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Who said: “Dangerous... to take shelter under a tree, during a thunder-gust. It has been fatal to many, both men and beasts.”
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Single Quotes (365 quotes)


…with common water. Its substance reaches everywhere; it touches the past and prepares the future; it moves under the poles and wanders thinly in the heights of air. It can assume forms of exquisite perfection in a snowflake, or strip the living to a single shining bone cast up by the sea.
From essay 'The Flow of the River', collected in The Immense Journey: An Imaginative Naturalist Explores the Mysteries of Man and Nature (1957, 1959), 16.
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[Aristotle formal logic thus far (1787)] has not been able to advance a single step, and hence is to all appearances closed and completed.
In Preface to second edition (1787) of Critique Of Pure Reason (1781) as translated by Werner Pluhar (1996), 15. An earlier translation by N. Kemp-Smith (1933) is similar, but ends with “appearance a closed and completed body of doctrine.”
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[Everyone should know:] The unity of life that comes about through evolution, since we’re all descended from a single common ancestor. It’s almost too good to be true, that on one planet this extraordinary complexity of life should have come about by what is pretty much an intelligible process. And we're the only species capable of understanding it.
From 'Interview: Of Mind and Matter: David Attenborough Meets Richard Dawkins', The Guardian (11 Sep 2010),
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[It] is not the nature of things for any one man to make a sudden, violent discovery; science goes step by step and every man depends on the work of his predecessors. When you hear of a sudden unexpected discovery—a bolt from the blue—you can always be sure that it has grown up by the influence of one man or another, and it is the mutual influence which makes the enormous possibility of scientific advance. Scientists are not dependent on the ideas of a single man, but on the combined wisdom of thousands of men, all thinking of the same problem and each doing his little bit to add to the great structure of knowledge which is gradually being erected.
Concluding remark in Lecture ii (1936) on 'Forty Years of Physics', revised and prepared for publication by J.A. Ratcliffe, collected in Needham and Pagel (eds.), Background to Modern Science: Ten Lectures at Cambridge Arranged by the History of Science Committee, (1938), 73-74. Note that the words as prepared for publication may not be verbatim as spoken in the original lecture by the then late Lord Rutherford.
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[Martin Gardner is] the single brightest beacon defending rationality and good science against the mysticism and anti-intellectualism that surround us.
As quoted in Kendrick Frazier, 'A Mind at Play: An Interview with Martin Gardner', Skeptical Inquirer (Mar/Apr 1998), 22, No. 2, 36.
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[On common water.] Its substance reaches everywhere; it touches the past and prepares the future; it moves under the poles and wanders thinly in the heights of air. It can assume forms of exquisite perfection in a snowflake, or strip the living to a single shining bone cast up by the sea.
From essay 'The Flow of the River', collected in The Immense Journey: An Imaginative Naturalist Explores the Mysteries of Man and Nature (1957, 1959), 16.
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[Simplicio] is much puzzled and perplexed. I think I hear him say, 'To whom then should we repair for the decision of our controversies if Aristotle were removed from the choir? What other author should we follow in the schools, academies, and studies? What philosopher has written all the divisions of Natural Philosophy, and so methodically, without omitting as much as a single conclusion? Shall we then overthrow the building under which so many voyagers find shelter? Shall we destroy that sanctuary, that Prytaneum, where so many students find commodious harbour; where without exposing himself to the injuries of the air, with only the turning over of a few leaves, one may learn all the secrets of Nature.'
Dialogue on the Great World Systems (1632). Revised and Annotated by Giorgio De Santillana (1953), 66.
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[The Royal Society] is quite simply the voice of science in Britain. It is intellectually rigorous, not afraid to be outspoken on controversial issues such as climate change, but it is not aggressively secular either, insisting on a single view of the world. In fact, there are plenty of eminent scientists – Robert Winston, for instance – who are also men of faith.
Quoted in Max Davidson, 'Bill Bryson: Have faith, science can solve our problems', Daily Telegraph (26 Sep 2010)
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[The] structural theory is of extreme simplicity. It assumes that the molecule is held together by links between one atom and the next: that every kind of atom can form a definite small number of such links: that these can be single, double or triple: that the groups may take up any position possible by rotation round the line of a single but not round that of a double link: finally that with all the elements of the first short period [of the periodic table], and with many others as well, the angles between the valencies are approximately those formed by joining the centre of a regular tetrahedron to its angular points. No assumption whatever is made as to the mechanism of the linkage. Through the whole development of organic chemistry this theory has always proved capable of providing a different structure for every different compound that can be isolated. Among the hundreds of thousands of known substances, there are never more isomeric forms than the theory permits.
Presidential Address to the Chemical Society (16 Apr 1936), Journal of the Chemical Society (1936), 533.
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The Mighty Task is Done

At last the mighty task is done;
Resplendent in the western sun
The Bridge looms mountain high;
Its titan piers grip ocean floor,
Its great steel arms link shore with shore,
Its towers pierce the sky.

On its broad decks in rightful pride,
The world in swift parade shall ride,
Throughout all time to be;
Beneath, fleet ships from every port,
Vast landlocked bay, historic fort,
And dwarfing all the sea.

To north, the Redwood Empires gates;
To south, a happy playground waits,
In Rapturous appeal;
Here nature, free since time began,
Yields to the restless moods of man,
Accepts his bonds of steel.

Launched midst a thousand hopes and fears,
Damned by a thousand hostile sneers,
Yet Neer its course was stayed,
But ask of those who met the foe
Who stood alone when faith was low,
Ask them the price they paid.

Ask of the steel, each strut and wire,
Ask of the searching, purging fire,
That marked their natal hour;
Ask of the mind, the hand, the heart,
Ask of each single, stalwart part,
What gave it force and power.

An Honored cause and nobly fought
And that which they so bravely wrought,
Now glorifies their deed,
No selfish urge shall stain its life,
Nor envy, greed, intrigue, nor strife,
Nor false, ignoble creed.

High overhead its lights shall gleam,
Far, far below lifes restless stream,
Unceasingly shall flow;
For this was spun its lithe fine form,
To fear not war, nor time, nor storm,
For Fate had meant it so.

Written upon completion of the building of the Golden Gate Bridge, May 1937. In Allen Brown, Golden Gate: biography of a Bridge (1965), 229.
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[On Typhoid Fever] How often have I seen in past days, in the single narrow chamber of the day-labourer’s cottage, the father in the coffin, the mother in the sick-bed in muttering delirium, and nothing to relieve the desolation of the children but the devotion of some poor neighbour, who in too many cases paid the penalty of her kindness in becoming herself the victim of the same disorder.
As quoted by John Tyndall in Lecture (19 Oct 1876) to Glasgow Science Lectures Association. Printed in 'Address Delivered Before The British Association Assembled at Belfast', The Fortnightly Review (1 Nov 1876), 26 N.S., No. 119, 572.
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Are coral reefs growing from the depths of the oceans? ... [The] reply is a simple negative; and a single fact establishes its truth. The reef-forming coral zoophytes, as has been shown, cannot grow at greater depths than 100 or 120 feet; and therefore in seas deeper than this, the formation or growth of reefs over the bottom is impossible.
On Coral Reefs and Islands (1853), 138.
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Nature is curious, and such worke may make,
That our dull sense can never finde, but scape.
For Creatures, small as Atomes, may be there,
If every Atome a Creatures Figure beare.
If foure Atomes a World can make, then see
What severall Worlds might in an Eare--ring bee:
For Millions of these Atomes may bee in
The Head of one Small, little, Single Pin.
And if thus Small, then Ladies may well weare
A World of Worlds, as Pendents in each Eare.
From 'Of Many Worlds in this World', in Poems and Fancies (1653), 44-5.
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The Charms of Statistics.—It is difficult to understand why statisticians commonly limit their inquiries to Averages, and do not revel in more comprehensive views. Their souls seem as dull to the charm of variety as that of the native of one of our flat English counties, whose retrospect of Switzerland was that, if its mountains could be thrown into its lakes, two nuisances would be got rid of at once. An Average is but a solitary fact, whereas if a single other fact be added to it, an entire Normal Scheme, which nearly corresponds to the observed one, starts potentially into existence. Some people hate the very name of statistics, but I find them full of beauty and interest. Whenever they are not brutalised, but delicately handled by the higher methods, and are warily interpreted, their power of dealing with complicated phenomena is extraordinary. They are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of those who pursue the Science of man.
Natural Inheritance (1889), 62-3.
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A distinguished writer [Siméon Denis Poisson] has thus stated the fundamental definitions of the science:
“The probability of an event is the reason we have to believe that it has taken place, or that it will take place.”
“The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible” (equally like to happen).
From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary. Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.
An Investigation of the Laws of Thought (1854), 243-244. The Poisson quote is footnoted as from Recherches sur la Probabilité des Jugemens.
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A great surgeon performs operations for stone by a single method; later he makes a statistical summary of deaths and recoveries, and he concludes from these statistics that the mortality law for this operation is two out of five. Well, I say that this ratio means literally nothing scientifically and gives us no certainty in performing the next operation; for we do not know whether the next case will be among the recoveries or the deaths. What really should be done, instead of gathering facts empirically, is to study them more accurately, each in its special determinism. We must study cases of death with great care and try to discover in them the cause of mortal accidents so as to master the cause and avoid the accidents.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 137-138. (Note that Bernard overlooks how the statistical method can be useful: a surgeon announcing a mortality rate of 40% invites comparison. A surgeon with worse outcomes should adopt this method. If a surgeon has a better results, that method should be adopted.)
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A single and distinct luminous body causes stronger relief in the objects than a diffused light; as may be seen by comparing one side of a landscape illuminated by the sun, and one overshadowed by clouds, and illuminated only by the diffused light of the atmosphere.
…...
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A single axis is harmless, but a murderous mathematician can go on a killing spree with a pair of axes.
Anonymous
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A single death is a tragedy, a million deaths is a statistic.
Anonymous
According to Ralph Keyes in The Quote Verifier this is not a quote by Joseph Stalin. Although a 1958 book review in the New York Times used similar words, no citation was provided, and likely because there is none. However, the quote is often seen incorrectly attributed to Stalin, and sometimes Lenin or Heinrich Himmler.
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A single idea, if it is right, saves us the labor of an infinity of experiences.
Reflections on America (1958), 97.
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A single kind of red cell is supposed to have an enormous number of different substances on it, and in the same way there are substances in the serum to react with many different animal cells. In addition, the substances which match each kind of cell are different in each kind of serum. The number of hypothetical different substances postulated makes this conception so uneconomical that the question must be asked whether it is the only one possible. ... We ourselves hold that another, simpler, explanation is possible.
Landsteiner and Adriano Sturli, 'Hamagglutinine normaler Sera', Wiener klinische Wochenschrift (1902), 15, 38-40. Trans. Pauline M. H. Mazumdar.
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A single ray of light from a distant star falling upon the eye of a tyrant in bygone times, may have altered the course of his life, may have changed the destiny of nations, may have transformed the surface of the globe, so intricate, so inconceivably complex are the processes of nature.
Lecture (Feb 1893) delivered before the Franklin Institute, Philadelphia, 'On Light and Other High Frequency Phenomena,' collected in Thomas Commerford Martin and Nikola Tesla, The Inventions, Researches and Writings of Nikola Tesla (1894), 298.
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A single swallow, it is said, devours ten millions of insects every year. The supplying of these insects I take to be a signal instance of the Creator's bounty in providing for the lives of His creatures.
Attributed to Henry Ward Beecher as a quote under the definition of 'Bounty' in Ambrose Bierce, The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary, 40. Webmaster has not yet found a primary print source confirming the quote is by Beecher, and thus presently lists it under Bierce. Please contact webmaster if you know a primary print source for Beecher.
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A single tree by itself is dependent upon all the adverse chances of shifting circumstances. The wind stunts it: the variations in temperature check its foliage: the rains denude its soil: its leaves are blown away and are lost for the purpose of fertilisation. You may obtain individual specimens of line trees either in exceptional circumstances, or where human cultivation had intervened. But in nature the normal way in which trees flourish is by their association in a forest. Each tree may lose something of its individual perfection of growth, but they mutually assist each other in preserving the conditions of survival. The soil is preserved and shaded; and the microbes necessary for its fertility are neither scorched, nor frozen, nor washed away. A forest is the triumph of the organisation of mutually dependent species.
In Science and the Modern World (1926), 296-7.
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According to the older view, for every single effect of a serum, there was a separate substance, or at least a particular chemical group... A normal serum contained as many different haemagglutinins as it agglutinated different cells. The situation was undoubtedly made much simpler if, to use the Ehrlich terminology... the separate haptophore groups can combine with an extremely large number of receptors in stepwise differing quantities as a stain does with different animal tissues, though not always with the same intensity. A normal serum would therefore visibly affect such a large number of different blood cells... not because it contained countless special substances, but because of the colloids of the serum, and therefore of the agglutinins by reason of their chemical constitution and the electrochemical properties resulting from it. That this manner of representation is a considerable simplification is clear; it also opens the way to direct experimental testing by the methods of structural chemistry.
'Die Theorien der Antikorperbildung ... ', Wiener klinische Wöchenschrift (1909), 22, 1623-1631. Trans. Pauline M. H. Mazumdar.
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All interesting issues in natural history are questions of relative frequency, not single examples. Everything happens once amidst the richness of nature. But when an unanticipated phenomenon occurs again and again–finally turning into an expectation–then theories are overturned.
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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 organs of an animal form a single system, the parts of which hang together, and act and re-act upon one another; and no modifications can appear in one part without bringing about corresponding modifications in all the rest.
Histoire des Progrès des Sciences naturelles depuis (1789), Vol. I, 310. Quoted in E. S. Russell, Form and Function(1916), 35.
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All the different classes of beings which taken together make up the universe are, in the ideas of God who knows distinctly their essential gradations, only so many ordinates of a single curve so closely united that it would be impossible to place others between any two of them, since that would imply disorder and imperfection. Thus men are linked with the animals, these with the plants and these with the fossils which in turn merge with those bodies which our senses and our imagination represent to us as absolutely inanimate. And, since the law of continuity requires that when the essential attributes of one being approximate those of another all the properties of the one must likewise gradually approximate those of the other, it is necessary that all the orders of natural beings form but a single chain, in which the various classes, like so many rings, are so closely linked one to another that it is impossible for the senses or the imagination to determine precisely the point at which one ends and the next begins?all the species which, so to say, lie near the borderlands being equivocal, at endowed with characters which might equally well be assigned to either of the neighboring species. Thus there is nothing monstrous in the existence zoophytes, or plant-animals, as Budaeus calls them; on the contrary, it is wholly in keeping with the order of nature that they should exist. And so great is the force of the principle of continuity, to my thinking, that not only should I not be surprised to hear that such beings had been discovered?creatures which in some of their properties, such as nutrition or reproduction, might pass equally well for animals or for plants, and which thus overturn the current laws based upon the supposition of a perfect and absolute separation of the different orders of coexistent beings which fill the universe;?not only, I say, should I not be surprised to hear that they had been discovered, but, in fact, I am convinced that there must be such creatures, and that natural history will perhaps some day become acquainted with them, when it has further studied that infinity of living things whose small size conceals them for ordinary observation and which are hidden in the bowels of the earth and the depth of the sea.
Lettre Prétendue de M. De Leibnitz, à M. Hermann dont M. Koenig a Cité le Fragment (1753), cxi-cxii, trans. in A. O. Lovejoy, Great Chain of Being: A Study of the History of an Idea (1936), 144-5.
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All the events which occur upon the earth result from Law: even those actions which are entirely dependent on the caprices of the memory, or the impulse of the passions, are shown by statistics to be, when taken in the gross, entirely independent of the human will. As a single atom, man is an enigma; as a whole, he is a mathematical problem. As an individual, he is a free agent; as a species, the offspring of necessity.
In The Martyrdom of Man (1876), 185-186.
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All the unhappiness of men arises from one single fact, that they cannot stay quietly in their own chamber.
In Pensées (1670), Section 4, No. 2. As translated in Blaise Pascal and W.F. Trotter (trans.), 'Thoughts', No. 139, collected in Charles W. Eliot (ed.), The Harvard Classics (1910), Vol. 48, 52. Also seen translated as, “The sole cause of man’s unhappiness is that he does not know how to stay quietly in his room.” From the original French, “Tout le malheur des hommes vient d’une seule chose, qui est de ne savoir pas demeurer en repos, dans une chambre,” in Ernest Havet (ed.), Pensées de Pascal (1892), 152.
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All things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence ... there is an enormous amount of information about the world.
His suggestion that the most valuable information on scientific knowledge in a single sentence using the fewest words is to state the atomic hypothesis.
Six Easy Pieces (1995), 4.
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Although [Charles Darwin] would patiently go on repeating experiments where there was any good to be gained, he could not endure having to repeat an experiment which ought, if complete care had been taken, to have told its story at first—and this gave him a continual anxiety that the experiment should not be wasted; he felt the experiment to be sacred, however slight a one it was. He wished to learn as much as possible from an experiment, so that he did not confine himself to observing the single point to which the experiment was directed, and his power of seeing a number of other things was wonderful. ... Any experiment done was to be of some use, and ... strongly he urged the necessity of keeping the notes of experiments which failed, and to this rule he always adhered.
In Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of his Published Letters (1908), 92.
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Among all the occurrences possible in the universe the a priori probability of any particular one of them verges upon zero. Yet the universe exists; particular events must take place in it, the probability of which (before the event) was infinitesimal. At the present time we have no legitimate grounds for either asserting or denying that life got off to but a single start on earth, and that, as a consequence, before it appeared its chances of occurring were next to nil. ... Destiny is written concurrently with the event, not prior to it.
In Jacques Monod and Austryn Wainhouse (trans.), Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology (1971), 145.
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An amino acid residue (other than glycine) has no symmetry elements. The general operation of conversion of one residue of a single chain into a second residue equivalent to the first is accordingly a rotation about an axis accompanied by translation along the axis. Hence the only configurations for a chain compatible with our postulate of equivalence of the residues are helical configurations.
[Co-author with American chemist, ert B. Corey (1897-1971) and H. R. Branson]
'The Structure of Proteins: Two Hydrogen-bonded Helical Configurations of the Polypeptide Chain', Proceedings of the National Academy of Sciences of the United States of America (1951), 37, 206.
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An aromatic compound may be defined as a cyclic compound with a large resonance energy where all the annular atoms take part in a single conjugated system.
Electronic Theory of Organic Chemistry (1949), 160.
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An extra-terrestrial philosopher, who had watched a single youth up to the age of twenty-one and had never come across any other human being, might conclude that it is the nature of human beings to grow continually taller and wiser in an indefinite progress towards perfection; and this generalization would be just as well founded as the generalization which evolutionists base upon the previous history of this planet.
Scientific Method in Philosophy (1914), 12.
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An irrefutable proof that such single-celled primaeval animals really existed as the direct ancestors of Man, is furnished according to the fundamental law of biogeny by the fact that the human egg is nothing more than a simple cell.
Natürlche Schöpfungsgeschichte, trans. E. R. Lankester, The History of Creation (1892), Vol. 2, 381.
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And now, as a germination of planetary dimensions, comes the thinking layer which over its full extent develops and intertwines its fibres, not to confuse and neutralise them but to reinforce them in the living unity of a single tissue.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 244. Originally published in French as Le Phénomene Humain (1955).
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Any opinion as to the form in which the energy of gravitation exists in space is of great importance, and whoever can make his opinion probable will have, made an enormous stride in physical speculation. The apparent universality of gravitation, and the equality of its effects on matter of all kinds are most remarkable facts, hitherto without exception; but they are purely experimental facts, liable to be corrected by a single observed exception. We cannot conceive of matter with negative inertia or mass; but we see no way of accounting for the proportionality of gravitation to mass by any legitimate method of demonstration. If we can see the tails of comets fly off in the direction opposed to the sun with an accelerated velocity, and if we believe these tails to be matter and not optical illusions or mere tracks of vibrating disturbance, then we must admit a force in that direction, and we may establish that it is caused by the sun if it always depends upon his position and distance.
Letter to William Huggins (13 Oct 1868). In P. M. Hannan (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 1862-1873, 451-2.
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Are God and Nature then at strife,
That Nature lends such evil dreams?
So careful of the type she seems,
So careless of the single life; ...
'So careful of the type', but no.
From scarped cliff and quarried stone
She cries, 'A thousand types are gone:
I care for nothing, all shall go' ...
Man, her last work, who seemed so fair,
Such splendid purpose in his eyes,
Who rolled the psalm to wintry skies,
Who built him fanes of fruitless prayer,
Who trusted God was love indeed
And love Creation's final law—
Tho’ Nature red in tooth and claw
With ravine, shrieked against his creed...
In Memoriam A. H. H. (1850), Cantos 56-57. Collected in Alfred Tennyson and William James Rolfe (ed.) The Poetic and Dramatic works of Alfred, Lord Tennyson (1898), 176.
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Are God and Nature then at strife,
That Nature lends such evil dreams?
So careful of the type she seems,
So careless of the single life…
So careful of the type, but no.
From scarped cliff and quarried stone
She cries, “A thousand types are gone;
I care for nothing, all shall go.”
From poem, 'In Memoriam A.H.H.' written between 1833-50, and first published anonymously in 1850. Collected in Poetical Works of Alfred Tennyson (1860), Vol.2, 64.
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As a single footstep will not make a path on the earth, so a single thought will not make a pathway in the mind. To make a deep physical path, we walk again and again. To make a deep mental path, we must think over and over the kind of thoughts we wish to dominate our lives.
From The Art of Living, Day by Day 91972), 77. Frequently misattributed to Henry David Thoreau.
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As Crystallography was born of a chance observation by Haüy of the cleavage-planes of a single fortunately fragile specimen, … so out of the slender study of the Norwich Spiral has sprung the vast and interminable Calculus of Cyclodes, which strikes such far-spreading and tenacious roots into the profoundest strata of denumeration, and, by this and the multitudinous and multifarious dependent theories which cluster around it, reminds one of the Scriptural comparison of the Kingdom of Heaven “to a grain of mustard-seed which a man took and cast into his garden, and it grew and waxed a great tree, and the fowls of the air lodged in the branches of it.”
From 'Outline Trace of the Theory of Reducible Cyclodes', Proceedings of the London Mathematical Society (1869), 2, 155, collected in Collected Mathematical Papers of James Joseph Sylvester (1908), Vol. 2, 683-684.
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As the human fetus develops, its changing form seems to retrace the whole of human evolution from the time we were cosmic dust to the time we were single-celled organisms in the primordial sea to the time we were four-legged, land-dwelling reptiles and beyond, to our current status as large­brained, bipedal mammals. Thus, humans seem to be the sum total of experience since the beginning of the cosmos.
From interview with James Reston, Jr., in Pamela Weintraub (ed.), The Omni Interviews (1984), 99. Previously published in magazine, Omni (May 1982).
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At fertilization, these two “haploid” nuclei are added together to make a “diploid” nucleus that now contains 2a, 2b and so on; and, by the splitting of each chromosome and the regulated karyokinetic separation of the daughter chromosomes, this double series is inherited by both of the primary blastomeres. In the resulting resting nuclei the individual chromosomes are apparently destroyed. But we have the strongest of indications that, in the stroma of the resting nucleus, every one of the chromosomes that enters the nucleus survives as a well-defined region; and as the cell prepares for its next division this region again gives rise to the same chromosome (Theory of the Individuality of the Chromosomes). In this way the two sets of chromosomes brought together at fertilization are inherited by all the cells of the new individual. It is only in the germinal cells that the so called reduction division converts the double series into a single one. Out of the diploid state, the haploid is once again generated.
In Arch. Zellforsch, 1909, 3, 181, trans. Henry Harris, The Birth of the Cell (1999), 171-2.
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At the origin, the [space travel] pioneers of the greatest adventure of all times were motivated by the drive to explore, by the pure spirit of conquest, by the lofty desire to open up new fields to human genius. … From their exceptional journeys, they all came back with the revelation of beauty. Beauty of the black sky, beauty and variety of our planet, beauty of the Earth seen from the Moon, girdled by a scintillating belt of equatorial thunderstorms. They all emphasize that our planet is one, that borderlines are artificial, that humankind is one single community on board spaceship Earth. They all insist that this fragile gem is at our mercy and that we must all endeavor to protect it.
Written for 'Foreword' to Kevin W. Kelley (ed.), The Home Planet (1988), paragraphs 6-7 (unpaginated).
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At the sight of a single bone, of a single piece of bone, I recognize and reconstruct the portion of the whole from which it would have been taken. The whole being to which this fragment belonged appears in my mind's eye.
Cited by Geoffroy Saint-Hilaire, Comptes-Rendus de l’Académie des Sciences. 1837, 7, 116. Trans. Franck Bourdier, 'Geoffroy Saint-Hilaire versus Cuvier: The Campaign for Paleontological Evolution (1825- 1838)', Cecil J. Schneer (ed.), Toward a History of Geology (1969), 44.
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At the voice of comparative anatomy, every bone, and fragment of a bone, resumed its place. I cannot find words to express the pleasure I have in seeing, as I discovered one character, how all the consequences, which I predicted from it, were successively confirmed; the feet were found in accordance with the characters announced by the teeth; the teeth in harmony with those indicated beforehand by the feet; the bones of the legs and thighs, and every connecting portion of the extremities, were found set together precisely as I had arranged them, before my conjectures were verified by the discovery of the parts entire: in short, each species was, as it were, reconstructed from a single one of its component elements.
Geology and Mineralogy (1836), Vol. I, 83-4.
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At this point, however, I have no intention whatever of criticizing the false teachings of Galen, who is easily first among the professors of dissection, for I certainly do not wish to start off by gaining a reputation for impiety toward him, the author of all good things, or by seeming insubordinate to his authority. For I am well aware how upset the practitioners (unlike the followers of Aristotle) invariably become nowadays, when they discover in the course of a single dissection that Galen has departed on two hundred or more occasions from the true description of the harmony, function, and action of the human parts, and how grimly they examine the dissected portions as they strive with all the zeal at their command to defend him. Yet even they, drawn by their love of truth, are gradually calming down and placing more faith in their own not ineffective eyes and reason than in Galen’s writings.
From De Humani Corporis Fabrica Libri Septem: (1543), Book I, iv, as translated by William Frank Richardson, in On The Fabric of the Human Body: Book I: The Bones and Cartilages (1998), Preface, liv.
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Because a child of one doubles its age after the passage of a single year, it can be said to be aging rapidly.
Speech at the Nobel Banquet (10 Dec 1983) for his Nobel Prize in Chemistry. In Wilhelm Odelberg (ed.), Les Prix Nobel: The Nobel Prizes (1984), 43.
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Before the seas and lands had been created, before the sky that covers everything, Nature displayed a single aspect only throughout the cosmos; Chaos was its name, a shapeless, unwrought mass of inert bulk and nothing more, with the discordant seeds of disconnected elements all heaped together in anarchic disarray.
Describing the creation of the universe from chaos, at the beginning of Book I of Metamorphoses, lines 5-9. As translated in Charles Martin (trans.), Metamorphoses (2004), 15.
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Between the lowest and the highest degree of spiritual and corporal perfection, there is an almost infinite number of intermediate degrees. The succession of degrees comprises the Universal Chain. It unites all beings, ties together all worlds, embraces all the spheres. One SINGLE BEING is outside this chain, and this is HE who made it.
Contemplation de la nature (1764), Vol. I, 27. Trans. Stephen Jay Gould, Ontogeny and Phylogeny (1977), 23.
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But how is it that they [astrologers] have never been able to explain why, in the life of twins, in their actions, in their experiences, their professions, their accomplishments, their positions—in all the other circumstances of human life, and even in death itself, there is often found such a diversity that in those respects many strangers show more resemblance to them than they show to one another, even though the smallest possible interval separated their births and though they were conceived at the same moment, by a single act of intercourse.
De Civitate Dei (The City of God) [413-426], Book V, chapter I, trans. H. Bettenson (1972),180-181.
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But the dreams about the modes of creation, enquiries whether our globe has been formed by the agency of fire or water, how many millions of years it has cost Vulcan or Neptune to produce what the fiat of the Creator would effect by a single act of will, is too idle to be worth a single hour of any man’s life.
Letter (2 May 1826) to Doctor John P. Emmet. Collected in The Writings of Thomas Jefferson (1854), Vol. 7, 443.
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Certain students of genetics inferred that the Mendelian units responsible for the selected character were genes producing only a single effect. This was careless logic. It took a good deal of hammering to get rid of this erroneous idea. As facts accumulated it became evident that each gene produces not a single effect, but in some cases a multitude of effects on the characters of the individual. It is true that in most genetic work only one of these character-effects is selected for study—the one that is most sharply defined and separable from its contrasted character—but in most cases minor differences also are recognizable that are just as much the product of the same gene as is the major effect.
'The Relation of Genetics to Physiology and Medicine', Nobel Lecture (4 Jun 1934). In Nobel Lectures, Physiology or Medicine 1922-1941 (1965), 317.
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Chemistry is an art that has furnished the world with a great number of useful facts, and has thereby contributed to the improvement of many arts; but these facts lie scattered in many different books, involved in obscure terms, mixed with many falsehoods, and joined to a great deal of false philosophy; so that it is not great wonder that chemistry has not been so much studied as might have been expected with regard to so useful a branch of knowledge, and that many professors are themselves but very superficially acquainted with it. But it was particularly to be expected, that, since it has been taught in universities, the difficulties in this study should have been in some measure removed, that the art should have been put into form, and a system of it attempted—the scattered facts collected and arranged in a proper order. But this has not yet been done; chemistry has not yet been taught but upon a very narrow plan. The teachers of it have still confined themselves to the purposes of pharmacy and medicine, and that comprehends a small branch of chemistry; and even that, by being a single branch, could not by itself be tolerably explained.
John Thomson, An Account of the Life, Lectures and Writings of William Cullen, M.D. (1832), Vol. 1, 40.
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Considering the difficulties represented by the lack of water, by extremes of temperature, by the full force of gravity unmitigated by the buoyancy of water, it must be understood that the spread to land of life forms that evolved to meet the conditions of the ocean represented the greatest single victory won by life over the inanimate environment.
(1965). In Isaac Asimov’s Book of Science and Nature Quotations (1988), 194.
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Controlled research … endeavors to pick out of the web of nature’s activities some single strand and trace it towards its origin and its terminus and determine its relation to other strands.
In 'The Influence of Research in Bringing into Closer Relationship the Practice of Medicine and Public Health Activities', American Journal of Medical Sciences (Dec 1929), No. 178.
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Do there exist many worlds, or is there but a single world? This is one of the most noble and exalted questions in the study of Nature.
Quoted in Grant McColley, 'The Seventeenth-Century Doctrine of a Plurality of Worlds', Annals of Science (1936), 1, 385. As cited in George Sarton and Frances Siegel, 'Forty-Ninth Critical Bibliography of the History and Philosophy of Science and of the History of Civilization', Isis (May 1937), 27, No. 1, 174-175.
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Doctors coin money when they do procedures—family practice doesn’t have any procedures. A urologist has cystoscopies, a gastroenterologist has gastroscopies, a dermatologist has biopsies. They can do three or four of those and make five or six hundred dollars in a single day. We get nothing for the use of our time to understand the lives of our patients. Technology is rewarded in medicine, it seems to me, and not thinking.
Quoted in John McPhee, 'Heirs of General Practice,' New Yorker (23 Jul 1984), 40-85. In David Barton Smith and Arnold D. Kaluzny, The White Labyrinth (2000), 227.
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Dr. M.L. von Franz has explained the circle (or sphere) as a symbol of Self. It expresses the totality of the psyche in all its aspects, including the relationship between man and the whole of nature. It always points to the single most vital aspect of life, its ultimate wholeness.
In Aniela Jaffé, 'Symbolism in the Visual Arts', collected in Carl Jung (ed.), Man and His Symbols (1964, 1968), 266.
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E.W. Goodpasture showed that the virus of fowl pox could be grown in the tissues of the developing chick embryo. Nearly all the later practical advances in the control of virus diseases in man and animals sprang from this single discovery.
In 'Filterable Viruses', Encyclopaedia Britannica (1954), Vol. 9, 237. As quoted and cited by Esmond R. Long, 'Ernest William Goodpasture', National Academy of Sciences Biographical Memoirs (1965), 122.
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Each species may have had its origin in a single pair, or individual, where an individual was sufficient, and species may have been created in succession at such times and in such places as to enable them to multiply and endure for an appointed period, and occupy an appointed space on the globe.
Principles of Geology(1830-3), Vol. 2, 124.
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Education in my family was not merely emphasized, it was our raison d'être. Virtually all of our aunts and uncles had Ph.D.s in science or engineering, and it was taken for granted that the next generation of Chu's were to follow the family tradition. When the dust had settled, my two brothers and four cousins collected three MDs, four Ph.D.s and a law degree. I could manage only a single advanced degree.
Autobiography in Gösta Ekspong (ed.), Nobel Lectures: Physics 1996-2000 (2002), 115.
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ELECTRICITY, n. The power that causes all natural phenomena not known to be caused by something else. It is the same thing as lightning, and its famous attempt to strike Dr. Franklin is one of the most picturesque incidents in that great and good man's career. The memory of Dr. Franklin is justly held in great reverence, particularly in France, where a waxen effigy of him was recently on exhibition, bearing the following touching account of his life and services to science:
Monsieur Franqulin, inventor of electricity. This illustrious savant, after having made several voyages around the world, died on the Sandwich Islands and was devoured by savages, of whom not a single fragment was ever recovered.
Electricity seems destined to play a most important part in the arts and industries. The question of its economical application to some purposes is still unsettled, but experiment has already proved that it will propel a street car better than a gas jet and give more light than a horse.
The Cynic's Word Book (1906), 87. Also published later as The Devil's Dictionary.
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Endowed with two qualities, which seemed incompatible with each other, a volcanic imagination and a pertinacity of intellect which the most tedious numerical calculations could not daunt, Kepler conjectured that the movements of the celestial bodies must be connected together by simple laws, or, to use his own expression, by harmonic laws. These laws he undertook to discover. A thousand fruitless attempts, errors of calculation inseparable from a colossal undertaking, did not prevent him a single instant from advancing resolutely toward the goal of which he imagined he had obtained a glimpse. Twenty-two years were employed by him in this investigation, and still he was not weary of it! What, in reality, are twenty-two years of labor to him who is about to become the legislator of worlds; who shall inscribe his name in ineffaceable characters upon the frontispiece of an immortal code; who shall be able to exclaim in dithyrambic language, and without incurring the reproach of anyone, “The die is cast; I have written my book; it will be read either in the present age or by posterity, it matters not which; it may well await a reader, since God has waited six thousand years for an interpreter of his words.”
In 'Eulogy on Laplace', in Smithsonian Report for the year 1874 (1875), 131-132.
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Enough for me the mystery of the eternity of life, and the inkling of the marvellous structure of reality, together with the single-hearted endeavour to comprehend a portion, be it never so tiny, of the reason that manifests itself in nature.
In Alan Harris (ed.), The World As I See It (1934), 242.
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Even more difficult to explain, than the breaking-up of a single mass into fragments, and the drifting apart of these blocks to form the foundations of the present-day continents, is the explanation of the original production of the single mass, or PANGAEA, by the concentration of the former holosphere of granitic sial into a hemisphere of compressed and crushed gneisses and schists. Creep and the effects of compression, due to shrinking or other causes, have been appealed to but this is hardly a satisfactory explanation. The earth could no more shrug itself out of its outer rock-shell unaided, than an animal could shrug itself out of its hide, or a man wriggle out of his skin, or even out of his closely buttoned coat, without assistance either of his own hands or those of others.
The Rhythm of Ages (1940), 9-10.
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Even those to whom Providence has allotted greater strength of understanding, can expect only to improve a single science. In every other part of learning, they must be content to follow opinions, which they are not able to examine; and, even in that which they claim as peculiarly their own, can seldom add more than some small particle of knowledge, to the hereditary stock devolved to them from ancient times, the collective labour of a thousand intellects.
In Samuel Johnson and W. Jackson Bate (Ed.), ',The Rambler, No. 121, Tuesday, 14 May 1751.' The Selected Essays from the Rambler, Adventurer, and Idler (1968), 172.
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Every breath you draw, every accelerated beat of your heart in the emotional periods of your oratory depend upon highly elaborated physical and chemical reactions and mechanisms which nature has been building up through a million centuries. If one of these mechanisms, which you owe entirely to your animal ancestry, were to be stopped for a single instant, you would fall lifeless on the stage. Not only this, but some of your highest ideals of human fellowship and comradeship were not created in a moment, but represent the work of ages.
Quoted in Closing Address by Dr. Henry Sloane Coffin, president of the Union Theological Seminary, New York, at the Memorial Service for Osborn at St. Bartholomew's Church, N.Y. (18 Dec 1935). In 'Henry Fairfield Osborn', Supplement to Natural History (Feb 1936), 37:2, 133-34. Bound in Kofoid Collection of Pamphlets on Biography, University of California.
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Every cent we earn from Crocodile Hunter goes straight back into conservation. Every single cent.
…...
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Fertilization of mammalian eggs is followed by successive cell divisions and progressive differentiation, first into the early embryo and subsequently into all of the cell types that make up the adult animal. Transfer of a single nucleus at a specific stage of development, to an enucleated unfertilized egg, provided an opportunity to investigate whether cellular differentiation to that stage involved irreversible genetic modification. The first offspring to develop from a differentiated cell were born after nuclear transfer from an embryo-derived cell line that had been induced to became quiescent. Using the same procedure, we now report the birth of live lambs from three new cell populations established from adult mammary gland, fetus and embryo. The fact that a lamb was derived from an adult cell confirms that differentiation of that cell did not involve the irreversible modification of genetic material required far development to term. The birth of lambs from differentiated fetal and adult cells also reinforces previous speculation that by inducing donor cells to became quiescent it will be possible to obtain normal development from a wide variety of differentiated cells.
[Co-author of paper announcing the cloned sheep, ‘Dolly’.]
In I. Wilmut, A. E. Schnieke, J. McWhir, et al., 'Viable Offspring Derived from Petal and Adult Mammalian Cells', Nature (1997), 385, 810.
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For a stone, when it is examined, will be found a mountain in miniature. The fineness of Nature’s work is so great, that, into a single block, a foot or two in diameter, she can compress as many changes of form and structure, on a small scale, as she needs for her mountains on a large one; and, taking moss for forests, and grains of crystal for crags, the surface of a stone, in by far the plurality of instances, is more interesting than the surface of an ordinary hill; more fantastic in form and incomparably richer in colour—the last quality being, in fact, so noble in most stones of good birth (that is to say, fallen from the crystalline mountain ranges).
Modern Painters, 4, Containing part 5 of Mountain Beauty (1860), 311.
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For more than half a century, Martin Gardner has been the single brightest beacon defending rationality and good science against the mysticism and anti-intellectualism that surround us.
As quoted on the back cover of several of the books by Martin Gardner.
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For nearly twelve years I travelled and lived mostly among uncivilised or completely savage races, and I became convinced that they all possessed good qualities, some of them in a very remarkable degree, and that in all the great characteristics of humanity they are wonderfully like ourselves. Some, indeed, among the brown Polynesians especially, are declared by numerous independent and unprejudiced observers, to be physically, mentally, and intellectually our equals, if not our superiors; and it has always seemed to me one of the disgraces of our civilisation that these fine people have not in a single case been protected from contamination by the vices and follies of our more degraded classes, and allowed to develope their own social and political organislll under the advice of some of our best and wisest men and the protection of our world-wide power. That would have been indeed a worthy trophy of our civilisation. What we have actually done, and left undone, resulting in the degradation and lingering extermination of so fine a people, is one of the most pathetic of its tragedies.
In 'The Native Problem in South Africa and Elsewhere', Independent Review (1906), 11, 182.
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For the sake of our children and our future, we must do more to combat climate change. Now, it’s true that no single event makes a trend. But the fact is the 12 hottest years on record have all come in the last 15. Heat waves, droughts, wildfires, floods—all are now more frequent and more intense. We can choose to believe that Superstorm Sandy, and the most severe drought in decades, and the worst wildfires some states have ever seen were all just a freak coincidence. Or we can choose to believe in the overwhelming judgment of science—and act before it’s too late.
From second State of the Union Address (12 Feb 2013) at the U.S. Capitol.
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Formerly Milton's Paradise Lost had been my chief favourite, and in my excursions during the voyage of the Beagle, when I could take only a single small volume, I always chose Milton.
Nora Barlow (ed.), The Autobiography of Charles Darwin, 1809-1882 (1958), 85.
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From a drop of water a logician could predict an Atlantic or a Niagara without having seen or heard of one or the other. So all life is a great chain, the nature of which is known whenever we are shown a single link of it.
In A Study in Scarlet (1887, 1892), 27.
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From all we have learnt about the structure of living matter, we must be prepared to find it working in a manner that cannot be reduced to the ordinary laws of physics. And that not on the ground that there is any “new force” or what not, directing the behavior of the single atoms within a living organism, but because the construction is different from anything we have yet tested in the physical laboratory.
What is Life? (1956), 74.
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Generalisations which are fruitful because they reveal in a single general principle the rationale of a great many particular truths, the connections and common origins of which had not previously been seen, are found in all the sciences, and particularly in mathematics. Such generalisations are the most important of all, and their discovery is the work of genius.
From Essai sur les Fondements de nos Connaissances et sur les Caractères de la Critique Philosophique (1851), 28, as translated by Merritt H Moore in An Essay on the Foundations of Our Knowledge (1956), 24. From the original French: “Il y a dans toutes les sciences, et en mathématiques particulièrement, des généralisations fécondes, parce qu’elles nous montrent dans une vérité générale la raison d’une multitude de vérités particulières dont les liens et la commune origine n’étaient point aperçus. De telles généralisations sont des découvertes du génie, et les plus importantes de toutes.”
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Generality of points of view and of methods, precision and elegance in presentation, have become, since Lagrange, the common property of all who would lay claim to the rank of scientific mathematicians. And, even if this generality leads at times to abstruseness at the expense of intuition and applicability, so that general theorems are formulated which fail to apply to a single special case, if furthermore precision at times degenerates into a studied brevity which makes it more difficult to read an article than it was to write it; if, finally, elegance of form has well-nigh become in our day the criterion of the worth or worthlessness of a proposition,—yet are these conditions of the highest importance to a wholesome development, in that they keep the scientific material within the limits which are necessary both intrinsically and extrinsically if mathematics is not to spend itself in trivialities or smother in profusion.
In Die Entwickdung der Mathematik in den letzten Jahrhunderten (1884), 14-15.
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Genius itself has been analyzed by the shrewdest observers into a higher capacity of attention. “Genius,” says Helvetius … “is nothing but a continued attention,” (une attention suivie). “Genius,” says Buffon, “is only a protracted patience,” (une longue patience). “In the exact sciences, at least,” says Cuvier, “it is the patience of a sound intellect, when invincible, which truly constitutes genius.” And Chesterfield has also observed, that “the power of applying an attention, steady and undissipated, to a single object, is the sure mark of a superior genius.”
In Lectures on Metaphysics and Logic (1860), Vol. 1, 179.
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God is infinite, so His universe must be too. Thus is the excellence of God magnified and the greatness of His kingdom made manifest; He is glorified not in one, but in countless suns; not in a single earth, a single world, but in a thousand thousand, I say in an infinity of worlds.
…...
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Having made a sufficient opening to admit my finger into the abdomen, I passed it between the intestines to the spine, and felt the aorta greatly enlarged, and beating with excessive force. By means of my finger nail, I scratched through the peritoneum on the left side of the aorta, and then gradually passed my finger between the aorta and the spine, and again penetrated the peritoneum, on the right side of the aorta. I had now my finger under the artery, and by its side I conveyed the blunt aneurismal needle, armed with a single ligature behind it...
Describing the first ligation of the aorta in 1817 for left femoral aneurysm.
Frederick Tyrell (Ed.), 'Lecture 15, On the Operation for Aneurism', The Lectures of Sir Astley Cooper (1824), Vol. 2, 58.
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Her [Nettie Stevens] single-mindedness and devotion, combined with keen powers of observation; her thoughtfulness and patience, united to a well-balanced judgment, account, in part, for her remarkable accomplishment.
In obituary, 'The Scientific Work of Miss N.M. Steves', Science (11 Oct 1912), 36, No. 928, 470.
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Heredity is the general expression of the periodicity of organic life. All generations belong to a continuous succession of waves, in which every single one resembles its predecessors and its followers.
In 'On the Principles of Animal Morphology', Proceedings of the Royal Society of Edinburgh (1888), 15, 295. Original as Letter to Mr John Murray, communicated to the Society by Professor Sir William Turner. Page given as in collected volume published 1889.
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High in the North in a land called Svithjod there is a mountain. It is a hundred miles long and a hundred miles high and once every thousand years a little bird comes to this mountain to sharpen its beak. When the mountain has thus been worn away a single day of eternity will have passed
In The Story of America (1921). As cited in David Blatner, Spectrums: Our Mind-boggling Universe from Infinitesimal to Infinity (2012), 24.
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His Majesty has, with great skill, constructed a cart, containing a corn mill, which is worked by the motion of the carriage. He has also contrived a carriage of such a magnitude as to contain several apartments, with a hot bath; and it is drawn by a single elephant. This movable bath is extremely useful, and refreshing on a journey. … He has also invented several hydraulic machines, which are worked by oxen. The pulleys and wheels of some of them are so adjusted that a single ox will at once draw water out of two wells, and at the same time turn a millstone.
From Ain-i-Akbery (c.1590). As translated from the original Persian, by Francis Gladwin in 'Akbar’s Conduct and Administrative Rules', 'Of Machines', Ayeen Akbery: Or, The Institutes of the Emperor Akber (1783), Vol. 1, 284. Note: Akbar (Akber) was a great ruler and enlightened statesman.
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I am a horse for single harness, not cut out for tandem or teamwork.
In Leopold Infeld, Quest, the Evolution of a Scientist (1941), 287.
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I am born into an environment–I know not whence I came nor whither I go nor who I am. This is my situation as yours, every single one of you. The fact that everyone always was in this same situation, and always will be, tells me nothing. Our burning question as to the whence and whither–all we can ourselves observe about it is the present environment. That is why we are eager to find out about it as much as we can. That is science, learning, knowledge; it is the true source of every spiritual endeavour of man. We try to find out as much as we can about the spatial and temporal surroundings of the place in which we find ourselves put by birth.
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I am mindful that scientific achievement is rooted in the past, is cultivated to full stature by many contemporaries and flourishes only in favorable environment. No individual is alone responsible for a single stepping stone along the path of progress, and where the path is smooth progress is most rapid. In my own work this has been particularly true.
Nobel Prize banquet speech (29 Feb 1940)
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I am more and more convinced that the ant colony is not so much composed of separate individuals as that the colony is a sort of individual, and each ant like a loose cell in it. Our own blood stream, for instance, contains hosts of white corpuscles which differ little from free-swimming amoebae. When bacteria invade the blood stream, the white corpuscles, like the ants defending the nest, are drawn mechanically to the infected spot, and will die defending the human cell colony. I admit that the comparison is imperfect, but the attempt to liken the individual human warrior to the individual ant in battle is even more inaccurate and misleading. The colony of ants with its component numbers stands half way, as a mechanical, intuitive, and psychical phenomenon, between our bodies as a collection of cells with separate functions and our armies made up of obedient privates. Until one learns both to deny real individual initiative to the single ant, and at the same time to divorce one's mind from the persuasion that the colony has a headquarters which directs activity … one can make nothing but pretty fallacies out of the polity of the ant heap.
In An Almanac for Moderns (1935), 121
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I am much occupied with the investigation of the physical causes [of motions in the Solar System]. My aim in this is to show that the celestial machine is to be likened not to a divine organism but rather to a clockwork … insofar as nearly all the manifold movements are carried out by means of a single, quite simple magnetic force. This physical conception is to be presented through calculation and geometry.
Letter to Ilerwart von Hohenburg (10 Feb 1605) Quoted in Holton, Johannes Kepler's Universe: Its Physics and Metaphysics, 342, as cited by Hylarie Kochiras, Force, Matter, and Metaphysics in Newton's Natural Philosophy (2008), 57.
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I am nothing more than a single narrow gasping lung, floating over the mists and summits.
In Everest: Expedition to the Ultimate (1979), 180.
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I am perhaps more proud of having helped to redeem the character of the cave-man than of any other single achievement of mine in the field of anthropology.
Quoted in Closing Address by Dr. Henry Sloane Coffin, president of the Union Theological Seminary, New York, at the Memorial Service for Osborn at St. Bartholomew's Church, N.Y. (18 Dec 1935). In 'Henry Fairfield Osborn', Supplement to Natural History (Feb 1936), 37:2, 134. Bound in Kofoid Collection of Pamphlets on Biography, University of California.
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I argued that it was important not to place too much reliance on any single piece of experimental evidence. It might turn out to be misleading, as the 5.1 Å reflection undoubtedly was. Jim was a little more brash, stating that no good model ever accounted for all the facts, since some data was bound to be misleading if not plain wrong. A theory that did fit all the data would have been “carpentered” to do so and would thus be open to suspicion.
In What Mad Pursuit: A Personal View of Scientific Discovery (1988), 59-60.
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I believe in “intelligence,” and I believe also that there are inherited differences in intellectual ability, but I do not believe that intelligence is a simple scalar endowment that can be quantified by attaching a single figure to it—an I.Q. or the like.
In Advice to a Young Scientist (1979), 25. Footnoted with reference to his own earlier review article of books about IQ, in which he stated “misgivings about whether it is indeed possible to attach a single-number valuation to an endowment as complex and as various as intelligence.” That review was titled 'Unnatural Science', in New York Review of Books (3 Feb 1977), 24, No. 1, 13,
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I can’t recall a single problem in my life, of any sort, that I ever started on that I didn't solve, or prove that I couldn’t solve it. I never let up, until I had done everything that I could think of, no matter how absurd it might seem as a means to the end I was after.
As quoted in French Strother, 'The Modern Profession of Inventing', World's Work and Play (Jul 1905), 6, No. 32, 186.
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I cannot think of a single field in biology or medicine in which we can claim genuine understanding, and it seems to me the more we learn about living creatures, especially ourselves, the stranger life becomes.
In 'On Science and Certainty', Discover Magazine (Oct 1980).
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I defend the following postulate as an indisputable principle: that each nerve fibre originates as a process from a single cell. This is its genetic, nutritive, and functional center; all other connections of the fibre are either indirect or secondary.
'Zur Geschichte des menschlichen Rückenmarkes und der Nervenwurzeln' (1887). Trans. Edwin Clarke and C. D. O'Malley, The Human Brain and Spinal Cord (1968), 103.
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I have devoted my whole life to the study of Nature, and yet a single sentence may express all that I have done. I have shown that there is a correspondence between the succession of Fishes in geological times and the different stages of their growth in the egg,—this is all. It chanced to be a result that was found to apply to other groups and has led to other conclusions of a like nature.
In Methods of Study in Natural History (1863), 23.
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I have mentioned mathematics as a way to settle in the mind a habit of reasoning closely and in train; not that I think it necessary that all men should be deep mathematicians, but that, having got the way of reasoning which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge, as they shall have occasion. For in all sorts of reasoning, every single argument should be managed as a mathematical demonstration; the connection and dependence of ideas should be followed till the mind is brought to the source on which it bottoms, and observes the coherence all along; …
In The Conduct of the Understanding, Sect. 7.
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I have no patience with attempts to identify science with measurement, which is but one of its tools, or with any definition of the scientist which would exclude a Darwin, a Pasteur or a Kekulé. The scientist is a practical man and his are practical aims. He does not seek the ultimate but the proximate. He does not speak of the last analysis but rather of the next approximation. His are not those beautiful structures so delicately designed that a single flaw may cause the collapse of the whole. The scientist builds slowly and with a gross but solid kind of masonry. If dissatisfied with any of his work, even if it be near the very foundations, he can replace that part without damage to the remainder. On the whole, he is satisfied with his work, for while science may never be wholly right it certainly is never wholly wrong; and it seems to be improving from decade to decade.
The Anatomy of Science (1926), 6-7.
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I have often thought that an interesting essay might be written on the influence of race on the selection of mathematical methods. methods. The Semitic races had a special genius for arithmetic and algebra, but as far as I know have never produced a single geometrician of any eminence. The Greeks on the other hand adopted a geometrical procedure wherever it was possible, and they even treated arithmetic as a branch of geometry by means of the device of representing numbers by lines.
In A History of the Study of Mathematics at Cambridge (1889), 123
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I much prefer the sharpest criticism of a single intelligent man to the thoughtless approval of the great masses.
Letter (13 Oct 1597) to Galileo, who had just replied with thanks for the book Kepler sent him. As quoted in translation in Jackson J. Spielvogel, Western Civilization: Alternate Volume: Since 1300 (2010), Vol. 2, 494.
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I see nothing wrong ethically with the idea of correcting single gene defects [through genetic engineering]. But I am concerned about any other kind of intervention, for anything else would be an experiment, [which would] impose our will on future generations [and take unreasonable chances] with their welfare ... [Thus] such intervention is beyond the scope of consideration.
in The Second Creation: Dolly and the Age of Biological Control
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I see the whole of humankind becoming a single, integrated organism. … I look upon each of us as I would an individual cell in the organism, each of us playing his or her respective role.
From interview with James Reston, Jr., in Pamela Weintraub (ed.), The Omni Interviews (1984), 109. Previously published in magazine, Omni (May 1982).
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I should be the last to discard the law of organic heredity ... but the single word “heredity” cannot dispense science from the duty of making every possible inquiry into the mechanism of organic growth and of organic formation. To think that heredity will build organic beings without mechanical means is a piece of unscientific mysticism.
In 'On the Principles of Animal Morphology', Proceedings of the Royal Society of Edinburgh (1888), 15, 294-295. Original as Letter to Mr John Murray, communicated to the Society by Professor Sir William Turner. Page given as in collected volume published 1889.
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I sometimes think there is a malign force loose in the universe that is the social equivalent of cancer, and it’s plastic. It infiltrates everything. It’s metastasis. It gets into every single pore of productive life. I mean there won’t be anything that isn’t made of plastic before long. They’ll be paving the roads with plastic before they’re done. Our bodies, our skeletons, will be replaced with plastic.
From Robert Begiebing, 'Twelfth Round: An Interview with Norman Mailer', collected in J. Michael Lennon (ed.), Conversations with Norman Mailer (1988), 321.
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I think each individual is never a plane but a polyhedron. Naturally, whenever a ray of light falls on a face, a vertex, an edge of this polyhedron; the arc that it reflects is undoubtedly variable, very complex and single or multicoloured. I don’t believe in plane men, I think we’re all multiple. We don’t have a double life, we have a multiple life. However, it is no less true that we’re thought to have a common denominator. I think I am or I aspire to be an honest man that tries not to bother too many people in this valley of tears.
From Cela Foundation biography webpage.
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I think there probably is life, maybe primitive life, in outer space. There might be very primitive life in our solar system—single-cell animals, that sort of thing. We may know the answer to that in five or ten years. There is very likely to be life in other solar systems, in planets around other stars. But we won’t know about that for a long time.
Interview conducted on Scholastic website (20 Nov 1998).
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I trust ... I have succeeded in convincing you that modern chemistry is not, as it has so long appeared, an ever-growing accumulation of isolated facts, as impossible for a single intellect to co-ordinate as for a single memory to grasp.
The intricate formulae that hang upon these walls, and the boundless variety of phenomena they illustrate, are beginning to be for us as a labyrinth once impassable, but to which we have at length discovered the clue. A sense of mastery and power succeeds in our minds to the sort of weary despair with which we at first contemplated their formidable array. For now, by the aid of a few general principles, we find ourselves able to unravel the complexities of these formulae, to marshal the compounds which they represent in orderly series; nay, even to multiply their numbers at our will, and in a great measure to forecast their nature ere we have called them into existence. It is the great movement of modern chemistry that we have thus, for an hour, seen passing before us. It is a movement as of light spreading itself over a waste of obscurity, as of law diffusing order throughout a wilderness of confusion, and there is surely in its contemplation something of the pleasure which attends the spectacle of a beautiful daybreak, something of the grandeur belonging to the conception of a world created out of chaos.
Concluding remark for paper presented at the Friday Discourse of the the Royal Institution (7 Apr 1865). 'On the Combining Power of Atoms', Proceedings of the Royal Institution (1865), 4, No. 42, 416.
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I trust I may be enabled in the treatment of patients always to act with a single eye to their good.
Letter to his sister Jane (3 Mar 1857). In John Vaughan, 'Lord Lister', The Living Age (1918), 297, 361. Reprinted from The Fortnightly Review (1918), 109, 417- .
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I would trade all my experimental works for the single idea of the benzene theory.
Quoted by B. L. Lepsius in 'Hofmann und die Deutsche Chemische Gesellschaft', Berichte der Deutschen Chemischen Gesellschaft (1918), 51, 51.
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I wouldn’t miss this opportunity for anything. For the chance to work on these conservation issues, to serve my country, to work for this president, I’d do it all over again, every single minute.
…...
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If a single cell, under appropriate conditions, becomes a man in the space of a few years, there can surely be no difficulty in understanding how, under appropriate conditions, a cell may, in the course of untold millions of years, give origin to the human race.
Principles of Biology (1865, 1872), 350.
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If all the parts of the universe are interchained in a certain measure, any one phenomenon will not be the effect of a single cause, but the resultant of causes infinitely numerous.
…...
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If I had to define life in a single phrase, I should clearly express my thought of throwing into relief one characteristic which, in my opinion, sharply differentiates biological science. I should say: life is creation.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 93.
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If the views we have ventured to advance be correct, we may almost consider {greek words} of the ancients to be realised in hydrogen, an opinion, by the by, not altogether new. If we actually consider the specific gravities of bodies in their gaseous state to represent the number of volumes condensed into one; or in other words, the number of the absolute weight of a single volume of the first matter ({greek words}) which they contain, which is extremely probable, multiples in weight must always indicate multiples in volume, and vice versa; and the specific gravities, or absolute weights of all bodies in a gaseous state, must be multiples of the specific gravity or absolute weight of the first matter, ({Greek words}), because all bodies in the gaseous state which unite with one another unite with reference to their volume.
'Correction of a Mistake in the Essay on the Relation between the Specific Gravities of Bodies in their Gaseous State and the Weights of their Atoms', Annals of Philosophy (1816), 7, 113.
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If the world has begun with a single quantum, the notions of space and would altogether fail to have any meaning at the beginning; they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time. I think that such a beginning of the world is far enough from the present order of Nature to be not at all repugnant. It may be difficult to follow up the idea in detail as we are not yet able to count the quantum packets in every case. For example, it may be that an atomic nucleus must be counted as a unique quantum, the atomic number acting as a kind of quantum number. If the future development of quantum theory happens to turn in that direction, we could conceive the beginning of the universe in the form of a unique atom, the atomic weight of which is the total mass of the universe. This highly unstable atom would divide in smaller and smaller atoms by a kind of super-radioactive process.
In a seminal short letter (457 words), 'The Beginning of the World from the Point of View of Quantum Theory', Nature (9 May 1931), 127, 706.
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If there is a lesson in our story it is that the manipulation, according to strictly self-consistent rules, of a set of symbols representing one single aspect of the phenomena may produce correct, verifiable predictions, and yet completely ignore all other aspects whose ensemble constitutes reality.
In 'Epilogue', The Sleepwalkers: A History of Man’s Changing Vision of the Universe (1959, 1968), 533.
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If we compare a mathematical problem with an immense rock, whose interior we wish to penetrate, then the work of the Greek mathematicians appears to us like that of a robust stonecutter, who, with indefatigable perseverance, attempts to demolish the rock gradually from the outside by means of hammer and chisel; but the modern mathematician resembles an expert miner, who first constructs a few passages through the rock and then explodes it with a single blast, bringing to light its inner treasures.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1869), 9. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 114. From the original German, “Vergleichen wir ein mathematisches Problem mit einem gewaltigen Felsen, in dessen Inneres wir eindringen wollen, so erscheint die Arbeit der griechischen Mathematiker uns als die eines rüstigen Steinhauers, der mit Hammer und Meissel in unermüdlicher Ausdauer den Felsen langsam von aussen her zu zerbröckeln beginnt; der moderne Mathematiker aber als ein trefflicher Minirer, der diesen Felsen zunächst mit wenigen Gängen durchzieht, von denen aus er dann den Felsblock mit einem gewaltigem Schlage zersprengt und die Schätze des Inneren zu Tage fördert.”
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If you disregard the very simplest cases, there is in all of mathematics not a single infinite series whose sum has been rigorously determined. In other words, the most important parts of mathematics stand without a foundation.
In Letter to a friend, as quoted in George Finlay Simmons, Calculus Gems (1992), 188.
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If you have a lot of loose papers to carry, or sticks of kindling-wood, you will do it more easily if they are tied together in a single bundle. That is what the scientist is always doing, tying up fugitive facts into compact and portable packages.
In Chats on Science (1924), 4.
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In 1946 [we visited] a rock called Le Veyron, around which sea life swarmed … an undersea paradise.… About thirty years later I returned … to the same depth, to the same caves, at the same time of year. The grotto was empty. Not one single fish lived among the rocks. The verdant gardens were gone.…
When I saw Le Veyron, I believed that the sea’s most monstrous force doesn’t live in Loch Ness. It lives in us.
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 40-41.
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In a sense cosmology contains all subjects because it is the story of everything, including biology, psychology and human history. In that single sense it can be said to contain an explanation also of time's arrow. But this is not what is meant by those who advocate the cosmological explanation of irreversibility. They imply that in some way the time arrow of cosmology imposes its sense on the thermodynamic arrow. I wish to disagree with this view. The explanation assumes that the universe is expanding. While this is current orthodoxy, there is no certainty about it. The red-shifts might be due to quite different causes. For example, when light passes through the expanding clouds of gas it will be red-shifted. A large number of such clouds might one day be invoked to explain these red shifts. It seems an odd procedure to attempt to 'explain' everyday occurrences, such as the diffusion of milk into coffee, by means of theories of the universe which are themselves less firmly established than the phenomena to be explained. Most people believe in explaining one set of things in terms of others about which they are more certain, and the explanation of normal irreversible phenomena in terms of the cosmological expansion is not in this category.
'Thermodynamics, Cosmology) and the Physical Constants', in J. T. Fraser (ed.), The Study of Time III (1973), 117-8.
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In all our academies we attempt far too much. ... In earlier times lectures were delivered upon chemistry and botany as branches of medicine, and the medical student learned enough of them. Now, however, chemistry and botany are become sciences of themselves, incapable of comprehension by a hasty survey, and each demanding the study of a whole life, yet we expect the medical student to understand them. He who is prudent, accordingly declines all distracting claims upon his time, and limits himself to a single branch and becomes expert in one thing.
Quoted in Johann Hermann Baas, Henry Ebenezer Handerson (trans.), Outlines of the History of Medicine and the Medical Profession (1889), 842-843.
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In man, then, let us take the amount that is extruded by the individual beats, and that cannot return into the heart because of the barrier set in its way by the valves, as half an ounce, or three drachms, or at least one drachm. In half an hour the heart makes over a thousand beats; indeed, in some individuals, and on occasion, two, three, or four thousand. If you multiply the drachms per beat by the number of beats you will see that in half an hour either a thousand times three drachms or times two drachms, or five hundred ounces, or other such proportionate quantity of blood has been passed through the heart into the arteries, that is, in all cases blood in greater amount than can be found in the whole of the body. Similarly in the sheep or the dog. Let us take it that one scruple passes in a single contraction of the heart; then in half an hour a thousand scruples, or three and a half pounds of blood, do so. In a body of this size, as I have found in the sheep, there is often not more than four pounds of blood.
In the above sort of way, by calculating the amount of blood transmitted [at each heart beat] and by making a count of the beats, let us convince ourselves that the whole amount of the blood mass goes through the heart from the veins to the arteries and similarly makes the pulmonary transit.
Even if this may take more than half an hour or an hour or a day for its accomplishment, it does nevertheless show that the beat of the heart is continuously driving through that organ more blood than the ingested food can supply, or all the veins together at any time contain.
De Motu Cordis (1628), The Circulation of the Blood and Other Writings, trans. Kenneth J. Franklin (1957), Chapter 9, 62-3.
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In my life as an architect, I found that the single thing which inhibits young professionals, new students most severely, is their acceptance of standards that are too low.
In 'Foreword' written for Richard P. Gabriel, Patterns of Software: Tales from the Software Community (1996), vii.
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In order that an inventory of plants may be begun and a classification of them correctly established, we must try to discover criteria of some sort for distinguishing what are called “species”. After a long and considerable investigation, no surer criterion for determining species had occurred to me than distinguishing features that perpetuate themselves in propagation from seed. Thus, no matter what variations occur in the individuals or the species, if they spring from the seed of one and the same plant, they are accidental variations and not such as to distinguish a species. For these variations do not perpetuate themselves in subsequent seeding. Thus, for example, we do not regard caryophylli with full or multiple blossoms as a species distinct from caryophylli with single blossoms, because the former owe their origin to the seed of the latter and if the former are sown from their own seed, they once more produce single-blossom caryophylli. But variations that never have as their source seed from one and the same species may finally be regarded as distinct species. Or, if you make a comparison between any two plants, plants which never spring from each other's seed and never, when their seed is sown, are transmuted one into the other, these plants finally are distinct species. For it is just as in animals: a difference in sex is not enough to prove a difference of species, because each sex is derived from the same seed as far as species is concerned and not infrequently from the same parents; no matter how many and how striking may be the accidental differences between them; no other proof that bull and cow, man and woman belong to the same species is required than the fact that both very frequently spring from the same parents or the same mother. Likewise in the case of plants, there is no surer index of identity of species than that of origin from the seed of one and the same plant, whether it is a matter of individuals or species. For animals that differ in species preserve their distinct species permanently; one species never springs from the seed of another nor vice versa.
John Ray
Historia Plantarum (1686), Vol. 1, 40. Trans. Edmund Silk. Quoted in Barbara G. Beddall, 'Historical Notes on Avian Classification', Systematic Zoology (1957), 6, 133-4.
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In questions of science the authority of a thousand is not worth the humble reasoning of a single individual.
(1632). Attributed in F. Arago, Eulogy on Laplace as quoted in Smithsonian Report (1874), 164. Cited in Robert Edouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 232.
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In scientific investigations it is grievously wrong to pander to the public’s impatience for results, or to let them think that for discovery it is necessary only to set up a great manufactory and a system of mass production. If in treatment team work is effective, in research it is the individual who counts first and above all. No great thought has ever sprung from anything but a single mind, suddenly conceiving. Throughout the whole world there has been too violent a forcing of the growth of ideas; too feverish a rush to perform experiments and publish conclusions. A year of vacation for calm detachment with all the individual workers thinking it all over in a desert should be proclaimed.
In Viewless Winds: Being the Recollections and Digressions of an Australian Surgeon (1939), 286.
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In scientific study, or, as I prefer to phrase it, in creative scholarship, the truth is the single end sought; all yields to that. The truth is supreme, not only in the vague mystical sense in which that expression has come to be a platitude, but in a special, definite, concrete sense. Facts and the immediate and necessary inductions from facts displace all pre-conceptions, all deductions from general principles, all favourite theories. Previous mental constructions are bowled over as childish play-structures by facts as they come rolling into the mind. The dearest doctrines, the most fascinating hypotheses, the most cherished creations of the reason and of the imagination perish from a mind thoroughly inspired with the scientific spirit in the presence of incompatible facts. Previous intellectual affections are crushed without hesitation and without remorse. Facts are placed before reasonings and before ideals, even though the reasonings and the ideals be more beautiful, be seemingly more lofty, be seemingly better, be seemingly truer. The seemingly absurd and the seemingly impossible are sometimes true. The scientific disposition is to accept facts upon evidence, however absurd they may appear to our pre-conceptions.
The Ethical Functions of Scientific Study: An Address Delivered at the Annual Commencement of the University of Michigan, 28 June 1888, 7-8.
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In the final, the positive, state, the mind has given over the vain search after absolute notions, the origin and destination of the universe, and the causes of phenomena, and applies itself to the study of their laws—that is, their invariable relations of succession and resemblance. Reasoning and observation, duly combined, are the means of this knowledge. What is now understood when we speak of an explanation of facts is simply the establishment of a connection between single phenomena and some general facts.
The Positive Philosophy, trans. Harriet Martineau (1853), Vol. 1, 2.
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In the gametes of an individual hybrid the Anlagen for each individual parental character are found in all possible combinations but never in a single gamete the Anlagen for a pair of characters. Each combination occurs with approximately the same frequency.
'Mendel's Regel über das Verhalten der Nachkommenschaft der Rassenbastarde', Der Deutsche Botanisch Gesellschaft, 1900, 18, 158-68. Trans. in Ernst Mayr, The Growth of Biological Thought: Diversity, Evolution and Inheritance (1982), 719.
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In the history of the discovery of zero will always stand out as one of the greatest single achievements of the human race.
Number: the Language of Science (1930), 35.
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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 space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the old Oolitic Silurian Period, must a million years ago next November, the Lower Mississippi River was upward of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-rod. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo and New Orleans will have their streets joined together, and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.
Life on the Mississippi (1883, 2000), 173.
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In war, science has proven itself an evil genius; it has made war more terrible than it ever was before. Man used to be content to slaughter his fellowmen on a single plane—the earth’s surface. Science has taught him to go down into the water and shoot up from below and to go up into the clouds and shoot down from above, thus making the battlefield three times as bloody as it was before; but science does not teach brotherly love. Science has made war so hellish that civilization was about to commit suicide; and now we are told that newly discovered instruments of destruction will make the cruelties of the late war seem trivial in comparison with the cruelties of wars that may come in the future.
Proposed summation written for the Scopes Monkey Trial (1925), in Genevieve Forbes Herrick and John Origen Herrick, The Life of William Jennings Bryan (1925), 405. This speech was prepared for delivery at the trial, but was never heard there, as both sides mutually agreed to forego arguments to the jury.
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It has been recognized that hydrogen bonds restrain protein molecules to their native configurations, and I believe that as the methods of structural chemistry are further applied to physiological problems it will be found that the significance of the hydrogen bond for physiology is greater than that of any other single structural feature.
Nature of the Chemical Bond and the Structure of Molecules and Crystals (1939), 265.
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It has sometimes been said that the success of the Origin proved “that the subject was in the air,” or “that men's minds were prepared for it.” I do not think that this is strictly true, for I occasionally sounded not a few naturalists, and never happened to come across a single one who seemed to doubt about the permanence of species.
In Charles Darwin and Francis Darwin (ed.), Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of His Published Letters (1892), 42.
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It is a strange feeling which comes over one as he stands in the centre of the tunnel, and knows that a mighty river is rolling on over his head, and that great ships with their thousands of tons burthen, sail over him. ... There is no single work of Art in London (with the exception of St. Paul's Cathedral) which excites so much curiosity and admiration among foreigners as the Tunnel. Great buildings are common to all parts of Europe, but the world has not such another Tunnel as this. There is something grand in the idea of walking under a broad river—making a pathway dry and secure beneath ships and navies!
[About visiting Brunel's Thames Tunnel, the first in the world under a navigable waterway.]
What I Saw in London: or, Men and Things in the Great Metropolis (1853), 168-169.
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It is a very strange thing to reflect that but for the invention of Professor Haber the Germans could not have continued the War after their original stack of nitrates was exhausted. The invention of this single man has enabled them, utilising the interval in which their accumulations were used up, not only to maintain an almost unlimited supply of explosives for all purposes, but to provide amply for the needs of agriculture in chemical manures. It is a remarkable fact, and shows on what obscure and accidental incidents the fortunes of possible the whole world may turn in these days of scientific discovery.
[During World War I, Fritz Haber and Karl Bosch invented a large scale process to cause the direct combination of hydrogen and nitrogen gases to chemically synthesize ammonia, thus providing a replacement for sodium nitrate in the manufacture of explosives and fertilizers.]
Parliamentary debate (25 Apr 1918). In Winston Churchill, Richard Langworth (ed.), Churchill by Himself: The Definitive Collection of Quotations (2008), 469. by Winston Churchill, Richard Langworth
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It is easy to get a thousand prescriptions, but hard to get one single remedy.
Chinese proverb.
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It is easy to make out three areas where scientists will be concentrating their efforts in the coming decades. One is in physics, where leading theorists are striving, with the help of experimentalists, to devise a single mathematical theory that embraces all the basic phenomena of matter and energy. The other two are in biology. Biologists—and the rest of us too—would like to know how the brain works and how a single cell, the fertilized egg cell, develops into an entire organism
Article 'The View From Mars', in Annals of the New York Academy of Sciences: Research Facilities of the Future (1994), 735, 37.
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It is grindingly, creakingly, crashingly obvious that, if Darwinism were really a theory of chance, it couldn’t work. You don't need to be a mathematician or physicist to calculate that an eye or a haemoglobin molecule would take from here to infinity to self-assemble by sheer higgledy-piggledy luck. Far from being a difficulty peculiar to Darwinism, the astronomic improbability of eyes and knees, enzymes and elbow joints and all the other living wonders is precisely the problem that any theory of life must solve, and that Darwinism uniquely does solve. It solves it by breaking the improbability up into small, manageable parts, smearing out the luck needed, going round the back of Mount Improbable and crawling up the gentle slopes, inch by million-year inch. Only God would essay the mad task of leaping up the precipice in a single bound.
In Climbing Mount Improbable (1996), 67-8.
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It is hard to sneak a look at God’s cards. But that he would choose to play dice with the world … is something I cannot believe for a single moment.
On quantum theory. In Letter (21 Mar 1942) to his student-colleague, Cornel Lanczos. In Yale Book of Quotations (2006), 229. Also seen paraphrased as, “I cannot believe that God would choose to play dice with the universe.”
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It is important to realize that life on this planet has spent about three-quarters of its existence in single-celled form, and even today the majority of organisms still exist as single cells. The evolutionary pressure to become complex is evidently not very great.
and Robert Shapiro
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It is impossible for us adequately to conceive the boldness of the measure which aimed at universal education through the establishment of free schools. ... it had no precedent in the world's history ... But time has ratified its soundness. Two centuries proclaim it to be as wise as it was courageous, as beneficient as it was disinterested. ... The establishment of free schools was one of those grand mental and moral experiments whose effects could not be developed and made manifest in a single generation. ... The sincerity of our gratitude must be tested by our efforts to perpetuate and improve what they established. The gratitude of the lips only is an unholy offering.
Tenth Report of the Secretary of the Massachusetts Board of Education (1946). Life and Works of Horace Mann (1891), Vol. 4, 111-112.
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It is impossible to put together a single prescription that will cure all ailing bodies.
As quoted in Fred Rosner, The Medical Legacy of Moses Maimonides (1998), 51.
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It is not Cayley’s way to analyze concepts into their ultimate elements. … But he is master of the empirical utilization of the material: in the way he combines it to form a single abstract concept which he generalizes and then subjects to computative tests, in the way the newly acquired data are made to yield at a single stroke the general comprehensive idea to the subsequent numerical verification of which years of labor are devoted. Cayley is thus the natural philosopher among mathematicians.
In Mathematische Annalen, Bd. 46 (1895), 479. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 146.
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It is not a simple life to be a single cell, although I have no right to say so, having been a single cell so long ago myself that I have no memory at all of that stage in my life.
In A Long Line of Cells: Collected Essays (1990), 244.
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It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
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It is now necessary to indicate more definitely the reason why mathematics not only carries conviction in itself, but also transmits conviction to the objects to which it is applied. The reason is found, first of all, in the perfect precision with which the elementary mathematical concepts are determined; in this respect each science must look to its own salvation .... But this is not all. As soon as human thought attempts long chains of conclusions, or difficult matters generally, there arises not only the danger of error but also the suspicion of error, because since all details cannot be surveyed with clearness at the same instant one must in the end be satisfied with a belief that nothing has been overlooked from the beginning. Every one knows how much this is the case even in arithmetic, the most elementary use of mathematics. No one would imagine that the higher parts of mathematics fare better in this respect; on the contrary, in more complicated conclusions the uncertainty and suspicion of hidden errors increases in rapid progression. How does mathematics manage to rid itself of this inconvenience which attaches to it in the highest degree? By making proofs more rigorous? By giving new rules according to which the old rules shall be applied? Not in the least. A very great uncertainty continues to attach to the result of each single computation. But there are checks. In the realm of mathematics each point may be reached by a hundred different ways; and if each of a hundred ways leads to the same point, one may be sure that the right point has been reached. A calculation without a check is as good as none. Just so it is with every isolated proof in any speculative science whatever; the proof may be ever so ingenious, and ever so perfectly true and correct, it will still fail to convince permanently. He will therefore be much deceived, who, in metaphysics, or in psychology which depends on metaphysics, hopes to see his greatest care in the precise determination of the concepts and in the logical conclusions rewarded by conviction, much less by success in transmitting conviction to others. Not only must the conclusions support each other, without coercion or suspicion of subreption, but in all matters originating in experience, or judging concerning experience, the results of speculation must be verified by experience, not only superficially, but in countless special cases.
In Werke [Kehrbach] (1890), Bd. 5, 105. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 19.
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It is presumed that there exists a great unity in nature, in respect of the adequacy of a single cause to account for many different kinds of consequences.
In Theoretical Philosophy, 1755-1770, trans. and ed. By David Walford (2003), 155.
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It is supposed that the ancients were ignorant of the law in hydraulics, by which water, in a tube, will rise as high as the fountain-head; and hence they carried their stupendous aqueducts horizontally, from hill-top to hill-top, upon lofty arches, with an incredible expenditure of labor and money. The knowledge of a single law, now familiar to every well-instructed school-boy,— namely, that water seeks a level, and, if not obstructed, will find it,—enables the poorest man of the present day to do what once demanded the wealth of an empire. The beautiful fragments of the ancient Roman aqueducts, which have survived the ravage of centuries, are often cited to attest the grandeur and power of their builders. To me, they are monuments, not of their power, but of their weakness.
In Thoughts Selected From the Writings of Horace Mann (1872), 231.
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It seems to me that every phenomenon, every fact, itself is the really interesting object. Whoever explains it, or connects it with other events, usually only amuses himself or makes sport of us, as, for instance, the naturalist or historian. But a single action or event is interesting, not because it is explainable, but because it is true.
Quoted in translated from Unterhaltungen deutscher Ausgewanderten in Franz Boas, 'The Study of Geography', Science Supplement (11 Feb 1881), 9, No. 210, 139.
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It was cold. Space, the air we breathed, the yellow rocks, were deadly cold. There was something ultimate, passionless, and eternal in this cold. It came to us as a single constant note from the depths of space. We stood on the very boundary of life and death.
…...
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It was my good fortune to be linked with Mme. Curie through twenty years of sublime and unclouded friendship. I came to admire her human grandeur to an ever growing degree. Her strength, her purity of will, her austerity toward herself, her objectivity, her incorruptible judgement—all these were of a kind seldom found joined in a single individual… The greatest scientific deed of her life—proving the existence of radioactive elements and isolating them—owes its accomplishment not merely to bold intuition but to a devotion and tenacity in execution under the most extreme hardships imaginable, such as the history of experimental science has not often witnessed.
Out of My Later Years (1950), 227-8.
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It was shortly after midday on December 12, 1901, [in a hut on the cliffs at St. John’s, Newfoundland] that I placed a single earphone to my ear and started listening. The receiver on the table before me was very crude—a few coils and condensers and a coherer—no valves [vacuum tubes], no amplifiers, not even a crystal. I was at last on the point of putting the correctness of all my beliefs to test. … [The] answer came at 12:30. … Suddenly, about half past twelve there sounded the sharp click of the “tapper” … Unmistakably, the three sharp clicks corresponding to three dots sounded in my ear. “Can you hear anything, Mr. Kemp?” I asked, handing the telephone to my assistant. Kemp heard the same thing as I. … I knew then that I had been absolutely right in my calculations. The electric waves which were being sent out from Poldhu [Cornwall, England] had travelled the Atlantic, serenely ignoring the curvature of the earth which so many doubters considered a fatal obstacle. … I knew that the day on which I should be able to send full messages without wires or cables across the Atlantic was not far distant.
As quoted in Degna Marconi, My Father, Marconi (2000), 93.
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Just as a tree constitutes a mass arranged in a definite manner, in which, in every single part, in the leaves as in the root, in the trunk as in the blossom, cells are discovered to be the ultimate elements, so is it also with the forms of animal life. Every animal presents itself as a sum of vital unities, every one of which manifests all the characteristics of life. The characteristics and unity of life cannot be limited to anyone particular spot in a highly developed organism (for example, to the brain of man), but are to be found only in the definite, constantly recurring structure, which every individual element displays. Hence it follows that the structural composition of a body of considerable size, a so-called individual, always represents a kind of social arrangement of parts, an arrangement of a social kind, in which a number of individual existences are mutually dependent, but in such a way, that every element has its own special action, and, even though it derive its stimulus to activity from other parts, yet alone effects the actual performance of its duties.
In Lecture I, 'Cells and the Cellular Theory' (1858), Rudolf Virchow and Frank Chance (trans.) ,Cellular Pathology (1860), 13-14.
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Just as Americans have discovered the hidden energy costs in a multitude of products—in refrigerating a steak, for example, on its way to the butcher—they are about to discover the hidden water costs. Beginning with the water that irrigated the corn that was fed to the steer, the steak may have accounted for 3,500 gallons. The water that goes into a 1,000-pound steer would float a destroyer. It takes 14,935 gallons of water to grow a bushel of wheat, 60,000 gallons to produce a ton of steel, 120 gallons to put a single egg on the breakfast table.
From 'The Browning of America: Drought, Waste and Pollution Threaten a Water Shortage', Newsweek (23 Feb 1981), 26-30. In long excerpt in William Shurtleff and Akiko Aoyagi, History of Soymilk and Other Non-Dairy Milks (1226-2013) (2013), 1126-1127.
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Language is simply alive, like an organism. We all tell each other this, in fact, when we speak of living languages, and I think we mean something more than an abstract metaphor. We mean alive. Words are the cells of language, moving the great body, on legs. Language grows and evolves, leaving fossils behind. The individual words are like different species of animals. Mutations occur. Words fuse, and then mate. Hybrid words and wild varieties or compound words are the progeny. Some mixed words are dominated by one parent while the other is recessive. The way a word is used this year is its phenotype, but it has deeply immutable meanings, often hidden, which is its genotype.... The separate languages of the Indo-European family were at one time, perhaps five thousand years ago, maybe much longer, a single language. The separation of the speakers by migrations had effects on language comparable to the speciation observed by Darwin on various islands of the Galapagos. Languages became different species, retaining enough resemblance to an original ancestor so that the family resemblance can still be seen.
in 'Living Language,' The Lives of a Cell: Notes of a Biology Watcher, (1974, 1984), 106.
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Leibnitz’s discoveries lay in the direction in which all modern progress in science lies, in establishing order, symmetry, and harmony, i.e., comprehensiveness and perspicuity,—rather than in dealing with single problems, in the solution of which followers soon attained greater dexterity than himself.
In Leibnitz (1884), 112.
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Let us only imagine that birds had studied their own development and that it was they in turn who investigated the structure of the adult mammal and of man. Wouldn’t their physiological textbooks teach the following? “Those four and two-legged animals bear many resemblances to embryos, for their cranial bones are separated, and they have no beak, just as we do in the first live or six days of incubation; their extremities are all very much alike, as ours are for about the same period; there is not a single true feather on their body, rather only thin feather-shafts, so that we, as fledglings in the nest, are more advanced than they shall ever be … And these mammals that cannot find their own food for such a long time after their birth, that can never rise freely from the earth, want to consider themselves more highly organized than we?”
Über Entwicklungsgeschichte der Thiere: Beobachtung und Reflexion (1828), 203. Trans. Stephen Jay Gould, Ontogeny and Phylogeny (1977), 54.
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Edwin Grant Conklin quote: Man cannot change a single law of nature, but can put himself into such relations to natural laws tha
Man cannot change a single law of nature, but can put himself into such relations to natural laws that he can profit by them.
In Heredity and Environment in the Development of Men (1920), 275.
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Man does not live by bread alone, there are other wants to be supplied, and even in a practical point of view, a single thought may be fraught with a thousand useful inventions.
Presidential Address (Aug 1853) to the American Association for the Advancement of Education, in Proceedings of the Third Session of the American Association for the Advancement of Education (1854), 29.
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Mastering the lawless science of our law,—
That codeless myriad of precedent,
That wilderness of single instances.
'Aylmer’s Field.' The Poetical Works of Alfred Tennyson, Poet Laureate (1869), 341.
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Mathematicians attach great importance to the elegance of their methods and their results. This is not pure dilettantism. What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details. But this is exactly what yields great results, in fact the more we see this aggregate clearly and at a single glance, the better we perceive its analogies with other neighboring objects, consequently the more chances we have of divining the possible generalizations. Elegance may produce the feeling of the unforeseen by the unexpected meeting of objects we are not accustomed to bring together; there again it is fruitful, since it thus unveils for us kinships before unrecognized. It is fruitful even when it results only from the contrast between the simplicity of the means and the complexity of the problem set; it makes us then think of the reason for this contrast and very often makes us see that chance is not the reason; that it is to be found in some unexpected law. In a word, the feeling of mathematical elegance is only the satisfaction due to any adaptation of the solution to the needs of our mind, and it is because of this very adaptation that this solution can be for us an instrument. Consequently this esthetic satisfaction is bound up with the economy of thought.
In 'The Future of Mathematics', Monist, 20, 80. Translated from the French by George Bruce Halsted.
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Mathematics … above all other subjects, makes the student lust after knowledge, fills him, as it were, with a longing to fathom the cause of things and to employ his own powers independently; it collects his mental forces and concentrates them on a single point and thus awakens the spirit of individual inquiry, self-confidence and the joy of doing; it fascinates because of the view-points which it offers and creates certainty and assurance, owing to the universal validity of its methods. Thus, both what he receives and what he himself contributes toward the proper conception and solution of a problem, combine to mature the student and to make him skillful, to lead him away from the surface of things and to exercise him in the perception of their essence. A student thus prepared thirsts after knowledge and is ready for the university and its sciences. Thus it appears, that higher mathematics is the best guide to philosophy and to the philosophic conception of the world (considered as a self-contained whole) and of one’s own being.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 40. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 49.
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Mathematics, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road. I believe, on the contrary, that there was a long period of tentative work (chiefly still among the Egyptians), and that the change is to be ascribed to a revolution, produced by the happy thought of a single man, whose experiments pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science. The history of that intellectual revolution, which was far more important than the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us. … A new light flashed on the first man who demonstrated the properties of the isosceles triangle (whether his name was Thales or any other name), for he found that he had not to investigate what he saw in the figure, or the mere concepts of that figure, and thus to learn its properties; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.
In Critique of Pure Reason, Preface to the Second Edition, (1900), 690.
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Maxwell's equations… originally consisted of eight equations. These equations are not “beautiful.” They do not possess much symmetry. In their original form, they are ugly. …However, when rewritten using time as the fourth dimension, this rather awkward set of eight equations collapses into a single tensor equation. This is what a physicist calls “beauty.”
In 'Quantum Heresy', Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (1995), 130. Note: For two “beauty” criteria, unifying symmetry and economy of expression, see quote on this page beginning “When physicists…”
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May God us keep
From Single vision & Newton’s sleep!
Letter to Thomas Butt (22 Nov 1802). Collected in William Blake and Archibald George Blomefield Russell (ed.), The Letters of William Blake (1906), Vol. 1, 112.
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Men are noisy, narrow-band devices, but their nervous systems have very many parallel and simultaneously active channels. Relative to men, computing machines are very fast and very accurate, but they are constrained to perform only one or a few elementary operations at a time. Men are flexible, capable of “programming themselves contingently” on the basis of newly received information. Computing machines are single-minded, constrained by their “pre-programming.”
From article 'Man-Computer Symbiosis', in IRE Transactions on Human Factors in Electronics (Mar 1960), Vol. HFE-1, 4-11.
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Microprocessors are getting into everything. We won’t be able to pick up a single piece of equipment in the near future, except maybe a broom, that hasn’t got a microprocessor in it.
(1979). Interview with Malcolm Kirk, in the magazine OMNI. Collected in Ben Bova and Don Myrus (eds.), The Best of Omni Science Fiction (1980), Issue 1, 143.
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Morphological information has provided the greatest single source of data in the formulation and development of the theory of evolution and that even now, when the preponderance of work is experimental, the basis for interpretation in many areas of study remains the form and relationships of structures.
'Morphology, Paleontology, and Evolution', in Sol Tax (ed.), Evolution After Darwin, Vol. 1, The Evolution of Life (1960), 524.
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My experiments with single traits all lead to the same result: that from the seeds of hybrids, plants are obtained half of which in turn carry the hybrid trait (Aa), the other half, however, receive the parental traits A and a in equal amounts. Thus, on the average, among four plants two have the hybrid trait Aa, one the parental trait A, and the other the parental trait a. Therefore, 2Aa+ A +a or A + 2Aa + a is the empirical simple series for two differing traits.
Letter to Carl Nägeli, 31 Dec 1866. In Curt Stern and Eva R. Sherwood (eds.), The Origin of Genetics: A Mendel Source Book (1966), 63.
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My guess is that well over eighty per cent. of the human race goes through life without having a single original thought..
Minority Report (1956, 2006 reprint), 10.
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My interest in Science had many roots. Some came from my mother … while I was in my early teens. She fell in love with science,… [from] classes on the Foundations of Physical Science. … I was infected by [her] professor second hand, through hundreds of hours of conversations at my mother’s knees. It was from my mother that I first learned of Archimedes, Leonardo da Vinci, Galileo, Kepler, Newton, and Darwin. We spent hours together collecting single-celled organisms from a local pond and watching them with a microscope.
From 'Richard E. Smalley: Biographical', collected in Tore Frängsmyr (ed.), Les Prix Nobel: The Nobel Prizes 1996 (1997).
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My visceral perception of brotherhood harmonizes with our best modern biological knowledge ... Many people think (or fear) that equality of human races represents a hope of liberal sentimentality probably squashed by the hard realities of history. They are wrong. This essay can be summarized in a single phrase, a motto if you will: Human equality is a contingent fact of history. Equality is not true by definition; it is neither an ethical principle (though equal treatment may be) nor a statement about norms of social action. It just worked out that way. A hundred different and plausible scenarios for human history would have yielded other results (and moral dilemmas of enormous magnitude). They didn’t happen.
…...
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Nature has not arranged her productions on a single and direct line. They branch at every step, and in every direction, and he who attempts to reduce them into departments is left to do it by the lines of his own fancy.
In Letter (22 Feb 1814) to Dr. John Manners. Collected in The Writings of Thomas Jefferson (1905), Vol 13, 99.
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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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New scientific ideas never spring from a communal body, however organized, but rather from the head of an individually inspired researcher who struggles with his problems in lonely thought and unites all his thought on one single point which is his whole world for the moment.
Address on the 25th anniversary of the Kaiser-Wilhelm Gesellschaft (Jan 1936). Quoted in Surviving the Swastika: Scientific Research in Nazi Germany (1993), 97.
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No amount of experimentation can ever prove me right; a single experiment can prove me wrong.
Attributed to Einstein. Quoted in Alice Calaprice, The Quotable Einstein (1996), 224.
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No aphorism is more frequently repeated in connection with field trials, than that we must ask Nature few questions, or, ideally, one question, at a time. The writer is convinced that this view is wholly mistaken. Nature, he suggests, will best respond to a logical and carefully thought out questionnaire; indeed, if we ask her a single question, she will often refuse to answer until some other topic has been discussed.
'The Arrangement of Field Experiments', The Journal of the Ministry of Agriculture, 1926, 33, 511.
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No man can be truly called an entomologist, sir; the subject is too vast for any single human intelligence to grasp.
In 'The Poet at the Breakfast Table: II', The Atlantic Monthly (Feb 1872), 29, 231.
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No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. … Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; … [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. … A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.
In A Mathematician's Apology (1941, reprint with Foreward by C.P. Snow 1992), 70-71.
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No Single Atom, once in Being, lost,…
The Complaint: or, Night-Thoughts on Life, Death, and Immortality (1742, 1750), Night 6, 140.
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Nomenclature, the other foundation of botany, should provide the names as soon as the classification is made... If the names are unknown knowledge of the things also perishes... For a single genus, a single name.
Philosophia Botanica (1751), aphorism 210. Trans. Frans A. Stafleu, Linnaeus and the Linnaeans: The Spreading of their Ideas in Systematic Botany, 1735-1789 (1971), 80.
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Not a single visible phenomenon of cell-division gives even a remote suggestion of qualitative division. All the facts, on the contrary, indicate that the division of the chromatin is carried out with the most exact equality.
In The Cell in Development and Inheritance (1896), 306.
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Not only are there meaningless questions, but many of the problems with which the human intellect has tortured itself turn out to be only 'pseudo problems,' because they can be formulated only in terms of questions which are meaningless. Many of the traditional problems of philosophy, of religion, or of ethics, are of this character. Consider, for example, the problem of the freedom of the will. You maintain that you are free to take either the right- or the left-hand fork in the road. I defy you to set up a single objective criterion by which you can prove after you have made the turn that you might have made the other. The problem has no meaning in the sphere of objective activity; it only relates to my personal subjective feelings while making the decision.
The Nature of Physical Theory (1936), 12.
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Nothing is known in our profession by guess; and I do not believe, that from the first dawn of medical science to the present moment, a single correct idea has ever emanated from conjecture: it is right therefore, that those who are studying their profession should be aware that there is no short road to knowledge; and that observation on the diseased living, examination of the dead, and experiments upon living animals, are the only sources of true knowledge; and that inductions from these are the sole bases of legitimate theory.
Astley Paston Cooper, Astley Cooper, Bransby Blake Cooper, A Treatise on Dislocations and Fractures of the Joints (1851), 155.
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Nothing is more symptomatic of the enervation, of the decompression of the Western imagination, than our incapacity to respond to the landings on the Moon. Not a single great poem, picture, metaphor has come of this breathtaking act, of Prometheus’ rescue of Icarus or of Phaeton in flight towards the stars.
…...
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Now, all causes of natural effects must be expressed by means of lines, angles and figures, for otherwise it is impossible to grasp their explanation. This is evident as follows. A natural agent multiplies its power from itself to the recipient, whether it acts on sense or on matter. This power is sometimes called species, sometimes a likeness, and it is the same thing whatever it may be called; and the agent sends the same power into sense and into matter, or into its own contrary, as heat sends the same thing into the sense of touch and into a cold body. For it does not act, by deliberation and choice, and therefore it acts in a single manner whatever it encounters, whether sense or something insensitive, whether something animate or inanimate. But the effects are diversified by the diversity of the recipient, for when this power is received by the senses, it produces an effect that is somehow spiritual and noble; on the other hand, when it is received by matter, it produces a material effect. Thus the sun produces different effects in different recipients by the same power, for it cakes mud and melts ice.
De Uneis, Angulis et Figuris seu Fractionibus Reflexionibus Radiorum (On Lines, Angles and Figures or On the Refraction and Reflection of Rays) [1230/31], trans. D. C. Lindberg, quoted in E. Grant (ed.), A Source Book in Medieval Science (1974), 385-6.
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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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Numbers written on restaurant checks [bills] within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe.
This single statement took the scientific world by storm. It completely revolutionized it. So many mathematical conferences got held in such good restaurants that many of the finest minds of a generation died of obesity and heart failure and the science of math was put back by years.
Life, the Universe and Everything (1982, 1995), 49.
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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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One [idea] was that the Universe started its life a finite time ago in a single huge explosion, and that the present expansion is a relic of the violence of this explosion. This big bang idea seemed to me to be unsatisfactory even before detailed examination showed that it leads to serious difficulties.
In radio talk on the BBC Third Programme, as subsequently printed in the BBC’s The Listener magazine (9 Mar 1950), Vol.43, 420. This was his further use of the term “big bang” that he first expressed in a radio talk on 28 Mar 1949.
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One of the grandest generalizations formulated by modern biological science is that of the continuity of life; the protoplasmic activity within each living body now on earth has continued without cessation from the remote beginnings of life on our planet, and from that period until the present no single organism has ever arisen save in the form of a bit of living protoplasm detached from a pre-existing portion; the eternal flame of life once kindled upon this earth has passed from organism to organism, and is still, going on existing and propagating, incarnated within the myriad animal and plant forms of everyday life.
In History of the Human Body (1919), 1.
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One of the main purposes of scientific inference is to justify beliefs which we entertain already; but as a rule they are justified with a difference. Our pre-scientific general beliefs are hardly ever without exceptions; in science, a law with exceptions can only be tolerated as a makeshift. Scientific laws, when we have reason to think them accurate, are different in form from the common-sense rules which have exceptions: they are always, at least in physics, either differential equations, or statistical averages. It might be thought that a statistical average is not very different from a rule with exceptions, but this would be a mistake. Statistics, ideally, are accurate laws about large groups; they differ from other laws only in being about groups, not about individuals. Statistical laws are inferred by induction from particular statistics, just as other laws are inferred from particular single occurrences.
The Analysis of Matter (1927), 191.
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One or two atoms can convert a fuel to a poison, change a color, render an inedible substance edible, or replace a pungent odor with a fragrant one. That changing a single atom can have such consequences is the wonder of the chemical world.
In Scientific American Library, Molecules (1987), 2.
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One single equation for the motion of the Moon covers some 250 large-size pages and represents the major effort of a lifetime.
In Earth, Moon and Planets (1963), 28.
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Our commercial and mercantile law was no sudden invention. It was not the work of a day, or of one set of minds… In the incipient, the early existence of this system, a single maxim obtained force, others succeeded; one rule of right formed a nucleus around which other kindred rules might cling; the necessities of trade originated customs, customs ripened into law; a few feeble decisions of courts laid the foundation for others; the wisdom and experience of each succeeding generation improved upon the wisdom and experience of generations that were past; and thus the edifice arose, perfect in its parts, beautiful in its proportions.
From biographical preface by T. Bigelow to Austin Abbott (ed.), Official Report of the Trial of Henry Ward Beecher (1875), Vol. 1, xi-xii.
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Felix Klein quote: Our science, in contrast with others, is not founded on a single period of human history, but has accompanied
Our science, in contrast with others, is not founded on a single period of human history, but has accompanied the development of culture through all its stages. Mathematics is as much interwoven with Greek culture as with the most modern problems in Engineering. She not only lends a hand to the progressive natural sciences but participates at the same time in the abstract investigations of logicians and philosophers.
In Klein und Riecke: Ueber angewandte Mathematik und Physik (1900), 228.
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Owing to his lack of knowledge, the ordinary man cannot attempt to resolve conflicting theories of conflicting advice into a single organized structure. He is likely to assume the information available to him is on the order of what we might think of as a few pieces of an enormous jigsaw puzzle. If a given piece fails to fit, it is not because it is fraudulent; more likely the contradictions and inconsistencies within his information are due to his lack of understanding and to the fact that he possesses only a few pieces of the puzzle. Differing statements about the nature of things, differing medical philosophies, different diagnoses and treatments—all of these are to be collected eagerly and be made a part of the individual's collection of puzzle pieces. Ultimately, after many lifetimes, the pieces will fit together and the individual will attain clear and certain knowledge.
'Strategies of Resort to Curers in South India', contributed in Charles M. Leslie (ed.), Asian Medical Systems: A Comparative Study (1976), 185.
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Painting is but one single small mode of expressing my own cosmology, which enables me, through my genius and paranoia, to create a synthesis of nature impossible even for the scientist, because the scientist is too much involved in his specialization.
As quoted in 'Playboy Interview: Salvador Dalí, a candid conversation with the flamboyantly eccentric grand vizier of surrealism', Playboy Magazine (Jul 1964), 46, 48. Quoted and cited in Michael R. Taylor, 'God and the Atom: Salvador Dalí’s Mystical Manifesto and the Contested Origins of Nuclear Painting', Avant-garde Studies (Fall 2016), No. 2, 10.
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Persons possessing great intellect and a capacity for excelling in the creative arts and also in the sciences are generally likely to have heavier brains than the ordinary individual. Arguing from this we might expect to find a corresponding lightness in the brain of the criminal, but this is not always the case ... Many criminals show not a single anomaly in their physical or mental make-up, while many persons with marked evidences of morphological aberration have never exhibited the criminal tendency.
Every attempt to prove crime to be due to a constitution peculiar only to criminals has failed signally. It is because most criminals are drawn from the ranks of the low, the degraded, the outcast, that investigators were ever deceived into attempting to set up a 'type' of criminal. The social conditions which foster the great majority of crimes are more needful of study and improvement.
From study of known normal brains we have learned that there is a certain range of variation. No two brains are exactly alike, and the greatest source of error in the assertions of Benedict and Lombroso has been the finding of this or that variation in a criminal’s brains, and maintaining such to be characteristic of the 'criminal constitution,' unmindful of the fact that like variations of structure may and do exist in the brains of normal, moral persons.
Address to the American Association for the Advancement of Science in Philadelphia (28 Dec 1904), as quoted in 'Americans of Future Will Have Best Brains', New York Times (29 Dec 1904), 6.
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Philosophy [the universe] is written in that great book which ever lies before our eyes ... We cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in the mathematical language ... without whose help it is humanly impossible to comprehend a single word of it, and without which one wanders in vain through a dark labyrinth.
…...
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Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.
In 'The Assayer' (1623), trans. Stillman Drake, Discoveries and Opinions of Galileo (1957), 237-8.
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Physical science enjoys the distinction of being the most fundamental of the experimental sciences, and its laws are obeyed universally, so far as is known, not merely by inanimate things, but also by living organisms, in their minutest parts, as single individuals, and also as whole communities. It results from this that, however complicated a series of phenomena may be and however many other sciences may enter into its complete presentation, the purely physical aspect, or the application of the known laws of matter and energy, can always be legitimately separated from the other aspects.
In Matter and Energy (1912), 9-10.
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Quite recently the human descent theory has been stigmatized as the “gorilla theory of human ancestry.” All this despite the fact that Darwin himself, in the days when not a single bit of evidence regarding the fossil ancestors of man was recognized, distinctly stated that none of the known anthropoid apes, much less any of the known monkeys, should be considered in any way as ancestral to the human stock.
In Henry Fairfield Osborn, 'Osborn States the Case For Evolution', New York Times (12 Jul 1925), XX1. Written at the time of the Scopes Monkey Trial, in rebuttal of the anti-evolution position publicized by William Jennings Bryan.
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Reason must approach nature with the view, indeed, of receiving information from it, not, however, in the character of a pupil, who listens to all that his master chooses to tell him, but in that of a judge, who compels the witnesses to reply to those questions which he himself thinks fit to propose. To this single idea must the revolution be ascribed, by which, after groping in the dark for so many centuries, natural science was at length conducted into the path of certain progress.
Critique of Pure Reason, translated by J.M.D. Meiklejohn (1855), Preface to the Second Edition, xxvii.
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Scheele, it was said, never forgot anything if it had to do with chemistry. He never forgot the look, the feel, the smell of a substance, or the way it was transformed in chemical reactions, never forgot anything he read, or was told, about the phenomena of chemistry. He seemed indifferent, or inattentive, to most things else, being wholly dedicated to his single passion, chemistry. It was this pure and passionate absorption in phenomena—noticing everything, forgetting nothing—that constituted Scheele's special strength.
Uncle Tungsten: Memories of a Chemical Boyhood (2001), 44.
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Science and technology, and the various forms of art, all unite humanity in a single and interconnected system. As science progresses, the worldwide cooperation of scientists and technologists becomes more and more of a special and distinct intellectual community of friendship, in which, in place of antagonism, there is growing up a mutually advantageous sharing of work, a coordination of efforts, a common language for the exchange of information, and a solidarity, which are in many cases independent of the social and political differences of individual states.
In The Medvedev Papers (1970).
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Science cannot avert a single thunderbolt.
In Sexual Personae: Art and Decadence from Nefertiti to Emily Dickinson (1990), 5.
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Science in England is not a profession: its cultivators are scarcely recognised even as a class. Our language itself contains no single term by which their occupation can be expressed. We borrow a foreign word [Savant] from another country whose high ambition it is to advance science, and whose deeper policy, in accord with more generous feelings, gives to the intellectual labourer reward and honour, in return for services which crown the nation with imperishable renown, and ultimately enrich the human race.
The Exposition of 1851: Or the Views of Industry, Science and Government of England (1851), 171.
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Science is a system of statements based on direct experience, and controlled by experimental verification. Verification in science is not, however, of single statements but of the entire system or a sub-system of such statements.
The Unity of Science (1934), trans. Max Black, 42.
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Science is neither a single tradition, nor the best tradition there is, except for people who have become accustomed to its presence, its benefits and its disadvantages. In a democracy it should be separated from the state just as churches are now separated from the state.
Against Method, p. 238 (1975).The author's warning against allowing scientists to become the new 'high priests' of society.
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Science means simplification. It substitutes a single rule for a million miscellaneous observations.
In Chats on Science (1924), 4.
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Shakespeare was pursuing two Methods at once; and besides the Psychological Method, he had also to attend to the Poetical. (Note) we beg pardon for the use of this insolent verbum: but it is one of which our Language stands in great need. We have no single term to express the Philosophy of the Human Mind.
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Simple as the law of gravity now appears, and beautifully in accordance with all the observations of past and of present times, consider what it has cost of intellectual study. Copernicus, Galileo, Kepler, Euler, Lagrange, Laplace, all the great names which have exalted the character of man, by carrying out trains of reasoning unparalleled in every other science; these, and a host of others, each of whom might have been the Newton of another field, have all labored to work out, the consequences which resulted from that single law which he discovered. All that the human mind has produced—the brightest in genius, the most persevering in application, has been lavished on the details of the law of gravity.
in The Ninth Bridgewater Treatise: A Fragment (1838), 57.
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Since many cases are known in which the specificities of antigens and enzymes appear to bear a direct relation to gene specificities, it seems reasonable to suppose that the gene’s primary and possibly sole function is in directing the final configurations of protein molecules.
Assuming that each specific protein of the organism has its unique configuration copied from that of a gene, it follows that every enzyme whose specificity depends on a protein should be subject to modification or inactivation through gene mutation. This would, of course, mean that the reaction normally catalyzed by the enzyme in question would either have its rate or products modified or be blocked entirely.
Such a view does not mean that genes directly “make” proteins. Regardless of precisely how proteins are synthesized, and from what component parts, these parts must themselves be synthesized by reactions which are enzymatically catalyzed and which in turn depend on the functioning of many genes. Thus in the synthesis of a single protein molecule, probably at least several hundred different genes contribute. But the final molecule corresponds to only one of them and this is the gene we visualize as being in primary control.
In 'Genetics and Metabolism in Neurospora', Physiological Reviews, 1945, 25, 660.
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Sites need to be able to interact in one single, universal space.
…...
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Some recent work by E. Fermi and L. Szilard, which has been communicated to me in manuscript, leads me to expect that the element uranium may be turned into a new and important source of energy in the immediate future. Certain aspects of the situation seem to call for watchfulness and, if necessary, quick action on the part of the Administration. …
In the course of the last four months it has been made probable … that it may become possible to set up nuclear chain reactions in a large mass of uranium, by which vast amounts of power and large quantities of new radium-like elements would be generated. Now it appears almost certain that this could be achieved in the immediate future.
This new phenomenon would also lead to the construction of bombs, and it is conceivable—though much less certain—that extremely powerful bombs of a new type may thus be constructed. A single bomb of this type, carried by boat or exploded in a port, might well destroy the whole port altogether with some of the surrounding territory. However, such bombs might well prove to be too heavy for transportation by air.
Letter to President Franklin P. Roosevelt, (2 Aug 1939, delivered 11 Oct 1939). In Otto Nathan and Heinz Norden (Eds.) Einstein on Peace (1960, reprinted 1981), 294-95.
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Such is the substance of my faith; and if I were to sum up my credo in a single word, it would be that proud motto of Fustel de Coulanges, Quaero, I seek to learn.
From Conclusion of Presidential Address (29 Dec 1950) read at the annual dinner of the American Historical Association, Chicago, 'Faith of a Historian', The American Historical Review (Jan 1951), 56, No. 2, 261-275.
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Superstring theories provide a framework in which the force of gravity may be united with the other three forces in nature: the weak, electromagnetic and strong forces. Recent progress has shown that the most promising superstring theories follow from a single theory. For the last generation, physicists have studied five string theories and one close cousin. Recently it has become clear that these five or six theories are different limiting cases of one theory which, though still scarcely understood, is the candidate for superunification of the forces of nature.
His synopsis of lecture, University of Maryland Distinguished Lecture Series (2 Mar 1998), on web page.
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Suppose physics soon succeeds, as Stephen Hawking and a few other physicists hope and believe, in reducing physics to a single equation or a small set of equations that will “explain” all of nature’s fundamental laws. We can then ask the unanswerable question, "Why this set of equations?”
In Introduction, The Night Is Large: Collected Essays 1938-1995 (1996), xvii.
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Tactics used by many practitioners of pseudoscience: make a large number of vaguely scientific arguments in the hope of making the desired conclusion seem inevitable. It is essential to recognize that a disconnected assemblage of weak arguments does not create a single, strong scientific argument.
Co-author with Matt Ford, Chris Lee and Jonathan Gitlin, in 'Diluting the Scientific Method: Ars Looks at Homeopathy' (11 Sep 2007) on arstechnica.com web site.
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That mathematics “do not cultivate the power of generalization,”; … will be admitted by no person of competent knowledge, except in a very qualified sense. The generalizations of mathematics, are, no doubt, a different thing from the generalizations of physical science; but in the difficulty of seizing them, and the mental tension they require, they are no contemptible preparation for the most arduous efforts of the scientific mind. Even the fundamental notions of the higher mathematics, from those of the differential calculus upwards are products of a very high abstraction. … To perceive the mathematical laws common to the results of many mathematical operations, even in so simple a case as that of the binomial theorem, involves a vigorous exercise of the same faculty which gave us Kepler’s laws, and rose through those laws to the theory of universal gravitation. Every process of what has been called Universal Geometry—the great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of them—is a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics.
In An Examination of Sir William Hamilton’s Philosophy (1878), 612-13.
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The actual evolution of mathematical theories proceeds by a process of induction strictly analogous to the method of induction employed in building up the physical sciences; observation, comparison, classification, trial, and generalisation are essential in both cases. Not only are special results, obtained independently of one another, frequently seen to be really included in some generalisation, but branches of the subject which have been developed quite independently of one another are sometimes found to have connections which enable them to be synthesised in one single body of doctrine. The essential nature of mathematical thought manifests itself in the discernment of fundamental identity in the mathematical aspects of what are superficially very different domains. A striking example of this species of immanent identity of mathematical form was exhibited by the discovery of that distinguished mathematician … Major MacMahon, that all possible Latin squares are capable of enumeration by the consideration of certain differential operators. Here we have a case in which an enumeration, which appears to be not amenable to direct treatment, can actually be carried out in a simple manner when the underlying identity of the operation is recognised with that involved in certain operations due to differential operators, the calculus of which belongs superficially to a wholly different region of thought from that relating to Latin squares.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 290.
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The advance from the simple to the complex, through a process of successive differentiations, is seen alike in the earliest changes of the Universe to which we can reason our way back, and in the earliest changes which we can inductively establish; it is seen in the geologic and climatic evolution of the Earth; it is seen in the unfolding of every single organism on its surface, and in the multiplication of kinds of organisms; it is seen in the evolution of Humanity, whether contemplated in the civilized individual, or in the aggregate of races; it is seen in the evolution of Society in respect alike of its political, its religious, and its economical organization; and it is seen in the evolution of all those endless concrete and abstract products of human activity which constitute the environment of our daily life. From the remotest past which Science can fathom, up to the novelties of yesterday, that in which Progress essentially consists, is the transformation of the homogeneous into the heterogeneous.
Progress: Its Law and Cause (1857), 35.
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The advantage is that mathematics is a field in which one’s blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It is a field which has often been compared with chess, but differs from the latter in that it is only one’s best moments that count and not one’s worst. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician’s reputation.
In Ex-Prodigy: My Childhood and Youth (1953), 21.
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The advantage which science gained by Gauss’ long-lingering method of publication is this: What he put into print is as true and important today as when first published; his publications are statutes, superior to other human statutes in this, that nowhere and never has a single error been detected in them. This justifies and makes intelligible the pride with which Gauss said in the evening of his life of the first larger work of his youth: “The Disquisitiones arithmeticae belong to history.”
In Allgemeine Deutsche Biographie (1878, 8, 435. As cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 158.
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The ancients had a taste, let us say rather a passion, for the marvellous, which caused … grouping together the lofty deeds of a great number of heroes, whose names they have not even deigned to preserve, and investing the single personage of Hercules with them. … In our own time the public delight in blending fable with history. In every career of life, in the pursuit of science especially, they enjoy a pleasure in creating Herculeses.
In François Arago, trans. by William Henry Smyth, Baden Powell and Robert Grant, 'Fourier', Biographies of Distinguished Scientific Men (1859), Vol. 1, 408. This comment indicates that a single scientist or inventor may be held as the exemplar, such as James Watt and the steam-engine, although groundwork was laid by predecessors.
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The application of algebra to geometry…, far more than any of his metaphysical speculations, immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences.
In An Examination of Sir William Hamilton’s Philosophy (1865), 531.
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The astronomers said, ‘Give us matter and a little motion and we will construct the universe. It is not enough that we should have matter, we must also have a single impulse, one shove to launch the mass and generate the harmony of the centrifugal and centripetal forces.’ ... There is no end to the consequences of the act. That famous aboriginal push propagates itself through all the balls of the system, and through every atom of every ball.
From essay, 'Nature', collected in Ralph Waldo Emerson and J.E. Cabot (ed.), Emerson's Complete Works: Essays, Second Series (1884), Vol. 3, 176-177.
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The attempt of Lavoisier to reform chemical nomenclature is premature. One single experiment may destroy the whole filiation of his terms; and his string of sulphates, sulphites, and sulphures, may have served no end than to have retarded the progress of science by a jargon, from the confusion of which time will be requisite to extricate us.
Letter to Rev. James Madison (Paris, 1788). In Thomas Jefferson and John P. Foley (ed.), The Jeffersonian Cyclopedia (1900), 135. From H.A. Washington, The Writings of Thomas Jefferson (1853-54). Vol 2, 432.
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The automatic computing engine now being designed at N.P.L. [National Physics Laboratory] is atypical large scale electronic digital computing machine. In a single lecture it will not be possible to give much technical detail of this machine, and most of what I shall say will apply equally to any other machine of this type now being planned. From the point of view of the mathematician the property of being digital should be of greater interest than that of being electronic. That it is electronic is certainly important because these machines owe their high speed to this, and without the speed it is doubtful if financial support for their construction would be forthcoming. But this is virtually all that there is to be said on that subject. That the machine is digital however has more subtle significance. It means firstly that numbers are represented by sequences of digits which can be as long as one wishes. One can therefore work to any desired degree of accuracy. This accuracy is not obtained by more careful machining of parts, control of temperature variations, and such means, but by a slight increase in the amount of equipment in the machine.
Lecture to the London Mathematical Society, 20 February 1947. Quoted in B. E. Carpenter and R. W. Doran (eds.), A. M. Turing's Ace Report of 1946 and Other Papers (1986), 106.
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The average gambler will say “The player who stakes his whole fortune on a single play is a fool, and the science of mathematics can not prove him to be otherwise.” The reply is obvious: “The science of mathematics never attempts the impossible, it merely shows that other players are greater fools.”
Concluding remarks to his mathematical proof, with certain assumptions, that the best betting strategy for “Gambler’s Ruin” would be to always make his largest stake on his first play. In 'Gambler’s Ruin', Annals of Mathematics (Jul 1909), 2nd Series, 10, No. 4, 189. This is also seen, without primary source, quoted as “It is true that a man who does this is a fool. I have only proved that a man who does anything else is an even bigger fool,” in Harold Eves, Return to Mathematical Circles (1988), 39.
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The chief art of learning, as Locke has observed, is to attempt but little at a time. The widest excursions of the mind are made by short flights frequently repeated; the most lofty fabrics of science are formed by the continued accumulation of single propositions.
'The Need For General Knowledge,' Rambler No. 137 (9 Jul 1751). In Samuel Johnson, Donald Greene (ed.), Samuel Johnson (1984), 223.
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The coastal zone may be the single most important portion of our planet. The loss of its biodiversity may have repercussions far beyond our worst fears.
In 'Ecological Diversity and Coastal Zones and Oceans', collected in E. O. Wilson (ed.), Biodiversity (1988), 48.
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The colors are stunning. In a single view, I see - looking out at the edge of the earth: red at the horizon line, blending to orange and yellow, followed by a thin white line, then light blue, gradually turning to dark blue and various gradually darker shades of gray, then black and a million stars above. It’s breathtaking.
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The creation of a science, like that of a world, demands more than a single day; but when our successors write the history of our science, I am convinced that they will say that the work of Suess marks the end of the first day, when there was light.
As translated to English, in Karl Alfred von Zittel, History of Geology and Palæontology to the End of the Nineteenth Century (1901), 321, from Bertrand’s Preface to the French translation by Emile de Margerie of Éduard Seuss, Das Antlitz der Erde (The Face of the Earth). The quote is the concluding sentence of La Face de la Terre (1897), Preface, xvi: “Il faut savoir attendre; la création d’une science, comme celle d’un monde, demande plus d’un jour; mais quand nos successeurs écriront l’histoire de la nôtre, ils diront, j’en suis persuadé, que l’œuvre de M. Suess marque dans cette histoire la fin du premier jour, celui où la lumière fut.”
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The days of the Mosaic creation are not to be strictly construed as implying the same length of time which is at present occupied by a single revolution of our globe, but PERIODS of a much longer extent.
Vindiciae Geologicae (1820),32.
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The dog [in Pavlov’s experiments] does not continue to salivate whenever it hears a bell unless sometimes at least an edible offering accompanies the bell. But there are innumerable instances in human life where a single association, never reinforced, results in the establishment of a life-long dynamic system. An experience associated only once with a bereavement, an accident, or a battle, may become the center of a permanent phobia or complex, not in the least dependent on a recurrence of the original shock.
Personality: A Psychological Interpretation(1938), 199.
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The Earth Speaks, clearly, distinctly, and, in many of the realms of Nature, loudly, to William Jennings Bryan, but he fails to hear a single sound. The earth speaks from the remotest periods in its wonderful life history in the Archaeozoic Age, when it reveals only a few tissues of its primitive plants. Fifty million years ago it begins to speak as “the waters bring forth abundantly the moving creatures that hath life.” In successive eons of time the various kinds of animals leave their remains in the rocks which compose the deeper layers of the earth, and when the rocks are laid bare by wind, frost, and storm we find wondrous lines of ascent invariably following the principles of creative evolution, whereby the simpler and more lowly forms always precede the higher and more specialized forms.
The earth speaks not of a succession of distinct creations but of a continuous ascent, in which, as the millions of years roll by, increasing perfection of structure and beauty of form are found; out of the water-breathing fish arises the air-breathing amphibian; out of the land-living amphibian arises the land-living, air-breathing reptile, these two kinds of creeping things resembling each other closely. The earth speaks loudly and clearly of the ascent of the bird from one kind of reptile and of the mammal from another kind of reptile.
This is not perhaps the way Bryan would have made the animals, but this is the way God made them!
The Earth Speaks to Bryan (1925), 5-6. Osborn wrote this book in response to the Scopes Monkey Trial, where William Jennings Bryan spoke against the theory of evolution. They had previously been engaged in the controversy about the theory for several years. The title refers to a Biblical verse from the Book of Job (12:8), “Speak to the earth and it shall teach thee.”
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The entire range of living matter on Earth from whales to viruses and from oaks to algae could be regarded as constituting a single living entity capable of maintaining the Earth’s atmosphere to suit its overall needs and endowed with faculties and powers far beyond those of its constituent parts.
In Gaia: A New Look at Life on Earth (1979), 9.
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The estimate we form of the intellectual capacity of our race, is founded on an examination of those productions which have resulted from the loftiest flights of individual genius, or from the accumulated labors of generations of men, by whose long-continued exertions a body of science has been raised up, surpassing in its extent the creative powers of any individual, and demanding for its development a length of time, to which no single life extends.
In The Ninth Bridgewater Treatise: A Fragment (1838), 30.
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The eventual goal of science is to provide a single theory that describes the whole universe.
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The first effect of the mind growing cultivated is that processes once multiple get to be performed in a single act. Lazarus has called this the progressive “condensation” of thought. ... Steps really sink from sight. An advanced thinker sees the relations of his topics is such masses and so instantaneously that when he comes to explain to younger minds it is often hard ... Bowditch, who translated and annotated Laplace's Méchanique Céleste, said that whenever his author prefaced a proposition by the words “it is evident,” he knew that many hours of hard study lay before him.
In The Principles of Psychology (1918), Vol. 2, 369-370.
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The first question which you will ask and which I must try to answer is this, “What is the use of climbing Mount Everest ?” and my answer must at once be, “It is no use.” There is not the slightest prospect of any gain whatsoever. Oh, we may learn a little about the behavior of the human body at high altitudes, and possibly medical men may turn our observation to some account for the purposes of aviation. But otherwise nothing will come of it. We shall not bring back a single bit of gold or silver, not a gem, nor any coal or iron. We shall not find a single foot of earth that can be planted with crops to raise food. It’s no use. So, if you cannot understand that there is something in man which responds to the challenge of this mountain and goes out to meet it, that the struggle is the struggle of life itself upward and forever upward, then you won’t see why we go. What we get from this adventure is just sheer joy. And joy is, after all, the end of life. We do not live to eat and make money. We eat and make money to be able to enjoy life. That is what life means and what life is for.
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The frillshark has many anatomical features similar to those of the ancient sharks that lived 25 to 30 million years ago. It has too many gills and too few dorsal fins for a modern shark, and its teeth, like those of fossil sharks, are three-pronged and briarlike. Some ichthyologists regard it as a relic derived from very ancient shark ancestors that have died out in the upper waters but, through this single species, are still carrying on their struggle for earthly survival, in the quiet of the deep sea.
In The Sea Around Us (1951), 54.
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The full story of successful organ transplantation in man weaves together three separate pathways: the study of renal disease, skin grafting in twins, and surgical determination. A leitmotif permeates each of these pathways, i.e. a single event or report was critical for medical progress.
In Tore Frängsmyr and Jan E. Lindsten (eds.), Nobel Lectures: Physiology Or Medicine: 1981-1990 (1993), 558.
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The general disposition of the land [in the Periodic Kingdom] is one of metals in the west, giving way, as you travel eastward, to a varied landscape of nonmetals, which terminates in largely inert elements at the eastern shoreline. To the south of the mainland, there is an offshore island, which we shall call the Southern Island. It consists entirely of metals of subtly modulated personality. North of the mainland, situated rather like Iceland off the northwestern edge of Europe, lies a single, isolated region-hydrogen. This simple but gifted element is an essential outpost of the kingdom, for despite its simplicity it is rich in chemical personality. It is also the most abundant element in the universe and the fuel of the stars.
In The Periodic Kingdom: A Journey Into the Land of the Chemical Elements (1995), 9.
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The geometrical problems and theorems of the Greeks always refer to definite, oftentimes to rather complicated figures. Now frequently the points and lines of such a figure may assume very many different relative positions; each of these possible cases is then considered separately. On the contrary, present day mathematicians generate their figures one from another, and are accustomed to consider them subject to variation; in this manner they unite the various cases and combine them as much as possible by employing negative and imaginary magnitudes. For example, the problems which Apollonius treats in his two books De sectione rationis, are solved today by means of a single, universally applicable construction; Apollonius, on the contrary, separates it into more than eighty different cases varying only in position. Thus, as Hermann Hankel has fittingly remarked, the ancient geometry sacrifices to a seeming simplicity the true simplicity which consists in the unity of principles; it attained a trivial sensual presentability at the cost of the recognition of the relations of geometric forms in all their changes and in all the variations of their sensually presentable positions.
In 'Die Synthetische Geometrie im Altertum und in der Neuzeit', Jahresbericht der Deutschen Mathematiker Vereinigung (1902), 2, 346-347. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112. The spelling of the first “Apollonius” has been corrected from “Appolonius” in the original English text. From the original German, “Die geometrischen Probleme und Sätze der Griechen beziehen sich allemal auf bestimmte, oft recht komplizierte Figuren. Nun können aber die Punkte und Linien einer solchen Figur häufig sehr verschiedene Lagen zu einander annehmen; jeder dieser möglichen Fälle wird alsdann für sich besonders erörtert. Dagegen lassen die heutigen Mathematiker ihre Figuren aus einander entstehen und sind gewohnt, sie als veränderlich zu betrachten; sie vereinigen so die speziellen Fälle und fassen sie möglichst zusammen unter Benutzung auch negativer und imaginärer Gröfsen. Das Problem z. B., welches Apollonius in seinen zwei Büchern de sectione rationis behandelt, löst man heutzutage durch eine einzige, allgemein anwendbare Konstruktion; Apollonius selber dagegen zerlegt es in mehr als 80 nur durch die Lage verschiedene Fälle. So opfert, wie Hermann Hankel treffend bemerkt, die antike Geometrie einer scheinbaren Einfachheit die wahre, in der Einheit der Prinzipien bestehende; sie erreicht eine triviale sinnliche Anschaulichkeit auf Kosten der Erkenntnis vom Zusammenhang geometrischer Gestalten in aller Wechsel und in aller Veränderlichkeit ihrer sinnlich vorstellbaren Lage.”
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The goddess of learning is fabled to have sprung full-grown from the brain of Zeus, but it is seldom that a scientific conception is born in its final form, or owns a single parent. More often it is the product of a series of minds, each in turn modifying the ideas of those that came before, and providing material for those that came after. The electron is no exception.
'Electronic Waves', Nobel Lecture (7 Jun 1938). Nobel Lectures: Physics 1922-1941 (1998), 397.
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The golden age of mathematics—that was not the age of Euclid, it is ours. Ours is the age when no less than six international congresses have been held in the course of nine years. It is in our day that more than a dozen mathematical societies contain a growing membership of more than two thousand men representing the centers of scientific light throughout the great culture nations of the world. It is in our time that over five hundred scientific journals are each devoted in part, while more than two score others are devoted exclusively, to the publication of mathematics. It is in our time that the Jahrbuch über die Fortschritte der Mathematik, though admitting only condensed abstracts with titles, and not reporting on all the journals, has, nevertheless, grown to nearly forty huge volumes in as many years. It is in our time that as many as two thousand books and memoirs drop from the mathematical press of the world in a single year, the estimated number mounting up to fifty thousand in the last generation. Finally, to adduce yet another evidence of a similar kind, it requires not less than seven ponderous tomes of the forthcoming Encyclopaedie der Mathematischen Wissenschaften to contain, not expositions, not demonstrations, but merely compact reports and bibliographic notices sketching developments that have taken place since the beginning of the nineteenth century.
In Lectures on Science, Philosophy and Art (1908), 8.
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The greatest single achievement of nature to date was surely the invention of the molecule DNA.
In The Medusa and the Snail: More Notes of a Biology Watcher (1974, 1979), 27.
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The highest of the world’s mountains, it seems, has to make but a single gesture of magnificence to be the lord of all, vast in unchallenged and isolated supremacy.
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The history of science teaches only too plainly the lesson that no single method is absolutely to be relied upon, that sources of error lurk where they are least expected, and that they may escape the notice of the most experienced and conscientious worker.
Transactions of the Sections', Reports of the British Association for the Advancement of Science (1883), 438.
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The human race, whose intelligence dates back only a single tick of the astronomical clock, could hardly hope to understand so soon what it all means.
The Stars in their Courses (1931, 1948), 153.
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The Humorless Person: I have a friend who has about as much sense of humor as the wooden Indian of commerce. Some time ago he made a trip through the Mammoth Cave of Kentucky. … He did his sight-seeing very thoroughly. He didn’t miss a single ramification in that great crack in the face of Mother Nature. … I asked him what he thought of the Mammoth Cave. “Well,” said he, “taking it as a hole, it is all right.”
In A Sample Case of Humor (1919), 15.
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The idea of a method that contains firm, unchanging, and absolutely binding principles for conducting the business of science meets considerable difficulty when confronted with the results of historical research. We find, then, that there is not a single rule, however plausible, and however firmly grounded in epistemology, that is not violated at some time or another.
Against Method: Outline of an Anarchistic Theory of Knowledge (1975, 1993), 14.
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The importance of a result is largely relative, is judged differently by different men, and changes with the times and circumstances. It has often happened that great importance has been attached to a problem merely on account of the difficulties which it presented; and indeed if for its solution it has been necessary to invent new methods, noteworthy artifices, etc., the science has gained more perhaps through these than through the final result. In general we may call important all investigations relating to things which in themselves are important; all those which have a large degree of generality, or which unite under a single point of view subjects apparently distinct, simplifying and elucidating them; all those which lead to results that promise to be the source of numerous consequences; etc.
From 'On Some Recent Tendencies in Geometric Investigations', Rivista di Matematica (1891), 44. In Bulletin American Mathematical Society (1904), 444.
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The incessant call in this country for practical results and the confounding of mechanical inventions with scientific discoveries has a very prejudicial influence on science. … A single scientific principle may include a thousand applications and is therefore though if not of immediate use of vastly more importance even in a practical view.
Presidential address to the American Association for the Advancement of Science (22 Aug 1850),The Papers of Joseph Henry, Vol. 8, 101-102.
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The individual feels the futility of human desires and aims and the sublimity and marvelous order which reveal themselves both in nature and in the world of thought. Individual existence impresses him as a sort of prison and he wants to experience the universe as a single significant whole. The beginnings of cosmic religious feeling already appear at an early stage of development, e.g., in many of the Psalms of David and in some of the Prophets. Buddhism, as we have learned especially from the wonderful writings of Schopenhauer, contains a much stronger element of this. The religious geniuses of all ages have been distinguished by this kind of religious feeling, which knows no dogma and no God conceived in man’s image; so that there can be no church whose central teachings are based on it. Hence it is precisely among the heretics of every age that we find men who were filled with this highest kind of religious feeling and were in many cases regarded by their contemporaries as atheists, sometimes also as saints. Looked at in this light, men like Democritus, Francis of Assisi, and Spinoza are closely akin to one another.
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The iron labor of conscious logical reasoning demands great perseverance and great caution; it moves on but slowly, and is rarely illuminated by brilliant flashes of genius. It knows little of that facility with which the most varied instances come thronging into the memory of the philologist or historian. Rather is it an essential condition of the methodical progress of mathematical reasoning that the mind should remain concentrated on a single point, undisturbed alike by collateral ideas on the one hand, and by wishes and hopes on the other, and moving on steadily in the direction it has deliberately chosen.
In Ueber das Verhältniss der Naturwissenschaften zur Gesammtheit der Wissenschaft, Vorträge und Reden (1896), Bd. 1, 178.
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The last few meters up to the summit no longer seem so hard. On reaching the top, I sit down and let my legs dangle into space. I don’t have to climb anymore. I pull my camera from my rucksack and, in my down mittens, fumble a long time with the batteries before I have it working properly. Then I film Peter. Now, after the hours of torment, which indeed I didn’t recognize as torment, now, when the monotonous motion of plodding upwards is at an end, and I have nothing more to do than breathe, a great peace floods my whole being. I breathe like someone who has run the race of his life and knows that he may now rest forever. I keep looking all around, because the first time I didn’t see anything of the panorama I had expected from Everest, neither indeed did I notice how the wind was continually chasing snow across the summit. In my state of spiritual abstraction, I no longer belong to myself and to my eyesight. I am nothing more than a single, narrow, gasping lung, floating over the mists and the summits.
In Everest: Expedition to the Ultimate (1979), 180.
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The laws of thermodynamics, as empirically determined, express the approximate and probable behavior of systems of a great number of particles, or, more precisely, they express the laws of mechanics for such systems as they appear to beings who have not the fineness of perception to enable them to appreciate quantities of the order of magnitude of those which relate to single particles, and who cannot repeat their experiments often enough to obtain any but the most probable results.
Elementary Principles in Statististical Mechanics (1902), Preface, viii.
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The line separating investment and speculation, which is never bright and clear, becomes blurred still further when most market participants have recently enjoyed triumphs. Nothing sedates rationality like large doses of effortless money. After a heady experience of that kind, normally sensible people drift into behavior akin to that of Cinderella at the ball. They know that overstaying the festivities—that is, continuing to speculate in companies that have gigantic valuations relative to the cash they are likely to generate in the future—will eventually bring on pumpkins and mice. But they nevertheless hate to miss a single minute of what is one helluva party. Therefore, the giddy participants all plan to leave just seconds before midnight. There’s a problem, though: They are dancing in a room in which the clocks have no hands.
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The majority of mathematical truths now possessed by us presuppose the intellectual toil of many centuries. A mathematician, therefore, who wishes today to acquire a thorough understanding of modern research in this department, must think over again in quickened tempo the mathematical labors of several centuries. This constant dependence of new truths on old ones stamps mathematics as a science of uncommon exclusiveness and renders it generally impossible to lay open to uninitiated readers a speedy path to the apprehension of the higher mathematical truths. For this reason, too, the theories and results of mathematics are rarely adapted for popular presentation … This same inaccessibility of mathematics, although it secures for it a lofty and aristocratic place among the sciences, also renders it odious to those who have never learned it, and who dread the great labor involved in acquiring an understanding of the questions of modern mathematics. Neither in the languages nor in the natural sciences are the investigations and results so closely interdependent as to make it impossible to acquaint the uninitiated student with single branches or with particular results of these sciences, without causing him to go through a long course of preliminary study.
In Mathematical Essays and Recreations (1898), 32.
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The mathematical universe is already so large and diversified that it is hardly possible for a single mind to grasp it, or, to put it in another way, so much energy would be needed for grasping it that there would be none left for creative research. A mathematical congress of today reminds one of the Tower of Babel, for few men can follow profitably the discussions of sections other than their own, and even there they are sometimes made to feel like strangers.
In The Study Of The History Of Mathematics (1936), 14.
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The mathematics of cooperation of men and tools is interesting. Separated men trying their individual experiments contribute in proportion to their numbers and their work may be called mathematically additive. The effect of a single piece of apparatus given to one man is also additive only, but when a group of men are cooperating, as distinct from merely operating, their work raises with some higher power of the number than the first power. It approaches the square for two men and the cube for three. Two men cooperating with two different pieces of apparatus, say a special furnace and a pyrometer or a hydraulic press and new chemical substances, are more powerful than their arithmetical sum. These facts doubtless assist as assets of a research laboratory.
Quoted from a speech delivered at the fiftieth anniversary of granting of M.I.T's charter, in Guy Suits, 'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 352.
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The meaning of life is contained in every single expression of life. It is present in the infinity of forms and phenomena that exist in all of creation.
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The most intensely social animals can only adapt to group behavior. Bees and ants have no option when isolated, except to die. There is really no such creature as a single individual; he has no more life of his own than a cast off cell marooned from the surface of your skin.
In The Lives of a Cell (1974), 63.
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The most revolutionary aspect of technology is its mobility. Anybody can learn it. It jumps easily over barriers of race and language. … The new technology of microchips and computer software is learned much faster than the old technology of coal and iron. It took three generations of misery for the older industrial countries to master the technology of coal and iron. The new industrial countries of East Asia, South Korea, and Singapore and Taiwan, mastered the new technology and made the jump from poverty to wealth in a single generation.
Infinite in All Directions: Gifford lectures given at Aberdeen, Scotland (2004), 270.
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The nations may be divided in everything else, but they all share a single body of science.
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 270.
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The nature of the atoms, and the forces called into play in their chemical union; the interactions between these atoms and the non-differentiated ether as manifested in the phenomena of light and electricity; the structures of the molecules and molecular systems of which the atoms are the units; the explanation of cohesion, elasticity, and gravitation—all these will be marshaled into a single compact and consistent body of scientific knowledge.
In Light Waves and Their Uses? (1902), 163.
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The night spread out of the east in a great flood, quenching the red sunlight in a single minute. We wriggled by breathless degrees deep into our sleeping bags. Our sole thought was of comfort; we were not alive to the beauty or the grandeur of our position; we did not reflect on the splendor of our elevation. A regret I shall always have is that I did not muster up the energy to spend a minute or two stargazing. One peep I did make between the tent flaps into the night, and I remember dimly an appalling wealth of stars, not pale and remote as they appear when viewed through the moisture-laden air of lower levels, but brilliant points of electric blue fire standing out almost stereoscopically. It was a sight an astronomer would have given much to see, and here were we lying dully in our sleeping bags concerned only with the importance of keeping warm and comfortable.
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The novel feature of the structure is the manner in which the two chains are held together by the purine and pyrimidine bases. The planes of the bases are perpendicular to the fibre axis. They are joined together in pairs, a single base from one chain being hydrogen-bonded to a single base from the other chain, so that the two lie side by side with identical z-co-ordinates. One of the pair must be 11 purine and the other a pyrimidine for bonding to occur. The hydrogen bonds are made as follows: purine position I to pyrimidine position I; purine position 6 to pyrimidine position 6.
[Co-author with Francis Crick]
In 'Molecular Structure of Nucleic Acids', Nature (1953), 171, 737.
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The object of geometry in all its measuring and computing, is to ascertain with exactness the plan of the great Geometer, to penetrate the veil of material forms, and disclose the thoughts which lie beneath them? When our researches are successful, and when a generous and heaven-eyed inspiration has elevated us above humanity, and raised us triumphantly into the very presence, as it were, of the divine intellect, how instantly and entirely are human pride and vanity repressed, and, by a single glance at the glories of the infinite mind, are we humbled to the dust.
From 'Mathematical Investigation of the Fractions Which Occur in Phyllotaxis', Proceedings of the American Association for the Advancement of Science (1850), 2, 447, as quoted by R. C. Archibald in 'Benjamin Peirce: V. Biographical Sketch', The American Mathematical Monthly (Jan 1925), 32, No. 1, 12.
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The present state of the system of nature is evidently a consequence of what is in the preceding moment, and if we conceive of an intelligence which at a given instant knew all the forces acting in nature and the position of every object in the universe—if endowed with a brain sufficiently vast to make all necessary calculations—could describe with a single formula the motions of the largest astronomical bodies and those of the smallest atoms. To such an intelligence, nothing would be uncertain; the future, like the past, would be an open book.
As quoted in The Fascination of Physics by Jacqueline D. Spears and Dean Zollman (1986). Alternate translation: “The present state of the system of nature is evidently a consequence of what is in the preceding moment, and if we conceive of an intelligence which at a given instant comprehends all the relations of the entities of this universe, it could state the respective positions, motions, and general effects of all these entities at any time in the past or future.” In Harry Woolf, The Analytic spirit: essays in the history of science in honor of Henry Guerlac (1981), 91, the author states that “the language Laplace used was obviously borrowed from Concdorset, though now the words were reshuffled to express a new idea.”
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The problem for a writer of a text-book has come now, in fact, to be this—to write a book so neatly trimmed and compacted that no coach, on looking through it, can mark a single passage which the candidate for a minimum pass can safely omit. Some of these text-books I have seen, where the scientific matter has been, like the lady’s waist in the nursery song, compressed “so gent and sma’,” that the thickness barely, if at all, surpasses what is devoted to the publisher’s advertisements. We shall return, I verily believe, to the Compendium of Martianus Capella. The result of all this is that science, in the hands of specialists, soars higher and higher into the light of day, while educators and the educated are left more and more to wander in primeval darkness.
In Presidential Address British Association for the Advancement of Science (1885), Nature, 32, 448. [Martianus Capella, who flourished c.410-320, wrote a compendium of the seven liberal arts. —Webmaster]
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The problems of the infinite have challenged man’s mind and have fired his imagination as no other single problem in the history of thought. The infinite appears both strange and familiar, at times beyond our grasp, at times easy and natural to understand. In conquering it, man broke the fetters that bound him to earth. All his faculties were required for this conquest—his reasoning powers, his poetic fancy, his desire to know.
With co-author James R Newman, in 'Beyond the Google', Mathematics and the Imagination (1940), 35.
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The prominent reason why a mathematician can be judged by none but mathematicians, is that he uses a peculiar language. The language of mathesis is special and untranslatable. In its simplest forms it can be translated, as, for instance, we say a right angle to mean a square corner. But you go a little higher in the science of mathematics, and it is impossible to dispense with a peculiar language. It would defy all the power of Mercury himself to explain to a person ignorant of the science what is meant by the single phrase “functional exponent.” How much more impossible, if we may say so, would it be to explain a whole treatise like Hamilton’s Quaternions, in such a wise as to make it possible to judge of its value! But to one who has learned this language, it is the most precise and clear of all modes of expression. It discloses the thought exactly as conceived by the writer, with more or less beauty of form, but never with obscurity. It may be prolix, as it often is among French writers; may delight in mere verbal metamorphoses, as in the Cambridge University of England; or adopt the briefest and clearest forms, as under the pens of the geometers of our Cambridge; but it always reveals to us precisely the writer’s thought.
In North American Review (Jul 1857), 85, 224-225.
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The publication in 1859 of the Origin of Species by Charles Darwin made a marked epoch in my own mental development, as it did in that of human thought generally. Its effect was to demolish a multitude of dogmatic barriers by a single stroke, and to arouse a spirit of rebellion against all ancient authorities whose positive and unauthenticated statements were contradicted by modern science.
Memories of My Life (1908), 287.
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The reduced variability of small populations is not always due to accidental gene loss, but sometimes to the fact that the entire population was started by a single pair or by a single fertilized female. These “founders” of the population carried with them only a very small proportion of the variability of the parent population. This “founder” principle sometimes explains even the uniformity of rather large populations, particularly if they are well isolated and near the borders of the range of the species.
Systematics and the Origin of Species: From the Viewpoint of a Zoologist (1942), 237.
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The result would inevitably be a state of universal rest and death, if the universe were finite and left to obey existing laws. But it is impossible to conceive a limit to the extent of matter in the universe; and therefore science points rather to an endless progress, through an endless space, of action involving the transformation of potential energy into palpable motion and thence into heat, than to a single finite mechanism, running down like a clock, and stopping for ever.
In 'On the Age of the Sun's Heat' (1862), Popular Lectures and Addresses (1891), Vol. 1, 349-50.
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The solution of problems is one of the lowest forms of mathematical research, … yet its educational value cannot be overestimated. It is the ladder by which the mind ascends into higher fields of original research and investigation. Many dormant minds have been aroused into activity through the mastery of a single problem.
With co-editor J. M. Colaw, Editorial introducing the first issue of The American Mathematical Monthly (Jan 1894), 1, No. 1, 2.
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The standard of proof is not very high for an investigation that announces that a plume is responsible for a bit of magma or a bit of chemistry found in, or near, or away from a volcano. The standard is being lowered all the time. Plumes were invented to explain small-scale features such as volcanoes. They were 100 kilometers wide. Then they were used to provide magmas 600 km away from a volcano, or to interact with distant ridges. Then the whole North Atlantic, from Canada to England needed to be serviced by a single plume. Then all of Africa. Then a bit of basalt on the East Pacific Rise was found to be similar to a Hawaiian basalt, so the plume influence was stretched to 5000 kilometers! No reviewer or editor has been found to complain yet. Superplumes are now routinely used to affect geology all around the Pacific. This is called creeping incredulity. It can also be called a Just-So Story.
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The statement that there is no single scientific method has become a truism only rather recently.
In 'On the Duality and Growth of Physical Science', American Scientist (Jan 1953), 41, No. 1, 89.
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The story of scientific discovery has its own epic unity—a unity of purpose and endeavour—the single torch passing from hand to hand through the centuries; and the great moments of science when, after long labour, the pioneers saw their accumulated facts falling into a significant order—sometimes in the form of a law that revolutionised the whole world of thought—have an intense human interest, and belong essentially to the creative imagination of poetry.
In Prefactory Note, Watchers of the Sky (1922), v.
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The sun rises. In that short phrase, in a single fact, is enough information to keep biology, physics, and philosophy busy for all the rest of time.
In Lifetide: A Biology of the Unconscious (1979), 23.
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The supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.
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The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them. In this methodological uncertainty, one might suppose that there were any number of possible systems of theoretical physics all equally well justified; and this opinion is no doubt correct, theoretically. But the development of physics has shown that at any given moment, out of all conceivable constructions, a single one has always proved itself decidedly superior to all the rest.
Address (1918) for Max Planck's 60th birthday, at Physical Society, Berlin, 'Principles of Research' in Essays in Science (1934), 4.
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The swelling and towering omnibuses, the huge trucks and wagons and carriages, the impetuous hansoms and the more sobered four-wheelers, the pony-carts, donkey-carts, hand-carts, and bicycles which fearlessly find their way amidst the turmoil, with foot-passengers winding in and out, and covering the sidewalks with their multitude, give the effect of a single monstrous organism, which writhes swiftly along the channel where it had run in the figure of a flood till you were tired of that metaphor. You are now a molecule of that vast organism.
Describing streets in London, from 'London Films', Harper’s Magazine (), 110, No. 655, 72.
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The term ‘community’ implies a diversity but at the same time a certain organized uniformity in the units. The units are the many individual plants that occur in every community, whether this be a beech-forest, a meadow, or a heath. Uniformity is established when certain atmospheric, terrestrial, and any of the other factors discussed in Section I are co-operating, and appears either because a certain, defined economy makes its impress on the community as a whole, or because a number of different growth-forms are combined to form a single aggregate which has a definite and constant guise.
Oecology of Plants: An Introduction to the Study of Plant Communities (1909), 91-92.
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The theory of punctuated equilibrium, proposed by Niles Eldredge and myself, is not, as so often misunderstood, a radical claim for truly sudden change, but a recognition that ordinary processes of speciation, properly conceived as glacially slow by the standard of our own life-span, do not resolve into geological time as long sequences of insensibly graded intermediates (the traditional, or gradualistic, view), but as geologically ‘sudden’ origins at single bedding planes.
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The three of us have worked on the development of the small and totally harmless fruit fly, Drosophila. This animal has been extremely cooperative in our hands - and has revealed to us some of its innermost secrets and tricks for developing from a single celled egg to a complex living being of great beauty and harmony. ... None of us expected that our work would be so successful or that our findings would ever have relevance to medicine.
Nobel Banquet Speech, 10 Dec 1995
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The uniformity of the earth’s life, more astonishing than its diversity, is accountable by the high probability that we derived, originally, from some single cell, fertilized in a bolt of lightning as the earth cooled. It is from the progeny of this parent cell that we take our looks; we still share genes around, and the resemblance of the enzymes of grasses to those of whales is a family resemblance.
In The Lives of a Cell (1974), 5.
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The universe…cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.
From Opere Il Saggiatore (1623), Sec. 6. (Title in English, The Assayer.) As translated in D. D. Raphael, Hobbes: Morals and Politics (2014), Vol. 6, 19.
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The variety of minds served the economy of nature in many ways. The Creator, who designed the human brain for activity, had insured the restlessness of all minds by enabling no single one to envisage all the qualities of the creation. Since no one by himself could aspire to a serene knowledge of the whole truth, all men had been drawn into an active, exploratory and cooperative attitude.
In The Lost World of Thomas Jefferson (1948, 1993), 125.
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The whole organism subsists only by means of the reciprocal action of the single elementary parts.
In Theodor Schwann and Henry Smith (trans.), 'Theory of the Cells', Microscopical Researches Into the Accordance in the Structure and Growth of Animals and Plants (1839, 1847), 191.
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The Wright Brothers created the single greatest cultural force since the invention of writing. The airplane became the first World Wide Web, bringing people, languages, ideas, and values together.
…...
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There are living systems; there is no living “matter.” No substance, no single molecule, extracted and isolated from a living being possess, of its own, the aforementioned paradoxical properties. They are present in living systems only; that is to say, nowhere below the level of the cell.
Inaugural lecture on taking the chair of molecular biology, Collège de France (3 Nov 1967). From Biology to Ethics (1969), 5.
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There is a single general space, a single vast immensity which we may freely call void: in it are unnumerable globes like this on which we live and grow, this space we declare to be infinite, since neither reason, convenience, sense-perception nor nature assign to it a limit.
Quoted in Joseph Silk, The Big Bang (1997), 89.
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There is a single light of science, and to brighten it anywhere is to brighten it everywhere.
In Erin Gruwell and Frank McCourt, The Gigantic Book of Teachers' Wisdom (2007), 578.
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There is not, we believe, a single example of a medicine having been received permanently into the Materia Medica upon the sole ground of its physical, chemical, or physiological properties. Nearly every one has become a popular remedy before being adopted or even tried by physicians; by far the greater number were first employed in countries which were and are now in a state of scientific ignorance....
Therapeutics and Materia Medica (2006), 31
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There is now a feeling that the pieces of physics are falling into place, not because of any single revolutionary idea or because of the efforts of any one physicist, but because of a flowering of many seeds of theory, most of them planted long ago.
In 'The Forces of Nature', Bulletin of the American Academy of Arts and Sciences (Jan 1976), 29:4, 14.
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There is only one subject matter for education, and that is Life in all its manifestations. Instead of this single unity, we offer children—Algebra, from which nothing follows; Geometry, from which nothing follows; Science, from which nothing follows; History, from which nothing follows; a Couple of Languages, never mastered; and lastly, most dreary of all, Literature, represented by plays of Shakespeare, with philological notes and short analyses of plot and character to be in substance committed to memory.
In 'The Aims of Education', The Aims of Education: & Other Essays (1917), 10.
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There is scarce a single Humour in the Body of a Man, or of any other Animal, in which our Glasses do not discover Myriads of living Creatures.
In The Spectator (25 Oct 1712), No. 519, as collected in Vol. 7 (1729, 10th ed.), 84.
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There’s no evolution of single individuals. Evolution is the property of populations.
In transcript of video interview story No. 112, 'What is Life?' on webofstories.com website.
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These duplicates in those parts of the body, without which a man might have very well subsisted, though not so well as with them, are a plain demonstration of an all-wise Contriver, as those more numerous copyings which are found among the vessels of the same body are evident demonstrations that they could not be the work of chance. This argument receives additional strength if we apply it to every animal and insect within our knowledge, as well as to those numberless living creatures that are objects too minute for a human eye: and if we consider how the several species in this whole world of life resemble one another in very many particulars, so far as is convenient for their respective states of existence, it is much more probable that a hundred millions of dice should be casually thrown a hundred millions of times in the same number than that the body of any single animal should be produced by the fortuitous concourse of matter.
In The Spectator (22 Nov 1712), No. 543, as collected in Vol. 4 (1721, 10th ed.), 48.
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These insecticides are not selective poisons; they do not single out the one species of which we desire to be rid. … Scientific observers at Sheldon described the symptoms of a meadowlark found near death: “Although it lacked muscular coordination and could not fly or stand, it continued to beat its wings and clutch with its toes while lying on its side. Its beak was held open and breathing was labored.”
In 'Needless Havoc', Silent Spring (1962), 99. [Note: Summarizing Carson (pp 92-93), for several years from 1954, Sheldon, in eastern Illinois, was subjected to extensive spraying of dieldrin (50 times more poisonous than DDT) by the Agriculture Departments of the U.S. and Illinois, to attempt to eradicate the Japanese beetle along the line of its invasive advance into Illinois. The dieldrin used was roughly equivalent to 150 pounds of DDT per acre. —Webmaster]
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Think of a single problem confronting the world today. Disease, poverty, global warming… If the problem is going to be solved, it is science that is going to solve it. Scientists tend to be unappreciated in the world at large, but you can hardly overstate the importance of the work they do. If anyone ever cures cancer, it will be a guy with a science degree. Or a woman with a science degree.
Quoted in Max Davidson, 'Bill Bryson: Have faith, science can solve our problems', Daily Telegraph (26 Sep 2010)
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Think of it: zillions and zillions of organisms running around, each under the hypnotic spell of a single truth, all these truths identical, and all logically incompatible with one another.
The Moral Animall: Evolutionary Psychology and Everyday Life (1994), 238.
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This Academy [at Lagado] is not an entire single Building, but a Continuation of several Houses on both Sides of a Street; which growing waste, was purchased and applied to that Use.
I was received very kindly by the Warden, and went for many Days to the Academy. Every Room hath in it ' one or more Projectors; and I believe I could not be in fewer than five Hundred Rooms.
The first Man I saw was of a meagre Aspect, with sooty Hands and Face, his Hair and Beard long, ragged and singed in several Places. His Clothes, Shirt, and Skin were all of the same Colour. He had been Eight Years upon a Project for extracting Sun-Beams out of Cucumbers, which were to be put into Vials hermetically sealed, and let out to warm the Air in raw inclement Summers. He told me, he did not doubt in Eight Years more, that he should be able to supply the Governor's Gardens with Sunshine at a reasonable Rate; but he complained that his Stock was low, and interested me to give him something as an Encouragement to Ingenuity, especially since this had been a very dear Season for Cucumbers. I made him a small Present, for my Lord had furnished me with Money on purpose, because he knew their Practice of begging from all who go to see them.
I saw another at work to calcine Ice into Gunpowder; who likewise shewed me a Treatise he had written concerning the Malleability of Fire, which he intended to publish.
There was a most ingenious Architect who had contrived a new Method for building Houses, by beginning at the Roof, and working downwards to the Foundation; which he justified to me by the life Practice of those two prudent Insects the Bee and the Spider.
In another Apartment I was highly pleased with a Projector, who had found a device of plowing the Ground with Hogs, to save the Charges of Plows, Cattle, and Labour. The Method is this: In an Acre of Ground you bury at six Inches Distance, and eight deep, a quantity of Acorns, Dates, Chestnuts, and other Masts or Vegetables whereof these Animals are fondest; then you drive six Hundred or more of them into the Field, where in a few Days they will root up the whole Ground in search of their Food, and make it fit for sowing, at the same time manuring it with their Dung. It is true, upon Experiment they found the Charge and Trouble very great, and they had little or no Crop. However, it is not doubted that this Invention may be capable of great Improvement.
I had hitherto seen only one Side of the Academy, the other being appropriated to the Advancers of speculative Learning.
Some were condensing Air into a dry tangible Substance, by extracting the Nitre, and letting the acqueous or fluid Particles percolate: Others softening Marble for Pillows and Pin-cushions. Another was, by a certain Composition of Gums, Minerals, and Vegetables outwardly applied, to prevent the Growth of Wool upon two young lambs; and he hoped in a reasonable Time to propagate the Breed of naked Sheep all over the Kingdom.
Gulliver's Travels (1726, Penguin ed. 1967), Part III, Chap. 5, 223.
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This fundamental discovery that all bodies owe their origin to arrangements of single initial corpuscular type is the beacon that lights the history of the universe to our eyes. In its own way, matter obeyed from the beginning that great law of biology to which we shall have to recur time and time again, the law of “complexification.”
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 48. Originally published in French as Le Phénomene Humain (1955).
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This is one of the greatest advantages of modern geometry over the ancient, to be able, through the consideration of positive and negative quantities, to include in a single enunciation the several cases which the same theorem may present by a change in the relative position of the different parts of a figure. Thus in our day the nine principal problems and the numerous particular cases, which form the object of eighty-three theorems in the two books De sectione determinata of Appolonius constitute only one problem which is resolved by a single equation.
In Histoire de la Géométrie, chap. 1, sect. 35.
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This prime matter which is proper for the form of the Elixir is taken from a single tree which grows in the lands of the West. It has two branches, which are too high for whoso seeks to eat the fruit thereof to reach them without labour and trouble; and two other branches, but the fruit of these is drier and more tanned than that of the two preceding. The blossom of one of the two is red [corresponding to gold], and the blossom of the second is between white and black [corresponding to silver]. Then there are two other branches weaker and softer than the four preceding, and the blossom of one of them is black [referring to iron] and the other between white and yellow [probably tin]. And this tree grows on the surface of the ocean [the material prima from which all metals are formed] as plants grow on the surface of the earth. This is the tree of which whosoever eats, man and jinn obey him; it is also the tree of which Adam (peace be upon him!) was forbidden to eat, and when he ate thereof he was transformed from his angelic form to human form. And this tree may be changed into every animal shape.
Al- Iraqi
'Cultivation of Gold', trans. E. J. Holmyard (1923), 23. Quoted and annotated in Seyyed Hossein Nasr, Science and Civilization in Islam (1968), 279.
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This single Stick, which you now behold ingloriously lying in that neglected Corner, I once knew in a flourishing State in a Forest: It was full of Sap, full of Leaves, and full of Boughs: But now, in vain does the busy Art of Man pretend to vie with Nature, by tying that withered Bundle of Twigs to its sapless Trunk: It is at best but the Reverse of what it was; a Tree turned upside down, the Branches on the Earth, and the Root in the Air.
'A Meditation Upon a Broom-stick: According to The Style and Manner of the Honorable Robert Boyle's Meditations' (1703), collected in 'Thoughts On Various Subjects', The Works of Jonathan Swift (1746), Vol. 1, 55-56.
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This very important property of rods, and indeed also of each kind of cone, this limitation of output to a single dimension of change, may be called the Principle of Univariance and stated thus: “The output of a receptor depends upon its quantum catch, but not upon what quanta are caught.” … Young's theory of colour vision may now be stated in terms of cone pigments. “There are three classes of cone each containing a different visual pigment. The output of each cone is univariant, depending simply upon the quantum catch of its pigment. Our sensation of colour depends upon the ratios of these three cone outputs.”
Principle of Univariance, concerning color vision, as stated in Lecture to a meeting of the Physiological Society at Chelsea College, London (17 Apr 1970), and reported in 'Pigments and Signals in Colour Vision', The Journal of Physiology (1972), 220 No. 3, 4P.
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Those who have long and carefully studied the Grand Cañon of the Colorado do not hesitate for a moment to pronounce it by far the most sublime of all earthly spectacles. If its sublimity consisted only in its dimensions, it could be sufficiently set forth in a single sentence. It is more than 200 miles long, from 5 to 12 miles wide, and from 5,000 to 6,000 feet deep. There are in the world valleys which are longer and a few which are deeper. There are valleys flanked by summits loftier than the palisades of the Kaibab. Still the Grand Cañon is the sublimest thing on earth. It is so not alone by virtue of its magnitudes, but by virtue of the whole—its ensemble.
In Tertiary History of the Grand Cañon District: With Atlas (1882), Vol. 2, 142-143.
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Thus I learned the single essential to qualify a dive as successful: a return.
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 38.
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Thus one becomes entangled in contradictions if one speaks of the probable position of the electron without considering the experiment used to determine it ... It must also be emphasized that the statistical character of the relation depends on the fact that the influence of the measuring device is treated in a different manner than the interaction of the various parts of the system on one another. This last interaction also causes changes in the direction of the vector representing the system in the Hilbert space, but these are completely determined. If one were to treat the measuring device as a part of the system—which would necessitate an extension of the Hilbert space—then the changes considered above as indeterminate would appear determinate. But no use could be made of this determinateness unless our observation of the measuring device were free of indeterminateness. For these observations, however, the same considerations are valid as those given above, and we should be forced, for example, to include our own eyes as part of the system, and so on. The chain of cause and effect could be quantitatively verified only if the whole universe were considered as a single system—but then physics has vanished, and only a mathematical scheme remains. The partition of the world into observing and observed system prevents a sharp formulation of the law of cause and effect. (The observing system need not always be a human being; it may also be an inanimate apparatus, such as a photographic plate.)
The Physical Principles of the Quantum Theory, trans. Carl Eckart and Frank C. Hoyt (1949), 58.
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Thus, we have three principles for increasing adequacy of data: if you must work with a single object, look for imperfections that record historical descent; if several objects are available, try to render them as stages of a single historical process; if processes can be directly observed, sum up their effects through time. One may discuss these principles directly or recognize the ‘little problems’ that Darwin used to exemplify them: orchids, coral reefs, and worms–the middle book, the first, and the last.
…...
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Time is in itself [not] a difficulty, but a time-rate, assumed on very insufficient grounds, is used as a master-key, whether or not it fits, to unravel all difficulties. What if it were suggested that the brick-built Pyramid of Hawara had been laid brick by brick by a single workman? Given time, this would not be beyond the bounds of possibility. But Nature, like the Pharaohs, had greater forces at her command to do the work better and more expeditiously than is admitted by Uniformitarians.
'The Position of Geology', The Nineteenth Century (1893), 34, 551.
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To a mathematician the eleventh means only a single unit: to the bushman who cannot count further than his ten fingers it is an incalculable myriad.
In 'Maxims for Revolutionists: Greatness', in Man and Superman (1903), 236.
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To be the first to enter the cosmos, to engage, single-handed, in an unprecedented duel with nature—could one dream of anything more?
From remarks made minutes before launch (12 Apr 1961), as quoted in Ulrike Landfester, Nina-Louisa Remuss, Kai-Uwe Schrogl, Jean-Claude Worms (eds.), Humans in Outer Space - Interdisciplinary Perspectives (2010), 225.
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To pray is to ask that the laws of the universe be annulled on behalf of a single petitioner confessedly unworthy.
From The Devil's Dictionary (1906). In The Collected Works of Ambrose Bierce: The Devil’s Dictionary (1911), 261.
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To regulate something always requires two opposing factors. You cannot regulate by a single factor. To give an example, the traffic in the streets could not be controlled by a green light or a red light alone. It needs a green light and a red light as well. The ratio between retine and promine determines whether there is any motion, any growth, or not. Two different inclinations have to be there in readiness to make the cells proliferate.
In Ralph W. Moss, Free Radical (1988), 186.
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To the natural philosopher, to whom the whole extent of nature belongs, all the individual branches of science constitute the links of an endless chain, from which not a single link can be detached without destroying the harmony of the whole.
'Astronomy', Friedrich Schoedler and Henry Medlock (trans.) The Book of Nature (1858), 140.
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Tobacco has not yet been fully tried before the bar of science. But the tribunal has been prepared and the gathering of evidence has begun and when the final verdict is rendered, it will appear that tobacco is evil and only evil; that as a drug it is far more deadly than alcohol, killing in a dose a thousand times smaller, and that it does not possess a single one of the quasi merits of alcohol.
In Tobaccoism: or, How Tobacco Kills (1922), Preface, 8.
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Tobacco, in its various forms, is one of the most mischievous of all drugs. There is perhaps no other drug which injures the body in so many ways and so universally as does tobacco. Some drugs offer a small degree of compensation for the evil effects which they produce; but tobacco has not a single redeeming feature and gives nothing in return.
In Tobaccoism: or, How Tobacco Kills (1922), Preface, 7.
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Today the greatest single source of wealth is between your ears.
…...
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Tonight, the moon came out, it was nearly full.
Way down here on earth, I could feel it’s pull.
The weight of gravity or just the lure of life,
Made me want to leave my only home tonight.
I’m just wondering how we know where we belong
Is it in the arc of the moon, leaving shadows on the lawn
In the path of fireflies and a single bird at dawn
Singing in between here and gone
…...
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Truly grand and powerful theories … do not and cannot rest upon single observations. Evolution is an inference from thousands of independent sources, the only conceptual structure that can make unified sense of all this disparate information. The failure of a particular claim usually records a local error, not the bankruptcy of a central theory … If I mistakenly identify your father’s brother as your own dad, you don’t become genealogically rootless and created de novo. You still have a father; we just haven’t located him properly.
Leonardo’s Mountain of Clams and the Diet of Worms: Essays on Natural History (1998), 155.
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Truly I say to you, a single number has more genuine and permanent value than an expensive library full of hypotheses.
Letter to Griesinger (20 Jul 1844). In Jacob J. Weyrauch (ed.), Kleinere Schriften und Briefe von Robert Milyer, nebst Mittheilungen aus seinem Leben (1893), 226. Trans. Kenneth L. Caneva, Robert Mayer and the Conservation of Energy (1993), 37.
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Tyndall, ... I must remain plain Michael Faraday to the last; and let me now tell you, that if accepted the honour which the Royal Society desires to confer upon me, I would not answer for the integrity of my intellect for a single year.
On being offered the Presidency of the Royal Society.
John Tyndall, Faraday as a Discoverer (1868), 157-8.
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Under certain given circumstances, and only under those circumstances, an agglomeration of men presents new characteristics very different from those of the individuals composing it. The sentiments and ideas of all the persons in the gathering take one and the same direction, and their conscious personality vanishes. A collective mind is formed, doubtless transitory, but presenting very clearly defined characteristics. The gathering has thus become what, in the absence of a better expression, I will call an organized crowd, or, if the term is considered preferable, a psychological crowd. It forms a single being and is subject to the law of the mental unity of crowds.
From Psychologie des Foules (1895), 12. English text in The Crowd: A Study of the Popular Mind (1897), Book 1, Chap. 1, 1-2. The original French text is, “Dans certaines circonstances données, et seulement dans ces circonstances, une agglomération d’hommes possède des caractères nouveaux fort différents de ceux des individus composant cette agglomération. La personnalité consciente s’évanouit, les sentiments et les idées de toutes les unités sont orientés dans une même direction. Il se forme une âme collective, transitoire sans doute, mais présentant des caractères très nets. La collectivité est alors devenue ce que, faute d’une expression meilleure, j’appellerai une foule organisée, ou, si l’on préfère, une foule psychologique. Elle forme un seul être et se trouve soumise à la loi de l'unité mentale des foules.”
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We build our personalities laboriously and through many years, and we cannot order fundamental changes just because we might value their utility; no button reading ‘positive attitude’ protrudes from our hearts, and no finger can coerce positivity into immediate action by a single and painless pressing.
…...
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We have not known a single great scientist who could not discourse freely and interestingly with a child. Can it be that haters of clarity have nothing to say, have observed nothing, have no clear picture of even their own fields?
In John Steinbeck and Edward Flanders Ricketts, Sea of Cortez: a Leisurely Journal of Travel and Research (1941), 73.
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We have seen that a proton of energy corresponding to 30,000 volts can effect the transformation of lithium into two fast α-particles, which together have an energy equivalent of more than 16 million volts. Considering the individual process, the output of energy in the transmutation is more than 500 times greater than the energy carried by the proton. There is thus a great gain of energy in the single transmutation, but we must not forget that on an average more than 1000 million protons of equal energy must be fired into the lithium before one happens to hit and enter the lithium nucleus. It is clear in this case that on the whole the energy derived from transmutation of the atom is small compared with the energy of the bombarding particles. There thus seems to be little prospect that we can hope to obtain a new source of power by these processes. It has sometimes been suggested, from analogy with ordinary explosives, that the transmutation of one atom might cause the transmutation of a neighbouring nucleus, so that the explosion would spread throughout all the material. If this were true, we should long ago have had a gigantic explosion in our laboratories with no one remaining to tell the tale. The absence of these accidents indicates, as we should expect, that the explosion is confined to the individual nucleus and does not spread to the neighbouring nuclei, which may be regarded as relatively far removed from the centre of the explosion.
The Transmutation of the Atom (1933), 23-4
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We hope to explain the universe in a single, simple formula that you can wear on your T-shirt.
In 'Quark City' by Richard Wolkomir, Omni, February 1984.
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We know only a single science, the science of history. History can be contemplated from two sides, it can be divided into the history of nature and the history of mankind. However, the two sides are not to be divided off; as long as men exist the history of nature and the history of men are mutually conditioned.
Karl Marx
Karl Marx and Frederick Engels, The German Ideology (1845-6), Vol. 1, 28. English translation 1965.
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We may lay it down that a happy person never phantasises, only an unsatisfied one... The motive forces of phantasies are unsatisfied wishes, and every single phantasy is the fulfilment of a wish, a correction of unsatisfying reality. These motivating wishes vary according to the sex, character and circumstances of the person who is having the phantasy; but they fall naturally into two main groups. They are either ambitious wishes, which serve to elevate the subject's personality; or they are erotic ones. It was shocking when Nietzsche said this, but today it is commonplace; our historical position—and no end to it is in sight—is that of having to philosophise without 'foundations'.
Creative Writers and Day-Dreaming (1906), In James Strachey (ed.), The Standard Edition of the Complete Psychcological Works of Sigmund Freud (1959), Vol 9, 146-7.
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We must ascribe to all cells an independent vitality; that is, such combinations of molecules as occur in any single cell are capable of setting free the power by which it is enabled to take up fresh molecules.
In Theodor Schwann and Henry Smith (trans.), 'Theory of the Cells', Microscopical Researches Into the Accordance in the Structure and Growth of Animals and Plants (1839, 1847), 192.
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We reverence ancient Greece as the cradle of western science. Here for the first time the world witnessed the miracle of a logical system which proceeded from step to step with such precision that every single one of its propositions was absolutely indubitable—I refer to Euclid’s geometry. This admirable triumph of reasoning gave the human intellect the necessary confidence in itself for its subsequent achievements. If Euclid failed to kindle your youthful enthusiasm, then you were not born to be a scientific thinker.
From 'On the Method of Theoretical Physics', in Essays in Science (1934, 2004), 13.
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We suppose ... that the constituent molecules of any simple gas whatever (i.e., the molecules which are at such a distance from each other that they cannot exercise their mutual action) are not formed of a solitary elementary molecule, but are made up of a certain number of these molecules united by attraction to form a single one.
'Essay on a Manner of Determining the Relative Masses of the Elementary Molecules of Bodies, and the Proportions in which they enter into these Compounds', Journal de Physique, 1811, 73, 58-76. In Foundations of the Molecular Theory: Alembic Club Reprints, Number 4 (1923), 31.
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We will be misguided in our intentions if we point at one single thing and say that it will prevent war, unless, of course, that thing happens to be the will, the determination, and the resolve of people everywhere that nations will never again clash on the battlefield.
Opening address (7 Nov 1945) of Town Hall’s annual lecture series, as quoted in 'Gen. Groves Warns on Atom ‘Suicide’', New York Times (8 Nov 1945), 4. (Just three months before he spoke, two atom bombs dropped on Japan in Aug 1945 effectively ended WW II.)
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What is the universal?
The single case.
What is the particular?
Millions of cases.
Jeremy Naydler (ed.), Goethe On Science: An Anthology of Goethe's Scientific Writings (1996), 92.
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When I came home not a single acre of Government, state, or private timberland was under systematic forest management anywhere on the most richly timbered of all continents. … When the Gay Nineties began, the common word for our forests was 'inexhaustible.' To waste timber was a virtue and not a crime. There would always be plenty of timber. … The lumbermen … regarded forest devastation as normal and second growth as a delusion of fools. … And as for sustained yield, no such idea had ever entered their heads. The few friends the forest had were spoken of, when they were spoken of at all, as impractical theorists, fanatics, or ‘denudatics,’ more or less touched in the head. What talk there was about forest protection was no more to the average American that the buzzing of a mosquito, and just about as irritating.
In Breaking New Ground (1947, 1998), 27.
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When I think of the floor of the deep sea, the single, overwhelming fact that possesses my imagination is the accumulation of sediments.
(1961).
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Wherever we seek to find constancy we discover change. Having looked at the old woodlands in Hutcheson Forest, at Isle Royale, and in the wilderness of the boundary waters, in the land of the moose and the wolf, and having uncovered the histories hidden within the trees and within the muds, we find that nature undisturbed is not constant in form, structure, or proportion, but changes at every scale of time and space. The old idea of a static landscape, like a single musical chord sounded forever, must be abandoned, for such a landscape never existed except in our imagination. Nature undisturbed by human influence seems more like a symphony whose harmonies arise from variation and change over many scales of time and space, changing with individual births and deaths, local disruptions and recoveries, larger scale responses to climate from one glacial age to another, and to the slower alterations of soils, and yet larger variations between glacial ages.
Discordant Harmonies (1990), 62.
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While no one can ascribe a single weather event to climate change with any degree of scientific certainty, higher maximum temperatures are one of the most predictable impacts of accelerated global warming, and the parallels—between global climate change and global terrorism—are becoming increasingly obvious.
In 'Global Warming is Now a Weapon of Mass Destruction', The Guardian (28 Jul 2003).
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While the method of the natural sciences is... analytic, the method of the social sciences is better described as compositive or synthetic. It is the so-called wholes, the groups of elements which are structurally connected, which we learn to single out from the totality of observed phenomena... Insofar as we analyze individual thought in the social sciences the purpose is not to explain that thought, but merely to distinguish the possible types of elements with which we shall have to reckon in the construction of different patterns of social relationships. It is a mistake... to believe that their aim is to explain conscious action ... The problems which they try to answer arise only insofar as the conscious action of many men produce undesigned results... If social phenomena showed no order except insofar as they were consciously designed, there would indeed be no room for theoretical sciences of society and there would be, as is often argued, only problems of psychology. It is only insofar as some sort of order arises as a result of individual action but without being designed by any individual that a problem is raised which demands a theoretical explanation... people dominated by the scientistic prejudice are often inclined to deny the existence of any such order... it can be shown briefly and without any technical apparatus how the independent actions of individuals will produce an order which is no part of their intentions... The way in which footpaths are formed in a wild broken country is such an instance. At first everyone will seek for himself what seems to him the best path. But the fact that such a path has been used once is likely to make it easier to traverse and therefore more likely to be used again; and thus gradually more and more clearly defined tracks arise and come to be used to the exclusion of other possible ways. Human movements through the region come to conform to a definite pattern which, although the result of deliberate decision of many people, has yet not be consciously designed by anyone.
…...
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Whoever would not remain in complete ignorance of the resources which cause him to act; whoever would seize, at a single philosophical glance, the nature of man and animals, and their relations to external objects; whoever would establish, on the intellectual and moral functions, a solid doctrine of mental diseases, of the general and governing influence of the brain in the states of health and disease, should know, that it is indispensable, that the study of the organization of the brain should march side by side with that of its functions.
On the Organ of the Moral Qualities and Intellectual Faculties, and the Plurality of the Cerebral Organs (1835), 45-6.
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Why, then, are we surprised that comets, such a rare spectacle in the universe, are not known, when their return is at vast intervals?. … The time will come when diligent research over long periods will bring to light things which now lie hidden. A single lifetime, even though entirely devoted to the sky, would not be enough for the investigation of so vast a subject … And so this knowledge will be unfolded only through long successive ages. There will come a time when our descendants will be amazed that we did not know things that are so plain to them …. Many discoveries are reserved for ages still to come, when memory of us will have been effaced. Our universe is a sorry little affair unless it has in it something for every age to investigate … Nature does not reveal her mysteries once and for all. Someday there will be a man who will show in what regions comets have their orbit, why they travel so remote from other celestial bodies, how large they are and what sort they are.
Natural Questions, Book 7. As translated by Thomas H. Corcoran in Seneca in Ten Volumes: Naturales Quaestiones II (1972), 279 and 293.
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Will power is only the tensile strength of one’s own disposition. One cannot increase it by a single ounce.
In The Burning Brand: Diaries 1935-1950 (1961), 88.
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With a tone control at a single touch
I can make Caruso sound like Hutch,
I never did care for music much—
It’s the high fidelity!
A parody of the hi-fi addict. From lyrics of 'Song of Reproduction', in the Michael Flanders and Donald Swann revue, At the Drop of a Hat (1959). As quoted in Steven D. Lubar, InfoCulture: The Smithsonian Book of Information Age Inventions (1993), 186. “Hutch” was the popularly used name of Leslie Hutchinson (1900-1969), one of the biggest London cabaret entertainers of the 1920s-30s.
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With the exception of the geometrical series, there does not exist in all of mathematics a single infinite series the sum of which has been rigorously determined. In other words, the things which are the most important in mathematics are also those which have the least foundation.
From letter (Jan 1828) to his former teacher Berndt Holmböe. In Morris Kline, Mathematics: The Loss of Certainty (1982), 170.
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With the extension of mathematical knowledge will it not finally become impossible for the single investigator to embrace all departments of this knowledge? In answer let me point out how thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.
In 'Mathematical Problems', Lecture at the International Congress of Mathematics, Paris, (8 Aug 1900). Translated by Dr. Maby Winton Newson in Bulletin of the American Mathematical Society (1902), 8, 479. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 94-95. It is reprinted in Jeremy Gray, The Hilbert Challenge (2000), 282.
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Without the slightest doubt there is something through which material and spiritual energy hold togehter and are complementary. In the last analysis, somehow or other, there must be a single energy operating in the world. And the first idea that occurs to us is that the 'soul' must be as it were the focal point of transformation at which, from all the points of nature, the forces of bodies converge, to become interiorised and sublimated in beauty and truth.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 63. Originally published in French as Le Phénomene Humain (1955).
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Without writing, the literate mind would not and could not think as it does, not only when engaged in writing but normally even when it is composing its thoughts in oral form. More than any other single invention writing has transformed human consciousness.
Orality and Literacy: The Technologizing of the Word (1982), 78.
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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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- 90 -
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- 80 -
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- 70 -
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- 60 -
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- 50 -
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- 40 -
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- 30 -
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- 20 -
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- 10 -
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