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Member Quotes (41 quotes)

A good method of discovery is to imagine certain members of a system removed and then see how what is left would behave: for example, where would we be if iron were absent from the world: this is an old example.
Aphorism 258 in Notebook J (1789-1793), as translated by R. J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 181.
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Although my Aachen colleagues and students at first regarded the “pure mathematician” with suspicion, I soon had the satisfaction of being accepted a useful member not merely in teaching but also engineering practice; thus I was requested to render expert opinions and to participate in the Ingenieurverein [engineering association].
As quoted in Paul Forman and Armin Hermann, 'Sommerfeld, Arnold (Johannes Wilhelm)', Biography in Dictionary of Scientific Biography (1975), Vol. 12, 527. Cited from 'Autobiographische Skizze', Gesammelte Schriften, Vol 4, 673–682.
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Any conception which is definitely and completely determined by means of a finite number of specifications, say by assigning a finite number of elements, is a mathematical conception. Mathematics has for its function to develop the consequences involved in the definition of a group of mathematical conceptions. Interdependence and mutual logical consistency among the members of the group are postulated, otherwise the group would either have to be treated as several distinct groups, or would lie beyond the sphere of mathematics.
In 'Mathematics', Encyclopedia Britannica (9th ed.).
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As man advances in civilisation, and small tribes are united into larger communities, the simplest reason would tell each individual that he ought to extend his social instincts and sympathies to all the members of the same nation, though personally unknown to him. This point being once reached, there is only an artificial barrier to prevent his sympathies extending to the men of all nations and races.
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As one of the elder members of the community of integrative biologists, I am overwhelmingly aware that during this continuing intellectual revolution, seniority is more likely to be correlated with obsolescence than with wisdom.
In 'Integrative Biology: An Organismic Biologist’s Point of View', Integrative and Comparative Biology (2005), 45, 330.
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As science, of necessity, becomes more involved with itself, so also, of necessity, it becomes more international. I am impressed to know that of the 670 members of this Academy [National Academy of Sciences], 163 were born in other lands.
From Address to the Centennial Convocation of the National Academy of Sciences (22 Oct 1963), 'A Century of Scientific Conquest.' Online at The American Presidency Project.
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Each species has evolved a special set of solutions to the general problems that all organisms must face. By the fact of its existence, a species demonstrates that its members are able to carry out adequately a series of general functions. … These general functions offer a framework within which one can integrate one’s view of biology and focus one’s research. Such a view helps one to avoid becoming lost in a morass of unstructured detail—even though the ways in which different species perform these functions may differ widely. A few obvious examples will suffice. Organisms must remain functionally integrated. They must obtain materials from their environments, and process and release energy from these materials. … They must differentiate and grow, and they must reproduce. By focusing one’s questions on one or another of these obligatory and universal capacities, one can ensure that one’s research will not be trivial and that it will have some chance of achieving broad general applicability.
In 'Integrative Biology: An Organismic Biologist’s Point of View', Integrative and Comparative Biology (2005), 45, 331.
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Euclidean mathematics assumes the completeness and invariability of mathematical forms; these forms it describes with appropriate accuracy and enumerates their inherent and related properties with perfect clearness, order, and completeness, that is, Euclidean mathematics operates on forms after the manner that anatomy operates on the dead body and its members. On the other hand, the mathematics of variable magnitudes—function theory or analysis—considers mathematical forms in their genesis. By writing the equation of the parabola, we express its law of generation, the law according to which the variable point moves. The path, produced before the eyes of the student by a point moving in accordance to this law, is the parabola.
If, then, Euclidean mathematics treats space and number forms after the manner in which anatomy treats the dead body, modern mathematics deals, as it were, with the living body, with growing and changing forms, and thus furnishes an insight, not only into nature as she is and appears, but also into nature as she generates and creates,—reveals her transition steps and in so doing creates a mind for and understanding of the laws of becoming. Thus modern mathematics bears the same relation to Euclidean mathematics that physiology or biology … bears to anatomy.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 38. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112-113.
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Euler was a believer in God, downright and straightforward. The following story is told by Thiebault, in his Souvenirs de vingt ans de séjour à Berlin, … Thiebault says that he has no personal knowledge of the truth of the story, but that it was believed throughout the whole of the north of Europe. Diderot paid a visit to the Russian Court at the invitation of the Empress. He conversed very freely, and gave the younger members of the Court circle a good deal of lively atheism. The Empress was much amused, but some of her counsellors suggested that it might be desirable to check these expositions of doctrine. The Empress did not like to put a direct muzzle on her guest’s tongue, so the following plot was contrived. Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of God, and would give it him before all the Court, if he desired to hear it. Diderot gladly consented: though the name of the mathematician is not given, it was Euler. He advanced toward Diderot, and said gravely, and in a tone of perfect conviction:
Monsieur, (a + bn) / n = x, donc Dieu existe; repondez!

Diderot, to whom algebra was Hebrew, was embarrassed and disconcerted; while peals of laughter rose on all sides. He asked permission to return to France at once, which was granted.
In Budget of Paradoxes (1878), 251. [The declaration in French expresses, “therefore God exists; please answer!” This Euler-Diderot anecdote, as embellished by De Morgan, is generally regarded as entirely fictional. Diderot before he became an encyclopedist was an accomplished mathematician and fully capable of recognizing—and responding to—the absurdity of an algebraic expression in proving the existence of God. See B.H. Brown, 'The Euler-Diderot Anecdote', The American Mathematical Monthly (May 1942), 49, No. 5, 392-303. —Webmaster.]
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How fortunate for civilization, that Beethoven, Michelangelo, Galileo and Faraday were not required by law to attend schools where their total personalities would have been operated upon to make them learn acceptable ways of participating as members of “the group.”
In speech, 'Education for Creativity in the Sciences', Conference at New York University, Washington Square. As quoted by Gene Currivan in 'I.Q. Tests Called Harmful to Pupil', New York Times (16 Jun 1963), 66.
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I am afraid I am not in the flight for “aerial navigation”. I was greatly interested in your work with kites; but I have not the smallest molecule of faith in aerial navigation other than ballooning or of expectation of good results from any of the trials we hear of. So you will understand that I would not care to be a member of the aëronautical Society.
Letter (8 Dec 1896) to Baden Powell. This is the full text of the letter. An image of the handwritten original is on the zapatopi.net website
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I couldn’t possibly have become a member of this Institute [the Salk Institute], you know, if I hadn’t organized it myself.
In R. Carier, Breakthrough: The Saga of Jonas Salk (1966), 413.
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I learned a lot of different things from different schools. MIT is a very good place…. It has developed for itself a spirit, so that every member of the whole place thinks that it’s the most wonderful place in the world—it’s the center, somehow, of scientific and technological development in the United States, if not the world … and while you don’t get a good sense of proportion there, you do get an excellent sense of being with it and in it, and having motivation and desire to keep on…
From Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character (1985), 51.
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If Darwin had printed “The Origin of Species” as a serial running twenty or thirty years he might have found himself, at the end of it, a member of the House of Lords or even Archbishop of Canterbury. But he disgorged it in one stupendous and appalling dose, and in consequence he alarmed millions, including many of his fellow scientists, and got an evil name.
From Baltimore Evening Sun (6 Apr 1931). Collected in A Mencken Chrestomathy (1949, 1956), 330.
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In my opinion, there is absolutely no trustworthy proof that talents have been improved by their exercise through the course of a long series of generations. The Bach family shows that musical talent, and the Bernoulli family that mathematical power, can be transmitted from generation to generation, but this teaches us nothing as to the origin of such talents. In both families the high-watermark of talent lies, not at the end of the series of generations, as it should do if the results of practice are transmitted, but in the middle. Again, talents frequently appear in some member of a family which has not been previously distinguished.
In 'On Heredity', Essays upon Heredity and Kindred Biological Problems (1889), Vol. 1, 95-96.
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In order to form an immaculate member of a flock of sheep one must, above all, be a sheep.
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Men and animals do not merely struggle to maintain their individual existence; they are members of larger social groups. And, all too often, it is the social unit, not the individual, whose survival comes first.
In 'The Clint Eastwood Conundrum', The Lucifer Principle: A Scientific Expedition Into the Forces of History (1997), 7.
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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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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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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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Not only do the various components of the cells form a living system, in which the capacity to live, react, and reproduce is dependent on the interactions of all the members of the system; but this living system is identical with the genetic system. The form of life is determined not only by the specific nature of the hereditary units but also by the structure and arrangement of the system. The whole system is more than the sum of its parts, and the effect of each of the components depends on and is influenced by all previous reactions, whose sequence is in turn determined by the whole idiotype.
'Cytoplasmic Inheritance in Epilobium and Its Theoretical Significance', Advances in Genetics (1954), 6, 320.
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Now, it may be stretching an analogy to compare epidemics of cholera—caused by a known agent—with that epidemic of violent crime which is destroying our cities. It is unlikely that our social problems can be traced to a single, clearly defined cause in the sense that a bacterial disease is ‘caused’ by a microbe. But, I daresay, social science is about as advanced in the late twentieth century as bacteriological science was in the mid nineteenth century. Our forerunners knew something about cholera; they sensed that its spread was associated with misdirected sewage, filth, and the influx of alien poor into crowded, urban tenements. And we know something about street crime; nowhere has it been reported that a member of the New York Stock Exchange has robbed ... at the point of a gun. Indeed, I am naively confident that an enlightened social scientist of the next century will be able to point out that we had available to us at least some of the clues to the cause of urban crime.
'Cholera at the Harvey,' Woods Hole Cantata: Essays on Science and Society (1985).
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Once it happened that all the other members of a man mutinied against the stomach, which they accused as the single, idle, uncontributing part in the entire body, while the rest were put to hardships and the expense of much labor to supply and minister to its appetites. However, the stomach merely ridiculed the fatuity of the members, who appeared not to be aware that the stomach certainly does receive the general nourishment, but only to return it again and distribute it amongst the rest.
Fable related by Menenius Agrippa to resolve a grievance of plebeians against the social hierarchy, described in 'Life of Coriolanus', collected in A.H. Clough (ed.), Plutarch’s Lives of Illustrious Men (1859, 1881), 155.
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Sciences distinguished have a dependence upon universal knowledge, to be augmented, and rectified by the superior light thereof; as well as the parts and members of a science have upon the maxims of the same science, and the mutual light and consent which one part receiveth of another.
From 'Interpretatio Naturæ' ('Of The Interpretation of Nature'), collected in The Works Of Francis Bacon (1803), Vol. 2, 140.
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Society is a self-regulating mechanism for preventing the fulfilment of its members.
In The Decline and Fall of Science (1976), 6.
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Something will have gone out of us as a people if we ever let the remaining wilderness be destroyed; if we permit the last virgin forests to be turned into comic books and plastic cigarette cases; if we drive the few remaining members of the wild species into zoos or to extinction; if we pollute the last clean air and dirty the last clean streams and push our paved roads through the last of the silence, so that never again will Americans be free in their own country from the noise, the exhausts, the stinks of human and automotive waste.
Letter (3 Dec 1960) written to David E. Pesonen of the Outdoor Recreation Resources Review Commission. Collected in 'Coda: Wilderness Letter', The Sound of Mountain Water: The Changing American West (1969), 146.
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Suppose it were perfectly certain that the life and fortune of every one of us would, one day or other, depend upon his winning or losing a game of chess. Don't you think that we should all consider it to be a primary duty to learn at least the names and the moves of the pieces; to have a notion of a gambit, and a keen eye for all the means of giving and getting out of check? Do you not think that we should look with a disapprobation amounting to scorn upon the father who allowed his son, or the state which allowed its members, to grow up without knowing a pawn from a knight?
Yet, it is a very plain and elementary truth that the life, the fortune, and the happiness of every one of us, and, more or less, of those who are connected with us, do depend upon our knowing something of the rules of a game infinitely more difficult and complicated than chess. It is a game which has been played for untold ages, every man and woman of us being one of the two players in a game of his or her own. The chess-board is the world, the pieces are the phenomena of the universe, the rules of the game are what we call the laws of nature. The player on the other side is hidden from us. We know that his play is always fair, just, and patient. But also we know, to our cost, that he never overlooks a mistake, or makes the smallest allowance for ignorance. To the man who plays well the highest stakes are paid with that sort of overflowing generosity with which the strong shows delight in strength. And one who plays ill is checkmated—without haste, but without remorse.
Address to the South London Working Men’s College. 'A Liberal Education; and Where to Find It', in David Masson, (ed.), Macmillan’s Magazine (Mar 1868), 17, 369. Also in 'A Liberal Education and Where to Find it' (1868). In Collected Essays (1893), Vol. 3, 82.
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The complexity of contemporary biology has led to an extreme specialization, which has inevitably been followed by a breakdown in communication between disciplines. Partly as a result of this, the members of each specialty tend to feel that their own work is fundamental and that the work of other groups, although sometimes technically ingenious, is trivial or at best only peripheral to an understanding of truly basic problems and issues. There is a familiar resolution to this problem but it is sometimes difficulty to accept emotionally. This is the idea that there are a number of levels of biological integration and that each level offers problems and insights that are unique to it; further, that each level finds its explanations of mechanism in the levels below, and its significances in the levels above it.
From 'Interaction of physiology and behavior under natural conditions', collected in R.I. Bowman (ed.), The Galapagos (1966), 39.
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The economic anarchy of capitalist society as it exists today is, in my opinion, the real source of the evil. We see before us a huge community of producers the members of which are unceasingly striving to deprive each other of the fruits of their collective labor–not by force, but on the whole in faithful compliance with legally established rules.
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The individual, if left alone from birth would remain primitive and beast-like in his thoughts and feelings to a degree that we can hardly conceive. The individual is what he is and has the significance that he has not so much in virtue of his individuality, but rather as a member of a great human society, which directs his material and spiritual existence from the cradle to the grave.
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The maintenance of security … required every member of the project to attend strictly to his own business. The result was an operation whose efficiency was without precedent.
In And Now It Can Be Told: The Story Of The Manhattan Project (1962), 414.
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The starting point of Darwin’s theory of evolution is precisely the existence of those differences between individual members of a race or species which morphologists for the most part rightly neglect. The first condition necessary, in order that any process of Natural Selection may begin among a race, or species, is the existence of differences among its members; and the first step in an enquiry into the possible effect of a selective process upon any character of a race must be an estimate of the frequency with which individuals, exhibiting any given degree of abnormality with respect to that, character, occur. The unit, with which such an enquiry must deal, is not an individual but a race, or a statistically representative sample of a race; and the result must take the form of a numerical statement, showing the relative frequency with which the various kinds of individuals composing the race occur.
Biometrika: A Joumal for the Statistical Study of Biological Problems (1901), 1, 1-2.
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Thus the radio elements formed strange and cruel families in which each member was created by spontaneous transformation of the mother substance: radium was a “descendant” of uranium, polonium a descendant of radium.
Eve Curie
In Eve Curie, Madame Curie: a Biography by Eve Curie (1937, 2007), 197.
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To expect a personality to survive the disintegration of the brain is like expecting a cricket club to survive when all of its members are dead.
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To your care and recommendation am I indebted for having replaced a half-blind mathematician with a mathematician with both eyes, which will especially please the anatomical members of my Academy.
Letter (26 Jul 1766) to Jean le Rond D’Alembert appreciating his recommendation to bring the younger Joseph-Louis Lagrange (age 30) to the Academy of Sciences in Berlin when Leonhart Euler (age 59), vacated the post of director of mathematics. Euler lost the sight of one eye to disease in 1740, and a cataract took the sight of the remaining eye in 1766. As quoted in Florian Cajori, 'Frederick the Great on Mathematics and Mathematicians', The American Mathematical Monthly (Mar 1927), 34, No. 3, 128.
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We are not to consider the world as the body of God: he is an uniform being, void of organs, members, or parts; and they are his creatures, subordinate to him, and subservient to his will.
From 'Query 31', Opticks (1704, 2nd ed., 1718), 379.
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We must therefore bear the undoubtedly bad effect s of the weak surviving and propagating their kind; but there appears to be at least one check in steady action, namely that the weaker and inferior members of society do not marry so freely as the sound; and this check might be indefinitely increased by the weak in body or mind refraining from marriage, though this is more to be hoped for than expected.
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When the principles of breeding and of inheritance are better understood, we shall not hear ignorant members of our legislature rejecting with scorn a plan for ascertaining by an easy method whether or not consanguineous marriages are injurious to man.
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When we survey our lives and endeavours we soon observe that almost the whole of our actions and desires are bound up with the existence of other human beings. We see that our whole nature resembles that of the social animals. We eat food that others have grown, wear clothes that others have made, live in houses that others have built. The greater part of our knowledge and beliefs has been communicated to us by other people through the medium of a language which others have created. Without language our mental capacities would be poor indeed, comparable to those of the higher animals; we have, therefore, to admit that we owe our principal advantage over the beasts to the fact of living in human society. The individual, if left alone from birth would remain primitive and beast-like in his thoughts and feelings to a degree that we can hardly conceive. The individual is what he is and has the significance that he has not so much in virtue of his individuality, but rather as a member of a great human society, which directs his material and spiritual existence from the cradle to the grave.
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With highly civilised nations continued progress depends in a subordinate degree on natural selection; for such nations do not supplant and exterminate one another as do savage tribes. Nevertheless the more intelligent members within the same community will succeed better in the long run than the inferior, and leave a more numerous progeny, and this is a form of natural selection.
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[In the Royal Society, there] has been, a constant Resolution, to reject all the amplifications, digressions, and swellings of style: to return back to the primitive purity, and shortness, when men deliver'd so many things, almost in an equal number of words. They have exacted from all their members, a close, naked, natural way of speaking; positive expressions; clear senses; a native easiness: bringing all things as near the Mathematical plainness, as they can: and preferring the language of Artizans, Countrymen, and Merchants, before that, of Wits, or Scholars.
The History of the Royal Society (1667), 113.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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