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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Occur Quotes (150 quotes)

... an analysis that puts the final link in the chain, for here we see correlations between cytological evidence and genetic results that are so strong and obvious that their validity cannot be denied. This paper has been called a landmark in experimental genetics. It is more than that—it is a cornerstone.
Describing the paper 'A Correlation of Cytological and Genetic Crossings-over in Zea mays' published by Barbara McClintock and her student Harriet Creighton in the Proceedings of the National Academy of Sciences (1931), demonstrating that the exchange of genetic information that occurs during the production of sex cells is accompanied by an exchange of chromosomal material.
Classic Papers in Genetics (1959), 156.
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...I may perhaps venture a short word on the question much discussed in certain quarters, whether in the work of excavation it is a good thing to have cooperation between men and women ... Of a mixed dig ... I have seen something, and it is an experiment that I would be reluctant to try again. I would grant if need be that women are admirable fitted for the work, yet I would uphold that they should undertake it by themselves ... the work of an excavator on the dig and off it lays on those who share it a bond of closer daily intercourse than is conceivable ... between men and women, except in chance cases, I do not believe that such close and unavoidable companionship can ever be other than a source of irritation; at any rate, I believe that however it may affect women, the ordinary male at least cannot stand it ... A minor ... objection lies in one particular form of contraint ... moments will occur on the best regulated dig when you want to say just what you think without translation, which before the ladies, whatever their feelings about it, cannot be done.
Archaeological Excavation (1915), 63-64. In Getzel M. Cohen and Martha Sharp Joukowsky Breaking Ground (2006), 557-558. By (), 163-164.
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1839—The fermentation satire
THE MYSTERY OF ALCOHOLIC FERMENTATION RESOLVED
(Preliminary Report by Letter) Schwindler
I am about to develop a new theory of wine fermentation … Depending on the weight, these seeds carry fermentation to completion somewhat less than as in the beginning, which is understandable … I shall develop a new theory of wine fermentation [showing] what simple means Nature employs in creating the most amazing phenomena. I owe it to the use of an excellent microscope designed by Pistorius.
When brewer’s yeast is mixed with water the microscope reveals that the yeast dissolves into endless small balls, which are scarcely 1/800th of a line in diameter … If these small balls are placed in sugar water, it can be seen that they consist of the eggs of animals. As they expand, they burst, and from them develop small creatures that multiply with unbelievable rapidity in a most unheard of way. The form of these animals differs from all of the 600 types described up until now. They possess the shape of a Beinsdorff still (without the cooling apparatus). The head of the tube is a sort of proboscis, the inside of which is filled with fine bristles 1/2000th of a line long. Teeth and eyes are not discernible; however, a stomach, intestinal canal, anus (a rose red dot), and organs for secretion of urine are plainly discernible. From the moment they are released from the egg one can see these animals swallow the sugar from the solution and pass it to the stomach. It is digested immediately, a process recognized easily by the resultant evacuation of excrements. In a word, these infusors eat sugar, evacuate ethyl alcohol from the intestinal canal, and carbon dioxide from the urinary organs. The bladder, in the filled state, has the form of a champagne bottle; when empty, it is a small button … As soon as the animals find no more sugar present, they eat each other up, which occurs through a peculiar manipulation; everything is digested down to the eggs which pass unchanged through the intestinal canal. Finally, one again fermentable yeast, namely the seed of the animals, which remain over.
In 'Das entriithselle Geheimiss der geisligen Giihrung', Annalen der Pharmacie und Chemie (1839), 29, 100-104; adapted from English translalion by Ralph E. Oesper, The Human Side of Scientists (1975), 203-205.
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Quam multa fieri non posse priusquam sunt facta indicantur
How many things are judged impossible before they actually occur?
In Pliny: Natural History (1947), Vol. 2, Book 7, 511, as translated by H. Rackham
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“Pieces” almost always appear 'as parts' in whole processes. ... To sever a “'part” from the organized whole in which it occurs—whether it itself be a subsidiary whole or an “element”—is a very real process usually involving alterations in that “part”. Modifications of a part frequently involve changes elsewhere in the whole itself. Nor is the nature of these alterations arbitrary, for they too are determined by whole-conditions.
From 'Untersuchungen zur Lehre von der Gestalt, I', Psychol. Forsch. (1922), 1, 47-58. As translated in 'The General Theoretical Situation' (1922), collected in W. D. Ellis (ed.), A Source Book of Gestalt Psychology (1938, 1967), Vol. 2, 14.
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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 first step in the study of civilization is to dissect it into details, and to classify these in their proper groups. Thus, in examining weapons, they are to be classed under spear, club, sling, bow and arrow, and so forth; among textile arts are to be ranged matting, netting, and several grades of making and weaving threads; myths are divided under such headings as myths of sunrise and sunset, eclipse-myths, earthquake-myths, local myths which account for the names of places by some fanciful tale, eponymic myths which account for the parentage of a tribe by turning its name into the name of an imaginary ancestor; under rites and ceremonies occur such practices as the various kinds of sacrifice to the ghosts of the dead and to other spiritual beings, the turning to the east in worship, the purification of ceremonial or moral uncleanness by means of water or fire. Such are a few miscellaneous examples from a list of hundreds … To the ethnographer, the bow and arrow is the species, the habit of flattening children’s skulls is a species, the practice of reckoning numbers by tens is a species. The geographical distribution of these things, and their transmission from region to region, have to be studied as the naturalist studies the geography of his botanical and zoological species.
In Primitive Culture (1871), Vol. 1, 7.
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A mind which has once imbibed a taste for scientific enquiry, and has learnt the habit of applying its principles readily to the cases which occur, has within itself an inexhaustable source of pure and exciting contemplations:— One would think that Shakespeare had such a mind in view when he describes a contemplative man as finding
    “Tongues in trees—books in running brooks—
    Sermons in stones—and good in everything.”
Accustomed to trace the operations of general causes and the exemplification of general laws, in circumstances where the uninformed and uninquiring eye, perceives neither novelty nor beauty, he walks in the midst of wonders; every object which falls in his way elucidates some principle, affords some instruction and impresses him with a sense of harmony and order. Nor is it a mere passive pleasure which is thus communicated. A thousand questions are continually arising in his mind, a thousand objects of enquiry presenting themselves, which keep his faculties in constant exercise, and his thoughts perpetually on the wing, so that lassitude is excluded from his life, and that craving after artificial excitement and dissipation of the mind, which leads so many into frivolous, unworthy, and destructive pursuits, is altogether eradicated from his bosom.
In Dionysius Lardner (ed.), Cabinet Cyclopaedia, Vol 1, Preliminary Discourse on the Study of Natural Philosophy (1831), 14-15.
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A mind which has once imbibed a taste for scientific enquiry, and has learnt the habit of applying its principles readily to the cases which occur, has within itself an inexhaustible source of pure and exciting contemplations.
In Dionysius Lardner (ed.), Cabinet Cyclopaedia, Vol 1, Preliminary Discourse on the Study of Natural Philosophy (1831), 14-15.
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A quarter-horse jockey learns to think of a twenty-second race as if it were occurring across twenty minutes—in distinct parts, spaced in his consciousness. Each nuance of the ride comes to him as he builds his race. If you can do the opposite with deep time, living in it and thinking in it until the large numbers settle into place, you can sense how swiftly the initial earth packed itself together, how swiftly continents have assembled and come apart, how far and rapidly continents travel, how quickly mountains rise and how quickly they disintegrate and disappear.
Annals of the Former World
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According to astronomers, next week Wednesday will occur twice. They say such a thing happens only once every 60,000 years and although they don’t know why it occurs, they’re glad they have an extra day to figure it out.
In Napalm and Silly Putty (2002), 105.
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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 our experience indicates that life can manifest itself only in a concrete form, and that it is bound to certain substantial loci. These loci are cells and cell formations. But we are far from seeking the last and highest level of understanding in the morphology of these loci of life. Anatomy does not exclude physiology, but physiology certainly presupposes anatomy. The phenomena that the physiologist investigates occur in special organs with quite characteristic anatomical arrangements; the various morphological parts disclosed by the anatomist are the bearers of properties or, if you will, of forces probed by the physiologist; when the physiologist has established a law, whether through physical or chemical investigation, the anatomist can still proudly state: This is the structure in which the law becomes manifest.
In 'Cellular-Pathologie', Archiv für pathologische Anatomie und Physiologie und fur klinische Medizin (1855), 8, 19, as translated in LellandJ. Rather, 'Cellular Pathology', Disease, Life, and Man: Selected Essays by Rudolf Virchow (1958), 84.
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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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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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Anybody who looks at living organisms knows perfectly well that they can produce other organisms like themselves. This is their normal function, they wouldn’t exist if they didn’t do this, and it’s not plausible that this is the reason why they abound in the world. In other words, living organisms are very complicated aggregations of elementary parts, and by any reasonable theory of probability or thermodynamics highly improbable. That they should occur in the world at all is a miracle of the first magnitude; the only thing which removes, or mitigates, this miracle is that they reproduce themselves. Therefore, if by any peculiar accident there should ever be one of them, from there on the rules of probability do not apply, and there will be many of them, at least if the milieu is reasonable. But a reasonable milieu is already a thermodynamically much less improbable thing. So, the operations of probability somehow leave a loophole at this point, and it is by the process of self-reproduction that they are pierced.
From lecture series on self-replicating machines at the University of Illinois, Lecture 5 (Dec 1949), 'Re-evaluation of the Problems of Complicated Automata—Problems of Hierarchy and Evolution', Theory of Self-Reproducing Automata (1966).
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As Karl Marx once noted: “Hegel remarks somewhere that all great, world-historical facts and personages occur, as it were, twice. He forgot to add: the first time as tragedy, the second as farce.” William Jennings Bryan and the Scopes trial was a tragedy. The creationists and intelligent design theorists are a farce.
In '75 Years and Still No Peace'. Humanist (Sep 2000)
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As soon as the circumstances of an experiment are well known, we stop gathering statistics. … The effect will occur always without exception, because the cause of the phenomena is accurately defined. Only when a phenomenon includes conditions as yet undefined,Only when a phenomenon includes conditions as yet undefined, can we compile statistics. … we must learn therefore that we compile statistics only when we cannot possibly help it; for in my opinion, statistics can never yield scientific truth.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 134-137.
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Available energy is energy which we can direct into any desired channel. Dissipated energy is energy which we cannot lay hold of and direct at pleasure, such as the energy of the confused agitation of molecules which we call heat. Now, confusion, like the correlative term order, is not a property of material things in themselves, but only in relation to the mind which perceives them. A memorandum-book does not, provided it is neatly written, appear confused to an illiterate person, or to the owner who understands it thoroughly, but to any other person able to read it appears to be inextricably confused. Similarly the notion of dissipated energy could not occur to a being who could not turn any of the energies of nature to his own account, or to one who could trace the motion of every molecule and seize it at the right moment. It is only to a being in the intermediate stage, who can lay hold of some forms of energy while others elude his grasp, that energy appears to be passing inevitably from the available to the dissipated state.
'Diffusion', Encyclopaedia Britannica (1878). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 646.
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Bradley is one of the few basketball players who have ever been appreciatively cheered by a disinterested away-from-home crowd while warming up. This curious event occurred last March, just before Princeton eliminated the Virginia Military Institute, the year’s Southern Conference champion, from the NCAA championships. The game was played in Philadelphia and was the last of a tripleheader. The people there were worn out, because most of them were emotionally committed to either Villanova or Temple-two local teams that had just been involved in enervating battles with Providence and Connecticut, respectively, scrambling for a chance at the rest of the country. A group of Princeton players shooting basketballs miscellaneously in preparation for still another game hardly promised to be a high point of the evening, but Bradley, whose routine in the warmup time is a gradual crescendo of activity, is more interesting to watch before a game than most players are in play. In Philadelphia that night, what he did was, for him, anything but unusual. As he does before all games, he began by shooting set shots close to the basket, gradually moving back until he was shooting long sets from 20 feet out, and nearly all of them dropped into the net with an almost mechanical rhythm of accuracy. Then he began a series of expandingly difficult jump shots, and one jumper after another went cleanly through the basket with so few exceptions that the crowd began to murmur. Then he started to perform whirling reverse moves before another cadence of almost steadily accurate jump shots, and the murmur increased. Then he began to sweep hook shots into the air. He moved in a semicircle around the court. First with his right hand, then with his left, he tried seven of these long, graceful shots-the most difficult ones in the orthodoxy of basketball-and ambidextrously made them all. The game had not even begun, but the presumably unimpressible Philadelphians were applauding like an audience at an opera.
A Sense of Where You Are: Bill Bradley at Princeton
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But in my opinion we can now be assured sufficiently that no animals, however small they may be, take their origin in putrefaction, but exclusively in procreation… For seeing that animals, from the largest down to the little despised animal, the flea, have animalcules in their semen, seeing also that some of the vessels of the lungs of horses and cows consist of rings and that these rings can occur on the flea's veins, why cannot we come to the conclusion that as well as the male sperm of that large animal the horse and similar animals, and of all manner of little animals, the flea included, is furnished with animalcules (and other intestines, for I have often been astonished when I beheld the numerous vessels in a flea), why, I say should not the male sperm of the smallest animals, smaller than a flea may even the very smallest animalcules have the perfection that we find in a flea.
Letter to Robert Hooke, 12 Nov 1680. In The Collected Letters of Antoni van Leeuwenhoek (1957), Vol. 3, 329.
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But in science the credit goes to the man who convinces the world, not to the man to whom the idea first occurs. Not the man who finds a grain of new and precious quality but to him who sows it, reaps it, grinds it and feeds the world on it.
First Galton Lecture before the Eugenics Society', Eugenics Review, 1914, 6, 9.
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Did it ever occur to you that there’s no limit to how complicated things can get, on account of one thing always leading to another?
In 'Quo Vadimus?, The Adelphi (Jan 1930), collected in Quo Vadimus?: Or, The Case For the Bicycle (1938) 26.
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EFFECT, n. The second of two phenomena which always occur together in the same order. The first, called a Cause, is said to generate the other—which is no more sensible than it would be for one who has never seen a dog except in pursuit of a rabbit to declare the rabbit the cause of the dog.
The Cynic's Word Book (1906), 86. Later published as The Devil's Dictionary.
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Error is often nourished by good sense. … The meaning is, that the powers of the understanding are frequently employed to defend favourite errors; and that a man of sense frequently fortifies himself in his prejudices, or in false opinions which he received without examination, by such arguments as would not have occurred to a fool.
In Maxims, Characters, and Reflections, Critical, Satyrical and Moral (2nd ed., 1757), 9. The meaning is given as a footnote.
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Firefly meteorites blazed against a dark background, and sometimes the lightning was frighteningly brilliant. Like a boy, I gazed open-mouthed at the fireworks, and suddenly, before my eyes, something magical occurred. A greenish radiance poured from Earth directly up to the station, a radiance resembling gigantic phosphorescent organ pipes, whose ends were glowing crimson, and overlapped by waves of swirling green mist.
“Consider yourself very lucky, Vladimir,” I said to myself, “to have watched the northern lights.”
…...
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Firm support has been found for the assertion that electricity occurs at thousands of points where we at most conjectured that it was present. Innumerable electrical particles oscillate in every flame and light source. We can in fact assume that every heat source is filled with electrons which will continue to oscillate ceaselessly and indefinitely. All these electrons leave their impression on the emitted rays. We can hope that experimental study of the radiation phenomena, which are exposed to various influences, but in particular to the effect of magnetism, will provide us with useful data concerning a new field, that of atomistic astronomy, as Lodge called it, populated with atoms and electrons instead of planets and worlds.
'Light Radiation in a Magnetic Field', Nobel Lecture, 2 May 1903. In Nobel Lectures: Physics 1901-1921 (1967), 40.
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Fractals are patterns which occur on many levels. This concept can be applied to any musical parameter. I make melodic fractals, where the pitches of a theme I dream up are used to determine a melodic shape on several levels, in space and time. I make rhythmic fractals, where a set of durations associated with a motive get stretched and compressed and maybe layered on top of each other. I make loudness fractals, where the characteristic loudness of a sound, its envelope shape, is found on several time scales. I even make fractals with the form of a piece, its instrumentation, density, range, and so on. Here I’ve separated the parameters of music, but in a real piece, all of these things are combined, so you might call it a fractal of fractals.
Interview (1999) on The Discovery Channel. As quoted by Benoit B. Manelbrot and Richard Hudson in The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward (2010), 133.
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From my numerous observations, I conclude that these tubercle bacilli occur in all tuberculous disorders, and that they are distinguishable from all other microorganisms.
'The Etiology of Tuberculosis' (1882), Essays of Robert Koch (1987), trans. K. Codell Carter, 87.
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His genius was in asking the right questions and seeing explanations that did not readily occur to others. He loved and lived science and was an inspiration to all who came in contact with him.
Co-author with Marilyn Taylor and Robert E. Connick, obituary, 'Melvin Calvin', Proceedings of the American Philosophical Society (Dec 2000), 144, No. 4, 457.
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His work was so great that it cannot be compassed in a few words. His death is one of the greatest losses ever to occur to British science.
Describing Ernest Rutherford upon his death at age 66. Thomson, then 80 years old, was once his teacher.
Quoted in Time Magazine (1 Nov 1937).
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How can altruism, which by definition reduces personal fitness, possibly evolve by natural selection? The answer is kinship: if the genes causing the altruism are shared by two organisms because of common descent, and if the altruistic act by one organism increases the joint contribution of these genes to the next generation, the propensity to altruism will spread through the gene pool. This occurs even though the altruist makes less of a solitary contribution to the gene pool as the price of its altruistic act.
In Sociobiology (1975), 3-4.
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How do we discover the individual laws of Physics, and what is their nature? It should be remarked, to begin with, that we have no right to assume that any physical law exists, or if they have existed up to now, that they will continue to exist in a similar manner in the future. It is perfectly conceivable that one fine day Nature should cause an unexpected event to occur which would baffle us all; and if this were to happen we would be powerless to make any objection, even if the result would be that, in spite of our endeavors, we should fail to introduce order into the resulting confusion. In such an event, the only course open to science would be to declare itself bankrupt. For this reason, science is compelled to begin by the general assumption that a general rule of law dominates throughout Nature.
Max Planck, Walter Henry Johnston, The Universe in the Light of Modern Physics (1931), 58.
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How often things occur by mere chance which we dared not even hope for.
Terence
In Phormio, v.1, 31, as quoted and cited in (1908), 109.
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However, on many occasions, I examined normal blood and normal tissues and there was no possibility of overlooking bacteria or confusing them with granular masses of equal size. I never found organisms. Thus, I conclude that bacteria do not occur in healthy human or animal tissues.
'Investigations of the Etiology of Wound Infections' (1878), Essays of Robert Koch (1987), trans. K. Codell Carter, 27.
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Hypochondriac symptoms commonly occur and may, if no discernible cause for the symptom is found, be due to exaggerated needs for attention and other psychological desires.
In Benjamin B. Wolman (editor), Handbook of Clinical Psychology (1965), 830-1.
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I am particularly concerned to determine the probability of causes and results, as exhibited in events that occur in large numbers, and to investigate the laws according to which that probability approaches a limit in proportion to the repetition of events. That investigation deserves the attention of mathematicians because of the analysis required. It is primarily there that the approximation of formulas that are functions of large numbers has its most important applications. The investigation will benefit observers in identifying the mean to be chosen among the results of their observations and the probability of the errors still to be apprehended. Lastly, the investigation is one that deserves the attention of philosophers in showing how in the final analysis there is a regularity underlying the very things that seem to us to pertain entirely to chance, and in unveiling the hidden but constant causes on which that regularity depends. It is on the regularity of the main outcomes of events taken in large numbers that various institutions depend, such as annuities, tontines, and insurance policies. Questions about those subjects, as well as about inoculation with vaccine and decisions of electoral assemblies, present no further difficulty in the light of my theory. I limit myself here to resolving the most general of them, but the importance of these concerns in civil life, the moral considerations that complicate them, and the voluminous data that they presuppose require a separate work.
Philosophical Essay on Probabilities (1825), trans. Andrew I. Dale (1995), Introduction.
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I do not see the possibility of comparison between his [H. G. Wells] work and mine. We do not proceed in the same manner. It occurs to me that his stories do not repose on a very scientific basis. ... I make use of physics. He invents. I go to the moon in a cannon-ball, discharged from a cannon. Here there is no invention. He goes to Mars in an airship, which he constructs of a metal which does not obey the law of gravitation. Ça c'est très joli ... but show me this metal. Let him produce it.
Quoted in R. H. Sherard, 'Jules Verne Re-Visited', T.P.'s Weekly (9 Oct 1903).
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I do not think there should be a limit on the rig's liability, because they are sitting on top of unlimited amounts of oil, and thus, there could be an explosion occur that could do untold damage. ... The amount of damage that an offshore oil rig can do is infinite.
Senate Floor Debate, 135 Cong. Rec. S9689-S9716 (3 Aug 1989). Reproduced in Russell V. Randle, Oil Pollution Deskbook (1991), 432.
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I had observed that there were different lines exhibited in the spectra of different metals when ignited in the voltaic arc; and if I had had any reasonable amount of wit I ought to have seen the converse, viz., that by ignition different bodies show in their spectral lines the materials of which they are formed. If that thought had occured to my mind, I should have discovered the spectroscope before Kirchoff; but it didn’t.
Address, in 'Report to the Chemical Society's Jubilee', Nature (26 Mar 1891), 43, 493. Words as in original text, occured and Kirchoff are sic.
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I have very often reflected on what it is that really distinguishes the great genius from the common crowd. Here are a few observations I have made. The common individual always conforms to the prevailing opinion and the prevailing fashion; he regards the State in which everything now exists as the only possible one and passively accepts it ail. It does not occur to him that everything, from the shape of the furniture up to the subtlest hypothesis, is decided by the great council of mankind of which he is a member. He wears thin-soled shoes even though the sharp stones of the Street hurt his feet, he allows fashion to dictate to him that the buckles of his shoes must extend as far as the toes even though that means the shoe is often hard to get on. He does not reflect that the form of the shoe depends as much upon him as it does upon the fool who first wore thin shoes on a cracked pavement. To the great genius it always occurs to ask: Could this too not be false! He never gives his vote without first reflecting.
Aphorism 24 in Notebook C (1772-1773), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 36.
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I must beg leave to propose a separate technical name ‘chromosome’ for those things which have been called by Boveri ‘chromatic elements’, in which there occurs one of the most important acts in karyokinesis, viz. the longitudinal splitting.
[Coining the word ‘chromosome,’ or ‘chromosom’ in the original German.]
Original German text by Waldeyer in Archiv für Mikroskopische Anatomie (1888), 27, translated by W.B. Benham in Quarterly Journal of Microscopical Science (1889), 30, 181.
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I use the word “attraction” here in a general sense for any endeavor whatever of bodies to approach one another, whether that endeavor occurs as a result of the action of the bodies either drawn toward one other or acting on one another by means of spirits emitted or whether it arises from the action of aether or of air or of any medium whatsoever—whether corporeal or incorporeal—in any way impelling toward one another the bodies floating therein. I use the word “impulse” in the same general sense, considering in this treatise not the species of forces and their physical qualities but their quantities and mathematical proportions, as I have explained in the definitions.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Book I, Section II, Scholium, 588.
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I would like to start by emphasizing the importance of surfaces. It is at a surface where many of our most interesting and useful phenomena occur. We live for example on the surface of a planet. It is at a surface where the catalysis of chemical reactions occur. It is essentially at a surface of a plant that sunlight is converted to a sugar. In electronics, most if not all active circuit elements involve non-equilibrium phenomena occurring at surfaces. Much of biology is concerned with reactions at a surface.
'Surface properties of semiconductors', Nobel Lecture (11 Dec 1956). In Nobel Lectures, Physics 1942-1962 (1967), 377.
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If we assume that there is only one enzyme present to act as an oxidizing agent, we must assume for it as many different degrees of activity as are required to explain the occurrence of the various colors known to mendelize (three in mice, yellow, brown, and black). If we assume that a different enzyme or group of enzymes is responsible for the production of each pigment we must suppose that in mice at least three such enzymes or groups of enzymes exist. To determine which of these conditions occurs in mice is not a problem for the biologist, but for the chemist. The biologist must confine his attention to determining the number of distinct agencies at work in pigment formation irrespective of their chemical nature. These agencies, because of their physiological behavior, the biologist chooses to call 'factors,' and attempts to learn what he can about their functions in the evolution of color varieties.
Experimental Studies of the Inheritance of Color in Mice (1913), 17-18.
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In 1963, when I assigned the name “quark” to the fundamental constituents of the nucleon, I had the sound first, without the spelling, which could have been “kwork.” Then, in one of my occasional perusals of Finnegans Wake, by James Joyce, I came across the word “quark” in the phrase “Three quarks for Muster Mark.” Since “quark” (meaning, for one thing, the cry of a gull) was clearly intended to rhyme with “Mark,” as well as “bark” and other such words, I had to find an excuse to pronounce it as “kwork.” But the book represents the dreams of a publican named Humphrey Chimpden Earwicker. Words in the text are typically drawn from several sources at once, like the “portmanteau words” in Through the Looking Glass. From time to time, phrases occur in the book that are partially determined by calls for drinks at the bar. I argued, therefore, that perhaps one of the multiple sources of the cry “Three quarks for Muster Mark” might be pronunciation for “Three quarts for Mister Mark,” in which case the pronunciation “kwork” would not be totally unjustified. In any case, the number three fitted perfectly the way quarks occur in nature.
The Quark and the Jaguar (1994), 180.
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In describing a protein it is now common to distinguish the primary, secondary and tertiary structures. The primary structure is simply the order, or sequence, of the amino-acid residues along the polypeptide chains. This was first determined by Sanger using chemical techniques for the protein insulin, and has since been elucidated for a number of peptides and, in part, for one or two other small proteins. The secondary structure is the type of folding, coiling or puckering adopted by the polypeptide chain: the a-helix structure and the pleated sheet are examples. Secondary structure has been assigned in broad outline to a number of librous proteins such as silk, keratin and collagen; but we are ignorant of the nature of the secondary structure of any globular protein. True, there is suggestive evidence, though as yet no proof, that a-helices occur in globular proteins, to an extent which is difficult to gauge quantitatively in any particular case. The tertiary structure is the way in which the folded or coiled polypeptide chains are disposed to form the protein molecule as a three-dimensional object, in space. The chemical and physical properties of a protein cannot be fully interpreted until all three levels of structure are understood, for these properties depend on the spatial relationships between the amino-acids, and these in turn depend on the tertiary and secondary structures as much as on the primary. Only X-ray diffraction methods seem capable, even in principle, of unravelling the tertiary and secondary structures.
Co-author with G. Bodo, H. M. Dintzis, R. G. Parrish, H. Wyckoff, and D. C. Phillips
'A Three-Dimensional Model of the Myoglobin Molecule Obtained by X-ray Analysis', Nature (1958) 181, 662.
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In early times, when the knowledge of nature was small, little attempt was made to divide science into parts, and men of science did not specialize. Aristotle was a master of all science known in his day, and wrote indifferently treatises on physics or animals. As increasing knowledge made it impossible for any one man to grasp all scientific subjects, lines of division were drawn for convenience of study and of teaching. Besides the broad distinction into physical and biological science, minute subdivisions arose, and, at a certain stage of development, much attention was, given to methods of classification, and much emphasis laid on the results, which were thought to have a significance beyond that of the mere convenience of mankind.
But we have reached the stage when the different streams of knowledge, followed by the different sciences, are coalescing, and the artificial barriers raised by calling those sciences by different names are breaking down. Geology uses the methods and data of physics, chemistry and biology; no one can say whether the science of radioactivity is to be classed as chemistry or physics, or whether sociology is properly grouped with biology or economics. Indeed, it is often just where this coalescence of two subjects occurs, when some connecting channel between them is opened suddenly, that the most striking advances in knowledge take place. The accumulated experience of one department of science, and the special methods which have been developed to deal with its problems, become suddenly available in the domain of another department, and many questions insoluble before may find answers in the new light cast upon them. Such considerations show us that science is in reality one, though we may agree to look on it now from one side and now from another as we approach it from the standpoint of physics, physiology or psychology.
In article 'Science', Encyclopedia Britannica (1911), 402.
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In mathematics, if a pattern occurs, we can go on to ask, Why does it occur? What does it signify? And we can find answers to these questions. In fact, for every pattern that appears, a mathematician feels he ought to know why it appears.
in Prelude to mathematics (1955), 23.
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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 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 higher walks of politics the same sort of thing occurs. The statesman who has gradually concentrated all power within himself … may have had anything but a public motive… The phrases which are customary on the platform and in the Party Press have gradually come to him to seem to express truths, and he mistakes the rhetoric of partisanship for a genuine analysis of motives… He retires from the world after the world has retired from him.
In The Conquest of Happiness (1930, 2006), 79.
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In the index to the six hundred odd pages of Arnold Toynbee’s A Study of History, abridged version, the names of Copernicus, Galileo, Descartes and Newton do not occur yet their cosmic quest destroyed the medieval vision of an immutable social order in a walled-in universe and transformed the European landscape, society, culture, habits and general outlook, as thoroughly as if a new species had arisen on this planet.
In The Sleepwalkers: A History of Man's Changing Vision of the Universe (1959), Preface, 13.
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In the index to the six hundred odd pages of Arnold Toynbee’s A Study of History, abridged version, the names of Copernicus, Galileo, Descartes and Newton do not occur … yet their cosmic quest destroyed the mediaeval vision of an immutable social order in a walled-in universe and transformed the European landscape, society, culture, habits and general outlook, as thoroughly as if a new species had arisen on this planet.
First lines of 'Preface', in The Sleepwalkers: A History of Man’s Changing Vision of the Universe (1959), 13.
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In the vestibule of the Manchester Town Hall are placed two life-sized marble statues facing each other. One of these is that of John Dalton … the other that of James Prescott Joule. … Thus honour is done to Manchester’s two greatest sons—to Dalton, the founder of modern Chemistry and of the Atomic Theory, and the laws of chemical-combining proportions; to Joule, the founder of modern Physics and the discoverer of the Law of Conservation of Energy. The one gave to the world the final and satisfactory proof … that in every kind of chemical change no loss of matter occurs; the other proved that in all the varied modes of physical change, no loss of energy takes place.
In John Dalton and the Rise of Modern Chemistry (1895), 7.
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In the whole of geophysics there is probably hardly another law of such clarity and reliability as this—that there are two preferential levels for the world’s surface which occur in alternation side by side and are represented by the continents and the ocean floors, respectively. It is therefore very surprising that scarcely anyone has tried to explain this law.
In The Origins of Continents and Oceans (4th ed. 1929), trans. John Biram (1966), 37.
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In this communication I wish first to show in the simplest case of the hydrogen atom (nonrelativistic and undistorted) that the usual rates for quantization can be replaced by another requirement, in which mention of “whole numbers” no longer occurs. Instead the integers occur in the same natural way as the integers specifying the number of nodes in a vibrating string. The new conception can be generalized, and I believe it touches the deepest meaning of the quantum rules.
'Quantisierung als Eigenwertproblem', Annalen der Physik (1926), 79, 361. Trans. Walter Moore, Schrödinger: Life and Thought (1989), 200-2.
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Investigating the conditions under which mutations occur … requires studies of mutation frequency under various methods of handling the organisms. As yet, extremely little has been done along this line. That is because, in the past, a mutation was considered a windfall, and the expression “mutation frequency” would have seemed a contradiction in terms. To attempt to study it would have seemed as absurd as to study the conditions affecting the distribution of dollar bills on the sidewalk. You were simply fortunate if you found one. … Of late, however, we may say that certain very exceptional banking houses have been found, in front of which the dollars fall more frequently—in other words, specially mutable genes have been discovered, that are beginning to yield abundant data at the hands of Nilsson-Ehle, Zeleny, Emerson, Anderson and others.
In 'Variation Due to Change in the Individual Gene', The American Naturalist (Jan-Feb 1922), 56, No. 642, 44.
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It does not matter what men say in words, so long as their activities are controlled by settled instincts. The words may ultimately destroy the instincts. But until this has occurred, words do not count.
In Science and the Modern World (1925), 4.
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It is an old saying, abundantly justified, that where sciences meet there growth occurs. It is true moreover to say that in scientific borderlands not only are facts gathered that [are] often new in kind, but it is in these regions that wholly new concepts arise. It is my own faith that just as the older biology from its faithful studies of external forms provided a new concept in the doctrine of evolution, so the new biology is yet fated to furnish entirely new fundamental concepts of science, at which physics and chemistry when concerned with the non-living alone could never arrive.
'Biological Thought and Chemical Thought: A Plea for Unification', Linacre Lecture, Cambridge (6 May 1938), published in Lancet (1938),2, 1204.
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It is in all cases unavoidable that the heart is afflicted when death occurs.
As quoted in Robert Taylor, White Coat Tales: Medicine's Heroes, Heritage, and Misadventures (2010), 125.
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It is not always possible to know what one has learned, or when the dawning will arrive. You will continue to shift, sift, to shake out and to double back. The synthesis that finally occurs can be in the most unexpected place and the most unexpected time. My charge ... is to be alert to the dawnings.
…...
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It is the reciprocity of these appearances—that each party should think the other has contracted—that is so difficult to realise. Here is a paradox beyond even the imagination of Dean Swift. Gulliver regarded the Lilliputians as a race of dwarfs; and the Lilliputians regarded Gulliver as a giant. That is natural. If the Lilliputians had appeared dwarfs to Gulliver, and Gulliver had appeared a dwarf to the Lilliputians—but no! that is too absurd for fiction, and is an idea only to be found in the sober pages of science. …It is not only in space but in time that these strange variations occur. If we observed the aviator carefully we should infer that he was unusually slow in his movements; and events in the conveyance moving with him would be similarly retarded—as though time had forgotten to go on. His cigar lasts twice as long as one of ours. …But here again reciprocity comes in, because in the aviator’s opinion it is we who are travelling at 161,000 miles a second past him; and when he has made all allowances, he finds that it is we who are sluggish. Our cigar lasts twice as long as his.
In Space, Time and Gravitation: An Outline of the General Relativity Theory (1920, 1921), 23-24.
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It is this mythical, or rather this symbolic, content of the religious traditions which is likely to come into conflict with science. This occurs whenever this religious stock of ideas contains dogmatically fixed statements on subjects which be long in the domain of science. Thus, it is of vital importance for the preservation of true religion that such conflicts be avoided when they arise from subjects which, in fact, are not really essential for the pursuance of the religious aims.
…...
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It is usual to say that the two sources of experience are Observation and Experiment. When we merely note and record the phenomena which occur around us in the ordinary course of nature we are said to observe. When we change the course of nature by the intervention of our will and muscular powers, and thus produce unusual combinations and conditions of phenomena, we are said to experiment. [Sir John] Herschel has justly remarked that we might properly call these two modes of experience passive and active observation. In both cases we must certainly employ our senses to observe, and an experiment differs from a mere observation in the fact that we more or less influence the character of the events which we observe. Experiment is thus observation plus alteration of conditions.
Principles of Science: A Treatise on Logic and Scientific Method (1874, 2nd ed., 1913), 400.
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It makes me feel both proud and rather humble that it shall be called Lonsdaleite. Certainly the name seems appropriate since the mineral only occurs in very small quantities (perhaps rare would be too flattering) and it is generally rather mixed up!
From Letter to Clifford Frondel, who had named a meteoritic form of diamond after Lonsdale (a petite person). As quoted in Maureen M. Julian, 'Women in Crystallography', in G. Kass-Simon and P. Farnes (eds.), Women of Science: Righting the Record (1990), 356.
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It seems sensible to discard all hope of observing hitherto unobservable quantities, such as the position and period of the electron... Instead it seems more reasonable to try to establish a theoretical quantum mechanics, analogous to classical mechanics, but in which only relations between observable quantities occur.
In Helge Kragh, Quantum Generations: A History of Physics in the Twentieth Century (1999), 161.
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It will be noticed that the fundamental theorem proved above bears some remarkable resemblances to the second law of thermodynamics. Both are properties of populations, or aggregates, true irrespective of the nature of the units which compose them; both are statistical laws; each requires the constant increase of a measurable quantity, in the one case the entropy of a physical system and in the other the fitness, measured by m, of a biological population. As in the physical world we can conceive the theoretical systems in which dissipative forces are wholly absent, and in which the entropy consequently remains constant, so we can conceive, though we need not expect to find, biological populations in which the genetic variance is absolutely zero, and in which fitness does not increase. Professor Eddington has recently remarked that “The law that entropy always increases—the second law of thermodynamics—holds, I think, the supreme position among the laws of nature.” It is not a little instructive that so similar a law should hold the supreme position among the biological sciences. While it is possible that both may ultimately be absorbed by some more general principle, for the present we should note that the laws as they stand present profound differences—-(1) The systems considered in thermodynamics are permanent; species on the contrary are liable to extinction, although biological improvement must be expected to occur up to the end of their existence. (2) Fitness, although measured by a uniform method, is qualitatively different for every different organism, whereas entropy, like temperature, is taken to have the same meaning for all physical systems. (3) Fitness may be increased or decreased by changes in the environment, without reacting quantitatively upon that environment. (4) Entropy changes are exceptional in the physical world in being irreversible, while irreversible evolutionary changes form no exception among biological phenomena. Finally, (5) entropy changes lead to a progressive disorganization of the physical world, at least from the human standpoint of the utilization of energy, while evolutionary changes are generally recognized as producing progressively higher organization in the organic world.
The Genetical Theory of Natural Selection (1930), 36.
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It... [can] be easily shown:
1. That all present mountains did not exist from the beginning of things.
2. That there is no growing of mountains.
3. That the rocks or mountains have nothing in common with the bones of animals except a certain resemblance in hardness, since they agree in neither matter nor manner of production, nor in composition, nor in function, if one may be permitted to affirm aught about a subject otherwise so little known as are the functions of things.
4. That the extension of crests of mountains, or chains, as some prefer to call them, along the lines of certain definite zones of the earth, accords with neither reason nor experience.
5. That mountains can be overthrown, and fields carried over from one side of a high road across to the other; that peaks of mountains can be raised and lowered, that the earth can be opened and closed again, and that other things of this kind occur which those who in their reading of history wish to escape the name of credulous, consider myths.
The Prodromus of Nicolaus Steno's Dissertation Concerning a Solid Body enclosed by Process of Nature within a Solid (1669), trans. J. G. Winter (1916), 232-4.
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It’s important to always bear in mind that life occurs in historical time. Everyone in every culture lives in some sort of historical time, though it might not be perceived in the same way an outside observer sees it. It’s an interesting question, “When is now?” “Now” can be drawn from some point like this hour, this day, this month, this lifetime, or this generation. “Now” can also have occurred centuries ago; things like unfair treaties, the Trail of Tears, and the Black Hawk War, for instance, remain part of the “Now” from which many Native Americans view their place in time today. Human beings respond today to people and events that actually occurred hundreds or even thousands of years ago. Ethnohistorians have played a major role in showing how now is a social concept of time, and that time is part of all social life. I can only hope that their work will further the understanding that the study of social life is a study of change over time.
From Robert S. Grumet, 'An Interview with Anthony F. C. Wallace', Ethnohistory (Winter 1998), 45, No. 1, 127.
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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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Laughter that occurs during tickling of the axillary region and the soles of the feet, as well as the laughter that occurs when seeing comical things or when hearing comical things, has no practical diagnostic significance.
As quoted in Fred Rosner, The Medical Legacy of Moses Maimonides (1998), 55.
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Mathematics is a public activity. It occurs in a social context and has social consequences. Posing a problem, formulating a definition, proving a theorem are none of them private acts. They are all part of that larger social process we call science.
In 'Mathematics as an Objective Science', The American Mathematical Monthly (Aug-Sep 1979), 86, No. 7, 542. Reprinted in The Mathematical Intelligencer (1983), 5, No. 3.
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Medical science has proven time and again that when the resources are provided, great progress in the treatment, cure and prevention of disease can occur.
Commencement Address, Medical School Convocation, University of Miami (10 May 2003). From website www.michaeljfox.org.
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Natural causes, as we know, are at work, which tend to modify, if they do not at length destroy, all the arrangements and dimensions of the earth and the whole solar system. But though in the course of ages catastrophes have occurred and may yet occur in the heavens, though ancient systems may be dissolved and new systems evolved out of their ruins, the molecules [i.e. atoms] out of which these systems are built—the foundation stones of the material universe—remain unbroken and unworn. They continue to this day as they were created—perfect in number and measure and weight.
Lecture to the British Association at Bradford, 'Molecules', Nature (1873), 8, 437-441. Reprinted in James Clerk Maxwell and W. D. Niven, editor, The Scientific Papers of James Clerk Maxwell (2003), 377. By
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Nature, … in order to carry out the marvelous operations [that occur] in animals and plants has been pleased to construct their organized bodies with a very large number of machines, which are of necessity made up of extremely minute parts so shaped and situated as to form a marvelous organ, the structure and composition of which are usually invisible to the naked eye without the aid of a microscope. … Just as Nature deserves praise and admiration for making machines so small, so too the physician who observes them to the best of his ability is worthy of praise, not blame, for he must also correct and repair these machines as well as he can every time they get out of order.
'Reply to Doctor Sbaraglia' in Opera Posthuma (1697), in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 1, 568.
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No hypothesis concerning the nature of this 'something' shall be advanced thereby or based thereon. Therefore it appears as most simple to use the last syllable 'gen' taken from Darwin's well-known word pangene since it alone is of interest to use, in order thereby to replace the poor, more ambiguous word, 'Anlage'. Thus, we will say for 'das pangene' and 'die pangene' simply 'Das Gen' and 'Die Gene,' The word Gen is fully free from every hypothesis; it expresses only the safely proved fact that in any case many properties of organisms are conditioned by separable and hence independent 'Zustiinde,' 'Grundlagen,' 'Anlagen'—in short what we will call 'just genes'—which occur specifically in the gametes.
Elemente der Exakten Erblichkeitslehre (1909), 124. Trans. G. E. Allen and quoted in G. E. Allen, Thomas Hunt Morgan: The Man and His Science (1978), 209-10 (Footnote 79).
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No isolated experiment, however significant in itself, can suffice for the experimental demonstration of any natural phenomenon; for the “one chance in a million” will undoubtedly occur, with no less and no more than its appropriate frequency, however surprised we may be that it should occur to us.
The Design of Experiments (1935, 1971), 13-14.
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Nobody before the Pythagoreans had thought that mathematical relations held the secret of the universe. Twenty-five centuries later, Europe is still blessed and cursed with their heritage. To non-European civilizations, the idea that numbers are the key to both wisdom and power, seems never to have occurred.
In The Sleepwalkers: A History of Man's Changing Vision of the Universe (1959), Preface, 40.
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Nothing is more humbling than to look with a strong magnifying glass at an insect so tiny that the naked eye sees only the barest speck and to discover that nevertheless it is sculpted and articulated and striped with the same care and imagination as a zebra. Apparently it does not occur to nature whether or not a creature is within our range of vision, and the suspicion arises that even the zebra was not designed for our benefit.
…...
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Nothing occurs at random, but everything for a reason and by necessity.
Leucippus
Aetius 1.25.4. In G. S. Kirk, J. E. Raven and M. Schofield (eds.), The Presocratic Philosophers (1983), 420.
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Now, rather than human development occurring in a matrix of natural landscape, natural areas occur in a matrix of human-dominated landscape.
[Co-author with J. Scheck]
As cited in Anthony B. Anderson and Clinton N. Jenkins, Applying Nature's Design: Corridors As A Strategy For Biodiversity Conservation (2006), 1.
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One never finds fossil bones bearing no resemblance to human bones. Egyptian mummies, which are at least three thousand years old, show that men were the same then. The same applies to other mummified animals such as cats, dogs, crocodiles, falcons, vultures, oxen, ibises, etc. Species, therefore, do not change by degrees, but emerged after the new world was formed. Nor do we find intermediate species between those of the earlier world and those of today's. For example, there is no intermediate bear between our bear and the very different cave bear. To our knowledge, no spontaneous generation occurs in the present-day world. All organized beings owe their life to their fathers. Thus all records corroborate the globe's modernity. Negative proof: the barbaritY of the human species four thousand years ago. Positive proof: the great revolutions and the floods preserved in the traditions of all peoples.
'Note prese al Corso di Cuvier. Corso di Geologia all'Ateneo nel 1805', quoted in Pietro Corsi, The Age of Lamarck, trans. J. Mandelbaum (1988), 183.
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One summer night, out on a flat headland, all but surrounded by the waters of the bay, the horizons were remote and distant rims on the edge of space. Millions of stars blazed in darkness, and on the far shore a few lights burned in cottages. Otherwise there was no reminder of human life. My companion and I were alone with the stars: the misty river of the Milky Way flowing across the sky, the patterns of the constellations standing out bright and clear, a blazing planet low on the horizon. It occurred to me that if this were a sight that could be seen only once in a century, this little headland would be thronged with spectators. But it can be seen many scores of nights in any year, and so the lights burned in the cottages and the inhabitants probably gave not a thought to the beauty overhead; and because they could see it almost any night, perhaps they never will.
In The Sense of Wonder (1956), as condensed in Reader’s Digest (1986), 129, 174.
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Our natural way of thinking about these coarser emotions is that the mental perception of some fact excites the mental affection called the emotion, and that this latter state of mind gives rise to the bodily expression. My theory, on the contrary, is that the bodily changes follow directly the perception of the exciting fact, and that our feeling of the same changes as they occur IS the emotion. Common-sense says, we lose our fortune, are sorry and weep; we meet a bear, are frightened and run; we are insulted by a rival, are angry and strike. The hypothesis here to be defended says that this order of sequence is incorrect, that the one mental state is not immediately induced by the other, that the bodily manifestations must first be interposed between, and that the more rational statement is that we feel sorry because we cry, angry because we strike, afraid because we tremble, and not that we cry, strike, or tremble, because we are sorry, angry, or fearful, as the case may be. Without the bodily states following on the perception, the latter would be purely cognitive in form, pale, colorless, destitute of emotional warmth. We might then see the bear, and judge it best to run, receive the insult and deem it right to strike, but we should not actually feel afraid or angry.
The Principles or Psychology (1890), Vol. 2, 449-50.
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Physicists often quote from T. H. White’s epic novel The Once and Future King, where a society of ants declares, “Everything not forbidden is compulsory.” In other words, if there isn't a basic principle of physics forbidding time travel, then time travel is necessarily a physical possibility. (The reason for this is the uncertainty principle. Unless something is forbidden, quantum effects and fluctuations will eventually make it possible if we wait long enough. Thus, unless there is a law forbidding it, it will eventually occur.)
In Parallel Worlds: a Journey Through Creation, Higher Dimensions, and the Future of the Cosmos (2006), 136.
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Professor Cayley has since informed me that the theorem about whose origin I was in doubt, will be found in Schläfli’s De Eliminatione. This is not the first unconscious plagiarism I have been guilty of towards this eminent man whose friendship I am proud to claim. A more glaring case occurs in a note by me in the Comptes Rendus, on the twenty-seven straight lines of cubic surfaces, where I believe I have followed (like one walking in his sleep), down to the very nomenclature and notation, the substance of a portion of a paper inserted by Schlafli in the Mathematical Journal, which bears my name as one of the editors upon the face.
In Philosophical Transactions of the Royal Society (1864), 642.
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Psychiatrist David Shainberg argued that mental illness, which appears chaotic, is actually the reverse. Mental illness occurs when images of the self become rigid and closed, restricting an open creative response to the world.[Co-author with David Peat]
In John F. Briggs and David Peat, Seven Life Lessons of Chaos: Spiritual Wisdom from the Science of Change (1999, 2000), 29. A footnote gives the source of this idea as from David Shainberg, The Transforming Self: New Dimensions in Psychoanalytic Process (1973).
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Revolutions never occur in mathematics.
Tenth Law in 'Ten “Laws” Concerning Patterns of Change in the History of Mathematics', Historia Mathematica (1975), 2, 165.
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Several days after looking at the Earth a childish thought occurred to me - that we the cosmonauts are being deceived. If we are the first ones in space, then who was it who made the globe correctly? Then this thought was replaced by pride in the human capacity to see with our mind.
Igor Volk
…...
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Since biological change occurs slowly and cultural changes occur in every generation, it is futile to try to explain the fleeting phenomena of culture by a racial constant. We can often explain them—in terms of contact with other peoples, of individual genius, of geography—but not by racial differences.
An Introduction to Cultural Anthropology (1934), 9.
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Since [World War I] we have seen the atomic age, the computer age, the space age, and the bio-engineering age, each as epochal as the Bronze Age, the Iron Age, the Renaissance and the Industrial Revolution. And all these have occurred in one generation. Man has stood on the moon and looked back on the earth, that small planet now reduced to a neighbourhood. But our material achievements have exceeded the managerial capacities of our human minds and institutions.
As quoted in Colin Bingham (ed.), Wit and Wisdom: A Public Affairs Miscellany (1982), 227.
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Society exists through a process of transmission quite as much as biological life. This transmission occurs by means of communication of habits of doing, thinking, and feeling from the older to the younger.
Democracy and Education: an Introduction to the Philosophy of Education (1916), 3.
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Some of my cousins who had the great advantage of University education used to tease me with arguments to prove that nothing has any existence except what we think of it. … These amusing mental acrobatics are all right to play with. They are perfectly harmless and perfectly useless. ... I always rested on the following argument. … We look up to the sky and see the sun. Our eyes are dazzled and our senses record the fact. So here is this great sun standing apparently on no better foundation than our physical senses. But happily there is a method, apart altogether from our physical senses, of testing the reality of the sun. It is by mathematics. By means of prolonged processes of mathematics, entirely separate from the senses, astronomers are able to calculate when an eclipse will occur. They predict by pure reason that a black spot will pass across the sun on a certain day. You go and look, and your sense of sight immediately tells you that their calculations are vindicated. So here you have the evidence of the senses reinforced by the entirely separate evidence of a vast independent process of mathematical reasoning. We have taken what is called in military map-making “a cross bearing.” When my metaphysical friends tell me that the data on which the astronomers made their calculations, were necessarily obtained originally through the evidence of the senses, I say, “no.” They might, in theory at any rate, be obtained by automatic calculating-machines set in motion by the light falling upon them without admixture of the human senses at any stage. When it is persisted that we should have to be told about the calculations and use our ears for that purpose, I reply that the mathematical process has a reality and virtue in itself, and that onie discovered it constitutes a new and independent factor. I am also at this point accustomed to reaffirm with emphasis my conviction that the sun is real, and also that it is hot— in fact hot as Hell, and that if the metaphysicians doubt it they should go there and see.
In My Early Life (1930).
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Spontaneous generation, to put the matter simply, takes place in smaller plants, especially in those that are annuals and herbaceous. But still it occasionally occurs too in larger plants whenever there is rainy weather or some peculiar condition of air or soil; for thus it is said that the silphium sprang up in Libya when a murky and heavy sort of wet weather condition occurred, and that the timber growth which is now there has come from some similar reason or other; for it was not there in former times.
De Causis Plantarum 1.5.1, in Robert Ewing Dengler (trans.) Theophrastus: De Causis Plantarum Book One: Text, Critical Apparatus, Translation, and Commentary, (1927), 31.
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Subatomic particles do not exist but rather show “tendencies to exist”, and atomic events do not occur with certainty at definite times and in definite ways, but rather show “tendencies to occur”.
In The Tao of Physics (1975), 133.
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The alternative to the Big Bang is not, in my opinion, the steady state; it is instead the more general theory of continuous creation. Continuous creation can occur in bursts and episodes. These mini-bangs can produce all the wonderful element-building that Fred Hoyle discovered and contributed to cosmology. This kind of element and galaxy formation can take place within an unbounded, non-expanding universe. It will also satisfy precisely the Friedmann solutions of general relativity. It can account very well for all the facts the Big Bang explains—and also for those devastating, contradictory observations which the Big Bang must, at all costs, pretend are not there
In 'Letters: Wrangling Over the Bang', Science News (27 Jul 1991), 140, No. 4, 51. Also quoted in Roy C. Martin, Astronomy on Trial: A Devastating and Complete Repudiation of the Big Bang Fiasco (1999), Appendix I, 217.
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The ancestors of the higher animals must be regarded as one-celled beings, similar to the Amœbæ which at the present day occur in our rivers, pools, and lakes. The incontrovertible fact that each human individual develops from an egg, which, in common with those of all animals, is a simple cell, most clearly proves that the most remote ancestors of man were primordial animals of this sort, of a form equivalent to a simple cell. When, therefore, the theory of the animal descent of man is condemned as a “horrible, shocking, and immoral” doctrine, tho unalterable fact, which can be proved at any moment under the microscope, that the human egg is a simple cell, which is in no way different to those of other mammals, must equally be pronounced “horrible, shocking, and immoral.”
Translated from his Ueber die Entstehung und den Stammbaum des Menschengeschlechts, (1873), Vol. 2, as an epigraph to Chap. 6, The Evolution of Man, (1879), Vol 1, 120-121.
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The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.
In 'A Mathematician's Gossip', Indiscrete Thoughts (2008), 214.
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The assumption we have made … is that marriages and the union of gametes occur at random. The validity of this assumption may now be examined. “Random mating” obviously does not mean promiscuity; it simply means, as already explained above, that in the choice of mates for marriage there is neither preference for nor aversion to the union of persons similar or dissimilar with respect to a given trait or gene. Not all gentlemen prefer blondes or brunettes. Since so few people know what their blood type is, it is even safer to say that the chances of mates being similar or dissimilar in blood type are determined simply by the incidence of these blood types in a given Mendelian population.
[Co-author with Theodosius Dobzhansky]
In Radiation, Genes and Man (1960), 107.
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The average English author [of mathematical texts] leaves one under the impression that he has made a bargain with his reader to put before him the truth, the greater part of the truth, and nothing but the truth; and that if he has put the facts of his subject into his book, however difficult it may be to unearth them, he has fulfilled his contract with his reader. This is a very much mistaken view, because effective teaching requires a great deal more than a bare recitation of facts, even if these are duly set forth in logical order—as in English books they often are not. The probable difficulties which will occur to the student, the objections which the intelligent student will naturally and necessarily raise to some statement of fact or theory—these things our authors seldom or never notice, and yet a recognition and anticipation of them by the author would be often of priceless value to the student. Again, a touch of humour (strange as the contention may seem) in mathematical works is not only possible with perfect propriety, but very helpful; and I could give instances of this even from the pure mathematics of Salmon and the physics of Clerk Maxwell.
In Perry, Teaching of Mathematics (1902), 59-61.
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The basic symptoms which occur in pneumonia and which are never lacking are acute fever, sticking pain in the side, short rapid breaths, serrated pulse, and cough, mostly with sputum.
As quoted in Robert Taylor, White Coat Tales: Medicine's Heroes, Heritage, and Misadventures (2010), 126.
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The cause of the six-sided shape of a snowflake is none other than that of the ordered shapes of plants and of numerical constants; and since in them nothing occurs without supreme reason—not, to be sure, such as discursive reasoning discovers, but such as existed from the first in the Creators's design and is preserved from that origin to this day in the wonderful nature of animal faculties, I do not believe that even in a snowflake this ordered pattern exists at random.
Di Nive Sexangula, On the Six-Cornered Snowflake (1611), K18, 1. 6-12. Trans. and ed. Colin Hardie (1966), 33.
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The cell, too, has a geography, and its reactions occur in colloidal apparatus, of which the form, and the catalytic activity of its manifold surfaces, must efficiently contribute to the due guidance of chemical reactions.
'Some Aspects of Biochemistry', The Irish Journal of Medical Science (1932), 79, 344.
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The concepts of ‘soul’ or ‘life’ do not occur in atomic physics, and they could not, even indirectly, be derived as complicated consequences of some natural law. Their existence certainly does not indicate the presence of any fundamental substance other than energy, but it shows only the action of other kinds of forms which we cannot match with the mathematical forms of modern atomic physics ... If we want to describe living or mental processes, we shall have to broaden these structures. It may be that we shall have to introduce yet other concepts.
…...
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The divine tape recorder holds a million scenarios, each perfectly sensible. Little quirks at the outset, occurring for no particular reason, unleash cascades of consequences that make a particular feature seem inevitable in retrospect. But the slightest early nudge contacts a different groove, and history veers into another plausible channel, diverging continually from its original pathway. The end results are so different, the initial perturbation so apparently trivial.
…...
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The dogma of the Ghost in the Machine ... maintains that there exist both bodies and minds; that there occur physical processes and mental processes; that there are mechanical causes of corporeal movements and mental causes of corporeal movements.
The Concept of Mind (1949), 22.
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The flights of the imagination which occur to the pure mathematician are in general so much better described in his formulas than in words, that it is not remarkable to find the subject treated by outsiders as something essentially cold and uninteresting— … the only successful attempt to invest mathematical reasoning with a halo of glory—that made in this section by Prof. Sylvester—is known to a comparative few, …
In Presidential Address British Association for the Advancement of Science (1871), Nature Vol. 4, 271,
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The greatest human evils are not those that individuals perform in private, the tiny transgressions against some arbitrary social standard we call sins. The ultimate evils are the mass murders that occur in revolution and war, the large-scale savageries that arise when one agglomeration of humans tries to dominate another: the deeds of the social group. … only group efforts can save us from the sporadic insanities of the group.
In 'The Clint Eastwood Conundrum', The Lucifer Principle: A Scientific Expedition Into the Forces of History (1997), 7.
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The human understanding is unquiet; it cannot stop or rest, and still presses onward, but in vain. Therefore it is that we cannot conceive of any end or limit to the world, but always as of necessity it occurs to us that there is something beyond... But he is no less an unskilled and shallow philosopher who seeks causes of that which is most general, than he who in things subordinate and subaltern omits to do so
From Aphorism 48, Novum Organum, Book I (1620). Collected in James Spedding (ed.), The Works of Francis Bacon (1858), Vol. 4, 57.
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The incomplete knowledge of a system must be an essential part of every formulation in quantum theory. Quantum theoretical laws must be of a statistical kind. To give an example: we know that the radium atom emits alpha-radiation. Quantum theory can give us an indication of the probability that the alpha-particle will leave the nucleus in unit time, but it cannot predict at what precise point in time the emission will occur, for this is uncertain in principle.
The Physicist's Conception of Nature (1958), 41.
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The most ordinary things are to philosophy a source of insoluble puzzles. In order to explain our perceptions it constructs the concept of matter and then finds matter quite useless either for itself having or for causing perceptions in a mind. With infinite ingenuity it constructs a concept of space or time and then finds it absolutely impossible that there be objects in this space or that processes occur during this time ... The source of this kind of logic lies in excessive confidence in the so-called laws of thought.
'On Statistical Mechanics' (1904), in Theoretical Physics and Philosophical Problems (1974), 164-5.
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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 only objections that have occurred to me are, 1st that you have loaded yourself with an unnecessary difficulty in adopting Natura non facit saltum so unreservedly. … And 2nd, it is not clear to me why, if continual physical conditions are of so little moment as you suppose, variation should occur at all. However, I must read the book two or three times more before I presume to begin picking holes.
Comments after reading Darwin's book, Origin of Species.]
Letter to Charles Darwin (23 Nov 1859). 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), 214.
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The phenomena of nature, especially those that fall under the inspection of the astronomer, are to be viewed, not only with the usual attention to facts as they occur, but with the eye of reason and experience.
'An Account of Three Volcanoes on the Moon', read before the Royal Society, Philosophical Transactions (1787). Reprinted in Edward Polehampton, The Gallery of Nature and Art; or, a Tour Through Creation and Science (1815), 183.
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The presentation of mathematics where you start with definitions, for example, is simply wrong. Definitions aren't the places where things start. Mathematics starts with ideas and general concepts, and then definitions are isolated from concepts. Definitions occur somewhere in the middle of a progression or the development of a mathematical concept. The same thing applies to theorems and other icons of mathematical progress. They occur in the middle of a progression of how we explore the unknown.
Interview for website of the Mathematical Association of America.
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The production of motion in the steam engine always occurs in circumstances which it is necessary to recognize, namely when the equilibrium of caloric is restored, or (to express this differently) when caloric passes from the body at one temperature to another body at a lower temperature.
'Réflexions sur la Puissance Motrice du Feu et sur les Machines Propres a Développer cette Puissance' (1824). Trans. Robert Fox, Reflexions on the Motive Power of Fire (1986), 64.
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The proof given by Wright, that non-adaptive differentiation will occur in small populations owing to “drift,” or the chance fixation of some new mutation or recombination, is one of the most important results of mathematical analysis applied to the facts of neo-mendelism. It gives accident as well as adaptation a place in evolution, and at one stroke explains many facts which puzzled earlier selectionists, notably the much greater degree of divergence shown by island than mainland forms, by forms in isolated lakes than in continuous river-systems.
Evolution: The Modern Synthesis (1942), 199-200.
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The Reason of making Experiments is, for the Discovery of the Method of Nature, in its Progress and Operations. Whosoever, therefore doth rightly make Experiments, doth design to enquire into some of these Operations; and, in order thereunto, doth consider what Circumstances and Effects, in the Experiment, will be material and instructive in that Enquiry, whether for the confirming or destroying of any preconceived Notion, or for the Limitation and Bounding thereof, either to this or that Part of the Hypothesis, by allowing a greater Latitude and Extent to one Part, and by diminishing or restraining another Part within narrower Bounds than were at first imagin'd, or hypothetically supposed. The Method therefore of making Experiments by the Royal Society I conceive should be this.
First, To propound the Design and Aim of the Curator in his present Enquiry.
Secondly, To make the Experiment, or Experiments, leisurely, and with Care and Exactness.
Thirdly, To be diligent, accurate, and curious, in taking Notice of, and shewing to the Assembly of Spectators, such Circumstances and Effects therein occurring, as are material, or at least, as he conceives such, in order to his Theory .
Fourthly, After finishing the Experiment, to discourse, argue, defend, and further explain, such Circumstances and Effects in the preceding Experiments, as may seem dubious or difficult: And to propound what new Difficulties and Queries do occur, that require other Trials and Experiments to be made, in order to their clearing and answering: And farther, to raise such Axioms and Propositions, as are thereby plainly demonstrated and proved.
Fifthly, To register the whole Process of the Proposal, Design, Experiment, Success, or Failure; the Objections and Objectors, the Explanation and Explainers, the Proposals and Propounders of new and farther Trials; the Theories and Axioms, and their Authors; and, in a Word the history of every Thing and Person, that is material and circumstantial in the whole Entertainment of the said Society; which shall be prepared and made ready, fairly written in a bound Book, to be read at the Beginning of the Sitting of the Society: The next Day of their Meeting, then to be read over and further discoursed, augmented or diminished, as the Matter shall require, and then to be sign'd by a certain Number of the Persons present, who have been present, and Witnesses of all the said Proceedings, who, by Subscribing their names, will prove undoubted testimony to Posterity of the whole History.
'Dr Hooke's Method of Making Experiments' (1664-5). In W. Derham (ed.), Philosophical Experiments and Observations Of the Late Eminent Dr. Robert Hooke, F.R.S. And Geom. Prof. Gresh. and Other Eminent Virtuoso's in his Time (1726), 26-8.
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The rule for life in the sea can be summed up in the well known expression “big fish eat little fish”. … Research shows that great losses occur in the fish cycle because small fish are eaten by larger ones, and in many cases the larger fish are not fit for human consumption.
In 'Man Explores the Sea', Journal of the Royal Society of Arts (Sep 1963), 111, No. 5086, 787-789.
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The signs of liver inflammation [hepatitis] are eight in number, as follows: high fever, thirst, complete anorexia, a tongue which is initially red and then turns black, biliary vomitus initially yellow egg yolk in color, which later turns dark green, pain on the right side which ascends up to the clavicle. … Occasionally a mild cough may occur and a sensation of heaviness which is first felt on the right side and then spreads widely.
As quoted in Fred Rosner, The Medical Legacy of Moses Maimonides (1998), 53-54.
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The starting point of Darwin’s theory of evolution is precisely the existence of those differences between individual members of a race or species which morphologists for the most part rightly neglect. The first condition necessary, in order that any process of Natural Selection may begin among a race, or species, is the existence of differences among its members; and the first step in an enquiry into the possible effect of a selective process upon any character of a race must be an estimate of the frequency with which individuals, exhibiting any given degree of abnormality with respect to that, character, occur. The unit, with which such an enquiry must deal, is not an individual but a race, or a statistically representative sample of a race; and the result must take the form of a numerical statement, showing the relative frequency with which the various kinds of individuals composing the race occur.
Biometrika: A Joumal for the Statistical Study of Biological Problems (1901), 1, 1-2.
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The student should read his author with the most sustained attention, in order to discover the meaning of every sentence. If the book is well written, it will endure and repay his close attention: the text ought to be fairly intelligible, even without illustrative examples. Often, far too often, a reader hurries over the text without any sincere and vigorous effort to understand it; and rushes to some example to clear up what ought not to have been obscure, if it had been adequately considered. The habit of scrupulously investigating the text seems to me important on several grounds. The close scrutiny of language is a very valuable exercise both for studious and practical life. In the higher departments of mathematics the habit is indispensable: in the long investigations which occur there it would be impossible to interpose illustrative examples at every stage, the student must therefore encounter and master, sentence by sentence, an extensive and complicated argument.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 67.
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The tendency of modern physics is to resolve the whole material universe into waves, and nothing but waves. These waves are of two kinds: bottled-up waves, which we call matter, and unbottled waves, which we call radiation or light. If annihilation of matter occurs, the process is merely that of unbottling imprisoned wave-energy and setting it free to travel through space. These concepts reduce the whole universe to a world of light, potential or existent, so that the whole story of its creation can be told with perfect accuracy and completeness in the six words: 'God said, Let there be light'.
In The Mysterious Universe (1930, 1932), 97-98
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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 here developed is that mega-evolution normally occurs among small populations that become preadaptive and evolve continuously (without saltation, but at exceptionally rapid rates) to radically different ecological positions. The typical pattern involved is probably this: A large population is fragmented into numerous small isolated lines of descent. Within these, inadaptive differentiation and random fixation of mutations occur. Among many such inadaptive lines one or a few are preadaptive, i.e., some of their characters tend to fit them for available ecological stations quite different from those occupied by their immediate ancestors. Such groups are subjected to strong selection pressure and evolve rapidly in the further direction of adaptation to the new status. The very few lines that successfully achieve this perfected adaptation then become abundant and expand widely, at the same time becoming differentiated and specialized on lower levels within the broad new ecological zone.
Tempo and Mode in Evolution (1944), 123.
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The traditional mathematics professor of the popular legend is absentminded. He usually appears in public with a lost umbrella in each hand. He prefers to face a blackboard and to turn his back on the class. He writes a, he says b, he means c, but it should be d. Some of his sayings are handed down from generation to generation:
“In order to solve this differential equation you look at it till a solution occurs to you.”
“This principle is so perfectly general that no particular application of it is possible.”
“Geometry is the science of correct reasoning on incorrect figures.”
“My method to overcome a difficulty is to go round it.”
“What is the difference between method and device? A method is a device which you used twice.”
In How to Solve It: A New Aspect of Mathematical Method (2004), 208.
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The trick in discovering evolutionary laws is the same as it is in discovering laws of physics or chemistry—namely, finding the right level of generalization to make prediction possible. We do not try to find a law that says when and where explosions will occur. We content ourselves with saying that certain sorts of compounds are explosive under the right conditions, and we predict that explosions will occur whenever those conditions are realized.
In 'Paleoanthropology: Science or Mythical Charter?', Journal of Anthropological Research (Summer 2002), 58, No. 2, 193.
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The word “chance” then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order. Probability is relative in part to this ignorance, and in part to our knowledge.
'Mémoire sur les Approximations des Formules qui sont Fonctions de Très Grands Nombres' (1783, published 1786). In Oeuvres complète de Laplace, 14 Vols. (1843-1912), Vol. 10, 296, trans. Charles Coulston Gillispie, Pierre-Simon Laplace 1749-1827: A Life in Exact Science (1997), 91.
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There are still many unsolved problems about bird life, among which are the age that birds attain, the exact time at which some birds acquire their adult dress, and the changes which occur in this with years. Little, too, is known about the laws and routes of bird migration, and much less about the final disposition of the untold thousands which are annually produced.
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There are things out there that are very simple and you never think would work. … Wikipedia is one of those that it would never occur to me that something like that would work. … But it does work. … People who have taken fairly simple ideas, … at a certain scale and after they gain a certain amount of momentum, they can really take off and work. And that’s really an amazing thing.
Guest Lecture, UC Berkeley, 'Search Engines, Technology, and Business' (3 Oct 2005). At 1:13 in the YouTube video.
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There are, as we have seen, a number of different modes of technological innovation. Before the seventeenth century inventions (empirical or scientific) were diffused by imitation and adaption while improvement was established by the survival of the fittest. Now, technology has become a complex but consciously directed group of social activities involving a wide range of skills, exemplified by scientific research, managerial expertise, and practical and inventive abilities. The powers of technology appear to be unlimited. If some of the dangers may be great, the potential rewards are greater still. This is not simply a matter of material benefits for, as we have seen, major changes in thought have, in the past, occurred as consequences of technological advances.
Concluding paragraph of "Technology," in Dictionary of the History of Ideas (1973), Vol. 4, 364.
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Therefore, these [geotectonic] models cannot be expected to assume that the deeper parts of the earth’s crust were put together and built in a simpler way. The myth about the increasing simplicity with depth results from a general pre-scientific trend according to which the unknown or little known has to be considered simpler than the known. Many examples of this myth occur in the history of geology as, for instance, the development of views on the nature of the seafloor from the past to the present.
In 'Stockwerktektonik und Madelle van Esteinsdifferentiation', in Geotektonisches Symposium zu Ehren von Hans Stille, als Festschrift zur Vollendung seines 80, Lebensjahres (1956), 17, trans. Albert V. and Marguerite Carozzi.
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These days, it’s really been uninteresting except when disasters occur.
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These neutrino observations are so exciting and significant that I think we're about to see the birth of an entirely new branch of astronomy: neutrino astronomy. Supernova explosions that are invisible to us because of dust clouds may occur in our galaxy as often as once every 10 years, and neutrino bursts could give us a way to study them.
New York Times (3 Apr 1987)
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Though the world does not change with a change of paradigm, the scientist afterward works in a different world... I am convinced that we must learn to make sense of statements that at least resemble these. What occurs during a scientific revolution is not fully reducible to a re-interpretation of individual and stable data. In the first place, the data are not unequivocally stable.
The Structure of Scientific Revolutions (1962), 120.
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Time has a different quality in a forest, a different kind of flow. Time moves in circles, and events are linked, even if it’s not obvious that they are linked. Events in a forest occur with precision in the flow of tree time, like the motions of an endless dance.
The Wild Trees: A Story of Passion and Daring
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To pick a hole–say in the 2nd law of Ωcs, that if two things are in contact the hotter cannot take heat from the colder without external agency.
Now let A & B be two vessels divided by a diaphragm and let them contain elastic molecules in a state of agitation which strike each other and the sides. Let the number of particles be equal in A & B but let those in A have equal velocities, if oblique collisions occur between them their velocities will become unequal & I have shown that there will be velocities of all magnitudes in A and the same in B only the sum of the squares of the velocities is greater in A than in B.
When a molecule is reflected from the fixed diaphragm CD no work is lost or gained.
If the molecule instead of being reflected were allowed to go through a hole in CD no work would be lost or gained, only its energy would be transferred from the one vessel to the other.
Now conceive a finite being who knows the paths and velocities of all the molecules by simple inspection but who can do no work, except to open and close a hole in the diaphragm, by means of a slide without mass.
Let him first observe the molecules in A and when lie sees one coming the square of whose velocity is less than the mean sq. vel. of the molecules in B let him open a hole & let it go into B. Next let him watch for a molecule in B the square of whose velocity is greater than the mean sq. vel. in A and when it comes to the hole let him draw and slide & let it go into A, keeping the slide shut for all other molecules.
Then the number of molecules in A & B are the same as at first but the energy in A is increased and that in B diminished that is the hot system has got hotter and the cold colder & yet no work has been done, only the intelligence of a very observant and neat fingered being has been employed. Or in short if heat is the motion of finite portions of matter and if we can apply tools to such portions of matter so as to deal with them separately then we can take advantage of the different motion of different portions to restore a uniformly hot system to unequal temperatures or to motions of large masses. Only we can't, not being clever enough.
Letter to Peter Guthrie Tait (11 Dec 1867). In P. M. Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 331-2.
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Truth is born into this world only with pangs and tribulations, and every fresh truth is received unwillingly. To expect the world to receive a new truth, or even an old truth, without challenging it, is to look for one of those miracles which do not occur.
In 'Alfred Russel Wallace: An interview by W. B. Northrop', The Outlook (1913), 105, 622.
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Twitching occurs in all parts that can stretch, but never occurs in bones and cartilages, because bones and cartilages do not stretch in any way.
As quoted in Robert Taylor, White Coat Tales: Medicine's Heroes, Heritage, and Misadventures (2010), 125.
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Two forms or species are sympatric, if they occur together, that is if their areas of distribution overlap or coincide. Two forms (or species) are allapatric, if they do not occur together, that is if they exclude each other geographically. The term allopatric is primarily useful in denoting geographic representatives.
Systematics and the Origin of Species: From the Viewpoint of a Zoologist (1942), 148-9.
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We cannot doubt of our existence while we doubt, and that this is the first knowledge we acquire when we philosophize in order. … The knowledge, I think, therefore I am, is the first and most certain that occurs to one who philosophizes orderly.
From the original Latin: “Non posse à nobis dubitari, quin existamus dum dubitamus; atque quod ordine philosophando cognoscimus. … Ac proinde hæc cognitio, ego cognito, ergo sum, est omnium | prima & certissima, quæ cuilibet ordine philosophanti occurant,” in Principia Philosophiæ (1644), Pars Prima, as collected in Charles Adam and Paul Tannery, Œuvres de Descartes (1905), Vol. 8, Proposition VII, 6-7. English version as given in John Veitch (trans.), The Method, Meditations, and Selections from the Principles of Descartes (1880), 195.
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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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When I worked on the polio vaccine, I had a theory. Experiments were done to determine what might or might not occur. I guided each one by imagining myself in the phenomenon in which I was interested. The intuitive realm is constantly active—the realm of imagination guides my thinking.
From interview with James Reston, Jr., in Pamela Weintraub (ed.), The Omni Interviews (1984), 98. Previously published in magazine, Omni (May 1982).
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While a glacier is moving, it rubs and wears down the bottom on which it moves, scrapes its surface (now smooth), triturates the broken-off material that is found between the ice and the rock, pulverizes or reduces it to a clayey paste, rounds angular blocks that resist its pressure, and polishes those having a larger surface. At the surface of the glacier, other processes occur. Fragments of rocks that are broken-off from the neighbouring walls and fall on the ice, remain there or can be transported to the sides; they advance in this way on the top of the glacier, without moving or rubbing against each other … and arrive at the extremity of the glacier with their angles, sharp edges, and their uneven surfaces intact.
La théorie des glaciers et ses progrès les plus récents. Bibl. universelle de Genève, (3), Vol. 41, p.127. Trans. Karin Verrecchia.
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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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You’ll be tempted to grouse about the instability of taxonomy; but stability occurs only where people stop thinking and stop working.
In 'Preface', Observing Marine Invertebrates: Drawings from the Laboratory (1987), xvi.
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[A contemporary study] predicted the loss of two-thirds of all tropical forests by the turn of the century. Hundreds of thousands of species will perish, and this reduction of 10 to 20 percent of the earth’s biota will occur in about half a human life span. … This reduction of the biological diversity of the planet is the most basic issue of our time.
Foreword, written for Michael Soulé and Bruce Wilcox (eds.), papers from the 1978 International Conference on Conservation Biology, collected as Conservation Biology (1980), ix. As quoted and cited in Timothy J. Farnham, Saving Nature's Legacy: Origins of the Idea of Biological Diversity (2007), 208.
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[My] numberless observations... made on the Strata... [have] made me confident of their uniformity throughout this Country & [have] led me to conclude that the same regularity... will be found to extend to every part of the Globe for Nature has done nothing by piecemeal. [T]here is no inconsistency in her productions. [T]he Horse never becomes an Ass nor the Crab an Apple by any intermixture or artificial combination whatever[. N]or will the Oak ever degenerate into an Ash or an Ash into an Elm. [H]owever varied by Soil or Climate the species will still be distinct on this ground. [T]hen I argue that what is found here may be found elsewhere[.] When proper allowances are made for such irregularities as often occur and the proper situation and natural agreement is well understood I am satisfied there will be no more difficulty in ascertaining the true quality of the Strata and the place of its possition [sic] than there is now in finding the true Class and Character of Plants by the Linean [sic] System.
Natural Order of the Strata in England and Wales Accurately Delineated and Described, unpublished manuscript, Department of Geology, University of Oxford, 1801, f. 7v.
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[When combustion occurs,] one body, at least, is oxygenated, and another restored, at the same time, to its combustible state... This view of combustion may serve to show how nature is always the same, and maintains her equilibrium by preserving the same quantities of air and water on the surface of our globe: for as fast as these are consumed in the various processes of combustion, equal quantities are formed, and rise regenerated like the Phoenix from her ashes.
Fulhame believed 'that water was the only source of oxygen, which oxygenates combustible bodies' and that 'the hydrogen of water is the only substance that restores bodies to their combustible state.'
An Essay on Combustion with a View to a New Art of Dyeing and Painting (1794), 179-180. In Marilyn Bailey Ogilvie and Joy Dorothy Harvey, The Biographical Dictionary of Women in Science (2000), 478.
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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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Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
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Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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