints, as when someone constructing an animal of wood or stone forms the backbone of one single and continuous component. Even if man were destined only to bend and straighten his back, it would not have been appropriate to construct the whole from one single bone. And in fact, since it was necessary that man, by virtue of his backbone, be able to perform a great variety of movements, it was better that it be constructed from many bones, even though as a result of this it was rendered more liable to injury.
From De Humani Corporis Fabrica Libri Septem: (1543), Book I, 57-58, as translated by William Frank Richardson, in 'Nature’s Skill in Creating a Backbone to Hold Us Erect', On The Fabric of the Human Body: Book I: The Bones and Cartilages (1998), 138.
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Necessity is not the mother of invention. Knowledge and experiment are its parents. It sometimes happens that successful search is made for unknown materials to fill well-recognized and predetermined requirements. It more often happens that the acquirement of knowledge of the previously unknown properties of a material suggests its trial for some new use. These facts strongly indicate the value of knowledge of properties of materials and indicate a way for research.
Quoted in Guy Suits, 'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 357.
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Nevertheless, scientific method is not the same as the scientific spirit. The scientific spirit does not rest content with applying that which is already known, but is a restless spirit, ever pressing forward towards the regions of the unknown, and endeavouring to lay under contribution for the special purpose in hand the knowledge acquired in all portions of the wide field of exact science. Lastly, it acts as a check, as well as a stimulus, sifting the value of the evidence, and rejecting that which is worthless, and restraining too eager flights of the imagination and too hasty conclusions.
'The Scientific Spirit in Medicine: Inaugural Sessional Address to the Abernethian Society', St. Bartholomew's Hospital Journal, 1912, 20, 19.
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No one, it has been said, will ever look at the Moon in the same way again. More significantly can one say that no one will ever look at the earth in the same way. Man had to free himself from earth to perceive both its diminutive place in a solar system and its inestimable value as a life-fostering planet. As earthmen, we may have taken another step into adulthood. We can see our planet earth with detachment, with tenderness, with some shame and pity, but at last also with love.
In Earth Shine (1969). As quoted and cited in Joseph J. Kerski, Interpreting Our World: 100 Discoveries That Revolutionized Geography (2016), 93.
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Nobody knows more than a tiny fragment of science well enough to judge its validity and value at first hand. For the rest he has to rely on views accepted at second hand on the authority of a community of people accredited as scientists. But this accrediting depends in its turn on a complex organization. For each member of the community can judge at first hand only a small number of his fellow members, and yet eventually each is accredited by all. What happens is that each recognizes as scientists a number of others by whom he is recognized as such in return, and these relations form chains which transmit these mutual recognitions at second hand through the whole community. This is how each member becomes directly or indirectly accredited by all. The system extends into the past. Its members recognize the same set of persons as their masters and derive from this allegiance a common tradition, of which each carries on a particular strand.
Personal Knowledge (1958), 163.
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Nothing in science has any value to society if it is not communicated, and scientists are beginning to learn their social obligations.
Anne Roe
The Making of a Scientist (1953), 17.
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Now having (I know not by what accident) engaged my thoughts upon the Bills of Mortality, and so far succeeded therein, as to have reduced several great confused Volumes into a few perspicuous Tables, and abridged such Observations as naturally flowed from them, into a few succinct Paragraphs, without any long Series of multiloquious Deductions, I have presumed to sacrifice these my small, but first publish'd, Labours unto your Lordship, as unto whose benign acceptance of some other of my Papers even the birth of these is due; hoping (if I may without vanity say it) they may be of as much use to persons in your Lordships place, as they are of none to me, which is no more than fairest Diamonds are to the Journeymen Jeweller that works them, or the poor Labourer that first digg'd them from Earth.
[An early account demonstrating the value of statistical analysis of public health data. Graunt lived in London at the time of the plague epidemics.]
From Graunt's 'Epistle Dedicatory', for Natural and Political Observations Mentioned in a Following Index and Made upon Bills of Mortality (1662). Reproduced in Cornelius Walford, The Insurance Cyclopaedia (1871), Vol. 1, 286. (This text used abbreviations for “Mort.” and “vols.”) The italicized words are given as from other sources. Note: bills of mortality are abstracts from parish registers showing the numbers that have died in each week, month or year.
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Now, when all these studies reach the point of inter-communion and connection with one another, and come to be considered in their mutual affinities, then, I think, but not till then, will the pursuit of them have a value for our objects: otherwise there is no profit in them.
Plato
From The Republic, Book 7, Chap. 7, 531. As translated in The Dialogues of Plato (1871), Vol. 2, 367.
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Nowhere is water so beautiful as in the desert for nowhere else is it so scarce. By definition. Water, like a human being or a tree or a bird or a song gains value by rarity, singularity, isolation. In a humid climate water is common. In the desert each drop is precious.
Essay in Desert Images, collected in Beyond the Wall: Essays from the Outside (1984), 82.
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Obviously, what our age has in common with the age of the Reformation is the fallout of disintegrating values. What needs explaining is the presence of a receptive audience. More significant than the fact that poets write abstrusely, painters paint abstractly, and composers compose unintelligible music is that people should admire what they cannot understand; indeed, admire that which has no meaning or principle.
In Reflections on the Human Condition (1973), 62.
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Oersted would never have made his great discovery of the action of galvanic currents on magnets had he stopped in his researches to consider in what manner they could possibly be turned to practical account; and so we would not now be able to boast of the wonders done by the electric telegraphs. Indeed, no great law in Natural Philosophy has ever been discovered for its practical implications, but the instances are innumerable of investigations apparently quite useless in this narrow sense of the word which have led to the most valuable results.
From Silvanus Phillips Thompson, 'Introductory Lecture to the Course on Natural Philosophy', The Life of Lord Kelvin (1910), Vol. 1, Appendix to Chap. 5, 249.
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On one occasion committee members were asked by the chairman, who was also in charge of the project, to agree that a certain machine be run at a power which was ten percent lower than the design value. [Franz Eugen] Simon objected, arguing that “design value” should mean what it said. Thereupon the chairman remarked, “Professor Simon, don’t you see that we are not talking about science, but about engineering, which is an art.” Simon was persistent: “What would happen if the machine were run at full power?” “It might get too hot.” “But, Mr. Chairman,” came Simon’s rejoinder, “Can’t artists use thermometers?”
(1908). From N. Kurti, 'Franz Eugen Simon', Biographical Memoirs of Fellows of the Royal Society (Nov 1958), 4, 247.
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On the appearance of anything new the mass of people ask: What is the use of it? And they are not wrong. For it is only through the use of anything that they can perceive its value.
In The Maxims and Reflections of Goethe (1906), 189.
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One has a feeling that one has a kind of home in this timeless community of human beings that strive for truth ... I have always believed that Jesus meant by the Kingdom of God the small group scattered all through time of intellectually and ethically valuable people.
…...
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One of the great problems of philosophy, is the relationship between the realm of knowledge and the realm of values. Knowledge is what is; values are what ought to be. I would say that all traditional philosophies up to and including Marxism have tried to derive the “ought” from the “is.” My point of view is that this is impossible, this is a farce.
Quoted in John C. Hess, 'French Nobel Biologist Says World Based On Chance', New York Times (15 Mar 1971), 6. Cited in Barbara Bennett, Linda Amster, Who Said what (and When, and Where, and How) in 1971 (1972, 168.
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One of the petty ideas of philosophers is to elaborate a classification, a hierarchy of sciences. They all try it, and they are generally so fond of their favorite scheme that they are prone to attach an absurd importance to it. We must not let ourselves be misled by this. Classifications are always artificial; none more than this, however. There is nothing of value to get out of a classification of science; it dissembles more beauty and order than it can possibly reveal.
In 'The Teaching of the History of Science', The Scientific Monthly (Sep 1918), 194.
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One should guard against inculcating a young man with the idea that success is the aim of life, for a successful man normally receives from his peers an incomparably greater portion than the services he has been able to render them deserve. The value of a man resides in what he gives and not in what he is capable of receiving. The most important motive for study at school, at the university, and in life is the pleasure of working and thereby obtaining results which will serve the community. The most important task for our educators is to awaken and encourage these psychological forces in a young man {or woman}. Such a basis alone can lead to the joy of possessing one of the most precious assets in the world - knowledge or artistic skill.
…...
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One should guard against preaching to the young man success in the customary sense as the aim in life. ... The most important motive for work in school and in life is pleasure in work, pleasure in its result, and the knowledge of the value of the result to the community.
'On Education', address at the State University of New York, Albany (15 Oct 1936) in celebration of the Tercentenary of Higher Education in America, translation prepared by Lina Arronet. In Albert Einstein, The Einstein Reader (2006), 30.
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One wonders whether a generation that demands instant satisfaction of all its needs and instant solution of the world’s problems will produce anything of lasting value. Such a generation, even when equipped with the most modern technology, will be essentially primitive - it will stand in awe of nature, and submit to the tutelage of medicine men.
In Reflections on the Human Condition (1973), 38.
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Only the individual can think, and thereby create new values for society–nay, even set up new moral standards to which the life of the community conforms. Without creative, independently thinking and judging personalities the upward development of society is as unthinkable as the development of the individual personality without the nourishing soil of the community.
…...
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Our time is distinguished by wonderful achievements in the fields of scientific understanding and the technical application of those insights. Who would not be cheered by this? But let us not forget that human knowledge and skills alone cannot lead humanity to a happy and dignified life. Humanity has every reason to place the proclaimers of high moral standards and values above the discoverers of objective truth. What humanity owes to personalities like Buddha, Moses, and Jesus ranks for me higher than all the achievements of the inquiring constructive mind.
(Sep 1937). In Helen Dukas and Banesh Hoffman (ed.), Albert Einstein, the Human Side by (1979).
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Over the years, many Americans have made sacrifices in order to promote freedom and human rights around the globe: the heroic actions of our veterans, the lifesaving work of our scientists and physicians, and generosity of countless individuals who voluntarily give of their time, talents, and energy to help others—all have enriched humankind and affirmed the importance of our Judeo-Christian heritage in shaping our government and values.
Message on the observance of Christmas (8 Dec 1992). In William J. Federer, A Treasury of Presidential Quotations (2004), 300.
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People exaggerate the value of things they haven’t got: everybody worships truth and unselfishness because they have no experience with them.
…...
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People still do not understand that a live fish is more valuable than a dead one, and that destructive fishing techniques are taking a wrecking ball to biodiversity.
In 'Can We Stop Killing Our Oceans Now, Please?', Huffington Post (14 Aug 2013).
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Perhaps the best reason for regarding mathematics as an art is not so much that it affords an outlet for creative activity as that it provides spiritual values. It puts man in touch with the highest aspirations and lofiest goals. It offers intellectual delight and the exultation of resolving the mysteries of the universe.
Mathematics: a Cultural Approach (1962), 671. Quoted in H. E. Hunter, The Divine Proportion (1970), 6.
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Pervasive depletion and overuse of water supplies, the high capital cost of new large water projects, rising pumping costs and worsening ecological damage call for a shift in the way water is valued, used and managed.
From a study Postel wrote for Worldwatch Institute, quoted in New York Times (22 Sep 1985), 19.
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Physical investigation, more than anything besides, helps to teach us the actual value and right use of the Imagination—of that wondrous faculty, which, left to ramble uncontrolled, leads us astray into a wilderness of perplexities and errors, a land of mists and shadows; but which, properly controlled by experience and reflection, becomes the noblest attribute of man; the source of poetic genius, the instrument of discovery in Science, without the aid of which Newton would never have invented fluxions, nor Davy have decomposed the earths and alkalies, nor would Columbus have found another Continent.
Presidential Address to Anniversary meeting of the Royal Society (30 Nov 1859), Proceedings of the Royal Society of London (1860), 10, 165.
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Positive, objective knowledge is public property. It can be transmitted directly from one person to another, it can be pooled, and it can be passed on from one generation to the next. Consequently, knowledge accumulates through the ages, each generation adding its contribution. Values are quite different. By values, I mean the standards by which we judge the significance of life. The meaning of good and evil, of joy and sorrow, of beauty, justice, success-all these are purely private convictions, and they constitute our store of wisdom. They are peculiar to the individual, and no methods exist by which universal agreement can be obtained. Therefore, wisdom cannot be readily transmitted from person to person, and there is no great accumulation through the ages. Each man starts from scratch and acquires his own wisdom from his own experience. About all that can be done in the way of communication is to expose others to vicarious experience in the hope of a favorable response.
The Nature of Science and other Lectures (1954), 7.
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Probably among all the pursuits of the University, mathematics pre-eminently demand self-denial, patience, and perseverance from youth, precisely at that period when they have liberty to act for themselves, and when on account of obvious temptations, habits of restraint and application are peculiarly valuable.
In The Conflict of Studies and other Essays (1873), 12.
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Probably our atomic weights merely represent a mean value around which the actual atomic weights of the atoms vary within certain narrow limits... when we say, the atomic weight of, for instance, calcium is 40, we really express the fact that, while the majority of calcium atoms have an actual atomic weight of 40, there are not but a few which are represented by 39 or 41, a less number by 38 or 42, and so on.
Presidential Address, 2 September 1886, Section B, Chemical Science. Reports of the British Association for the Advancement of Science (1886), 569.
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Psychology, as the behaviorist views it, is a purely objective, experimental branch of natural science which needs introspection as little as do the sciences of chemistry and physics. It is granted that the behavior of animals can be investigated without appeal to consciousness. Heretofore the viewpoint has been that such data have value only in so far as they can be interpreted by analogy in terms of consciousness. The position is taken here that the behavior of man and the behavior of animals must be considered in the same plane.
In Psychology as the Behaviorist Views It (1913), 176.
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Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics. … The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible. … I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s Algebra published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.
In Presidential Address British Association for the Advancement of Science, Section A (1890), Nature, 42, 466.
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Reliable scientific knowledge is value free and has no moral or ethical value. Science tells us how the world is. … Dangers and ethical issue arise only when science is applied as technology.
Nobel Symposium, at Stockholm, Sweden on 'Virtual Museums and Public Understanding of Science and Culture' (26-29 May 2002), Lecture 'Is Science Dangerous'. Published in 'Is Cell Science Dangerous?', Journal of Medical Ethics (Jun 2007), 33, No. 6, 345.
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Research may start from definite problems whose importance it recognizes and whose solution is sought more or less directly by all forces. But equally legitimate is the other method of research which only selects the field of its activity and, contrary to the first method, freely reconnoitres in the search for problems which are capable of solution. Different individuals will hold different views as to the relative value of these two methods. If the first method leads to greater penetration it is also easily exposed to the danger of unproductivity. To the second method we owe the acquisition of large and new fields, in which the details of many things remain to be determined and explored by the first method.
In Zum Gedächtniss an Julius Plucker', Göttinger Abhandlungen (1871), 16, Mathematische Classe, 6.
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Research! A mere excuse for idleness; it has never achieved, and will never achieve any results of the slightest value.
As quoted from author’s conversation with Jowett, in Logan Pearsall Smith, Unforgotten Years (1938, 1939), 186-187.
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Science and poetry are, in fact, inseparable. By providing a vision of life, of Earth, of the universe in all its splendor, science does not challenge human values; it can inspire human values. It does not negate faith; it celebrates faith.
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 201.
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Science and technology revolutionize our lives, but memory, tradition and myth frame our response. Expelled from individual consciousness by the rush of change, history finds its revenge by stamping the collective unconsciousness with habits, values, expectations, dreams. The dialectic between past and future will continue to form our lives.
…...
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Science develops best when its concepts and conclusions are integrated into the broader human culture and its concerns for ultimate meaning and value. Scientists cannot, therefore, hold themselves entirely aloof from the sorts of issues dealt with by philosophers and theologians. By devoting to these issues something of the energy and care they give to their research in science, they can help others realize more fully the human potentialities of their discoveries. They can also come to appreciate for themselves that these discoveries cannot be a genuine substitute for knowledge of the truly ultimate.
In Letter (1 Jun 1988) to Father George V. Coyne, Director of the Vatican Observatory. On vatican.va website.
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Science enhances the moral value of life, because it furthers a love of truth and reverence—love of truth displaying itself in the constant endeavor to arrive at a more exact knowledge of the world of mind and matter around us, and reverence, because every advance in knowledge brings us face to face with the mystery of our own being.
In Max Planck and James Vincent Murphy (trans.), Where is Science Going?, (1932), 169.
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Science has nothing to be ashamed of even in the ruins of Nagasaki. The shame is theirs who appeal to other values than the human imaginative values which science has evolved. The shame is ours if we do not make science part of our world...
Lecture, 'The Sense of Human Dignity', at the Massachusetts Institute of Technology (19 Mar 1953), printed in Science and Human Values (1959), 94.
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Science has now been for a long time—and to an ever-increasing extent—a collective enterprise. Actually, new results are always, in fact, the work of specific individuals; but, save perhaps for rare exceptions, the value of any result depends on such a complex set of interrelations with past discoveries and possible future researches that even the mind of the inventor cannot embrace the whole.
In Oppression and Liberty (1955, 1958), 109.
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Martin Luther King quote: Science investigates; religion interprets. Science gives man knowledge which is power; religion gives
Science investigates; religion interprets. Science gives man knowledge which is power; religion gives man wisdom which is control. Science deals mainly with facts; religion deals mainly with values. The two are not rivals. They are complementary.
In 'A Tough Mind and a Tender Heart', Strength To Love (1963), 3.
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Science is now the craft of the manipulation, substitution and deflection of the forces of nature. What I see coming is a gigantic slaughterhouse, an Auschwitz, in which valuable enzymes, hormones, and so on will be extracted instead of gold teeth.
In Columbia Forum (Summer 1969). As quoted and cited in Rob Kaplan, Science Says (2000), 58.
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Science through its physical technological consequences is now determining the relations which human beings, severally and in groups, sustain to one another. If it is incapable of developing moral techniques which will also determine those relations, the split in modern culture goes so deep that not only democracy but all civilized values are doomed.
In Freedom and Culture (1939).
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Science will never be able to reduce the value of a sunset to arithmetic. Nor can it reduce friendship or statesmanship to a formula. Laughter and love, pain and loneliness, the challenge of beauty and truth: these will always surpass the scientific mastery of nature.
Louis Orr
As President, American Medical Association. From Commencement address at Emory University, Atlanta, 6 Jun 60
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Science, in the immediate, produces knowledge and, indirectly, means of action. It leads to methodical action if definite goals are set up in advance. For the function of setting up goals and passing statements of value transcends its domain. While it is true that science, to the extent of its grasp of causative connections, may reach important conclusions as to the compatibility and incompatibility of goals and evaluations, the independent and fundamental definitions regarding goals and values remain beyond science’s reach.
…...
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Scientific wealth tends to accumulate according to the law of compound interest. Every addition to knowledge of the properties of matter supplies the physical scientist with new instrumental means for discovering and interpreting phenomena of nature, which in their turn afford foundations of fresh generalisations, bringing gains of permanent value into the great storehouse of natural philosophy.
From Inaugural Address of the President to British Association for the Advancement of Science, Edinburgh (2 Aug 1871). Printed in The Chemical News (4 Aug 1871), 24, No. 610., 53.
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Shall an invention be patented or donated to the public freely? I have known some well-meaning scientific men to look askance at the patenting of inventions, as if it were a rather selfish and ungracious act, essentially unworthy. The answer is very simple. Publish an invention freely, and it will almost surely die from lack of interest in its development. It will not be developed and the world will not be benefited. Patent it, and if valuable, it will be taken up and developed into a business.
Address as M.I.T. acting president, to the graduating class (11 Jun 1920). Published in Massachusetts Institute of Technology, Technology Review (Jul 1920), 22, 420.
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She is a reflection of comfortable middle-class values that do not take seriously the continuing unemployment. What I particularly regret is that she does not take seriously the intellectual decline. Having given up the Empire and the mass production of industrial goods, Britain's future lay in its scientific and artistic pre-eminence. Mrs Thatcher will be long remembered for the damage she has done.
On Mrs Margaret H. Thatcher.
The Guardian, 15 Oct 1988.
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So far no chemist has ever discovered exchange-value either in a pearl or a diamond.
Karl Marx
Capital: A Critique of Political Economy (1867), trans. Ben Fowkes (1976), Vol. 1, 177.
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Sociology should... be thought of as a science of action—of the ultimate common value element in its relations to the other elements of action.
The Structure of Social Action (1937), Vol. 1, 440.
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Some of my youthful readers are developing wonderful imaginations. This pleases me. Imagination has brought mankind through the Dark Ages to its present state of civilization. Imagination led Columbus to discover America. Imagination led Franklin to discover electricity. Imagination has given us the steam engine, the telephone, the talking-machine and the automobile, for these things had to be dreamed of before they became realities. So I believe that dreams—day dreams, you know, with your eyes wide open and your brain-machinery whizzing—are likely to lead to the betterment of the world. The imaginative child will become the imaginative man or woman most apt to create, to invent, and therefore to foster civilization. A prominent educator tells me that fairy tales are of untold value in developing imagination in the young. I believe it.
Opening paragraph of preface, 'To My Readers', The Lost Princess of Oz (1917), 13.
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Statistical accounts are to be referred to as a dictionary by men of riper years, and by young men as a grammar, to teach them the relations and proportions of different statistical subjects, and to imprint them on the mind at a time when the memory is capable of being impressed in a lasting and durable manner, thereby laying the foundation for accurate and valuable knowledge.
In The Statistical Breviary: Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe (1801), 5-6.
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Success is achievable without public recognition, and the world has many unsung heroes. The teacher who inspires you to pursue your education to your ultimate ability is a success. The parents who taught you the noblest human principles are a success. The coach who shows you the importance of teamwork is a success. The spiritual leader who instills in you spiritual values and faith is a success. The relatives, friends, and neighbors with whom you develop a reciprocal relationship of respect and support - they, too, are successes. The most menial workers can properly consider themselves successful if they perform their best and if the product of their work is of service to humanity.
From 'Getting to the Heart of Success', in Jim Stovall, Success Secrets of Super Achievers: Winning Insights from Those Who Are at the Top (1999), 42-43.
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Such biological ideas as the “survival of the fittest,” whatever their doubtful value in natural science, are utterly useless in attempting to understand society … The life of a man in society, while it is incidentally a biological fact, has characteristics that are not reducible to biology and must be explained in the distinctive terms of a cultural analysis … the physical well-being of men is a result of their social organization and not vice versa … Social improvement is a product of advances in technology and social organization, not of breeding or selective elimination … Judgments as to the value of competition between men or enterprises or nations must be based upon social and not allegedly biological consequences; and … there is nothing in nature or a naturalistic philosophy of life to make impossible the acceptance of moral sanctions that can be employed for the common good.
Social Darwinism in American Thought 1860-1915 (1945), 176.
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Teaching should be such that what is offered is perceived as a valuable gift, and not as a hard duty.
From interview with Benjamin Fine, 'Einstein Stresses Critical Thinking', New York Times (5 Oct 1952), 37.
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That ability to impart knowledge … what does it consist of? … a deep belief in the interest and importance of the thing taught, a concern about it amounting to a sort of passion. A man who knows a subject thoroughly, a man so soaked in it that he eats it, sleeps it and dreams it—this man can always teach it with success, no matter how little he knows of technical pedagogy. That is because there is enthusiasm in him, and because enthusiasm is almost as contagious as fear or the barber’s itch. An enthusiast is willing to go to any trouble to impart the glad news bubbling within him. He thinks that it is important and valuable for to know; given the slightest glow of interest in a pupil to start with, he will fan that glow to a flame. No hollow formalism cripples him and slows him down. He drags his best pupils along as fast as they can go, and he is so full of the thing that he never tires of expounding its elements to the dullest.
This passion, so unordered and yet so potent, explains the capacity for teaching that one frequently observes in scientific men of high attainments in their specialties—for example, Huxley, Ostwald, Karl Ludwig, Virchow, Billroth, Jowett, William G. Sumner, Halsted and Osler—men who knew nothing whatever about the so-called science of pedagogy, and would have derided its alleged principles if they had heard them stated.
In Prejudices: third series (1922), 241-2.
For a longer excerpt, see H.L. Mencken on Teaching, Enthusiasm and Pedagogy.
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That the main results of the astronomer’s work are not so immediately practical does not detract from their value. They are, I venture to think, the more to be prized on that account. Astronomy has profoundly influenced the thought of the race. In fact, it has been the keystone in the arch of the sciences under which we have marched out from the darkness of the fifteenth and preceding centuries to the comparative light of to-day.
In 'The Nature of the Astronomer’s Work', North American Review (Jun 1908), 187, No. 631, 915.
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The alchemists in their search for gold discovered other things [of greater value].
With the phrase “of greater value” in James Wood, Dictionary of Quotations from Ancient and Modern, English and Foreign Sources (1893), 415. The more specific description '—gunpowder, china, medicines, the laws of nature' is given for 'of greater value' in Counsels and Maxims: Being the Second Part of Arthur Schopenhauer's Aphorismen Zur Lebensweisheit translated by Thomas Bailey Saunders (2nd Ed., 1890), 16.
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The average English author [of mathematical texts] leaves one under the impression that he has made a bargain with his reader to put before him the truth, the greater part of the truth, and nothing but the truth; and that if he has put the facts of his subject into his book, however difficult it may be to unearth them, he has fulfilled his contract with his reader. This is a very much mistaken view, because effective teaching requires a great deal more than a bare recitation of facts, even if these are duly set forth in logical order—as in English books they often are not. The probable difficulties which will occur to the student, the objections which the intelligent student will naturally and necessarily raise to some statement of fact or theory—these things our authors seldom or never notice, and yet a recognition and anticipation of them by the author would be often of priceless value to the student. Again, a touch of humour (strange as the contention may seem) in mathematical works is not only possible with perfect propriety, but very helpful; and I could give instances of this even from the pure mathematics of Salmon and the physics of Clerk Maxwell.
In Perry, Teaching of Mathematics (1902), 59-61.
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The Biblical value of pi, by comparison, is exactly three, as is clear from a verse in 1 Kings vii 23: 'and he made a molten sea, ten cubits from brim to brim, and his height was five cubit; and a line of thirty cubits did encompass him round about.'
Eli Maor
From To Infinity and Beyond (1991), 4.
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The by-product is sometimes more valuable than the product.
In Little Essays on Love and Virtue (1922), 66.
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The conclusion forced upon me in the course of a life devoted to natural science is that the universe as it is assumed to be in physical science is only an idealized world, while the real universe is the spiritual universe in which spiritual values count for everything.
The Sciences and Philosophy: Gifford Lectures, University of Glasgow, 1927 & 1925 (1929), 273.
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