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Follow Quotes (389 quotes)

... every chemical combination is wholly and solely dependent on two opposing forces, positive and negative electricity, and every chemical compound must be composed of two parts combined by the agency of their electrochemical reaction, since there is no third force. Hence it follows that every compound body, whatever the number of its constituents, can be divided into two parts, one of which is positively and the other negatively electrical.
Essai sur la théorie des proportions chemiques (1819), 98. Quoted by Henry M. Leicester in article on Bessel in Charles Coulston Gillespie (editor), Dictionary of Scientific Biography (1981), Vol. 2, 94.
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… the three positive characteristics that distinguish mathematical knowledge from other knowledge … may be briefly expressed as follows: first, mathematical knowledge bears more distinctly the imprint of truth on all its results than any other kind of knowledge; secondly, it is always a sure preliminary step to the attainment of other correct knowledge; thirdly, it has no need of other knowledge.
In Mathematical Essays and Recreations (1898), 35.
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…the Form or true definition of heat … is in few words as follows: Heat is a motion; expansive, restrained, and acting in its strife upon the smaller particles of bodies. But the expansion is thus modified; while it expands all ways, it has at the same time an inclination upward. And the struggle in the particles is modified also; it is not sluggish, but hurried and with violence.
Novum Organum (1620), Book 2, Aphorism 20. Translated as 'First Vintage Concerning the Form of Heat', The New Organon: Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man), collected in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 4, 154-5.
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…The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science. Einstein’s special theory of relativity, which explains the indeterminateness of the frame of space and time, crowns the work of Copernicus who first led us to give up our insistence on a geocentric outlook on nature; Einstein's general theory of relativity, which reveals the curvature or non-Euclidean geometry of space and time, carries forward the rudimentary thought of those earlier astronomers who first contemplated the possibility that their existence lay on something which was not flat. These earlier revolutions are still a source of perplexity in childhood, which we soon outgrow; and a time will come when Einstein’s amazing revelations have likewise sunk into the commonplaces of educated thought.
In The Theory of Relativity and its Influence on Scientific Thought (1922), 31-32
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…there is no prescribed route to follow to arrive at a new idea. You have to make the intuitive leap. But the difference is that once you’ve made the intuitive leap you have to justify it by filling in the intermediate steps. In my case, it often happens that I have an idea, but then I try to fill in the intermediate steps and find that they don’t work, so I have to give it up.
In Michael Harwood, 'The Universe and Dr. Hawking', New York Times Magazine (23 Jan 1983), 53.
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“Every moment dies a man,/ Every moment one is born”:
I need hardly point out to you that this calculation would tend to keep the sum total of the world's population in a state of perpetual equipoise whereas it is a well-known fact that the said sum total is constantly on the increase. I would therefore take the liberty of suggesting that in the next edition of your excellent poem the erroneous calculation to which I refer should be corrected as follows:
'Every moment dies a man / And one and a sixteenth is born.” I may add that the exact figures are 1.167, but something must, of course, be conceded to the laws of metre.
Unpublished letter to Tennyson in response to his Vision of Sin (1842). Quoted in Philip and Emily Morrison, Charles Babbage and his Calculating Engines: Selected Writings by Charles Babbage and Others (1961), xxiii.
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[Animals] do not so much act as be put into action, and that objects make an impression on their senses such that it is necessary for them to follow it just as it is necessary for the wheels of a clock to follow the weights and the spring that pulls them.
[In his philosophy, he regarded animals to be merely automatons.].
'Traitez de la voix', Harmonie Universelle (1637), Vol. 1, prop. lii, 79. In Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 318.
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[Benjamin Peirce's] lectures were not easy to follow. They were never carefully prepared. The work with which he rapidly covered the blackboard was very illegible, marred with frequent erasures, and not infrequent mistakes (he worked too fast for accuracy). He was always ready to digress from the straight path and explore some sidetrack that had suddenly attracted his attention, but which was likely to have led nowhere when the college bell announced the close of the hour and we filed out, leaving him abstractedly staring at his work, still with chalk and eraser in his hands, entirely oblivious of his departing class.
Writing as a Professor Emeritus at Harvard University, a former student of Peirce, in 'Benjamin Peirce: II. Reminiscences', The American Mathematical Monthly (Jan 1925), 32, No. 1, 6.
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[Euclid's Elements] has been for nearly twenty-two centuries the encouragement and guide of that scientific thought which is one thing with the progress of man from a worse to a better state. The encouragement; for it contained a body of knowledge that was really known and could be relied on, and that moreover was growing in extent and application. For even at the time this book was written—shortly after the foundation of the Alexandrian Museum—Mathematics was no longer the merely ideal science of the Platonic school, but had started on her career of conquest over the whole world of Phenomena. The guide; for the aim of every scientific student of every subject was to bring his knowledge of that subject into a form as perfect as that which geometry had attained. Far up on the great mountain of Truth, which all the sciences hope to scale, the foremost of that sacred sisterhood was seen, beckoning for the rest to follow her. And hence she was called, in the dialect of the Pythagoreans, ‘the purifier of the reasonable soul.’
From a lecture delivered at the Royal Institution (Mar 1873), collected postumously in W.K. Clifford, edited by Leslie Stephen and Frederick Pollock, Lectures and Essays, (1879), Vol. 1, 296.
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[J.J.] Sylvester’s methods! He had none. “Three lectures will be delivered on a New Universal Algebra,” he would say; then, “The course must be extended to twelve.” It did last all the rest of that year. The following year the course was to be Substitutions-Théorie, by Netto. We all got the text. He lectured about three times, following the text closely and stopping sharp at the end of the hour. Then he began to think about matrices again. “I must give one lecture a week on those,” he said. He could not confine himself to the hour, nor to the one lecture a week. Two weeks were passed, and Netto was forgotten entirely and never mentioned again. Statements like the following were not unfrequent in his lectures: “I haven’t proved this, but I am as sure as I can be of anything that it must be so. From this it will follow, etc.” At the next lecture it turned out that what he was so sure of was false. Never mind, he kept on forever guessing and trying, and presently a wonderful discovery followed, then another and another. Afterward he would go back and work it all over again, and surprise us with all sorts of side lights. He then made another leap in the dark, more treasures were discovered, and so on forever.
As quoted by Florian Cajori, in Teaching and History of Mathematics in the United States (1890), 265-266.
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[Simplicio] is much puzzled and perplexed. I think I hear him say, 'To whom then should we repair for the decision of our controversies if Aristotle were removed from the choir? What other author should we follow in the schools, academies, and studies? What philosopher has written all the divisions of Natural Philosophy, and so methodically, without omitting as much as a single conclusion? Shall we then overthrow the building under which so many voyagers find shelter? Shall we destroy that sanctuary, that Prytaneum, where so many students find commodious harbour; where without exposing himself to the injuries of the air, with only the turning over of a few leaves, one may learn all the secrets of Nature.'
Dialogue on the Great World Systems (1632). Revised and Annotated by Giorgio De Santillana (1953), 66.
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Considerate la vostra semenza:
Fatti non foste a viver come bruti,
Ma per seguir virtute e conoscenza
.
Consider your origins: you were not made to live as brutes, but to follow virtue and knowledge.
Divina Commedia 'Inferno', canto 26, l.118.
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Every teacher certainly should know something of non-euclidean geometry. Thus, it forms one of the few parts of mathematics which, at least in scattered catch-words, is talked about in wide circles, so that any teacher may be asked about it at any moment. … Imagine a teacher of physics who is unable to say anything about Röntgen rays, or about radium. A teacher of mathematics who could give no answer to questions about non-euclidean geometry would not make a better impression.
On the other hand, I should like to advise emphatically against bringing non-euclidean into regular school instruction (i.e., beyond occasional suggestions, upon inquiry by interested pupils), as enthusiasts are always recommending. Let us be satisfied if the preceding advice is followed and if the pupils learn to really understand euclidean geometry. After all, it is in order for the teacher to know a little more than the average pupil.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 72.
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Indiana Jones: Archaeology is the search for fact… not truth. If it’s truth you're looking for, Dr. Tyree’s philosophy class is right down the hall. … So forget any ideas you've got about lost cities, exotic travel, and digging up the world. We do not follow maps to buried treasure, and “X” never, ever marks the spot. Seventy percent of all archaeology is done in the library. Research. Reading.
Spoken by actor Harrison Ford as character Indiana Jones in movie, Indiana Jones and the Last Crusade (1989).
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L’homme ne poursuit que des chimères.
Man follows only phantoms.
His true last words, according to De Morgan. As quoted in Augustus De Morgan, Budget of Paradoxes (1915), Vol. 2, 3.
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La vérité est sur une courbe dont notre ésprit suit éternellement l'asymptote. (Oct 1879)
Truth is on a curve whose asymptote our spirit follows eternally.
In Recueil d'Œuvres de Léo Errera: Botanique Générale (1908), 193. As translated in John Arthur Thomson, Introduction to Science (1911), 57,
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Steckt keine Poesie in der Lokomotive, die brausend durch die Nacht zieht und über die zitternde Erde hintobt, als wollte sie Raum und Zeit zermalmen, in dem hastigen, aber wohl geregelten Zucken und Zerren ihrer gewaltigen Glieder, in dem stieren, nur auf ein Ziel losstürmenden Blick ihrer roten Augen, in dem emsigen, willenlosen Gefolge der Wagen, die kreischend und klappernd, aber mit unfehlbarer Sicherheit dem verkörperten Willen aus Eisen und Stahl folge leisten?
Is there no poetry in the locomotive roaring through the night and charging over the quivering earth as if it wanted to crush time and space? Is there no poetry in the hasty but regular jerking and tugging of its powerful limbs, in the stare of its red eyes that never lose sight of their goal? Is there no poetry in the bustling, will-less retinue of cars that follow, screeching and clattering with unmistakable surety, the steel and iron embodiment of will?
Max Eyth
From 'Poesie und Technik' (1904) (Poetry and Technology), in Schweizerische Techniker-Zeitung (1907), Vol 4, 306, as translated in Paul A. Youngman, Black Devil and Iron Angel: The Railway in Nineteenth-Century German Realism (2005), 128.
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~~[Unverified]~~ Why has elegance found so little following? Elegance has the disadvantage that hard work is needed to achieve it and a good education to appreciate it.
Webmaster has thus far found no primary source for verification. (Can you help?)
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A closer look at the course followed by developing theory reveals for a start that it is by no means as continuous as one might expect, but full of breaks and at least apparently not along the shortest logical path. Certain methods often afforded the most handsome results only the other day, and many might well have thought that the development of science to infinity would consist in no more than their constant application. Instead, on the contrary, they suddenly reveal themselves as exhausted and the attempt is made to find other quite disparate methods. In that event there may develop a struggle between the followers of the old methods and those of the newer ones. The former's point of view will be termed by their opponents as out-dated and outworn, while its holders in turn belittle the innovators as corrupters of true classical science.
In 'On the Development of the Methods of Theoretical Physics in Recent Times', Populäre Schriften, Essay 14. Address (22 Sep 1899) to the Meeting of Natural Scientists at Munich. Collected in Brian McGuinness (ed.), Ludwig Boltzmann: Theoretical Physics and Philosophical Problems, Selected Writings (1974), 79.
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A contradiction (between science and religion) is out of the question. What follows from science are, again and again, clear indications of God’s activity which can be so strongly perceived that Kepler dared to say (for us it seems daring, not for him) that he could ‘almost touch God with his hand in the Universe.’
…...
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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 good theoretical physicist today might find it useful to have a wide range of physical viewpoints and mathematical expressions of the same theory (for example, of quantum electrodynamics) available to him. This may be asking too much of one man. Then new students should as a class have this. If every individual student follows the same current fashion in expressing and thinking about electrodynamics or field theory, then the variety of hypotheses being generated to understand strong interactions, say, is limited. Perhaps rightly so, for possibly the chance is high that the truth lies in the fashionable direction. But, on the off-chance that it is in another direction—a direction obvious from an unfashionable view of field theory—who will find it?
In his Nobel Prize Lecture (11 Dec 1965), 'The Development of the Space-Time View of Quantum Electrodynamics'. Collected in Stig Lundqvist, Nobel Lectures: Physics, 1963-1970 (1998), 177.
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A good title should aim at making what follows as far as possible superfluous to those who know anything of the subject.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 229.
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A hundred years ago … an engineer, Herbert Spencer, was willing to expound every aspect of life, with an effect on his admiring readers which has not worn off today.
Things do not happen quite in this way nowadays. This, we are told, is an age of specialists. The pursuit of knowledge has become a profession. The time when a man could master several sciences is past. He must now, they say, put all his efforts into one subject. And presumably, he must get all his ideas from this one subject. The world, to be sure, needs men who will follow such a rule with enthusiasm. It needs the greatest numbers of the ablest technicians. But apart from them it also needs men who will converse and think and even work in more than one science and know how to combine or connect them. Such men, I believe, are still to be found today. They are still as glad to exchange ideas as they have been in the past. But we cannot say that our way of life is well-fitted to help them. Why is this?
In 'The Unification of Biology', New Scientist (11 Jan 1962), 13, No. 269, 72.
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Sigmund Freud quote: A layman will no doubt find it hard to understand how pathological disorders of the body and mind can be el
A layman will no doubt find it hard to understand how pathological disorders of the body and mind can be eliminated by 'mere' words. He will feel that he is being asked to believe in magic. And he will not be so very wrong, for the words which we use in our everyday speech are nothing other than watered-down magic. But we shall have to follow a roundabout path in order to explain how science sets about restoring to words a part at least of their former magical power.
Psychical (or Mental) Treatment (1905), In James Strachey (ed.), The Standard Edition of the Complete Psychological Works of Sigmund Freud (1953), Vol. 7, 283.
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A vital phenomenon can only be regarded as explained if it has been proven that it appears as the result of the material components of living organisms interacting according to the laws which those same components follow in their interactions outside of living systems.
Gesammelte Schriften (1904), Vol. 3, 767. Trans. Paul F. Cranefield, 'The Organic Physics of 1847 and the Biophysics of Today', Journal of the History of Medicine and Allied Sciences, 1957, 12, 410.
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Accordingly the primordial state of things which I picture is an even distribution of protons and electrons, extremely diffuse and filling all (spherical) space, remaining nearly balanced for an exceedingly long time until its inherent instability prevails. We shall see later that the density of this distribution can be calculated; it was about one proton and electron per litre. There is no hurry for anything to begin to happen. But at last small irregular tendencies accumulate, and evolution gets under way. The first stage is the formation of condensations ultimately to become the galaxies; this, as we have seen, started off an expansion, which then automatically increased in speed until it is now manifested to us in the recession of the spiral nebulae.
As the matter drew closer together in the condensations, the various evolutionary processes followed—evolution of stars, evolution of the more complex elements, evolution of planets and life.
The Expanding Universe (1933), 56-57.
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After I had addressed myself to this very difficult and almost insoluble problem, the suggestion at length came to me how it could be solved with fewer and much simpler constructions than were formerly used, if some assumptions (which are called axioms) were granted me. They follow in this order.
There is no one center of all the celestial circles or spheres.
The center of the earth is not the center of the universe, but only of gravity and of the lunar sphere.
All the spheres revolve about the sun as their mid-point, and therefore the sun is the center of the universe.
The ratio of the earth’s distance from the sun to the height of the firmament is so much smaller than the ratio of the earth’s radius to its distance from the sun that the distance from the earth to the sun is imperceptible in comparison with the height of the firmament.
Whatever motion appears in the firmament arises not from any motion of the firmament, but from the earth’s motion. The earth together with its circumjacent elements performs a complete rotation on its fixed poles in a daily motion, while the firmament and highest heaven abide unchanged.
What appears to us as motions of the sun arise not from its motion but from the motion of the earth and our sphere, with which we revolve about the sun like any other planet. The earth has, then, more than one motion.
The apparent retrograde and direct motion of the planets arises not from their motion but from the earth’s. The motion of the earth alone, therefore, suffices to explain so many apparent inequalities in the heavens.
'The Commentariolus', in Three Copernican Treatises (c.1510), trans. E. Rosen (1939), 58-9.
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All err the more dangerously because each follows a truth. Their mistake lies not in following a falsehood but in not following another truth.
From Pensées, as translated in W.H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms (1966), 325. From the original French, “Tous errent d'autant plus dangereusement qu’ils suivent chacun une vérité. Leur faute n’est pas de suivre une fausseté, mais de ne pas suivre une autre vérité,” in Oeuvres Complètes (1864), Vol. 1, 363.
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All human affairs follow nature's great analogue, the growth of vegetation. There are three periods of growth in every plant. The first, and slowest, is the invisible growth by the root; the second and much accelerated is the visible growth by the stem; but when root and stem have gathered their forces, there comes the third period, in which the plant quickly flashes into blossom and rushes into fruit.
The beginnings of moral enterprises in this world are never to be measured by any apparent growth. ... At length comes the sudden ripeness and the full success, and he who is called in at the final moment deems this success his own. He is but the reaper and not the labourer. Other men sowed and tilled and he but enters into their labours.
Life Thoughts (1858), 20.
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All our knowledge has been built communally; there would be no astrophysics, there would be no history, there would not even be language, if man were a solitary animal. What follows? It follows that we must be able to rely on other people; we must be able to trust their word. That is, it follows that there is a principle, which binds society together because without it the individual would be helpless to tell the truth from the false. This principle is truthfulness.
In Lecture at M.I.T. (19 Mar 1953), collected in 'The Sense of Human Dignity', Science and Human Values (1956, 1990), 57.
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All that comes above that surface [of the globe] lies within the province of Geography. All that comes below that surface lies inside the realm of Geology. The surface of the earth is that which, so to speak, divides them and at the same time “binds them together in indissoluble union.” We may, perhaps, put the case metaphorically. The relationships of the two are rather like that of man and wife. Geography, like a prudent woman, has followed the sage advice of Shakespeare and taken unto her “an elder than herself;” but she does not trespass on the domain of her consort, nor could she possibly maintain the respect of her children were she to flaunt before the world the assertion that she is “a woman with a past.”
From Anniversary Address to Geological Society of London (20 Feb 1903), 'The Relations of Geology', published in Quarterly Journal of the Geological Society of London (22 May 1903), 59, Part 2, lxxviii. As reprinted in Annual Report of the Board of Regents of the Smithsonian Institution (1904), 373.
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All that we can hope from these inspirations, which are the fruits of unconscious work, is to obtain points of departure for such calculations. As for the calculations themselves, they must be made in the second period of conscious work which follows the inspiration, and in which the results of the inspiration are verified and the consequences deduced.
Science and Method (1914, 2003), 62.
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Always be suspicious of conclusions that reinforce uncritical hope and follow comforting traditions of Western thought.
From The Flamingo's Smile (1987), 401.
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America has always been greatest when we dared to be great. We can reach for greatness again. We can follow our dreams to distant stars, living and working in space for peaceful, economic, and scientific gain. Tonight, I am directing NASA to develop a permanently manned space station and to do it within a decade.
From State of the Union Address (25 Jan 1984).
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Among all highly civilized peoples the golden age of art has always been closely coincident with the golden age of the pure sciences, particularly with mathematics, the most ancient among them.
This coincidence must not be looked upon as accidental, but as natural, due to an inner necessity. Just as art can thrive only when the artist, relieved of the anxieties of existence, can listen to the inspirations of his spirit and follow in their lead, so mathematics, the most ideal of the sciences, will yield its choicest blossoms only when life’s dismal phantom dissolves and fades away, when the striving after naked truth alone predominates, conditions which prevail only in nations while in the prime of their development.
From Die Entwickelung der Mathematik im Zusammenhange mit der Ausbreitung der Kultur (1893), 4. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 191-192. From the original German, “Bei allen Kulturvölkern ist die Blüthezeit der Kunst auch immer zeitlich eng verbunden mit einer Blüthezeit der reinen Wissenschaften, insbesondere der ältesten unter ihnen, der Mathematik.
Dieses Zusammentreffen dürfte auch nicht ein zufälliges, sondern ein natürliches, ein Ergebniss innerer Notwendigkeit sein. Wie die Kunst nur gedeihen kann, wenn der Künstler, unbekümmert um die Bedrängnisse des Daseins, den Eingebungen seines Geistes lauschen und ihnen folgen kann, so kann die idealste Wissenschaft, die Mathematik, erst dann ihre schönsten Blüthen treiben, wenn des Erdenlebens schweres Traumbild sinkt und sinkt und sinkt, wenn das Streben nach der nackten Wahrheit allein bestimmend ist, was nur bei Nationen in der Vollkraft ihrer Entwickelung vorkommt.”
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Among natural bodies some have, and some have not, life; and by life we mean the faculties of self-nourishment, self-growth and self-decay. Thus every natural body partaking of life may be regarded as an essential existence; … but then it is an existence only in combination. … And since the organism is such a combination, being possessed of life, it cannot be the Vital Principle. Therefore it follows that the Vital Principle most be an essence, as being the form of a natural body, holding life in potentiality; but essence is a reality (entetechie). The Vital Principle is the original reality of a natural body endowed with potential life; this, however, is to be understood only of a body which may be organized. Thus the parts even of plants are organs, but they are organs that are altogether simple; as the leaf which is the covering of the pericarp, the pericarp of the fruit. If, then, there be any general formula for every kind of Vital Principle, it is—tthe primary reality of an organism.
Aristotle
In George Henry Lewes, Aristotle (1864), 231.
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And from this such small difference of eight minutes [of arc] it is clear why Ptolemy, since he was working with bisection [of the linear eccentricity], accepted a fixed equant point… . For Ptolemy set out that he actually did not get below ten minutes [of arc], that is a sixth of a degree, in making observations. To us, on whom Divine benevolence has bestowed the most diligent of observers, Tycho Brahe, from whose observations this eight-minute error of Ptolemy’s in regard to Mars is deduced, it is fitting that we accept with grateful minds this gift from God, and both acknowledge and build upon it. So let us work upon it so as to at last track down the real form of celestial motions (these arguments giving support to our belief that the assumptions are incorrect). This is the path I shall, in my own way, strike out in what follows. For if I thought the eight minutes in [ecliptic] longitude were unimportant, I could make a sufficient correction (by bisecting the [linear] eccentricity) to the hypothesis found in Chapter 16. Now, because they could not be disregarded, these eight minutes alone will lead us along a path to the reform of the whole of Astronomy, and they are the matter for a great part of this work.
Astronomia Nova, New Astronomy (1609), ch. 19, 113-4, Johannes Kepler Gesammelte Werke (1937-), Vol. 3, 177-8.
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And from true lordship it follows that the true God is living, intelligent, and powerful; from the other perfections, that he is supreme, or supremely perfect. He is eternal and infinite, omnipotent and omniscient; that is, he endures from eternity to eternity; and he is present from infinity to infinity; he rules all things, and he knows all things that happen or can happen.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), General Scholium, 941.
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And this grey spirit yearning in desire, To follow knowledge like a sinking star, beyond the utmost bound of human thought.
From poem, 'Ulysses', collected in The Complete Poetical Works of Tennyson (1909), Vol. 2, 89.
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And this is a miracle of nature in part known, namely, that iron follows the part of a magnet that touches it, and flies from the other part of the same magnet. And the iron turns itself after moving to the part of the heavens conformed to the part of the magnet which it touched.
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As a teenage fisherman, I watched and followed terns to find fish. Later I studied terns for my Ph.D. During those studies I came to see and love other seabirds. Albatrosses are the biggest, so they get your attention.
In 'Field Notes', National Geographic (Dec 2007).
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As ideas are preserved and communicated by means of words, it necessarily follows that we cannot improve the language of any science, without at the same time improving the science itself; neither can we, on the other hand, improve a science without improving the language or nomenclature which belongs to it.
Elements of Chemistry (1790), trans. R. Kerr, Preface, xiv-v.
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As mineralogy constitutes a part of chemistry, it is clear that this arrangement [of minerals] must derive its principles from chemistry. The most perfect mode of arrangement would certainly be to allow bodies to follow each other according to the order of their electro-chemical properties, from the most electro-negative, oxygen, to the most electro-positive, potassium; and to place every compound body according to its most electro-positive ingredient.
An Attempt to Establish a Pure Scientific System of Mineralogy (1814), trans. J. Black, 48.
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As we discern a fine line between crank and genius, so also (and unfortunately) we must acknowledge an equally graded trajectory from crank to demagogue. When people learn no tools of judgment and merely follow their hopes, the seeds of political manipulation are sown.
…...
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Before delivering your lectures, the manuscript should be in such a perfect form that, if need be, it could be set in type. Whether you follow the manuscript during the delivery of the lecture is purely incidental. The essential point is that you are thus master of the subject matter.
Advice to his son. As quoted in Ralph Oesper, The Human Side Of Scientists (1975), 185.
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Before his [Sir Astley Cooper’s] time, operations were too often frightful alternatives or hazardous compromises; and they were not seldom considered rather as the resource of despair than as a means of remedy; he always made them follow, as it were, in the natural course of treatment; he gave them a scientific character; and he moreover, succeeded, in a great degree, in divesting them of their terrors, by performing them unostentatiously, simply, confidently, and cheerfully, and thereby inspiring the patient with hope of relief, where previously resignation under misfortune had too often been all that could be expected from the sufferer.
In John Forbes (ed.), British and Foreign Medical Review (Jul 1840), 10, No. 19, 104. In Bransby Blake Cooper, The Life of Sir Astley Cooper (1843), Vol. 2, 37.
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Before Kuhn, most scientists followed the place-a-stone-in-the-bright-temple-of-knowledge tradition, and would have told you that they hoped, above all, to lay many of the bricks, perhaps even the keystone, of truth’s temple. Now most scientists of vision hope to foment revolution. We are, therefore, awash in revolutions, most self-proclaimed.
…...
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Books must follow sciences, and not sciences books.
In 'A Proposal for Amending the Laws of England' (1616). Collected in The Works, with Several Additional Pieces Never Before Printed (1740), Vol. 4, 5.
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But … the working scientist … is not consciously following any prescribed course of action, but feels complete freedom to utilize any method or device whatever which in the particular situation before him seems likely to yield the correct answer. … No one standing on the outside can predict what the individual scientist will do or what method he will follow.
In Reflections of a Physicist: A Collection of Essays (1955, 1980), 83.
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But no pursuit at Cambridge was followed with nearly so much eagerness or gave me so much pleasure as collecting beetles. It was the mere passion for collecting, for I did not dissect them, and rarely compared their external characters with published descriptions, but got them named anyhow. I will give a proof of my zeal: one day, on tearing off some old bark, I saw two rare beetles, and seized one in each hand; then I saw a third and new kind, which I could not bear to lose, so that I popped the one which I held in my right hand into my mouth. Alas! it ejected some intensely acrid fluid, which burnt my tongue so that I was forced to spit the beetle out, which was lost, as was the third one.
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), 20.
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By the fruit one judges the tree; the tree of science grows exceedingly slowly; centuries elapse before one can pluck the ripe fruits; even today it is hardly possible for us to shell and appraise the kernel of the teachings that blossomed in the seventeenth century. He who sows cannot therefore judge the worth of the corn. He must have faith in the fruitfulness of the seed in order that he may follow untiringly his chosen furrow when he casts his ideas to the four winds of heaven.
As quoted in Philipp Frank, Modern Science and its Philosophy (1949), 62, which cites Évolution de la Mécanique (1903).
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Can the cause be reached from knowledge of the effect with the same certainty as the effect can be shown to follow from its cause? Is it possible for one effect to have many causes? If one determinate cause cannot be reached from the effect, since there is no effect which has not some cause, it follows that an effect, when it has one cause, may have another, and so that there may be several causes of it.
As quoted in Alistair Cameron Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100-1700 (1971), 81.
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Characteristically skeptical of the idea that living things would faithfully follow mathematical formulas, [Robert Harper] seized upon factors in corn which seemed to blend in the hybrid—rather than be represented by plus or minus signs, and put several seasons into throwing doubt upon the concept of immutable hypothetical units of inheritance concocted to account for selected results.
In 'Robert Almer Harper', National Academy Biographical Memoirs (1948), 25, 233-234.
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Consider the hateful brew compounded with gleaming, deadly white lead whose fresh colour is like milk…. Over the victim’s jaws and in the grooves of the gums is plastered an astringent froth, and the furrow of the tongue turns rough on either side, and the depth of the throat grows somewhat dry, and from the pernicious venom follows a dry retching and hawking, for this affliction is severe; meanwhile his spirit sickens and he is worn out with mortal suffering. His body too grows chill, while sometimes his eyes behold strange illusions or else he drowses; nor can he bestir his limbs as heretofore, and he succumbs to the overmastering fatigue.
Nicander
As translated by A.S.F. Gow and A.F. Scholfield in Nicander: The Poems and Portical Fragments (1953), 99.
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Contrary to popular parlance, Darwin didn't discover evolution. He uncovered one (most would say the) essential mechanism by which it operates: natural selection. Even then, his brainstorm was incomplete until the Modern Synthesis of the early/mid-20th century when (among other things) the complementary role of genetic heredity was fully realized. Thousands upon thousands of studies have followed, providing millions of data points that support this understanding of how life on Earth has come to be as it is.
In online article, 'The Day That Botany Took on Bobby Jindal by Just Being Itself', Huffington Post (5 Aug 2013).
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Deprived, therefore, as regards this period, of any assistance from history, but relieved at the same time from the embarrassing interference of tradition, the archaeologist is free to follow the methods which have been so successfully pursued in geology—the rude bone and stone implements of bygone ages being to the one what the remains of extinct animals are to the other. The analogy may be pursued even further than this. Many mammalia which are extinct in Europe have representatives still living in other countries. Our fossil pachyderms, for instance, would be almost unintelligible but for the species which still inhabit some parts of Asia and Africa; the secondary marsupials are illustrated by their existing representatives in Australia and South America; and in the same manner, if we wish clearly to understand the antiquities of Europe, we must compare them with the rude implements and weapons still, or until lately, used by the savage races in other parts of the world. In fact, the Van Diemaner and South American are to the antiquary what the opossum and the sloth are to the geologist.
Pre-historic Times, as Illustrated by Ancient Remains, and the Manners and Customs of Modern Savages, (2nd ed. 1869, 1890), 429-430.
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Describing laughter: The sound is produced by a deep inspiration followed by short, interrupted, spasmodic contractions of the chest, and especially the diaphragm... the mouth is open more or less widely, with the corners drawn much backwards, as well as a little upwards; and the upper lip is somewhat raised.
The Expression of Emotions in Man and Animals
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Discovery follows discovery, each both raising and answering questions, each ending a long search, and each providing the new instruments for a new search.
In 'Prospects in the Arts and Sciences,' in Fifty Famous Essays (1964).
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Do not follow where the path may lead. Go instead where there is no path and leave a trail.
Anonymous
In Richard Alan Krieger, Civilization’s Quotations: Life’s Ideal (2002), 6. Although this source, and a number of others, attribute the quote to Ralph Waldo Emerson, none that the webmaster found have a citation, and a number of other sources treat it as anonymous. Thus, the webmaster references Emerson with doubt. If you know a definitive primary print source, please contact the webmaster.
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Doubtless the reasoning faculty, the mind, is the leading and characteristic attribute of the human race. By the exercise of this, man arrives at the properties of the natural bodies. This is science, properly and emphatically so called. It is the science of pure mathematics; and in the high branches of this science lies the truly sublime of human acquisition. If any attainment deserves that epithet, it is the knowledge, which, from the mensuration of the minutest dust of the balance, proceeds on the rising scale of material bodies, everywhere weighing, everywhere measuring, everywhere detecting and explaining the laws of force and motion, penetrating into the secret principles which hold the universe of God together, and balancing worlds against worlds, and system against system. When we seek to accompany those who pursue studies at once so high, so vast, and so exact; when we arrive at the discoveries of Newton, which pour in day on the works of God, as if a second fiat had gone forth from his own mouth; when, further, we attempt to follow those who set out where Newton paused, making his goal their starting-place, and, proceeding with demonstration upon demonstration, and discovery upon discovery, bring new worlds and new systems of worlds within the limits of the known universe, failing to learn all only because all is infinite; however we may say of man, in admiration of his physical structure, that “in form and moving he is express and admirable,” it is here, and here without irreverence, we may exclaim, “In apprehension how like a god!” The study of the pure mathematics will of course not be extensively pursued in an institution, which, like this [Boston Mechanics’ Institute], has a direct practical tendency and aim. But it is still to be remembered, that pure mathematics lie at the foundation of mechanical philosophy, and that it is ignorance only which can speak or think of that sublime science as useless research or barren speculation.
In Works (1872), Vol. 1, 180.
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During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true
In Augustus De Morgan and Sophia Elizabeth De Morgan (ed.), A Budget of Paradoxes (1872), 2.
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Each nerve cell receives connections from other nerve cells at six sites called synapses. But here is an astonishing fact—there are about one million billion connections in the cortical sheet. If you were to count them, one connection (or synapse) per second, you would finish counting some thirty-two million years after you began. Another way of getting a feeling for the numbers of connections in this extraordinary structure is to consider that a large match-head’s worth of your brain contains about a billion connections. Notice that I only mention counting connections. If we consider how connections might be variously combined, the number would be hyperastronomical—on the order of ten followed by millions of zeros. (There are about ten followed by eighty zero’s worth of positively charged particles in the whole known universe!)
Bright and Brilliant Fire, On the Matters of the Mind (1992), 17.
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Education consists in co-operating with what is already inside a child's mind … The best way to learn geometry is to follow the road which the human race originally followed: Do things, make things, notice things, arrange things, and only then reason about things.
In Mathematician's Delight (1943), 27.
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Education in my family was not merely emphasized, it was our raison d'être. Virtually all of our aunts and uncles had Ph.D.s in science or engineering, and it was taken for granted that the next generation of Chu's were to follow the family tradition. When the dust had settled, my two brothers and four cousins collected three MDs, four Ph.D.s and a law degree. I could manage only a single advanced degree.
Autobiography in Gösta Ekspong (ed.), Nobel Lectures: Physics 1996-2000 (2002), 115.
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Euler was a believer in God, downright and straightforward. The following story is told by Thiebault, in his Souvenirs de vingt ans de séjour à Berlin, … Thiebault says that he has no personal knowledge of the truth of the story, but that it was believed throughout the whole of the north of Europe. Diderot paid a visit to the Russian Court at the invitation of the Empress. He conversed very freely, and gave the younger members of the Court circle a good deal of lively atheism. The Empress was much amused, but some of her counsellors suggested that it might be desirable to check these expositions of doctrine. The Empress did not like to put a direct muzzle on her guest’s tongue, so the following plot was contrived. Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of God, and would give it him before all the Court, if he desired to hear it. Diderot gladly consented: though the name of the mathematician is not given, it was Euler. He advanced toward Diderot, and said gravely, and in a tone of perfect conviction:
Monsieur, (a + bn) / n = x, donc Dieu existe; repondez!

Diderot, to whom algebra was Hebrew, was embarrassed and disconcerted; while peals of laughter rose on all sides. He asked permission to return to France at once, which was granted.
In Budget of Paradoxes (1878), 251. [The declaration in French expresses, “therefore God exists; please answer!” This Euler-Diderot anecdote, as embellished by De Morgan, is generally regarded as entirely fictional. Diderot before he became an encyclopedist was an accomplished mathematician and fully capable of recognizing—and responding to—the absurdity of an algebraic expression in proving the existence of God. See B.H. Brown, 'The Euler-Diderot Anecdote', The American Mathematical Monthly (May 1942), 49, No. 5, 392-303. —Webmaster.]
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Even those to whom Providence has allotted greater strength of understanding, can expect only to improve a single science. In every other part of learning, they must be content to follow opinions, which they are not able to examine; and, even in that which they claim as peculiarly their own, can seldom add more than some small particle of knowledge, to the hereditary stock devolved to them from ancient times, the collective labour of a thousand intellects.
In Samuel Johnson and W. Jackson Bate (Ed.), ',The Rambler, No. 121, Tuesday, 14 May 1751.' The Selected Essays from the Rambler, Adventurer, and Idler (1968), 172.
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Every time a significant discovery is being made one sets in motion a tremendous activity in laboratories and industrial enterprises throughout the world. It is like the ant who suddenly finds food and walks back to the anthill while sending out material called food attracting substance. The other ants follow the path immediately in order to benefit from the finding and continue to do so as long as the supply is rich.
Nobel Banquet speech (10 Dec 1982). In Wilhelm Odelberg (ed.), Les Prix Nobel. The Nobel Prizes 1982 (1983)
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Everyone has talent. What is rare is the courage to follow that talent to dark place where it leads.
…...
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Everything material which is the subject of knowledge has number, order, or position; and these are her first outlines for a sketch of the universe. If our feeble hands cannot follow out the details, still her part has been drawn with an unerring pen, and her work cannot be gainsaid. So wide is the range of mathematical sciences, so indefinitely may it extend beyond our actual powers of manipulation that at some moments we are inclined to fall down with even more than reverence before her majestic presence. But so strictly limited are her promises and powers, about so much that we might wish to know does she offer no information whatever, that at other moments we are fain to call her results but a vain thing, and to reject them as a stone where we had asked for bread. If one aspect of the subject encourages our hopes, so does the other tend to chasten our desires, and he is perhaps the wisest, and in the long run the happiest, among his fellows, who has learned not only this science, but also the larger lesson which it directly teaches, namely, to temper our aspirations to that which is possible, to moderate our desires to that which is attainable, to restrict our hopes to that of which accomplishment, if not immediately practicable, is at least distinctly within the range of conception.
From Presidential Address (Aug 1878) to the British Association, Dublin, published in the Report of the 48th Meeting of the British Association for the Advancement of Science (1878), 31.
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Experience is never at fault; it is only your judgment that is in error in promising itself such results from experience as are not caused by our experiments. For having given a beginning, what follows from it must necessarily be a natural development of such a beginning, unless it has been subject to a contrary influence, while, if it is affected by any contrary influence, the result which ought to follow from the aforesaid beginning will be found to partake of this contrary influence in a greater or less degree in proportion as the said influence is more or less powerful than the aforesaid beginning.
'Philosophy', in The Notebooks of Leonardo da Vinci, trans. E. MacCurdy (1938), Vol. 1, 70.
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Fatware has been a nasty little dance that we’ve endured for most of this decade. Intel builds a hot new machine and Microsoft follows quickly with new and ever more bulky software that consumes all of the new machine’s resources to do its stuff. So, Intel builds another machine…
In The Chicago Tribune (1 Feb 1998).
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Fertilization of mammalian eggs is followed by successive cell divisions and progressive differentiation, first into the early embryo and subsequently into all of the cell types that make up the adult animal. Transfer of a single nucleus at a specific stage of development, to an enucleated unfertilized egg, provided an opportunity to investigate whether cellular differentiation to that stage involved irreversible genetic modification. The first offspring to develop from a differentiated cell were born after nuclear transfer from an embryo-derived cell line that had been induced to became quiescent. Using the same procedure, we now report the birth of live lambs from three new cell populations established from adult mammary gland, fetus and embryo. The fact that a lamb was derived from an adult cell confirms that differentiation of that cell did not involve the irreversible modification of genetic material required far development to term. The birth of lambs from differentiated fetal and adult cells also reinforces previous speculation that by inducing donor cells to became quiescent it will be possible to obtain normal development from a wide variety of differentiated cells.
[Co-author of paper announcing the cloned sheep, ‘Dolly’.]
In I. Wilmut, A. E. Schnieke, J. McWhir, et al., 'Viable Offspring Derived from Petal and Adult Mammalian Cells', Nature (1997), 385, 810.
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Finally, since I thought that we could have all the same thoughts, while asleep, as we have while we are awake, although none of them is true at that time, I decided to pretend that nothing that ever entered my mind was any more true than the illusions of my dreams. But I noticed, immediately afterwards, that while I thus wished to think that everything was false, it was necessarily the case that I, who was thinking this, was something. When I noticed that this truth “I think, therefore I am” was so firm and certain that all the most extravagant assumptions of the sceptics were unable to shake it, I judged that I could accept it without scruple as the first principle of the philosophy for which I was searching. Then, when I was examining what I was, I realized that I could pretend that I had no body, and that there was no world nor any place in which I was present, but I could not pretend in the same way that I did not exist. On the contrary, from the very fact that I was thinking of doubting the truth of other things, it followed very evidently and very certainly that I existed; whereas if I merely ceased to think, even if all the rest of what I had ever imagined were true, I would have no reason to believe that I existed. I knew from this that I was a substance, the whole essence or nature of which was to think and which, in order to exist, has no need of any place and does not depend on anything material. Thus this self—that is, the soul by which I am what I am—is completely distinct from the body and is even easier to know than it, and even if the body did not exist the soul would still be everything that it is.
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 4, 24-5.
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First follow Nature, and your judgment frame
By her just standard, which is still the same:
Unerring nature, still divinely bright,
One clear, unchanged, and universal light,
Life, force, and beauty must to all impart,
At once the source, and end, and test of art.
#039;Essay On Criticism#039;, Miscellaneous Poems and Translations: by Several Hands (1720), 38.
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First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
In Ueber den Mathematischen Unterricht an den hoheren Schulen; Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 11, 131.
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Follow Descartes! Do not give up the religion of your youth until you get a better one.
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Following the example of Archimedes who wished his tomb decorated with his most beautiful discovery in geometry and ordered it inscribed with a cylinder circumscribed by a sphere, James Bernoulli requested that his tomb be inscribed with his logarithmic spiral together with the words, “Eadem mutata resurgo,” a happy allusion to the hope of the Christians, which is in a way symbolized by the properties of that curve.
From 'Eloge de M. Bernoulli', Oeuvres de Fontenelle, t. 5 (1768), 112. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 143-144. [The Latin phrase, Eadem numero mutata resurgo means as “Though changed, I arise again exactly the same”. —Webmaster]
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Following the light of the sun, we left the Old World.
…...
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For chemistry is no science form’d à priori; ’tis no production of the human mind, framed by reasoning and deduction: it took its rise from a number of experiments casually made, without any expectation of what follow’d; and was only reduced into an art or system, by collecting and comparing the effects of such unpremeditated experiments, and observing the uniform tendency thereof. So far, then, as a number of experimenters agree to establish any undoubted truth; so far they may be consider'd as constituting the theory of chemistry.
From 'The Author's Preface', in A New Method of Chemistry (1727), vi.
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For it is too bad that there are so few who seek the truth and so few who do not follow a mistaken method in philosophy. This is not, however, the place to lament the misery of our century, but to rejoice with you over such beautiful ideas for proving the truth. So I add only, and I promise, that I shall read your book at leisure; for I am certain that I shall find the noblest things in it. And this I shall do the more gladly, because I accepted the view of Copernicus many years ago, and from this standpoint I have discovered from their origins many natural phenomena, which doubtless cannot be explained on the basis of the more commonly accepted hypothesis.
Letter (4 Aug 1597) to Kepler, expressing thanks and interest in the book Kepler sent him. As quoted in translation in Jackson J. Spielvogel, Western Civilization: Alternate Volume: Since 1300 (2010), Vol. 2, 494.
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For it is too bad that there are so few who seek the truth and so few who do not follow a mistaken method in philosophy. This is not, however, the place to lament the misery of our century, but to rejoice with you over such beautiful ideas for proving the truth. So I add only, and I promise, that I shall read your book at leisure; for I am certain that I shall find the noblest things in it. And this I shall do the more gladly, because I accepted the view of Copernicus many years ago, and from this standpoint I have discovered from their origins many natural phenomena, which doubtless cannot be explained on the basis of the more commonly accepted hypothesis.
In Letter to Johannes Kepler. As quoted in The Portable Renaissance Reader (1968), 597.
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For the philosopher, order is the entirety of repetitions manifested, in the form of types or of laws, by perceived objects. Order is an intelligible relation. For the biologist, order is a sequence in space and time. However, according to Plato, all things arise out of their opposites. Order was born of the original disorder, and the long evolution responsible for the present biological order necessarily had to engender disorder.
An organism is a molecular society, and biological order is a kind of social order. Social order is opposed to revolution, which is an abrupt change of order, and to anarchy, which is the absence of order.
I am presenting here today both revolution and anarchy, for which I am fortunately not the only one responsible. However, anarchy cannot survive and prosper except in an ordered society, and revolution becomes sooner or later the new order. Viruses have not failed to follow the general law. They are strict parasites which, born of disorder, have created a very remarkable new order to ensure their own perpetuation.
'Interaction Among Virus, Cell, and Organism', Nobel Lecture (11 Dec 1965). In Nobel Lectures: Physiology or Medicine 1963-1970 (1972), 174.
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For the truth of the conclusions of physical science, observation is the supreme Court of Appeal. It does not follow that every item which we confidently accept as physical knowledge has actually been certified by the Court; our confidence is that it would be certified by the Court if it were submitted. But it does follow that every item of physical knowledge is of a form which might be submitted to the Court. It must be such that we can specify (although it may be impracticable to carry out) an observational procedure which would decide whether it is true or not. Clearly a statement cannot be tested by observation unless it is an assertion about the results of observation. Every item of physical knowledge must therefore be an assertion of what has been or would be the result of carrying out a specified observational procedure.
In ’Scientific Epistemology', The Philosophy of Physical Science (1938, 2012), 9.
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For there are two modes of acquiring knowledge, namely, by reasoning and experience. Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth, unless the mind discovers it by the path of experience; since many have the arguments relating to what can be known, but because they lack experience they neglect the arguments, and neither avoid what is harmful nor follow what is good. For if a man who has never seen fire should prove by adequate reasoning that fire burns and injures things and destroys them, his mind would not be satisfied thereby, nor would he avoid fire, until he placed his hand or some combustible substance in the fire, so that he might prove by experience that which reasoning taught. But when he has had actual experience of combustion his mind is made certain and rests in the full light of truth. Therefore reasoning does not suffice, but experience does.
Opus Majus [1266-1268], Part VI, chapter I, trans. R. B. Burke, The Opus Majus of Roger Bacon (1928), Vol. 2, 583.
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For they are not given to idleness, nor go in a proud habit, or plush and velvet garments, often showing their rings upon their fingers, or wearing swords with silver hilts by their sides, or fine and gay gloves upon their hands, but diligently follow their labours, sweating whole days and nights by their furnaces. They do not spend their time abroad for recreation, but take delight in their laboratory. They wear leather garments with a pouch, and an apron wherewith they wipe their hands. They put their fingers amongst coals, into clay, and filth, not into gold rings. They are sooty and black like smiths and colliers, and do not pride themselves upon clean and beautiful faces.
As translated in Paracelsus and Arthur Edward Waite (ed.), The Hermetic and Alchemical Writings of Paracelsus (1894, 1976), Vol. 1, 167.
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From the infinitely great down to the infinitely small, all things are subject to [the laws of nature]. The sun and the planets follow the laws discovered by Newton and Laplace, just as the atoms in their combinations follow the laws of chemistry, as living creatures follow the laws of biology. It is only the imperfections of the human mind which multiply the divisions of the sciences, separating astronomy from physics or chemistry, the natural sciences from the social sciences. In essence, science is one. It is none other than the truth.
From Cours d’Economie Politique (1896-97), as given in Archives Internationales d’Histoire des Sciences (1993), Issues 131-133, 67.
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From the point of view of the physicist, a theory of matter is a policy rather than a creed; its object is to connect or co-ordinate apparently diverse phenomena, and above all to suggest, stimulate and direct experiment. It ought to furnish a compass which, if followed, will lead the observer further and further into previously unexplored regions.
The Corpuscular Theory of Matter (1907), 1.
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From the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows. There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.
Concluding paragraph in The Origin of Species (1859), 490. In the second edition, Darwin changed “breathed” to “breathed by the Creator”.
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From this fountain (the free will of God) it is those laws, which we call the laws of nature, have flowed, in which there appear many traces of the most wise contrivance, but not the least shadow of necessity. These therefore we must not seek from uncertain conjectures, but learn them from observations and experimental. He who is presumptuous enough to think that he can find the true principles of physics and the laws of natural things by the force alone of his own mind, and the internal light of his reason, must either suppose the world exists by necessity, and by the same necessity follows the law proposed; or if the order of Nature was established by the will of God, the [man] himself, a miserable reptile, can tell what was fittest to be done.
…...
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From whence it is obvious to conclude that, since our Faculties are not fitted to penetrate into the internal Fabrick and real Essences of Bodies; but yet plainly discover to us the Being of a GOD, and the Knowledge of our selves, enough to lead us into a full and clear discovery of our Duty, and great Concernment, it will become us, as rational Creatures, to imploy those Faculties we have about what they are most adapted to, and follow the direction of Nature, where it seems to point us out the way.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 4, Chapter 12, Section 11, 646.
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Further study of the division phenomena requires a brief discussion of the material which thus far I have called the stainable substance of the nucleus. Since the term nuclear substance could easily result in misinterpretation..., I shall coin the term chromatin for the time being. This does not indicate that this substance must be a chemical compound of a definite composition, remaining the same in all nuclei. Although this may be the case, we simply do not know enough about the nuclear substances to make such an assumption. Therefore, we will designate as chromatin that substance, in the nucleus, which upon treatment with dyes known as nuclear stains does absorb the dye. From my description of the results of staining resting and dividing cells... it follows that the chromatin is distributed throughout the whole resting nucleus, mostly in the nucleoli, the network, and the membrane, but also in the ground-substance. In nuclear division it accumulates exclusively in the thread figures. The term achromatin suggests itself automatically for the unstainable substance of the nucleus. The terms chromatic and achromatic which will be used henceforth are thus explained.
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He who ascribes the movement of the seas to the movement of the earth assumes a purely forced movement; but he who lets the seas follow the moon makes this movement in a certain way a natural one.
As quoted in James Bruce Ross and Mary Martin McLaughlin, The Portable Renaissance Reader (1968), 603.
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He who knows not, and knows not he knows not, he is a fool—shun him;
He who knows not, and knows he knows not, he is simple—teach him;
He who knows, and knows not he knows, he is asleep—wake him;
He who knows, and knows he knows, he is wise—follow him.
Anonymous
Hesiod, 'Works and Days,' 293-7. In William White, Notes and Queries (1904), Series 10, Vol. 1, 235, the correspondent H.A. Strong says that the origin of these lines is to be found in Hesiod [Greek, 8th Century B.C.], Works and Days, 293-7; that the passage was very celebrated in antiquity, and is quoted by Aristotle, Nic. Eth., i. 4; and that both Livy (xxii. 29) and Cicero (Pro Cluent., 31) refer to it. Another correspondent (J.H.K.) said it was stated to be an Arab proverb in Lady [Isabel] Burton, Life of [Captain] Sir Richard [F.] Burton (1893), Vol. 1, 548, footnote, which prepends to the quote, “Men are four.”
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Hence dusky Iron sleeps in dark abodes,
And ferny foliage nestles in the nodes;
Till with wide lungs the panting bellows blow,
And waked by fire the glittering torrents flow;
Quick whirls the wheel, the ponderous hammer falls,
Loud anvils ring amid the trembling walls,
Strokes follow strokes, the sparkling ingot shines,
Flows the red slag, the lengthening bar refines;
Cold waves, immersed, the glowing mass congeal,
And turn to adamant the hissing Steel.
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His [Marvin Minsky’s] basic interest seemed to be in the workings of the human mind and in making machine models of the mind. Indeed, about that time he and a friend made one of the first electronic machines that could actually teach itself to do something interesting. It monitored electronic “rats” that learned to run mazes. It was being financed by the Navy. On one notable occasion, I remember descending to the basement of Memorial Hall, while Minsky worked on it. It had an illuminated display panel that enabled one to follow the progress of the “rats.” Near the machine was a hamster in a cage. When the machine blinked, the hamster would run around its cage happily. Minsky, with his characteristic elfin grin, remarked that on a previous day the Navy contract officer had been down to see the machine. Noting the man’s interest in the hamster, Minsky had told him laconically, “The next one we build will look like a bird.”
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How often people speak of art and science as though they were two entirely different things, with no interconnection. An artist is emotional, they think, and uses only his intuition; he sees all at once and has no need of reason. A scientist is cold, they think, and uses only his reason; he argues carefully step by step, and needs no imagination. That is all wrong. The true artist is quite rational as well as imaginative and knows what he is doing; if he does not, his art suffers. The true scientist is quite imaginative as well as rational, and sometimes leaps to solutions where reason can follow only slowly; if he does not, his science suffers.
'Prometheus.' The Roving Mind (1983), Chap 25.
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Human society is made up of partialities. Each citizen has an interest and a view of his own, which, if followed out to the extreme, would leave no room for any other citizen.
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I always tried to live up to Leo Szilard's commandment, “don't lie if you don't have to.” I had to. I filled up pages with words and plans I knew I would not follow. When I go home from my laboratory in the late afternoon, I often do not know what I am going to do the next day. I expect to think that up during the night. How could I tell them what I would do a year hence?
In 'Dionysians and Apollonians', Science (2 Jun 1972), 176, 966. Reprinted in Mary Ritchie Key, The Relationship of Verbal and Nonverbal Communication (1980), 318.
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I am a believer in unconscious cerebration. The brain is working all the time, though we do not know it. At night it follows up what we think in the daytime. When I have worked a long time on one thing, I make it a point to bring all the facts regarding it together before I retire; I have often been surprised at the results… We are thinking all the time; it is impossible not to think.
In Orison Swett Marden, 'Bell Telephone Talk: Hints on Success by Alexander G. Bell', How They Succeeded: Life Stories of Successful Men Told by Themselves (1901), 33.
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I am a strong advocate for free thought on all subjects, yet it appears to me (whether rightly or wrongly) that direct arguments against christianity & theism produce hardly any effect on the public; & freedom of thought is best promoted by the gradual illumination of men's minds, which follow[s] from the advance of science. It has, therefore, been always my object to avoid writing on religion, & I have confined myself to science. I may, however, have been unduly biassed by the pain which it would give some members of my family, if I aided in any way direct attacks on religion.
Letter to E.B. Aveling (13 Oct 1880).
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I am told that the wall paintings which we had the happiness of admiring in all their beauty and freshness [in the chapel she discovered at Abu Simbel] are already much injured. Such is the fate of every Egyptian monument, great or small. The tourist carves it over with names and dates, and in some instances with caricatures. The student of Egyptology, by taking wet paper “squeezes” sponges away every vestige of the original colour. The “Collector” buys and carries off everything of value that he can, and the Arab steals it for him. The work of destruction, meanwhile goes on apace. The Museums of Berlin, of Turin, of Florence are rich in spoils which tell their lamentable tale. When science leads the way, is it wonderful that ignorance should follow?
Quoted in Margaret S. Drower, The Early Years, in T.G.H. James, (ed.), Excavating in Egypt: The Egypt Exploration Society, 1882-1982 (1982), 10. As cited in Wendy M.K. Shaw, Possessors and Possessed: Museums, Archaeology, and the Visualization of History in the Late Ottoman Empire (2003), 37. Also quoted in Margaret S. Drower, Flinders Petrie: A Life in Archaeology (1995), 57.
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I believed that, instead of the multiplicity of rules that comprise logic, I would have enough in the following four, as long as I made a firm and steadfast resolution never to fail to observe them.
The first was never to accept anything as true if I did not know clearly that it was so; that is, carefully to avoid prejudice and jumping to conclusions, and to include nothing in my judgments apart from whatever appeared so clearly and distinctly to my mind that I had no opportunity to cast doubt upon it.
The second was to subdivide each on the problems I was about to examine: into as many parts as would be possible and necessary to resolve them better.
The third was to guide my thoughts in an orderly way by beginning, as if by steps, to knowledge of the most complex, and even by assuming an order of the most complex, and even by assuming an order among objects in! cases where there is no natural order among them.
And the final rule was: in all cases, to make such comprehensive enumerations and such general review that I was certain not to omit anything.
The long chains of inferences, all of them simple and easy, that geometers normally use to construct their most difficult demonstrations had given me an opportunity to think that all the things that can fall within the scope of human knowledge follow from each other in a similar way, and as long as one avoids accepting something as true which is not so, and as long as one always observes the order required to deduce them from each other, there cannot be anything so remote that it cannot be reached nor anything so hidden that it cannot be uncovered.
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 2, 16.
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I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
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I cannot find anything showing early aptitude for acquiring languages; but that he [Clifford] had it and was fond of exercising it in later life is certain. One practical reason for it was the desire of being able to read mathematical papers in foreign journals; but this would not account for his taking up Spanish, of which he acquired a competent knowledge in the course of a tour to the Pyrenees. When he was at Algiers in 1876 he began Arabic, and made progress enough to follow in a general way a course of lessons given in that language. He read modern Greek fluently, and at one time he was furious about Sanskrit. He even spent some time on hieroglyphics. A new language is a riddle before it is conquered, a power in the hand afterwards: to Clifford every riddle was a challenge, and every chance of new power a divine opportunity to be seized. Hence he was likewise interested in the various modes of conveying and expressing language invented for special purposes, such as the Morse alphabet and shorthand. … I have forgotten to mention his command of French and German, the former of which he knew very well, and the latter quite sufficiently; …
In paper, 'William Kingdon Clifford', The Fortnightly Review (1879), 31, 671. Published in advance of Leslie Stephen and Frederick Pollock (eds.), Clifford’s Lectures and Essays (1879), Vol. 1, Introduction, 9. The 'Introduction' was written by Pollock.
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I cannot serve as an example for younger scientists to follow. What I teach cannot be learned. I have never been a “100 percent scientist.” My reading has always been shamefully nonprofessional. I do not own an attaché case, and therefore cannot carry it home at night, full of journals and papers to read. I like long vacations, and a catalogue of my activities in general would be a scandal in the ears of the apostles of cost-effectiveness. I do not play the recorder, nor do I like to attend NATO workshops on a Greek island or a Sicilian mountain top; this shows that I am not even a molecular biologist. In fact, the list of what I have not got makes up the American Dream. Readers, if any, will conclude rightly that the Gradus ad Parnassum will have to be learned at somebody else’s feet.
In Heraclitean Fire: Sketches from a Life before Nature (1978), 7.
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I consider it extremely doubtful whether the happiness of the human race has been enhanced by the technical and industrial developments that followed in the wake of rapidly progressing natural science.
…...
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I do not intend to go deeply into the question how far mathematical studies, as the representatives of conscious logical reasoning, should take a more important place in school education. But it is, in reality, one of the questions of the day. In proportion as the range of science extends, its system and organization must be improved, and it must inevitably come about that individual students will find themselves compelled to go through a stricter course of training than grammar is in a position to supply. What strikes me in my own experience with students who pass from our classical schools to scientific and medical studies, is first, a certain laxity in the application of strictly universal laws. The grammatical rules, in which they have been exercised, are for the most part followed by long lists of exceptions; accordingly they are not in the habit of relying implicitly on the certainty of a legitimate deduction from a strictly universal law. Secondly, I find them for the most part too much inclined to trust to authority, even in cases where they might form an independent judgment. In fact, in philological studies, inasmuch as it is seldom possible to take in the whole of the premises at a glance, and inasmuch as the decision of disputed questions often depends on an aesthetic feeling for beauty of expression, or for the genius of the language, attainable only by long training, it must often happen that the student is referred to authorities even by the best teachers. Both faults are traceable to certain indolence and vagueness of thought, the sad effects of which are not confined to subsequent scientific studies. But certainly the best remedy for both is to be found in mathematics, where there is absolute certainty in the reasoning, and no authority is recognized but that of one’s own intelligence.
In 'On the Relation of Natural Science to Science in general', Popular Lectures on Scientific Subjects, translated by E. Atkinson (1900), 25-26.
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I do not think that G. H. Hardy was talking nonsense when he insisted that the mathematician was discovering rather than creating, nor was it wholly nonsense for Kepler to exult that he was thinking God's thoughts after him. The world for me is a necessary system, and in the degree to which the thinker can surrender his thought to that system and follow it, he is in a sense participating in that which is timeless or eternal.
'Reply to Lewis Edwin Hahn', The Philosophy of Brand Blanshard (1980), 901.
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I had … during many years, followed a golden rule, namely, that whenever a published fact, a new observation or thought came across me, which was opposed by my general results, to make a memorandum of it without fail and at once; for I had found by experience that such facts and thoughts were far more apt to escape from memory than favorable ones.
In The Autobiography of Charles Darwin with original omissions restored, edited by Nora Barlow (1958).
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I had a feeling of exhilaration that the 'gadget' had gone off properly followed by one of deep relief. I wouldn't have to go to the tower to see what had gone wrong.
Bulletin of the Atomic Scientists (1975)
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I have always felt that astronomical hypotheses should not be regarded as articles of faith, but should only serve as a framework for astronomical calculations, so that it does not matter whether they were right or wrong, as long as the phenomena can be characterized precisely. For who could possibly be certain as to whether the uneven movement of the sun, if we follow the hypotheses of Ptolemy, can be explained by assuming an epicycle or eccentricity. Both assumptions are plausible. That’s why I would consider it quite desirable for you to tell something about that in the preface. In this way you would appease the Aristotelians and the theologians, whose opposition you dread.
From surviving fragment of a Letter (20 Apr 1541) answering a query from Copernicus as to whether he should publish his book (De Revolutionibus). From the German in Leopold Friedrich Prowe, Nicolaus Coppernicus (1883), Vol. 1, Part 2, 521-522. Translated from Prowe by Webmaster using web resources. Original German: “Hypothesen nicht als Glaubens-Artikel zu betrachten seien, sondern nur als Grundlage für die astronomischen Rechnungen zu dienen hätten, so dass es nicht darauf ankomme, ob sie richtig oder falsch seien, wofern sich nur die Erscheinungen dadurch genau bestimmen liessen. »Denn wer dürfte uns wohl darüber sichere Auskunft geben, ob die ungleiche Bewegung der Sonne, wenn wir den Hypothesen des Ptolemaeus folgen, durch Annahme eines Epicykels oder der Ekcentricität zu erklären sei. Beide Annahmen sind gestattet. Daher würde ich—so schliesst Osiander—es für recht wünschenswerth erachten, wenn Du hierüber in der Vorrede etwas beibrächtest. Auf diese Weise würdest Du die Aristoteliker und die Theologen milder stimmen, von denen Du befürchtest, dass sie heftigen Widerspruch kundthun werden.«” Compare Latin text, from Johannes Kepler, 'Apologia Tychonia', Astronomi Opera Omnia (1858), Vol. 1, 246: “De hypothesibus ego sic sensi semper, non esse articulos fidei, sed fundamenta calculi ita ut, etiamsi falsae sint, modo motuum φαινομενα exacte exhibeant, nihil referat; quis enim nos certiores reddet, an Solis inaequalis motus nomine epicycli an nomine eccentricitatis contingat, si Ptolemaei hypotheses sequamur, cum id possit utrumque. Quare plausibile fore videretur, si hac de re in praefatione nonnihil attingeres. Sic enim placidiores redderes peripatheticos et theologos, quos contradicturos metuis.”
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I have mentioned mathematics as a way to settle in the mind a habit of reasoning closely and in train; not that I think it necessary that all men should be deep mathematicians, but that, having got the way of reasoning which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge, as they shall have occasion. For in all sorts of reasoning, every single argument should be managed as a mathematical demonstration; the connection and dependence of ideas should be followed till the mind is brought to the source on which it bottoms, and observes the coherence all along; …
In The Conduct of the Understanding, Sect. 7.
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I have now said enough to show you that it is indispensable for this country to have a scientific education in connexion with manufacturers, if we wish to outstrip the intellectual competition which now, happily for the world, prevails in all departments of industry. As surely as darkness follows the setting of the sun, so surely will England recede as a manufacturing nation, unless her industrial population become much more conversant with science than they are now.
In 'The Study of Abstract Science Essential to the Progress of Industry', Records of the School of Mines (1852) 1, 48.
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I have said that the investigation for which the teeth of the shark had furnished an opportunity, was very near an end... But thereafter, while I was examining more carefully these details of both places and bodies [sedimentary deposits and shells], these day by day presented points of doubt to me as they followed one another in indissoluble connection, so that I saw myself again and again brought back to the starting-place, as it were, when I thought I was nearest the goal. I might compare those doubts to the heads of the Lernean Hydra, since when one of them had been got rid of, numberless others were born; at any rate, I saw that I was wandering about in a sort of labyrinth, where the nearer one approaches the exit, the wider circuits does one tread.
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), 206.
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I immediately loved working with flies. They fascinated me, and followed me around in my dreams.
1995 Nobel Prize - Nobel Autobiography
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I knew, however, that it would cost ten times what I had available in order to build a molecular beam machine. I decided to follow a byway, rather than the highway. It is a procedure I have subsequently recommended to beginning scientists in this country, where research strategy is best modelled on that used by Wolfe at the Plains of Abraham.
(British General James Wolfe defeated the French defending Quebec in 1759 after scaling a cliff for a surprise attack.)
'A Scientist and the World He Lives In', Speech to the Empire Club of Canada (27 Nov 1986) in C. Frank Turner and Tim Dickson (eds.), The Empire Club of Canada Speeches 1986-1987 (1987), 149-161.
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I like to summarize what I regard as the pedestal-smashing messages of Darwin’s revolution in the following statement, which might be chanted several times a day, like a Hare Krishna mantra, to encourage penetration into the soul: Humans are not the end result of predictable evolutionary progress, but rather a fortuitous cosmic afterthought, a tiny little twig on the enormously arborescent bush of life, which, if replanted from seed, would almost surely not grow this twig again, or perhaps any twig with any property that we would care to call consciousness.
…...
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I notice that, in the lecture … which Prof. Lowry gave recently, in Paris … he brought forward certain freak formulae for tartaric acid, in which hydrogen figures as bigamist … I may say, he but follows the loose example set by certain Uesanians, especially one G. N. Lewis, a Californian thermodynamiter, who has chosen to disregard the fundamental canons of chemistry—for no obvious reason other than that of indulging in premature speculation upon electrons as the cause of valency…
'Bigamist Hydrogen. A Protest', Nature (1926), 117, 553.
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I regret that it has been necessary for me in this lecture to administer such a large dose of four-dimensional geometry. I do not apologize, because I am really not responsible for the fact that nature in its most fundamental aspect is four-dimensional. Things are what they are; and it is useless to disguise the fact that “what things are” is often very difficult for our intellects to follow.
From The Concept of Nature (1920, 1964), 118.
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I remember my first look at the great treatise of Maxwell’s when I was a young man… I saw that it was great, greater and greatest, with prodigious possibilities in its power… I was determined to master the book and set to work. I was very ignorant. I had no knowledge of mathematical analysis (having learned only school algebra and trigonometry which I had largely forgotten) and thus my work was laid out for me. It took me several years before I could understand as much as I possibly could. Then I set Maxwell aside and followed my own course. And I progressed much more quickly… It will be understood that I preach the gospel according to my interpretation of Maxwell.
From translations of a letter (24 Feb 1918), cited in Paul J. Nahin, Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age (2002), 24. Nahin footnotes that the words are not verbatim, but are the result of two translations. Heaviside's original letter in English was quoted, translated in to French by J. Bethenode, for the obituary he wrote, "Oliver Heaviside", in Annales des Posies Telegraphs (1925), 14, 521-538. The quote was retranslated back to English in Nadin's book. Bethenode footnoted that he made the original translation "as literally as possible in order not to change the meaning." Nadin assures that the retranslation was done likewise. Heaviside studyied Maxwell's two-volume Treatise on Electricity and Magnetism.
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I see with much pleasure that you are working on a large work on the integral Calculus [ ... ] The reconciliation of the methods which you are planning to make, serves to clarify them mutually, and what they have in common contains very often their true metaphysics; this is why that metaphysics is almost the last thing that one discovers. The spirit arrives at the results as if by instinct; it is only on reflecting upon the route that it and others have followed that it succeeds in generalising the methods and in discovering its metaphysics.
Letter to S. F. Lacroix, 1792. Quoted in S. F. Lacroix, Traité du calcul differentiel et du calcul integral (1797), Vol. 1, xxiv, trans. Ivor Grattan-Guinness.
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I shall never forget my first encounter with gorillas. Sound preceded sight. Odor preceded sound in the form of an overwhelming, musky-barnyard, humanlike scent. The air was suddenly rent by a high-pitched series of screams followed by the rhythmic rondo of sharp pok-pok chestbeats from a great silverbacked male obscured behind what seemed an impenetrable wall of vegetation.
Describing her 1963 trip to Kabara in Gorillas in the Mist (1983), 3. (The screams and chest-beating were of alarm, not ferocity.)
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I should study Nature’s laws in all their crossings and unions; I should follow magnetic streams to their source and follow the shores of our magnetic oceans. I should go among the rays of the aurora, and follow them to their beginnings, and study their dealings and communications with other powers and expressions of matter.
John Muir
…...
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I think it perfectly just, that he who, from the love of experiment, quits an approved for an uncertain practice, should suffer the full penalty of Egyptian law against medical innovation; as I would consign to the pillory, the wretch, who out of regard to his character, that is, to his fees, should follow the routine, when, from constant experience he is sure that his patient will die under it, provided any, not inhuman, deviation would give his patient a chance.
From his researches in Fever, 196. In John Edmonds Stock, Memoirs of the life of Thomas Beddoes (1810), 400.
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I think, and I am not the only one who does, that it is important never to introduce any conception which may not be completely defined by a finite number of words. Whatever may be the remedy adopted, we can promise ourselves the joy of the physician called in to follow a beautiful pathological case [beau cas pathologique].
From address read at the general session of the Fourth International Congress of Mathematicians in Rome (10 Apr 1908). As translated in 'The Future of Mathematics: by Henri Poincaré', General Appendix, Annual Report of the Boars of Regents of The Smithsonian Institution: For the Year Ending June 1909 (1910), 140.
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I thought it was a miracle that I got this faculty appointment and was so happy to be there for a few years that I just wanted to follow what was exciting for me. I didn’t have expectations of getting tenure. So this was an aspect of gender inequality that was extremely positive. It allowed me to be fearless.
As quoted in Anna Azvolinsky, 'Fearless About Folding', The Scientist (Jan 2016).
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I undertake my scientific research with the confident assumption that the earth follows the laws of nature which God established at creation. … My studies are performed with the confidence that God will not capriciously confound scientific results by “slipping in” a miracle.
Quoted in Lenny Flank, Deception by Design: The Intelligent Design Movement in America (2007), 81. Also seen as cited from Arthur Newell Strahler, Science and Earth History: the Evolution/Creation Controversy (1987), 40-41.
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I venture to assert that the feelings one has when the beautiful symbolism of the infinitesimal calculus first gets a meaning, or when the delicate analysis of Fourier has been mastered, or while one follows Clerk Maxwell or Thomson into the strange world of electricity, now growing so rapidly in form and being, or can almost feel with Stokes the pulsations of light that gives nature to our eyes, or track with Clausius the courses of molecules we can measure, even if we know with certainty that we can never see them I venture to assert that these feelings are altogether comparable to those aroused in us by an exquisite poem or a lofty thought.
In paper (May 1891) read before Bath Branch of the Teachers’ Guild, published in The Practical Teacher (July 1891), reprinted as 'Geometry', in Frederic Spencer, Chapters on the Aims and Practice of Teaching (1897), 194.
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I was interested in truth from the point of view of salvation just as much as in truth from the point of view of scientific certainty. It appeared to me that there were two paths to truth, and I decided to follow both of them.
Explaining his decision, made at age 9, to become a scientist, followed within a month by his decision to also become a priest. In interview with Duncan Aikman, 'Lemaître Follows Two Paths to Truth', New York Times Magazine (19 Feb 1933), 3.
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Ideas are like stars: You will not succeed in touching them with your hands, but like the seafaring man on the ocean desert of waters, you choose them as your guides, and following them, you reach your destiny.
…...
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If … the motion of the earth were circular, it would be violent and contrary to nature, and could not be eternal since … nothing violent is eternal. ... It follows, therefore, that the earth is not moved with a circular motion.
In Commentaria in Libros Aristotelis de Caelo et Mundo (c. 1270).
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If a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics.
In Men of Mathematics (1937), Vol. 2, 232. Also in J.R. Newman (ed.) The World of Mathematics (1956, 1960), Vol. 1, 308.
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If feeling be not a property of matter, but owing to a superior principle, it must follow, that the motions of the heart, and other muscles of animals, after being separated from their bodies, are to be ascribed to this principle; and that any difficulties which may appear in this matter are owing to our ignorance of the nature of the soul, of the manner of its existence, and of its wonderful union with, and action upon the body.
In An Essay on the Vital and Other Involuntary Motions of Animals (1751), 389-390.
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If I had my life to live over again I would not devote it to develop new industrial processes: I would try to add my humble efforts to use Science to the betterment of the human race.
I despair of the helter-skelter methods of our vaulted homo sapiens, misguided by his ignorance and his politicians. If we continue our ways, there is every possibility that the human race may follow the road of former living races of animals whose fossils proclaim that they were not fit to continue. Religion, laws and morals is not enough. We need more. Science can help us.
Letter to a friend (14 Jan 1934). In Savage Grace (1985, 2007), 62.
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If I set out to prove something, I am no real scientist—I have to learn to follow where the facts lead me—I have to learn to whip my prejudices.
Attributed, as cited in Peter McDonald (ed.), Oxford Dictionary of Medical Quotations (2004), 95. Quoted earlier without citation as “If I want to find truth, I must have an open mind. I have to learn to follow where the facts lead me—I have to learn to whip my prejudices,” in World Order (1948), 14, 76.
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If I would follow your advice and Jesus could perceive it, he, as a Jewish teacher, surely would not approve of such behavior.
…...
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If it was the warmth of the sun, and not its light, that produced this operation, it would follow, that, by warming the water near the fire about as much as it would have been in the sun, this very air would be produced; but this is far from being the case.
In Tobias George Smollett (ed.), 'Experiments Upon Vegetables', The Critical Review, Or, Annals of Literature (1779), 48, 336.
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If on occasion Mr. Casson exhibits an insularity of judgment when it comes to the evaluation of the contribution made by various men to the development of modern anthropology, he may be forgiven upon the ground that, where anthropology is concerned, he is only following an old English custom!
In 'Review: The Discovery of Man by Stanley Casson', Isis (Jun 1941), 33, No. 2, 302.
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If the man of science chose to follow the example of historians and pulpit-orators, and to obscure strange and peculiar phenomena by employing a hollow pomp of big and sounding words, this would be his opportunity; for we have approached one of the greatest mysteries which surround the problem of animated nature and distinguish it above all other problems of science. To discover the relations of man and woman to the egg-cell would be almost equivalent of the egg-cell in the body of the mother, the transfer to it by means of the seed, of the physical and mental characteristics of the father, affect all the questions which the human mind has ever raised in regard to existence.
Quoted in Ernst Heinrich Philipp August Haeckel, The Evolution of Man (1897), vol 1, 148.
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If the Weismann idea triumphs, it will be in a sense a triumph of fatalism; for, according to it, while we may indefinitely improve the forces of our education and surroundings, and this civilizing nurture will improve the individuals of each generation, its actual effects will not be cumulative as regards the race itself, but only as regards the environment of the race; each new generation must start de novo, receiving no increment of the moral and intellectual advance made during the lifetime of its predecessors. It would follow that one deep, almost instinctive motive for a higher life would be removed if the race were only superficially benefited by its nurture, and the only possible channel of actual improvement were in the selection of the fittest chains of race plasma.
'The Present Problem of Heredity', The Atlantic Monthly (1891), 57, 363.
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If the world has begun with a single quantum, the notions of space and would altogether fail to have any meaning at the beginning; they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time. I think that such a beginning of the world is far enough from the present order of Nature to be not at all repugnant. It may be difficult to follow up the idea in detail as we are not yet able to count the quantum packets in every case. For example, it may be that an atomic nucleus must be counted as a unique quantum, the atomic number acting as a kind of quantum number. If the future development of quantum theory happens to turn in that direction, we could conceive the beginning of the universe in the form of a unique atom, the atomic weight of which is the total mass of the universe. This highly unstable atom would divide in smaller and smaller atoms by a kind of super-radioactive process.
In a seminal short letter (457 words), 'The Beginning of the World from the Point of View of Quantum Theory', Nature (9 May 1931), 127, 706.
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If the world may be thought of as a certain definite quantity of force and as a certain definite number of centers of force—and every other representation remains indefinite and therefore useless—it follows that, in the great dice game of existence, it must pass through calculable number of combinations. In infinite time, every possible combination would at some time or another be realized; more: it would be realized an infinite number of times. And since between every combination and its next recurrence all other possible combinations would have to take place, and each of these combination conditions of the entire sequence of combinations in the same series, a circular movement of absolutely identical series is thus demonstrated: the world as a circular movement that has already repeated itself infinitely often and plays its game in infinitum. This conception is not simply a mechanistic conception; for if it were that, it would not condition an infinite recurrence of identical cases, but a final state. Because the world has not reached this, mechanistic theory must be considered an imperfect and merely provisional hypothesis.
The Will to Power (Notes written 1883-1888), book 4, no. 1066. Trans. W. Kaufmann and R. J. Hollingdale and ed. W. Kaufmann (1968), 549.
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If we are to follow in the wake of other countries in the pursuit of material prosperity, we must give up aimless activities and bring our ideals into line with the standards of the West, namely, to spread education in all grades, multiply occupations and increase production and wealth. All other activities should conform themselves to the economic ideal.
Speech (16 Mar 1912), at Central College Bangalore Visvesvaraya. Collected in Speeches: 1910-11 to 1916-17: by Sir Mokshagundam Visvesvaraya (1917), 23.
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If we betake ourselves to the statistical method, we do so confessing that we are unable to follow the details of each individual case, and expecting that the effects of widespread causes, though very different in each individual, will produce an average result on the whole nation, from a study of which we may estimate the character and propensities of an imaginary being called the Mean Man.
'Does the Progress of Physical Science tend to give any advantage to the opinion of necessity (or determinism) over that of the continuency of Events and the Freedom of the Will?' In P. M. Hannan (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 1862-1873, 818.
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If we had nothing but pecuniary rewards and worldly honours to look to, our profession would not be one to be desired. But in its practice you will find it to be attended with peculiar privileges, second to none in intense interest and pure pleasures. It is our proud office to tend the fleshly tabernacle of the immortal spirit, and our path, rightly followed, will be guided by unfettered truth and love unfeigned. In the pursuit of this noble and holy calling I wish you all God-speed.
Conclusion of Graduation Address, University of Edinburgh (1876). In John Vaughan, 'Lord Lister', The Living Age (1918), 297, 361.
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If we succeed in giving the love of learning, the learning itself is sure to follow.
The Pleasures of Life (1887, 2007), 73.
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In acute diseases the physician must conduct his inquiries in the following way. First he must examine the face of the patient, and see whether it is like the faces of healthy people, and especially whether it is like its usual self. Such likeness will be the best sign, and the greatest unlikeness will be the most dangerous sign. The latter will be as follows. Nose sharp, eyes hollow, temples sunken, ears cold and contracted with their lobes turned outwards, the skin about the face hard and tense and parched, the colour of the face as a whole being yellow or black.
Prognostic, in Hippocrates, trans. W. H. S. Jones (1923), Vol. 2, 9.
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In all disciplines in which there is systematic knowledge of things with principles, causes, or elements, it arises from a grasp of those: we think we have knowledge of a thing when we have found its primary causes and principles, and followed it back to its elements. Clearly, then, systematic knowledge of nature must start with an attempt to settle questions about principles.
Aristotle
In Physics Book 1, Chap 1, as translated in J.L. Ackrill, A New Aristotle Reader (1988), 81.
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In defining an element let us not take an external boundary, Let us say, e.g., the smallest ponderable quantity of yttrium is an assemblage of ultimate atoms almost infinitely more like each other than they are to the atoms of any other approximating element. It does not necessarily follow that the atoms shall all be absolutely alike among themselves. The atomic weight which we ascribe to yttrium, therefore, merely represents a mean value around which the actual weights of the individual atoms of the “element” range within certain limits. But if my conjecture is tenable, could we separate atom from atom, we should find them varying within narrow limits on each side of the mean.
Address to Annual General Meeting of the Chemical Society (28 Mar 1888), printed in Journal of the Chemical Society (1888), 491.
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In 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 no subject is there a rule, compliance with which will lead to new knowledge or better understanding. Skilful observations, ingenious ideas, cunning tricks, daring suggestions, laborious calculations, all these may be required to advance a subject. Occasionally the conventional approach in a subject has to be studiously followed; on other occasions it has to be ruthlessly disregarded. Which of these methods, or in what order they should be employed is generally unpredictable. Analogies drawn from the history of science are frequently claimed to be a guide; but, as with forecasting the next game of roulette, the existence of the best analogy to the present is no guide whatever to the future. The most valuable lesson to be learnt from the history of scientific progress is how misleading and strangling such analogies have been, and how success has come to those who ignored them.
'Cosmology', in Arthur Beer (ed.), Vistas in Astronomy (1956), Vol. 2, 1722.
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In one of my lectures many years ago I used the phrase “following the trail of light”. The word “light” was not meant in its literal sense, but in the sense of following an intellectual concept or idea to where it might lead. My interest in living things is probably a fundamental motivation for the scientific work in the laboratory, and we created here in Berkeley one of the first and foremost interdisciplinary laboratories in the world.
In autobiography, Following the Trail of Light: A Scientific Odyssey (1992), 134.
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In place of infinity we usually put some really big number, like 15.
Perhaps referring to the programmer’s hexadecimal counting scheme which has 16 digits (0-9 followed by digits A-F), useful in binary context as a power of 2.
Anonymous
Attributed to a Computer Science Professor on various web pages. Webmaster has found no print source for this wording and comments, but its originality makes it worthy of inclusion here. Webmaster comments: perhaps one of those infinite number of monkeys typed it! Please make contact if you know a primary print source.
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In reality, all Arguments from Experience are founded on the Similarity which we discover among natural Objects, and by which we are induc'd to expect effects similar to those which we have found to follow from such Objects. And tho' none but a Fool or Madman will ever pretend to dispute the Authority of Experience, or to reject that great Guide of human Life, it may surely be allow'd a Philosopher to have so much Curiosity at least as to examine the Principle of human Nature, which gives this mighty Authority to Experience, and makes us draw Advantage from that Similarity which Nature has plac'd among different Objects. From Causes which appear similar we expect similar Effects. This is the Sum of our experimental Conclusions.
An Enquiry Concerning Human Understanding (1748), 63.
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In science, attempts at formulating hierarchies are always doomed to eventual failure. A Newton will always be followed by an Einstein, a Stahl by a Lavoisier; and who can say who will come after us? What the human mind has fabricated must be subject to all the changes—which are not progress—that the human mind must undergo. The 'last words' of the sciences are often replaced, more often forgotten. Science is a relentlessly dialectical process, though it suffers continuously under the necessary relativation of equally indispensable absolutes. It is, however, possible that the ever-growing intellectual and moral pollution of our scientific atmosphere will bring this process to a standstill. The immense library of ancient Alexandria was both symptom and cause of the ossification of the Greek intellect. Even now I know of some who feel that we know too much about the wrong things.
Voices in the Labyrinth: Nature, Man, and Science (1979), 46.
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In science, the more discovered, the more new paths open for exploration. It is usual in science, when things are vague and unclear, for the path to be like that of a drunkard, wandering in a zigzag. As we stagger back from what lastly dawns upon our befuddled wits is the wrong way, we cross over the true path and move nearly as far to the, equally wrong, opposite side. If all goes well, our deviations lessen and the path converges towards, but never completely follows, the true one. It gives a new insight to the old tag in vino veritas.
In The Ages of Gaia: A Biography of Our Living Earth (1999), 199.
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In the beginning (if there was such a thing), God created Newton’s laws of motion together with the necessary masses and forces. This is all; everything beyond this follows from the development of appropriate mathematical methods by means of deduction.
Autobiographical Notes (1946), 19. In Albert Einstein, Alice Calaprice, Freeman Dyson , The Ultimate Quotable Einstein (2011), 397.
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In the benzene nucleus we have been given a soil out of which we can see with surprise the already-known realm of organic chemistry multiply, not once or twice but three, four, five or six times just like an equivalent number of trees. What an amount of work had suddenly become necessary, and how quickly were busy hands found to carry it out! First the eye moves up the six stems opening out from the tremendous benzene trunk. But already the branches of the neighbouring stems have become intertwined, and a canopy of leaves has developed which becomes more spacious as the giant soars upwards into the air. The top of the tree rises into the clouds where the eye cannot yet follow it. And to what an extent is this wonderful benzene tree thronged with blossoms! Everywhere in the sea of leaves one can spy the slender hydroxyl bud: hardly rarer is the forked blossom [Gabelblüte] which we call the amine group, the most frequent is the beautiful cross-shaped blossom we call the methyl group. And inside this embellishment of blossoms, what a richness of fruit, some of them shining in a wonderful blaze of color, others giving off an overwhelming fragrance.
A. W. Hofmann, after-dinner speech at Kekulé Benzolfest (Mar 1890). Trans. in W. H. Brock, O. Theodor Benfrey and Susanne Stark, 'Hofmann's Benzene Tree at the Kekulé Festivities', Journal of Chemical Education (1991), 68, 887-8.
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In the course of normal speaking the inhibitory function of the will is continuously directed to bringing the course of ideas and the articulatory movements into harmony with each other. If the expressive movement which which follows the idea is retarded through mechanical causes, as is the case in writing ... such anticipations make their appearance with particular ease.
Folk Psychology (1900)
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In the great debates of early-nineteenth century geology, catastrophists followed the stereotypical method of objective science-empirical literalism. They believed what they saw, interpolated nothing, and read the record of the rocks directly.
'The Stinkstones of Oeningen', In Hen's Teeth and Horse's Toes (1983), 105.
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In the main, Bacon prophesied the direction of subsequent progress. But he “anticipated” the advance. He did not see that the new science was for a long time to be worked in the interest of old ends of human exploitation. He thought that it would rapidly give man new ends. Instead, it put at the disposal of a class the means to secure their old ends of aggrandizement at the expense of another class. The industrial revolution followed, as he foresaw, upon a revolution in scientific method. But it is taking the revolution many centuries to produce a new mind.
In Democracy and Education: An Introduction to the Philosophy of Education (1916), 330-331.
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In the past we see that periods of great intellectual activity have followed certain events which have acted by freeing the mind from dogma, extending the domain in which knowledge can be sought, and stimulating the imagination. … [For example,] the development of the cell theory and the theory of evolution.
From address, 'A Medical Retrospect'. Published in Yale Medical Journal (Oct 1910), 17, No. 2, 59.
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In the preface to his great History of Europe, H. A. L. Fisher wrote: “Men wiser than and more learned than I have discerned in history a plot, a rhythm, a predetermined pattern. These harmonies are concealed from me. I can see only one emergency following upon another as wave follows upon wave …” It seems to me that the same is true of the much older [geological stratigraphical] history of Europe.
In The Nature of the Stratigraphical Record (1973), 79.
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In the twenties the late Dr. Glenn Frank, an eminent social scientist, developed a new statement of the scientific code, which has been referred to as the “Five Fingers of the Scientific Method.” It may be outlined as follows: find the facts; filter the facts; focus the facts; face the facts; follow the facts. The facts or truths are found by experimentation; the motivation is material. The facts are filtered by research into the literature; the motivation is material. The facts are focused by the publication of results; again the motivation is material. Thus the first three-fifths of the scientific method have a material motivation. It is about time scientists acknowledge that there is more to the scientific convention than the material aspect. Returning to the fourth and fifth fingers of Dr. Frank's conception of the scientific method, the facts should be faced by the proper interpretation of them for society. In other words, a scientist must assume social responsibility for his discoveries, which means that he must have a moral motivation. Finally, in the fifth definition of the scientific method, the facts are to be followed by their proper application to everyday life in society, which means moral motivation through responsibility to society.
From 'Scientists and Society', American Scientist (Jul 1954), 42, No. 3, 495.
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In the world’s history certain inventions and discoveries occurred of peculiar value, on account of their great efficiency in facilitating all other inventions and discoveries. Of these were the art of writing and of printing, the discovery of America, and the introduction of patent laws. The date of the first … is unknown; but it certainly was as much as fifteen hundred years before the Christian era; the second—printing—came in 1436, or nearly three thousand years after the first. The others followed more rapidly—the discovery of America in 1492, and the first patent laws in 1624.
Lecture 'Discoveries, Inventions and Improvements' (22 Feb 1860) in John George Nicolay and John Hay (eds.), Complete Works of Abraham Lincoln (1894), Vol. 5, 109-10.
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In the year of our Lord 729, two comets appeared around the sun, striking terror into all who saw them. One comet rose early and preceded the sun, while the other followed the setting sun at evening, seeming to portend awful calamity to east and west alike. Or else, since one comet was the precursor of day and the other of night, they indicated that mankind was menaced by evils at both times. They appeared in the month of January, and remained visible for about a fortnight, pointing their fiery torches northward as though to set the welkin aflame. At this time, a swarm of Saracens ravaged Gaul with horrible slaughter; … Both the outset and course of Ceolwulfs reign were filled by so many grave disturbances that it is quite impossible to know what to write about them or what the outcome will be.
Bede
From Historia Ecclesiastica Gentis Anglorum, Book V, Chap. XXIII., as translated by Leo Sherley-Price, revised by R.E. Latham, Ecclesiastical History of the English People (1955, 1990), 323. Note: The observation likely was on a single comet seen twice each day. The event is also in both the Laud and Parker manuscripts of The Anglo-Saxon Chronicle.
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In the year of our Lord’s incarnation 729, two comets appeared about the sun, to the great terror of the beholders. One of them went before the rising sun in the morning, the other followed him when he set at night, as it were presaging much destruction to the east and west; one was the forerunner of the day, and the other of the night, to signify that mortals were threatened with calamities at both times. They carried their flaming tails towards the north, as it were ready to set the world on fire. They appeared in January, and continued nearly a fortnight. At which time a dreadful plague of Saracens ravaged France with miserable slaughter; … the beginning and progress of Ceolwulf’s reign were so filled with commotions, that it cannot yet be known what is to be said concerning them, or what end they will have.
Bede
From Historia Ecclesiastica Gentis Anglorum, Book V, Chap. XXIII, as translated in J.A. Giles (ed.), The Venerable Bede’s Ecclesiastical History of England. Also the Anglo-Saxon Chronicle (1894), 291-292. The editor reprinted the translation based on the 1723 work of John Stevens into modern English. Note: The observation likely was on a single comet seen twice each day. The event is also in both the Laud and Parker manuscripts of The Anglo-Saxon Chronicle.
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In these researches I followed the principles of the experimental method that we have established, i.e., that, in presence of a well-noted, new fact which contradicts a theory, instead of keeping the theory and abandoning the fact, I should keep and study the fact, and I hastened to give up the theory.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 164.
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In this lecture I would like to conclude with … some characteristics [of] gravity … The most impressive fact is that gravity is simple. It is simple to state the principles completely and not have left any vagueness for anybody to change the ideas of the law. It is simple, and therefore it is beautiful. It is simple in its pattern. I do not mean it is simple in its action—the motions of the various planets and the perturbations of one on the other can be quite complicated to work out, and to follow how all those stars in a globular cluster move is quite beyond our ability. It is complicated in its actions, but the basic pattern or the system beneath the whole thing is simple. This is common to all our laws; they all turn out to be simple things, although complex in their actual actions.
In 'The Law of Gravitation, as Example of Physical Law', the first of his Messenger Lectures (1964), Cornell University. Collected in The Character of Physical Law (1967), 33-34.
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In time, manufacturing will to a great extent follow the sun.
[Speculating that with development of solar power the deserts would become great industrial areas.]
As quoted in Rene Bache, 'Harnessing the Sun', Popular Mechanics (Apr 1928), 602.
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Inexact method of observation, as I believe, is one flaw in clinical pathology to-day. Prematurity of conclusion is another, and in part follows from the first; but in chief part an unusual craving and veneration for hypothesis, which besets the minds of most medical men, is responsible. Except in those sciences which deal with the intangible or with events of long past ages, no treatises are to be found in which hypothesis figures as it does in medical writings. The purity of a science is to be judged by the paucity of its recorded hypotheses. Hypothesis has its right place, it forms a working basis; but it is an acknowledged makeshift, and, at the best, of purpose unaccomplished. Hypothesis is the heart which no man with right purpose wears willingly upon his sleeve. He who vaunts his lady love, ere yet she is won, is apt to display himself as frivolous or his lady a wanton.
The Mechanism and Graphic Registration of the Heart Beat (1920), vii.
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INSECTIVORA, n.
'See,' cries the chorus of admiring preachers,
'How Providence provides for all His creatures!"'
'His care,' the gnat said, 'even the insects follows: For us
He has provided wrens and swallows.'
[Under pen-name Sempen Railey.]
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  169.
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Instead of saying that a man behaves because of the consequences which are to follow his behavior, we simply say that he behaves because of the consequences which have followed similar behavior in the past. This is, of course, the Law of Effect or operant conditioning.
In Science and Human Behavior (1953), 87.
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Is evolution a theory, a system or a hypothesis? It is much more: it is a general condition to which all theories, all hypotheses, all systems must bow and which they must satisfy henceforth if they are to be thinkable and true. Evolution is a light illuminating all facts, a curve that all lines must follow. ... The consciousness of each of us is evolution looking at itself and reflecting upon itself....Man is not the center of the universe as once we thought in our simplicity, but something much more wonderful—the arrow pointing the way to the final unification of the world in terms of life. Man alone constitutes the last-born, the freshest, the most complicated, the most subtle of all the successive layers of life. ... The universe has always been in motion and at this moment continues to be in motion. But will it still be in motion tomorrow? ... What makes the world in which we live specifically modern is our discovery in it and around it of evolution. ... Thus in all probability, between our modern earth and the ultimate earth, there stretches an immense period, characterized not by a slowing-down but a speeding up and by the definitive florescence of the forces of evolution along the line of the human shoot.
In The Phenomenon of Man (1975), pp 218, 220, 223, 227, 228, 277.
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It does not follow that because something can be counted it therefore should be counted.
In a speech to the Society for College and University Planning, September 1975.
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It follows from the supreme perfection of God, that in creating the universe has chosen the best possible plan, in which there is the greatest variety together with the greatest order; the best arranged ground, place, time; the most results produced in the most simple ways; the most of power, knowledge, happiness and goodness the creatures that the universe could permit. For since all the possibles in I understanding of God laid claim to existence in proportion to their perfections, the actual world, as the resultant of all these claims, must be the most perfect possible. And without this it would not be possible to give a reason why things have turned out so rather than otherwise.
The Principles of Nature and Grace (1714), The Philosophical Works of Leibnitz (1890), ed. G. M. Duncan, 213-4.
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It follows from the theory of relativity that mass and energy are both different manifestations of the same thing—a somewhat unfamiliar conception for the average man. Furthermore E=MC2, in which energy is put equal to mass multiplied with the square of the velocity of light, showed that a very small amount of mass may be converted into a very large amount of energy... the mass and energy were in fact equivalent.
As expressed in the Einstein film, produced by Nova Television (1979). Quoted in Alice Calaprice, The Quotable Einstein (1996), 183.
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It has been said that no science is established on a firm basis unless its generalisations can be expressed in terms of number, and it is the special province of mathematics to assist the investigator in finding numerical relations between phenomena. After experiment, then mathematics. While a science is in the experimental or observational stage, there is little scope for discerning numerical relations. It is only after the different workers have “collected data” that the mathematician is able to deduce the required generalisation. Thus a Maxwell followed Faraday and a Newton completed Kepler.
In Higher Mathematics for Students of Chemistry and Physics (1902), 3.
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It is … genius which has given motion and progress to society; prevented the ossification of the human heart and brain; and though, in its processes, it may not ever have followed the rules laid down in primers, it has, at least, saved history from being the region of geology, and our present society from being a collection of fossil remains.
In 'Genius', Wellman’s Miscellany (Dec 1871), 4, No. 6, 204.
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It is a serious question whether America, following England’s lead, has not gone into problem-solving too extensively. Certain it is that we are producing no text-books in which the theory is presented in the delightful style which characterizes many of the French works … , or those of the recent Italian school, or, indeed, those of the continental writers in general.
In The Teaching of Elementary Mathematics (1902), 219.
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It is admitted by all that a finished or even a competent reasoner is not the work of nature alone; the experience of every day makes it evident that education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history, may be chosen for this purpose. Now of all these, it is desirable to choose the one which admits of the reasoning being verified, that is, in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. When the guiding property of the loadstone was first ascertained, and it was necessary to learn how to use this new discovery, and to find out how far it might be relied on, it would have been thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.
In On the Study and Difficulties of Mathematics (1898), chap. 1.
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It is almost as difficult to make a man unlearn his errors, as his knowledge. Mal-information is more hopeless than non-information: for error is always more busy than ignorance. Ignorance is a blank sheet on which we may write; but error is a scribbled one on which we first erase. Ignorance is contented to stand still with her back to the truth; but error is more presumptuous, and proceeds, in the same direction. Ignorance has no light, but error follows a false one. The consequence is, that error, when she retraces her footsteps, has farther to go, before we can arrive at the truth, than ignorance.
Reflection 1, in Lacon: or Many things in Few Words; Addressed to Those Who Think (1820), 15.
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It is because simplicity and vastness are both beautiful that we seek by preference simple facts and vast facts; that we take delight, now in following the giant courses of the stars, now in scrutinizing the microscope that prodigious smallness which is also a vastness, and now in seeking in geological ages the traces of a past that attracts us because of its remoteness.
…...
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It is easy for men to give advice, but difficult for one’s self to follow; we have an example in physicians: for their patients they order a strict regime, for themselves, on going to bed, they do all that they have forbidden to others.
Philemon
'The Sicilian.' In Gustave Jules Witkowski, The Evil that Has Been Said of Doctors (1889), 4-5
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It is easy to follow in the sacred writings of the Jewish people the development of the religion of fear into the moral religion, which is carried further in the New Testament. The religions of all civilized peoples, especially those of the Orient, are principally moral religions. An important advance in the life of a people is the transformation of the religion of fear into the moral religion.
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It is interesting thus to follow the intellectual truths of analysis in the phenomena of nature. This correspondence, of which the system of the world will offer us numerous examples, makes one of the greatest charms attached to mathematical speculations.
Exposition du système du monde (1799)
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It is interesting to transport one’s self back to the times when Astronomy began; to observe how discoveries were connected together, how errors have got mixed up with truth, have delayed the knowledge of it, and retarded its progress; and, after having followed the various epochs and traversed every climate, finally to contemplate the edifice founded on the labours of successive centuries and of various nations.
Description of Bailly’s plan when writing his history of astronomy books, quoted by François Arago, trans. by William Henry Smyth, Baden Powell and Robert Grant, in 'Bailly', Biographies of Distinguished Scientific Men (1859), Vol. 1, 114. Arago first presented this biography of Bailly when he read it to the Academy of Sciences (26 Feb 1844).
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It is known that there are an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so the average population of all the planets in the Universe can be said to be zero. From this it follows that the population of the whole Universe is also zero, and that any people you may meet from time to time are merely the products of a deranged imagination.
In The Restaurant at the End of the Universe (1980, 2005), 142-143. Slightly revised from 'Fit the Fifth', The Original Hitchhiker Radio Scripts (1985), 102. The show was recorded for the BBC on 21 Feb 1978.
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It is not an easy paper to follow, for the items that require retention throughout the analysis are many, and it is fatal to one's understanding to lose track of any of them. Mastery of this paper, however, can give one the strong feeling of being ableto master anything else [one] might have to wrestle within biology.
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).
Classic Papers in Genetics (1959), 156.
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It is often claimed that knowledge multiplies so rapidly that nobody can follow it. I believe this is incorrect. At least in science it is not true. The main purpose of science is simplicity and as we understand more things, everything is becoming simpler. This, of course, goes contrary to what everyone accepts.
Edward Teller, Wendy Teller, Wilson Talley, Conversations on the Dark Secrets of Physics (1991, 2002), 2.
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It is said that the composing of the Lilavati was occasioned by the following circumstance. Lilavati was the name of the author’s daughter, concerning whom it appeared, from the qualities of the ascendant at her birth, that she was destined to pass her life unmarried, and to remain without children. The father ascertained a lucky hour for contracting her in marriage, that she might be firmly connected and have children. It is said that when that hour approached, he brought his daughter and his intended son near him. He left the hour cup on the vessel of water and kept in attendance a time-knowing astrologer, in order that when the cup should subside in the water, those two precious jewels should be united. But, as the intended arrangement was not according to destiny, it happened that the girl, from a curiosity natural to children, looked into the cup, to observe the water coming in at the hole, when by chance a pearl separated from her bridal dress, fell into the cup, and, rolling down to the hole, stopped the influx of water. So the astrologer waited in expectation of the promised hour. When the operation of the cup had thus been delayed beyond all moderate time, the father was in consternation, and examining, he found that a small pearl had stopped the course of the water, and that the long-expected hour was passed. In short, the father, thus disappointed, said to his unfortunate daughter, I will write a book of your name, which shall remain to the latest times—for a good name is a second life, and the ground-work of eternal existence.
In Preface to the Persian translation of the Lilavati by Faizi (1587), itself translated into English by Strachey and quoted in John Taylor (trans.) Lilawati, or, A Treatise on Arithmetic and Geometry by Bhascara Acharya (1816), Introduction, 3. [The Lilavati is the 12th century treatise on mathematics by Indian mathematician, Bhaskara Acharya, born 1114.]
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It is the flash which appears, the thunderbolt will follow.
Translation of the original French, “C'est l'éclair qui paraît, la foudre va partir.” From the play, Oreste, Act 2, Scene 7. Accompanied with the translation in Craufurd Tait Ramage, Beautiful Thoughts from French and Italian Authors (1866), 365.
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It is the modest, not the presumptuous, inquirer who makes a real and safe progress in the discovery of divine truths. One follows Nature and Nature’s God; that is, he follows God in his works and in his word.
Letter to Alexander Pope. As cited in John Bartlett, Familiar Quotations (1875, 10th ed., 1919), 304. The quote has a footnote to compare from Pope’s philosophical poem, Essay on Man (1733-34), epistle iv, lines 331-32: “Slave to no sect, who takes no private road, But looks through Nature up to Nature’s God.”
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It is very desirable to have a word to express the Availability for work of the heat in a given magazine; a term for that possession, the waste of which is called Dissipation. Unfortunately the excellent word Entropy, which Clausius has introduced in this connexion, is applied by him to the negative of the idea we most naturally wish to express. It would only confuse the student if we were to endeavour to invent another term for our purpose. But the necessity for some such term will be obvious from the beautiful examples which follow. And we take the liberty of using the term Entropy in this altered sense ... The entropy of the universe tends continually to zero.
Sketch of Thermodynamics (1868), 100-2.
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It is well to observe the force and virtue and consequence of discoveries, and these are to be seen nowhere more conspicuously than in those three which were unknown to the ancients, and of which the origins, although recent, are obscure and inglorious; namely, printing, gunpowder, and the magnet. For these three have changed the whole face and state of things throughout the world; the first in literature, the second in warfare, the third in navigation; whence have followed innumerable changes, insomuch that no empire, no sect, no star seems to have exerted greater power and influence in human affairs than these mechanical discoveries.
From Novum Organum (1620), Book 1, Aphorism 129. Translated as The New Organon: Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man), collected in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 4, 114.
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It is with our entire past ... that we desire, will and act ... from this survival of the past it follows that consciousness cannot go through the same state twice. The circumstances may still be the same, but they will act no longer on the same person ... that is why our duration is irreversible.
Creative Evolution (1911), trans. Arthur Mitchell, 6.
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It must be for truth’s sake, and not for the sake of its usefulness to humanity, that the scientific man studies Nature. The application of science to the useful arts requires other abilities, other qualities, other tools than his; and therefore I say that the man of science who follows his studies into their practical application is false to his calling. The practical man stands ever ready to take up the work where the scientific man leaves it, and adapt it to the material wants and uses of daily life.
Methods of Study in Natural History (1863),24.
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It needs scarcely be pointed out that in placing Mathematics at the head of Positive Philosophy, we are only extending the application of the principle which has governed our whole Classification. We are simply carrying back our principle to its first manifestation. Geometrical and Mechanical phenomena are the most general, the most simple, the most abstract of all,— the most irreducible to others, the most independent of them; serving, in fact, as a basis to all others. It follows that the study of them is an indispensable preliminary to that of all others. Therefore must Mathematics hold the first place in the hierarchy of the sciences, and be the point of departure of all Education whether general or special.
In Auguste Comte and Harriet Martineau (trans.), The Positive Philosophy (1858), Introduction, Chap. 2, 50.
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It was badly received by the generation to which it was first addressed, and the outpouring of angry nonsense to which it gave rise is sad to think upon. But the present generation will probably behave just as badly if another Darwin should arise, and inflict upon them that which the generality of mankind most hate—the necessity of revising their convictions. Let them, then, be charitable to us ancients; and if they behave no better than the men of my day to some new benefactor, let them recollect that, after all, our wrath did not come to much, and vented itself chiefly in the bad language of sanctimonious scolds. Let them as speedily perform a strategic right-about-face, and follow the truth wherever it leads.
'On the Reception of the Origin of Species'. In F. Darwin (ed.), The Life and Letters of Charles Darwin, Including an Autobiographical Chapter (1888), Vol. 2, 204.
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It was not alone the striving for universal culture which attracted the great masters of the Renaissance, such as Brunellesco, Leonardo da Vinci, Raphael, Michelangelo and especially Albrecht Dürer, with irresistible power to the mathematical sciences. They were conscious that, with all the freedom of the individual fantasy, art is subject to necessary laws, and conversely, with all its rigor of logical structure, mathematics follows aesthetic laws.
From Lecture (5 Feb 1891) held at the Rathhaus, Zürich, printed as Ueber den Antheil der mathematischen Wissenschaft an der Kultur der Renaissance (1892), 19. (The Contribution of the Mathematical Sciences to the Culture of the Renaissance.) As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 183.
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It would follow that “significant form” was form behind which we catch a sense of ultimate reality.
In Art (1913), 54.
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Its [mathematical analysis] chief attribute is clearness; it has no means for expressing confused ideas. It compares the most diverse phenomena and discovers the secret analogies which unite them. If matter escapes us, as that of air and light because of its extreme tenuity, if bodies are placed far from us in the immensity of space, if man wishes to know the aspect of the heavens at successive periods separated by many centuries, if gravity and heat act in the interior of the solid earth at depths which will forever be inaccessible, mathematical analysis is still able to trace the laws of these phenomena. It renders them present and measurable, and appears to be the faculty of the human mind destined to supplement the brevity of life and the imperfection of the senses, and what is even more remarkable, it follows the same course in the study of all phenomena; it explains them in the same language, as if in witness to the unity and simplicity of the plan of the universe, and to make more manifest the unchangeable order which presides over all natural causes.
From Théorie Analytique de la Chaleur (1822), Discours Préliminaire, xiv, (Theory of Heat, Introduction), as translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.
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Jesus tapped me on the shoulder and said, “Bob, why are you resisting me?” I said, “I’m not resisting You!” He said, “You gonna follow Me?” I said, “I’ve never thought about that before!” He said, “When you’re not following Me, you’re resisting Me.”
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 156
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John Dalton was a very singular Man, a quaker by profession & practice: He has none of the manners or ways of the world. A tolerable mathematician He gained his livelihood I believe by teaching the mathematics to young people. He pursued science always with mathematical views. He seemed little attentive to the labours of men except when they countenanced or confirmed his own ideas... He was a very disinterested man, seemed to have no ambition beyond that of being thought a good Philosopher. He was a very coarse Experimenter & almost always found the results he required.—Memory & observation were subordinate qualities in his mind. He followed with ardour analogies & inductions & however his claims to originality may admit of question I have no doubt that he was one of the most original philosophers of his time & one of the most ingenious.
J. Z. Fullmer, 'Davy's Sketches of his Contemporaries', Chymia, 1967, 12, 133-134.
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Journalism must find the facts, it must not prejudge things in terms of conservatism or liberalism or radicalism; it must not decide in advance that it is to be conformist or non-conformist; it cannot fly in the face of facts without courting ultimate disaster.
Journalism must focus the facts; facts are not important for their own sake; they are important only as a basis for action; journalism must focus the facts it finds upon the issues its readers face.
Journalism must filter the facts; it must with conscientious care separate the facts from admixtures of prejudice, passion, partisanship, and selfish interest; facts that are diluted, colored, or perverted are valueless as a basis for action.
Journalism must face the facts; it must learn that the energy spent in trying to find ways to get around, under, or over the facts is wasted energy; facts have a ruthless way of winning the day sooner or later.
Journalism must follow the facts; journalism must say of facts as Job said, of God: though they slay us, yet shall we trust them; if the facts threaten to upset a paper's cherished policy, it always pays the journalist to re-examine his policy; that way lies realism, and realism is the ultimate good.
From address as president of the Wisconsin local chapter of Theta Sigma Phi, at its first annual Matrix Table (9 Jan 1926). quoted in 'Journalism News and Notes', in Robert S. Crawford (ed.), The Wisconsin Alumni Magazine (Feb 1926), 27, No. 4, 101. If you know any other example of Glenn Frank speaking about his five themes on facts, please contact Webmaster.
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Just as a tree constitutes a mass arranged in a definite manner, in which, in every single part, in the leaves as in the root, in the trunk as in the blossom, cells are discovered to be the ultimate elements, so is it also with the forms of animal life. Every animal presents itself as a sum of vital unities, every one of which manifests all the characteristics of life. The characteristics and unity of life cannot be limited to anyone particular spot in a highly developed organism (for example, to the brain of man), but are to be found only in the definite, constantly recurring structure, which every individual element displays. Hence it follows that the structural composition of a body of considerable size, a so-called individual, always represents a kind of social arrangement of parts, an arrangement of a social kind, in which a number of individual existences are mutually dependent, but in such a way, that every element has its own special action, and, even though it derive its stimulus to activity from other parts, yet alone effects the actual performance of its duties.
In Lecture I, 'Cells and the Cellular Theory' (1858), Rudolf Virchow and Frank Chance (trans.) ,Cellular Pathology (1860), 13-14.
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Keep in mind that new ideas are commonplace, and almost always wrong. Most flashes of insight lead nowhere; statistically, they have a half-life of hours or maybe days. Most experiments to follow up the surviving insights are tedious and consume large amounts of time, only to yield negative or (worse!) ambiguous results.
In Consilience: The Unity of Knowledge (1998, 1999), 60
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Louis Agassiz quote: Lay aside all conceit Learn to read the book of Nature for yourself. Those who have succeeded best have fol
Lay aside all conceit. Learn to read the book of Nature for yourself. Those who have succeeded best have followed for years some slim thread which once in a while has broadened out and disclosed some treasure worth a life-long search.
Lecture at a teaching laboratory on Penikese Island, Buzzard's Bay. Quoted from the lecture notes by David Starr Jordan, Science Sketches (1911), 145.
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Leave the beaten track occasionally and dive into the woods. Every time you do so you will be certain to find something that you have never seen before. Of course, it will be a little thing, but do not ignore it. Follow it up, explore all around it: one discovery will lead to another, and before you know it, you will have something worth thinking about to occupy your mind. All really big discoveries are the results of thought.
Address (22 May 1914) to the graduating class of the Friends’ School, Washington, D.C. Printed in 'Discovery and Invention', The National Geographic Magazine (1914), 25, 650.
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Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past … I shall use the phrase “time's arrow” to express this one-way property of time which has no analogue in space.
Gifford Lectures (1927), The Nature of The Physical World (1928), 69.
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Let us follow the natural order and begin with the primary facts.
Aristotle
In Ingram Bywater (trans.), Aristotle, On the Art of Poetry (1909), 3.
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Let us now declare the means whereby our understanding can rise to knowledge without fear of error. There are two such means: intuition and deduction. By intuition I mean not the varying testimony of the senses, nor the deductive judgment of imagination naturally extravagant, but the conception of an attentive mind so distinct and so clear that no doubt remains to it with regard to that which it comprehends; or, what amounts to the same thing, the self-evidencing conception of a sound and attentive mind, a conception which springs from the light of reason alone, and is more certain, because more simple, than deduction itself. …
It may perhaps be asked why to intuition we add this other mode of knowing, by deduction, that is to say, the process which, from something of which we have certain knowledge, draws consequences which necessarily follow therefrom. But we are obliged to admit this second step; for there are a great many things which, without being evident of themselves, nevertheless bear the marks of certainty if only they are deduced from true and incontestable principles by a continuous and uninterrupted movement of thought, with distinct intuition of each thing; just as we know that the last link of a long chain holds to the first, although we can not take in with one glance of the eye the intermediate links, provided that, after having run over them in succession, we can recall them all, each as being joined to its fellows, from the first up to the last. Thus we distinguish intuition from deduction, inasmuch as in the latter case there is conceived a certain progress or succession, while it is not so in the former; … whence it follows that primary propositions, derived immediately from principles, may be said to be known, according to the way we view them, now by intuition, now by deduction; although the principles themselves can be known only by intuition, the remote consequences only by deduction.
In Rules for the Direction of the Mind, Philosophy of Descartes. [Torrey] (1892), 64-65.
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Life itself is but the expression of a sum of phenomena, each of which follows the ordinary physical and chemical laws. (1845)
In Jonathan Miller, Freud: the Man, his World, His Influence (1972), 25
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Like water, be gentle and strong. Be gentle enough to follow the natural paths of the earth, and strong enough to rise up and reshape the world.
…...
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Logic is not concerned with human behavior in the same sense that physiology, psychology, and social sciences are concerned with it. These sciences formulate laws or universal statements which have as their subject matter human activities as processes in time. Logic, on the contrary, is concerned with relations between factual sentences (or thoughts). If logic ever discusses the truth of factual sentences it does so only conditionally, somewhat as follows: if such-and-such a sentence is true, then such-and-such another sentence is true. Logic itself does not decide whether the first sentence is true, but surrenders that question to one or the other of the empirical sciences.
Logic (1937). In The Language of Wisdom and Folly: Background Readings in Semantics (1967), 44.
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Look somewhere else for someone who can follow you in your researches about numbers. For my part, I confess that they are far beyond me, and I am competent only to admire them.
In Letter (27 Oct 1654), the third from Pascal to Fermat. As translated in George F. Simmons, Calculus Gems: Brief Lives and Memorable Mathematics (2007), 103. From the original French, “Cherchez ailleurs qui vous suive dans vos inventions numériques,… pour moi je vous confesse que cela me passé de bien loin: je ne fuis capable que de les admirer,” in Francis Maseres,Scriptores Logarithmici: Or, a Collection of Several Curious Tracts on the Nature and Construction of Logarithms (1801), Vol. 4, 495.
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Man is a part of nature, not something contrasted with nature. His thoughts and his bodily movements follow the same laws that describe the motions of stars and atoms.
Opening of What I Believe (1925), 1.
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Man is naturally metaphysical and arrogant, and is thus capable of believing that the ideal creations of his mind, which express his feelings, are identical with reality. From this it follows that the experimental method is not really natural to him.
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Many Species of Animals have been lost out of the World, which Philosophers and Divines are unwilling to admit, esteeming the Destruction of anyone Species a Dismembring of the Universe, and rendring the World imperfect; whereas they think the Divine Providence is especially concerned, and solicitous to secure and preserve the Works of the Creation. And truly so it is, as appears, in that it was so careful to lodge all Land Animals in the Ark at the Time of the general Deluge; and in that, of all Animals recorded in Natural Histories, we cannot say that there hath been anyone Species lost, no not of the most infirm, and most exposed to Injury and Ravine. Moreover, it is likely, that as there neither is nor can be any new Species of Animals produced, all proceeding from Seeds at first created; so Providence, without which one individual Sparrow falls not to the ground, doth in that manner watch over all that are created, that an entire Species shall not be lost or destroyed by any Accident. Now, I say, if these Bodies were sometimes the Shells and Bones of Fish, it will thence follow, that many Species have been lost out of the World... To which I have nothing to reply, but that there may be some of them remaining some where or other in the Seas, though as yet they have not come to my Knowledge. Far though they may have perished, or by some Accident been destroyed out of our Seas, yet the Race of them may be preserved and continued still in others.
John Ray
Three Physico-Theological Discourses (1713), Discourse II, 'Of the General Deluge, in the Days of Noah; its Causes and Effects', 172-3.
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Mathematics, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road. I believe, on the contrary, that there was a long period of tentative work (chiefly still among the Egyptians), and that the change is to be ascribed to a revolution, produced by the happy thought of a single man, whose experiments pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science. The history of that intellectual revolution, which was far more important than the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us. … A new light flashed on the first man who demonstrated the properties of the isosceles triangle (whether his name was Thales or any other name), for he found that he had not to investigate what he saw in the figure, or the mere concepts of that figure, and thus to learn its properties; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.
In Critique of Pure Reason, Preface to the Second Edition, (1900), 690.
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Men go into space to see whether it is the kind of place where other men, and their families and their children, can eventually follow them. A disturbingly high proportion of the intelligent young are discontented because they find the life before them intolerably confining. The moon offers a new frontier. It is as simple and splendid as that.
Editorial on the moon landing, The Economist (1969).
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More discoveries have arisen from intense observation of very limited material than from statistics applied to large groups. The value of the latter lies mainly in testing hypotheses arising from the former. While observing one should cultivate a speculative, contemplative attitude of mind and search for clues to be followed up. Training in observation follows the same principles as training in any activity. At first one must do things consciously and laboriously, but with practice the activities gradually become automatic and unconscious and a habit is established. Effective scientific observation also requires a good background, for only by being familiar with the usual can we notice something as being unusual or unexplained.
The Art of Scientific Investigation (1950), 101.
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Mortal as I am, I know that I am born for a day. But when I follow at my pleasure the serried multitude of the stars in their circular course, my feet no longer touch the earth.
Ptolemy
…...
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My definition of science is … somewhat as follows: Science is an interconnected series of concepts and conceptual schemes that have developed as a result of experimentation and observation and are fruitful of further experimentation and observations. In this definition the emphasis is on the word “fruitful.”
In Science and Common Sense (1951), 25.
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Newton’s and Darwin’s world were different from the worlds of most men, and yet their worlds were not the world, but more and better than mine, as they had followed out further and better the teachings of the sense.
In Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), xlviii.
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Ninety-nine [students] out of a hundred are automata, careful to walk in prescribed paths, careful to follow the prescribed custom. This is not an accident but the result of substantial education, which, scientifically defined, is the subsumption of the individual.
As quoted in various 21st century books, each time cited only as from the The Philosophy of Education (1906), with no page number. For example, in John Taylor Gatto, A Different Kind of Teacher: Solving the Crisis of American Schooling (2000), 61. Note: Webmaster is suspicious of the attribution of this quote. The Library of Congress lists no such title by Harris in 1906. The LOC does catalog this title by Harris for 1893, which is a 9-page pamphlet printing the text of a series of five lectures. These lectures do not contain this quote. William Torrey Harris was editor of the International Education Series of books, of which Vol. 1 was the translation by Anna Callender Bracket of The Philosophy of Education by Johann Karl Friedrich Rosenkranz (2nd ed. rev. 1886). The translation was previously published in The Journal of Speculative Philosophy (1872, -73, -74), Vols vi-viii. Webmaster does not find the quote in that book, either. Webmaster has so far been unable to verify this quote, in these words, or even find the quote in any 19th or 20th century publication (which causes more suspicion). If you have access to the primary source for this quote, please contact Webmaster.
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Nor can it be supposed that the diversity of chemical structure and process stops at the boundary of the species, and that within that boundary, which has no real finality, rigid uniformity reigns. Such a conception is at variance with any evolutionary conception of the nature and origin of species. The existence of chemical individuality follows of necessity from that of chemical specificity, but we should expect the differences between individuals to be still more subtle and difficult of detection. Indications of their existence are seen, even in man, in the various tints of skin, hair, and eyes, and in the quantitative differences in those portions of the end-products of metabolism which are endogenous and are not affected by diet, such as recent researches have revealed in increasing numbers. Even those idiosyncrasies with regard to drugs and articles of food which are summed up in the proverbial saying that what is one man's meat is another man's poison presumably have a chemical basis.
Inborn Errors of Metabolism: The Croonian Lectures delivered before the Royal College of Physicians of London, in June, 1908 (1909), 2-3.
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Nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus, which he declined to do before he had worked out his problem to a demonstration; the soldier, enraged, drew his sword and ran him through. Others write, that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate, that as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is, that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honoured them with signal favours.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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Nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus, which he declined to do before he had worked out his problem to a demonstration; the soldier, enraged, drew his sword and ran him through. Others write, that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate, that as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is, that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honoured them with signal favours.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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Nothing could be more admirable than the manner in which for forty years he [Joseph Black] performed this useful and dignified office. His style of lecturing was as nearly perfect as can well be conceived; for it had all the simplicity which is so entirely suited to scientific discourse, while it partook largely of the elegance which characterized all he said or did … I have heard the greatest understandings of the age giving forth their efforts in its most eloquent tongues—have heard the commanding periods of Pitt’s majestic oratory—the vehemence of Fox’s burning declamation—have followed the close-compacted chain of Grant’s pure reasoning—been carried away by the mingled fancy, epigram, and argumentation of Plunket; but I should without hesitation prefer, for mere intellectual gratification (though aware how much of it is derived from association), to be once more allowed the privilege which I in those days enjoyed of being present while the first philosopher of his age was the historian of his own discoveries, and be an eyewitness of those experiments by which he had formerly made them, once more performed with his own hands.
In 'Philosophers of the Time of George III', The Works of Henry, Lord Brougham, F.R.S. (1855), Vol. I, 19-21.
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Now I must take you to a very interesting part of our subject—to the relation between the combustion of a candle and that living kind of combustion which goes on within us. In every one of us there is a living process of combustion going on very similar to that of a candle, and I must try to make that plain to you. For it is not merely true in a poetical sense—the relation of the life of man to a taper; and if you will follow, I think I can make this clear.
A Course of Six Lectures on the Chemical History of a Candle (1861), 155-6.
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Now it came to me: … the independence of the gravitational acceleration from the nature of the falling substance, may be expressed as follows: In a gravitational field (of small spatial extension) things behave as they do in a space free of gravitation. … This happened in 1908. Why were another seven years required for the construction of the general theory of relativity? The main reason lies in the fact that it is not so easy to free oneself from the idea that coordinates must have an immediate metrical meaning.
In Paul Arthur Schilpp, 'Autobiographical Notes', Albert Einstein: Philosopher-Scientist (1949), 65-67.
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Now, all causes of natural effects must be expressed by means of lines, angles and figures, for otherwise it is impossible to grasp their explanation. This is evident as follows. A natural agent multiplies its power from itself to the recipient, whether it acts on sense or on matter. This power is sometimes called species, sometimes a likeness, and it is the same thing whatever it may be called; and the agent sends the same power into sense and into matter, or into its own contrary, as heat sends the same thing into the sense of touch and into a cold body. For it does not act, by deliberation and choice, and therefore it acts in a single manner whatever it encounters, whether sense or something insensitive, whether something animate or inanimate. But the effects are diversified by the diversity of the recipient, for when this power is received by the senses, it produces an effect that is somehow spiritual and noble; on the other hand, when it is received by matter, it produces a material effect. Thus the sun produces different effects in different recipients by the same power, for it cakes mud and melts ice.
De Uneis, Angulis et Figuris seu Fractionibus Reflexionibus Radiorum (On Lines, Angles and Figures or On the Refraction and Reflection of Rays) [1230/31], trans. D. C. Lindberg, quoted in E. Grant (ed.), A Source Book in Medieval Science (1974), 385-6.
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Nowadays the field naturalist—who is usually at all points superior to the mere closet naturalist—follows a profession as full of hazard and interest as that of the explorer or of the big-game hunter in the remote wilderness.
African Game Trails (1910), 414-415.
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Numbers written on restaurant checks [bills] within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe.
This single statement took the scientific world by storm. It completely revolutionized it. So many mathematical conferences got held in such good restaurants that many of the finest minds of a generation died of obesity and heart failure and the science of math was put back by years.
Life, the Universe and Everything (1982, 1995), 49.
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Oddly enough, eccentrics are happier and healthier than conformists. A study of 1,000 people found that eccentrics visit a doctor an average of just once every eight years, while conformists go twice a year. Eccentrics apparently enjoy better health because they feel less pressured to follow society’s rules, said the researcher who did the study at Royal Edinburgh Hospital in Scotland.
Eccentrics (1995).Study results in SELF magazine - 1992 National Enquirer.
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On CBS Radio the news of [Ed Murrow’s] death, reportedly from lung cancer, was followed by a cigarette commercial.
Prime Time: the Life of Edward R. Murrow (1969), 34.
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On the basis of the results recorded in this review, it can be claimed that the average sand grain has taken many hundreds of millions of years to lose 10 per cent. of its weight by abrasion and become subangular. It is a platitude to point to the slowness of geological processes. But much depends on the way things are put. For it can also be said that a sand grain travelling on the bottom of a river loses 10 million molecules each time it rolls over on its side and that representation impresses us with the high rate of this loss. The properties of quartz have led to the concentration of its grains on the continents, where they could now form a layer averaging several hundred metres thick. But to my mind the most astounding numerical estimate that follows from the present evaluations, is that during each and every second of the incredibly long geological past the number of quartz grains on earth has increased by 1,000 million.
'Sand-its Origin, Transportation, Abrasion and Accumulation', The Geological Society of South Africa (1959), Annexure to Volume 62, 31.
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On the terrace of the Pepiniere, the 150 pupils of the Institut Chemique talk chemistry as they leave the auditoria and the laboratory. The echoes of the magnificent public garden of the city of Nancy make the words reverberate; coupling, condensation, grignardization. Moreover, their clothes stay impregnated with strong and characteristic odours; we follow the initiates of Hermes by their scent. In such an environment, how is it possible not to be productive?
Charles Courtot, 'Notice sur la vie de Victor Grignard', Bulletin Societé Chemie, 1936, 3, 1445. Trans. in Mary Jo Nye, Science in the Provinces (1986),184.
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Once the data are in, the theory has to follow along meekly.
Hardfought (1983). Quoted in Gary Westfahl, Science Fiction Quotations (2005), 322.
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One may say that predictions are dangerous particularly for the future. If the danger involved in a prediction is not incurred, no consequence follows and the uncertainty principle is not violated.
Edward Teller , Wendy Teller and Wilson Talley, Conversations from the Dark Side of Physics (1991, 2002), 235.
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One of the great commandments of science is, 'Mistrust arguments from authority'. (Scientists, being primates, and thus given to dominance hierarchies, of course do not always follow this commandment.)
The Demon-Haunted World: Science as a Candle in the Dark (1996), 31.
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One of the things that makes the history of science so endlessly fascinating is to follow the slow education of our species in the sort of beauty to expect in nature.
In Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature (1992), 158.
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Ordinarily logic is divided into the examination of ideas, judgments, arguments, and methods. The two latter are generally reduced to judgments, that is, arguments are reduced to apodictic judgments that such and such conclusions follow from such and such premises, and method is reduced to judgments that prescribe the procedure that should be followed in the search for truth.
Ampére expresses how arguments have a logical structure which he expected should be applied to relate scientific theories to experimental evidence. In James R. Hofmann, André-Marie Ampère (1996), 158. Cites Académie des Sciences Ampère Archives, École Normale lecture 15 notes, box 261.
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Ostwald was a great protagonist and an inspiring teacher. He had the gift of saying the right thing in the right way. When we consider the development of chemistry as a whole, Ostwald's name like Abou ben Adhem's leads all the rest ... Ostwald was absolutely the right man in the right place. He was loved and followed by more people than any chemist of our time.
'Ostwald', Journal of Chemical Education, 1933, 10, 612, as cited by Erwin N. Hiebert and Hans-Gunther Korber in article on Ostwald in Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography Supplement 1, Vol 15-16, 466, which also says Wilder Bancroft "received his doctorate under Ostwald in 1892."
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Our great mistake in education is ... the worship of book-learning—the confusion of instruction and education. We strain the memory instead of cultivating the mind. … We ought to follow exactly the opposite course with children—to give them a wholesome variety of mental food, and endeavour to cultivate their tastes, rather than to fill their minds with dry facts.
The Pleasures of Life (Appleton, 1887), 183-184, or (2007), 71.
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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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Our progress in education has truly been a curious one. We have gone from the hard and arbitrary curriculum, with its primary insistence upon training the memory and the consequent devitalization of valuable and beneficial subjects, to the free elective system, with its wholesale invitations to follow the paths of least resistance, back to a half-hearted compromise somewhere between the two extremes, and we have arrived at what? Certainly at little more than an educational jumble. A maelstrom in which the maximum amount of theory and the minimum amount of practice whirl those who are thrown into it round and round for definitely fixed periods of time, to be cast out as flotsam for another period until corporate business and industrial organizations can accomplish that which could and should have been done by general education.
Co-author with Louis Jay Heath, in A New Basis for Social Progress (1917), 151-152.
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Philosophers no longer write for the intelligent, only for their fellow professionals. The few thousand academic philosophers in the world do not stint themselves: they maintain more than seventy learned journals. But in the handful that cover more than one subdivision of philosophy, any given philosopher can hardly follow more than one or two articles in each issue. This hermetic condition is attributed to “technical problems” in the subject. Since William James, Russell, and Whitehead, philosophy, like history, has been confiscated by scholarship and locked away from the contamination of general use.
In The Culture We Deserve (1989), 9.
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Philosophers, if they have much imagination, are apt to let it loose as well as other people, and in such cases are sometimes led to mistake a fancy for a fact. Geologists, in particular, have very frequently amused themselves in this way, and it is not a little amusing to follow them in their fancies and their waking dreams. Geology, indeed, in this view, may be called a romantic science.
Conversations on Geology (1840), 5.
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Physical Science and Industrialism may be conceived as a pair of dancers, both of whom know their steps and have an ear for the rhythm of the music. If the partner who has been leading chooses to change parts and to follow instead, there is perhaps no reason to expect that he will dance less correctly than before.
From 'Introduction: The Geneses of Civilizations', A Study of History (1948), Vol. 1, 3, footnote.
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Physicists still tend to regard biologists as men condemned by their lack of mathematics to follow an imprecise science. Some biologists think that, life is too complex to be amenable to mathematical study.
From A.S. Curtis, 'The Value of Mathematics in Biology',New Scientist (25 Jan 1962), 223.
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Plants, generally speaking, meet the impact of the terrestrial environment head on, although of course they in turn modify the physical environment by adventitious group activity. The individual plant cannot select its habitat; its location is largely determined by the vagaries of the dispersal of seeds or spores and is thus profoundly affected by chance. Because of their mobility and their capacity for acceptance or rejection terrestrial animals, in contrast, can and do actively seek out and utilize the facets of the environment that allow their physiological capacities to function adequately. This means that an animal by its behavior can fit the environment to its physiology by selecting situations in which its physiological capacities can cope with physical conditions. If one accepts this idea, it follows that there is no such thing as The Environment, for there exist as many different terrestrial environments as there are species of animals.
From 'The role of physiology in the distribution of terrestrial vertebrates', collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 84.
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Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.
In The Man who Knew Infinity: A Life of the Genius Ramanujan (1975), 226.
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Preferring a search for objective reality over revelation is another way of satisfying religious hunger. It is an endeavor almost as old as civilization and intertwined with traditional religion, but it follows a very different course—a stoic’s creed, an acquired taste, a guidebook to adventure plotted across rough terrain. It aims to save the spirit, not by surrender but by liberation of the human mind. Its central tenet, as Einstein knew, is the unification of knowledge. When we have unified enough certain knowledge, we will understand who we are and why we are here. If those committed to the quest fail, they will be forgiven. When lost, they will find another way.
In Consilience: The Unity of Knowledge (1998), 5.
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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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Progress has not followed a straight ascending line, but a spiral with rhythms of progress and retrogression, of evolution and dissolution.
As given, without citation, in Kate Louise Roberts (ed.), Hoyt’s New Cyclopedia of Practical Quotations (1922), 635.
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Pure mathematics … reveals itself as nothing but symbolic or formal logic. It is concerned with implications, not applications. On the other hand, natural science, which is empirical and ultimately dependent upon observation and experiment, and therefore incapable of absolute exactness, cannot become strictly mathematical. The certainty of geometry is thus merely the certainty with which conclusions follow from non-contradictory premises. As to whether these conclusions are true of the material world or not, pure mathematics is indifferent.
In 'Non-Euclidian Geometry of the Fourth Dimension', collected in Henry Parker Manning (ed.), The Fourth Dimension Simply Explained (1910), 58.
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Pure mathematics is a collection of hypothetical, deductive theories, each consisting of a definite system of primitive, undefined, concepts or symbols and primitive, unproved, but self-consistent assumptions (commonly called axioms) together with their logically deducible consequences following by rigidly deductive processes without appeal to intuition.
In 'Non-Euclidian Geometry of the Fourth Dimension', collected in Henry Parker Manning (ed.), The Fourth Dimension Simply Explained (1910), 58.
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Quantitative work shows clearly that natural selection is a reality, and that, among other things, it selects Mendelian genes, which are known to be distributed at random through wild populations, and to follow the laws of chance in their distribution to offspring. In other words, they are an agency producing variation of the kind which Darwin postulated as the raw material on which selection acts.
'Natural Selection', Nature, 1929, 124, 444.
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Science is a cosy, friendly club of specialists who follow their numerous different stars; it is proud and wonderfully productive but never certain and always hampered by the persistence of incomplete world views.
In 'The State of Earth', The Revenge of Gaia: Earth’s Climate Crisis & The Fate of Humanity (2006), Chap. 1, 5.
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Science seems to me to teach in the highest and strongest manner the great truth which is embodied in the Christian conception of entire surrender to the will of God. Sit down before fact as a little child, be prepared to give up every preconceived notion, follow humbly wherever and to whatever abysses nature leads, or you shall learn nothing. I have only begun to learn content and peace of mind since I have resolved at all risks to do this.
Letter to Charles Kingsley (23 Sep 1860). In L. Huxley, The Life and Letters of Thomas Henry Huxley (1903), Vol. 1, 316.
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Science—we have loved her well, and followed her diligently, what will she do? I fear she is too much in the pay of the counting-houses, and the drill-serjent, that she is too busy, and will for the present do nothing. Yet there are matters which I should have thought easy for her; say, for example, teaching Manchester how to consume its town smoke, or Leeds how to get rid of its superfluous black dye without turning it into the river, which would be as much worth her attention as the production of the heaviest black silks, or the biggest of useless guns.
In The Lesser Arts (1878).
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Self-esteem must be earned! When you dare to dream, dare to follow that dream, dare to suffer through the pain, sacrifice, self-doubts, and friction from the world, you will genuinely impress yourself.
…...
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Signs and symptoms indicate the present, past and future states of the three states of the body (health, illness, neutrality). According to Galen, knowledge of the present state is of advantage only to the patient as it helps him to follow the proper course of management. Knowledge of the past state is useful only to the physician inasmuch as its disclosure by him to the patient brings him a greater respect for his professional advice. Knowledge of the future state is useful to both. It gives an opportunity to the patient to be forewarned to adopt necessary preventative measures and it enhances the reputation of the physician by correctly forecasting the future developments.
Avicenna
'The Signs and Symptoms (Diagnosis): General Remarks,' in The Canon of Medicine, adapted by L. Bakhtiar (1999), 259.
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Since many cases are known in which the specificities of antigens and enzymes appear to bear a direct relation to gene specificities, it seems reasonable to suppose that the gene’s primary and possibly sole function is in directing the final configurations of protein molecules.
Assuming that each specific protein of the organism has its unique configuration copied from that of a gene, it follows that every enzyme whose specificity depends on a protein should be subject to modification or inactivation through gene mutation. This would, of course, mean that the reaction normally catalyzed by the enzyme in question would either have its rate or products modified or be blocked entirely.
Such a view does not mean that genes directly “make” proteins. Regardless of precisely how proteins are synthesized, and from what component parts, these parts must themselves be synthesized by reactions which are enzymatically catalyzed and which in turn depend on the functioning of many genes. Thus in the synthesis of a single protein molecule, probably at least several hundred different genes contribute. But the final molecule corresponds to only one of them and this is the gene we visualize as being in primary control.
In 'Genetics and Metabolism in Neurospora', Physiological Reviews, 1945, 25, 660.
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Speaking concretely, when we say “making experiments or making observations,” we mean that we devote ourselves to investigation and to research, that we make attempts and trials in order to gain facts from which the mind, through reasoning, may draw knowledge or instruction.
Speaking in the abstract, when we say “relying on observation and gaining experience,” we mean that observation is the mind's support in reasoning, and experience the mind's support in deciding, or still better, the fruit of exact reasoning applied to the interpretation of facts. It follows from this that we can gain experience without making experiments, solely by reasoning appropriately about well-established facts, just as we can make experiments and observations without gaining experience, if we limit ourselves to noting facts.
Observation, then, is what shows facts; experiment is what teaches about facts and gives experience in relation to anything.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 11.
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Spirituality leaps where science cannot yet follow, because science must always test and measure, and much of reality and human experience is immeasurable.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 43
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Statisticians tell us that for many years the death-rate from cancer has been slowly but steadily rising: and not unnaturally, many people conclude from this that for some reason or other we are becoming more susceptible to cancer. Actually, that conclusion does not follow at all. The rise in the cancer death-rate is probably due entirely to the fact that other causes of death have been reduced. Numbers of people who, if they had been born a century earlier, would have died in their twenties of typhoid or smallpox, say, are now living on into their seventies and dying of cancer.
From 'Figures Can Lie', Science Digest (Sep 1951), 30, No. 3, 53. (As condensed from The Listener). Excerpted in Meta Riley Emberger and Marian Ross Hall, Scientific Writing (1955), 407.
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Superstring theories provide a framework in which the force of gravity may be united with the other three forces in nature: the weak, electromagnetic and strong forces. Recent progress has shown that the most promising superstring theories follow from a single theory. For the last generation, physicists have studied five string theories and one close cousin. Recently it has become clear that these five or six theories are different limiting cases of one theory which, though still scarcely understood, is the candidate for superunification of the forces of nature.
His synopsis of lecture, University of Maryland Distinguished Lecture Series (2 Mar 1998), on web page.
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Symbolism is useful because it makes things difficult. Now in the beginning everything is self-evident, and it is hard to see whether one self-evident proposition follows from another or not. Obviousness is always the enemy to correctness. Hence we must invent a new and difficult symbolism in which nothing is obvious. … Thus the whole of Arithmetic and Algebra has been shown to require three indefinable notions and five indemonstrable propositions.
In International Monthly (1901), 4, 85-86.
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The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform. It can follow analysis; but it has no power of anticipating any analytical relations or truths. Its province is to assist us to making available what we are already acquainted with.
[Describing Charles Babbage's machine.]
In her notes as translator, following her translation of I. F. Menabrea, 'Sketch of the Analytical Engine Invented by Charles Babbage, Esq.', (from Bibliothègue Universelle de Génève (Oct 1842), No. 82) in Richard Taylor (ed.), Scientific Memoirs (1843), 3, 722.
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The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.
In 'What Knowledge is of Most Worth?', Presidential address to the National Education Association, Denver, Colorado (9 Jul 1895). In Educational Review (Sep 1895), 10, 109.
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The cause, then, philosophically speaking, is the sum total of the conditions, positive and negative, taken together; the whole of the contingencies of every description, which being realized, the consequent invariably follows.
A System of Logic, Ratiocinative and Inductive (1858), 200.
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The colors are stunning. In a single view, I see - looking out at the edge of the earth: red at the horizon line, blending to orange and yellow, followed by a thin white line, then light blue, gradually turning to dark blue and various gradually darker shades of gray, then black and a million stars above. It’s breathtaking.
…...
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The complexity of contemporary biology has led to an extreme specialization, which has inevitably been followed by a breakdown in communication between disciplines. Partly as a result of this, the members of each specialty tend to feel that their own work is fundamental and that the work of other groups, although sometimes technically ingenious, is trivial or at best only peripheral to an understanding of truly basic problems and issues. There is a familiar resolution to this problem but it is sometimes difficulty to accept emotionally. This is the idea that there are a number of levels of biological integration and that each level offers problems and insights that are unique to it; further, that each level finds its explanations of mechanism in the levels below, and its significances in the levels above it.
From 'Interaction of physiology and behavior under natural conditions', collected in R.I. Bowman (ed.), The Galapagos (1966), 39.
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The doctor is the servant and the interpreter of nature. Whatever he thinks or does, if he follows not in nature’s footsteps he will never be able to control her.
De Praxi Medica (1696), Introduction.
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The domain, over which the language of analysis extends its sway, is, indeed, relatively limited, but within this domain it so infinitely excels ordinary language that its attempt to follow the former must be given up after a few steps. The mathematician, who knows how to think in this marvelously condensed language, is as different from the mechanical computer as heaven from earth.
In Jahresberichte der Deutschen Mathematiker Vereinigung, 13, 367. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 197.
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The examples which a beginner should choose for practice should be simple and should not contain very large numbers. The powers of the mind cannot be directed to two things at once; if the complexity of the numbers used requires all the student’s attention, he cannot observe the principle of the rule which he is following.
In Study and Difficulties of Mathematics (1902), chap. 3.
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The extracellular genesis of cells in animals seemed to me, ever since the publication of the cell theory [of Schwann], just as unlikely as the spontaneous generation of organisms. These doubts produced my observations on the multiplication of blood cells by division in bird and mammalian embryos and on the division of muscle bundles in frog larvae. Since then I have continued these observations in frog larvae, where it is possible to follow the history of tissues back to segmentation.
'Ueber extracellulare Eutstehung thierischer Zelleu und üüber Vermehrung derselben durch Theilung', Archiv für Anatomie, Physiologie und Wissenschaftliche Medicin (1852), 1, 49-50. Quoted in Erwin H. Ackerknecht, Rudolf Virchow: Doctor Statesman Anthropologist (1953), 83-4.
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The fact that stares one in the face is that people of the greatest sincerity and of all levels of intelligence differ and have always differed in their religious beliefs. Since at most one faith can be true, it follows that human beings are extremely liable to believe firmly and honestly in something untrue in the field of revealed religion. One would have expected this obvious fact to lead to some humility, to some thought that however deep one's faith, one may conceivably be mistaken. Nothing is further from the believer, any believer, than this elementary humility. All in his power … must have his faith rammed down their throats. In many cases children are indeed indoctrinated with the disgraceful thought that they belong to the one group with superior knowledge who alone have a private wire to the office of the Almighty, all others being less fortunate than they themselves.
From 'Religion is a Good Thing', collected in R. Duncan and M. Wesson-Smith (eds.) Lying Truths: A Critical Scruting of Current Beliefs and Conventions (1979), 205. As quoted in Paul Davies, God and the New Physics (1984), 6-7.
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The fateful question for the human species seems to me to be whether and to what extent their cultural development will succeed in mastering the disturbance of their communal life by the human instinct of aggression and self-destruction … One thing only do I know for certain and that is that man's judgements of value follow directly from his wihes for happiness—that, accordingly, they are an attempt to support his illusions with arguments. (1930)
Civilization and its Discontents (2005), 154.
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The follow-on space shuttle program has fallen far short of the Apollo program in its appeal to human aspirations. The launching of the Hubble Space Telescope and the subsequent repair and servicing missions by skilled crews are highlights of the shuttle’s service to science. … Otherwise, the shuttle’s contribution to science has been modest, and its contribution to utilitarian applications of space technology has been insignificant.
In 'Is Human Spaceflight Obsolete?', Issues in Science and Technology (Summer 2004).
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The Foundation of Empire is Art & Science. Remove them, or Degrade them, & the Empire is No More. Empire follows Art, & not Vice Versa as Englishmen suppose.
Marginal note (c. 1808) written in his copy of The Works of Sir Joshua Reynolds (1798), at foot of first page of table of contents. As given in William Blake, Edwin John Ellis (ed.) and William Butler Yeats (ed.), The Works of William Blake (1893), Vol. 2, 319.
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The framing of hypotheses is, for the enquirer after truth, not the end, but the beginning of his work. Each of his systems is invented, not that he may admire it and follow it into all its consistent consequences, but that he may make it the occasion of a course of active experiment and observation. And if the results of this process contradict his fundamental assumptions, however ingenious, however symmetrical, however elegant his system may be, he rejects it without hesitation. He allows no natural yearning for the offspring of his own mind to draw him aside from the higher duty of loyalty to his sovereign, Truth, to her he not only gives his affections and his wishes, but strenuous labour and scrupulous minuteness of attention.
Philosophy of the Inductive Sciences (1847), Vol. 2, 57.
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The great difference between science and technology is a difference of initial attitude. The scientific man follows his method whithersoever it may take him. He seeks acquaintance with his subject­matter, and he does not at all care about what he shall find, what shall be the content of his knowledge when acquaintance-with is transformed into knowledge-about. The technologist moves in another universe; he seeks the attainment of some determinate end, which is his sole and obsessing care; and he therefore takes no heed of anything that he cannot put to use as means toward that end.
Systematic Psychology: Prolegomena (1929), 66.
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The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible.
In History of Mathematics (3rd Ed., 1901), 468.
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The Greeks in the first vigour of their pursuit of mathematical truth, at the time of Plato and soon after, had by no means confined themselves to those propositions which had a visible bearing on the phenomena of nature; but had followed out many beautiful trains of research concerning various kinds of figures, for the sake of their beauty alone; as for instance in their doctrine of Conic Sections, of which curves they had discovered all the principal properties. But it is curious to remark, that these investigations, thus pursued at first as mere matters of curiosity and intellectual gratification, were destined, two thousand years later, to play a very important part in establishing that system of celestial motions which succeeded the Platonic scheme of cycles and epicycles. If the properties of conic sections had not been demonstrated by the Greeks and thus rendered familiar to the mathematicians of succeeding ages, Kepler would probably not have been able to discover those laws respecting the orbits and motions of planets which were the occasion of the greatest revolution that ever happened in the history of science.
In History of Scientific Ideas, Bk. 9, chap. 14, sect. 3.
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The history of acceptance of new theories frequently shows the following steps: At first the new idea is treated as pure nonsense, not worth looking at. Then comes a time when a multitude of contradictory objections are raised, such as: the new theory is too fancy, or merely a new terminology; it is not fruitful, or simply wrong. Finally a state is reached when everyone seems to claim that he had always followed this theory. This usually marks the last state before general acceptance.
In 'Field Theory and the Phase Space', collected in Melvin Herman Marx, Psychological Theory: Contemporary Readings (1951), 299.
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The history of penicillin is one of the disgraces of medical research. Fleming published his classic paper in the British Journal of Experimental Pathology for June, 1929, but it was not until 1939 that Florey followed up the clue. An antiseptic which is almost ideal, inasmuch as it has no toxic effects, was allowed to slumber for ten years. Had it not been for the exigencies of the present war it might be slumbering still.
In book review, 'The Story of a Neglected Miracle', New York Times (25 Mar 1945), BR3. (The book being reviewed was J.D. Ratcliff, Yellow Magic: The Story of Penicillin.)
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The key to success for Sony, and to everything in business, science and technology for that matter, is never to follow the others.
Founder of Sony, quoted in Fortune (24 Feb 1992). In Julia Vitullo-Martin and J. Robert Moskin, The Executive's Book of Quotations (2002), 271.
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The legends of fieldwork locate all important sites deep in inaccessible jungles inhabited by fierce beasts and restless natives, and surrounded by miasmas of putrefaction and swarms of tsetse flies. (Alternative models include the hundredth dune after the death of all camels, or the thousandth crevasse following the demise of all sled dogs.)
In Wonderful Life: The Burgess Shale and the Nature of History (1990), 65.
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The logic of the subject [algebra], which, both educationally and scientifically speaking, is the most important part of it, is wholly neglected. The whole training consists in example grinding. What should have been merely the help to attain the end has become the end itself. The result is that algebra, as we teach it, is neither an art nor a science, but an ill-digested farrago of rules, whose object is the solution of examination problems. … The result, so far as problems worked in examinations go, is, after all, very miserable, as the reiterated complaints of examiners show; the effect on the examinee is a well-known enervation of mind, an almost incurable superficiality, which might be called Problematic Paralysis—a disease which unfits a man to follow an argument extending beyond the length of a printed octavo page.
In Presidential Address British Association for the Advancement of Science (1885), Nature, 32, 447-448.
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The main difficulty the student of groups meets is not that of following the argument, which is nearly always straightforward, but of grasping the purpose of the investigation.
In 'On Groups', Prelude to Mathematics (1955), 201.
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The mathematical universe is already so large and diversified that it is hardly possible for a single mind to grasp it, or, to put it in another way, so much energy would be needed for grasping it that there would be none left for creative research. A mathematical congress of today reminds one of the Tower of Babel, for few men can follow profitably the discussions of sections other than their own, and even there they are sometimes made to feel like strangers.
In The Study Of The History Of Mathematics (1936), 14.
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The method of inquiry which all our ingenious Theorists of the Earth have pursued is certainly erroneous. They first form an hypothesis to solve the phenomena, but in fact the Phenomena are always used as a prop to the hypothesis.
Instead therefore of attempting to cut the gordian knot by Hypothetical analysis, we shall follow the synthetic method of inquiry and content ourselves with endeavouring to establish facts rather than attempt solutions and try by experiments how far that method may leave us thro' the mazes of this subject
Introduction to his lecture course. In Robert Jameson, edited by H. W. Scott, Lectures on Geology, (1966), 27. In Patrick Wyse Jackson, Four Centuries of Geological Travel (2007), 33.
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The most important distinction between the two qualities [talent and genius] is this: one, in conception, follows mechanical processes; the other, vital. Talent feebly conceives objects with the senses and understanding; genius, fusing all its powers together in the alembic of an impassioned imagination, clutches every thing in the concrete, conceives objects as living realities, gives body to spiritual abstractions, and spirit to bodily appearances, and like
“A gate of steel
Fronting the sun, receives and renders back
His figure and his heat!”
In 'Genius', Wellman’s Miscellany (Dec 1871), 4, No. 6, 203. The quotation at the end is from Wiliam Shakespeare, Tr. & Cress. iii, 3.
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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 OATH. I swear by Apollo [the healing God], the physician and Aesclepius [son of Apollo], and Health [Hygeia], and All-heal [Panacea], and all the gods and goddesses, that, according to my ability and judgment, I will keep this Oath and this stipulation—to reckon him who taught me this Art equally dear to me as my parents, to share my substance with him, and relieve his necessities if required; to look upon his offspring in the same footing as my own brothers, and to teach them this art, if they shall wish to learn it, without fee or stipulation; and that by precept, lecture, and every other mode of instruction, I will impart a knowledge of the Art to my own sons, and those of my teachers, and to disciples bound by a stipulation and oath according to the law of medicine, but to none others. I will follow that system of regimen which, according to my ability and judgment, I consider for the benefit of my patients, and abstain from whatever is deleterious and mischievous. I will give no deadly medicine to any one if asked, nor suggest any such counsel; and in like manner I will not give to a woman a pessary to produce abortion. With purity and with holiness I will pass my life and practice my Art. I will not cut persons laboring under the stone, but will leave this to be done by men who are practitioners of this work. Into whatever houses I enter, I will go into them for the benefit of the sick, and will abstain from every voluntary act of mischief and corruption; and, further, from the seduction of females or males, of freemen and slaves. Whatever, in connection with my professional practice or not, in connection with it, I see or hear, in the life of men, which ought not to be spoken of abroad, I will not divulge, as reckoning that all such should be kept secret. While I continue to keep this Oath unviolated, may it be granted to me to enjoy life and the practice of the art, respected by all men, in all times! But should I trespass and violate this Oath, may the reverse be my lot!
The Genuine Works of Hippocrates, trans. Francis Adams (1886), Vol. 2, 344-5.
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The opinion I formed from attentive observation of the facts and phenomena, is as follows. When ice, for example, or any other solid substance, is changing into a fluid by heat, I am of opinion that it receives a much greater quantity of heat than that what is perceptible in it immediately after by the thermometer. A great quantity of heat enters into it, on this occasion, without making it apparently warmer, when tried by that instrument. This heat, however, must be thrown into it, in order to give it the form of a fluid; and I affirm, that this great addition of heat is the principal, and most immediate cause of the fluidity induced. And, on the other hand, when we deprive such a body of its fluidity again, by a diminution of its heat, a very great quantity of heat comes out of it, while it is assuming a solid form, the loss of which heat is not to be perceived by the common manner of using the thermometer. The apparent heat of the body, as measured by that instrument, is not diminished, or not in proportion to the loss of heat which the body actually gives out on this occasion; and it appears from a number of facts, that the state of solidity cannot be induced without the abstraction of this great quantity of heat. And this confirms the opinion, that this quantity of heat, absorbed, and, as it were, concealed in the composition of fluids, is the most necessary and immediate cause of their fluidity.
Lectures on the Elements of Chemistry, delivered in the University of Edinburgh (1803), Vol. I, 116-7.
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The picture of scientific method drafted by modern philosophy is very different from traditional conceptions. Gone is the ideal of a universe whose course follows strict rules, a predetermined cosmos that unwinds itself like an unwinding clock. Gone is the ideal of the scientist who knows the absolute truth. The happenings of nature are like rolling dice rather than like revolving stars; they are controlled by probability laws, not by causality, and the scientist resembles a gambler more than a prophet. He can tell you only his best posits—he never knows beforehand whether they will come true. He is a better gambler, though, than the man at the green table, because his statistical methods are superior. And his goal is staked higher—the goal of foretelling the rolling dice of the cosmos. If he is asked why he follows his methods, with what title he makes his predictions, he cannot answer that he has an irrefutable knowledge of the future; he can only lay his best bets. But he can prove that they are best bets, that making them is the best he can do—and if a man does his best, what else can you ask of him?
The Rise of Scientific Philosophy (1951, 1973), 248-9. Collected in James Louis Jarrett and Sterling M. McMurrin (eds.), Contemporary Philosophy: A Book of Readings (1954), 376.
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The plan followed by nature in producing animals clearly comprises a predominant prime cause. This endows animal life with the power to make organization gradually more complex, and to bring increasing complexity and perfection not only to the total organization but also to each individual apparatus when it comes to be established by animal life. This progressive complication of organisms was in effect accomplished by the said principal cause in all existing animals. Occasionally a foreign, accidental, and therefore variable cause has interfered with the execution of the plan, without, however, destroying it. This has created gaps in the series, in the form either of terminal branches that depart from the series in several points and alter its simplicity, or of anomalies observable in specific apparatuses of various organisms.
Histoire Naturelle des Animaux sans Vertèbres (1815-22), Vol. 1, 133. In Pietro Corsi, The Age of Lamarck: Evolutionary Theories in France 1790-1830, trans. J. Mandelbaum (1988), 189.
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The plexus called rectiform [rete mirabile] by anatomists, is the most wonderful of the bodies located in this region. It encircles the gland [the hypophysis] itself and extends far to the rear; for nearly the whole base of the encephalon has this plexus lying beneath it. It is not a simple network but [looks] as if you had taken several fisherman’s nets and superimposed them. It is characteristic of this net of Nature’s, however, that the meshes of one layer are always attached to those of another, and it is impossible to remove anyone of them alone; for, one after another, the rest follow the one you are removing, because they are all attached to one another successively.
Galen
On the Usefulness of the Parts of the Body, Book IX, 4. Trans. Margaret Tallmadge May (1968), Vol. 1, 430-1.
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The position of the anthropologist of to-day resembles in some sort the position of classical scholars at the revival of learning. To these men the rediscovery of ancient literature came like a revelation, disclosing to their wondering eyes a splendid vision of the antique world, such as the cloistered of the Middle Ages never dreamed of under the gloomy shadow of the minster and within the sound of its solemn bells. To us moderns a still wider vista is vouchsafed, a greater panorama is unrolled by the study which aims at bringing home to us the faith and the practice, the hopes and the ideals, not of two highly gifted races only, but of all mankind, and thus at enabling us to follow the long march, the slow and toilsome ascent, of humanity from savagery to civilization. And as the scholar of the Renaissance found not merely fresh food for thought but a new field of labour in the dusty and faded manuscripts of Greece and Rome, so in the mass of materials that is steadily pouring in from many sides—from buried cities of remotest antiquity as well as from the rudest savages of the desert and the jungle—we of to-day must recognise a new province of knowledge which will task the energies of generations of students to master.
'Author’s Introduction' (1900). In Dr Theodor H. Gaster (ed.), The New Golden Bough (1959), xxv-xxvi.
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The present state of the system of nature is evidently a consequence of what it was in the preceding moment, and if we conceive of an intelligence that at a given instant comprehends all the relations of the entities of this universe, it could state the respective position, motions, and general affects of all these entities at any time in the past or future. Physical astronomy, the branch of knowledge that does the greatest honor to the human mind, gives us an idea, albeit imperfect, of what such an intelligence would be. The simplicity of the law by which the celestial bodies move, and the relations of their masses and distances, permit analysis to follow their motions up to a certain point; and in order to determine the state of the system of these great bodies in past or future centuries, it suffices for the mathematician that their position and their velocity be given by observation for any moment in time. Man owes that advantage to the power of the instrument he employs, and to the small number of relations that it embraces in its calculations. But ignorance of the different causes involved in the production of events, as well as their complexity, taken together with the imperfection of analysis, prevents our reaching the same certainty about the vast majority of phenomena. Thus there are things that are uncertain for us, things more or less probable, and we seek to compensate for the impossibility of knowing them by determining their different degrees of likelihood. So it was that we owe to the weakness of the human mind one of the most delicate and ingenious of mathematical theories, the science of chance or probability.
'Recherches, 1º, sur l'Intégration des Équations Différentielles aux Différences Finies, et sur leur Usage dans la Théorie des Hasards' (1773, published 1776). In Oeuvres complètes de Laplace, 14 Vols. (1843-1912), Vol. 8, 144-5, trans. Charles Coulston Gillispie, Pierre-Simon Laplace 1749-1827: A Life in Exact Science (1997), 26.
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The process of self-estrangement and its removal underlies all education. The mind must fix its attention upon what is alien to it and penetrate its disguise, making it become familiar. … Wonder is only the first stage of this estrangement. It must be followed by recognition.
In Psychologic Foundations of Education: An Attempt to Show the Genesis of the Higher Faculties of the Mind (1907), 289.
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The process of tracing regularity in any complicated, and at first sight confused, set of appearances, is necessarily tentative; we begin by making any supposition, even a false one, to see what consequences will follow from it ; and by observing how these differ from the real phenomena, we learn what corrections to make in our assumption.
A System of Logic, Ratiocinative and Inductive (1858), 295.
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The progress of Science is generally regarded as a kind of clean, rational advance along a straight ascending line; in fact it has followed a zig-zag course, at times almost more bewildering than the evolution of political thought. The history of cosmic theories, in particular, may without exaggeration be called a history of collective obsessions and controlled schizophrenias; and the manner in which some of the most important individual discoveries were arrived at reminds one more of a sleepwalker’s performance than an electronic brain’s.
From 'Preface', in The Sleepwalkers: A History of Man’s Changing Vision of the Universe (1959), 15.
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The radius of space began at zero; the first stages of the expansion consisted of a rapid expansion determined by the mass of the initial atom, almost equal to the present mass of the universe. If this mass is sufficient, and the estimates which we can make indicate that this is indeed so, the initial expansion was able to permit the radius to exceed the value of the equilibrium radius. The expansion thus took place in three phases: a first period of rapid expansion in which the atom-universe was broken into atomic stars, a period of slowing-down, followed by a third period of accelerated expansion. It is doubtless in this third period that we find ourselves today, and the acceleration of space which followed the period of slow expansion could well be responsible for the separation of stars into extra-galactic nebulae.
From 'La formation des Nebuleuses dans l’Univers en Expansion', Comptes Rendus (1933), 196, 903-904. As translated in Helge Kragh, Cosmology and Controversy: The Historical Development of Two Theories of the Universe (1996), 52.
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The reactions follow a pattern, which is valid for the blood of all humans... Basically, in fact, there are four different types of human blood, the so-called blood groups. The number of the groups follows from the fact that the erythrocytes evidently contain substances (iso-agglutinogens) with two different structures, of which both may be absent, or one or both present, in the erythrocytes of a person. This alone would still not explain the reactions; the active substances of the sera, the iso-agglutinins, must also be present in a specific distribution. This is actually the case, since every serum contains those agglutinins which react with the agglutinogens not present in the cells—a remarkable phenomenon, the cause of which is not yet known for certain.
'On Individual Differences in Human Blood', Nobel Lecture (11 Dec 1930). In Nobel Lectures: Physiology or Medicine 1922-1941 (1965), 235.
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The result of all these experiments has given place to a new division of the parts of the human body, which I shall follow in this short essay, by distinguishing those which are susceptible of Irritability and Sensibility, from those which are not. But the theory, why some parts of the human body are endowed with these properties, while others are not, I shall not at all meddle with. For I am persuaded that the source of both lies concealed beyond the reach of the knife and microscope, beyond which I do not chuse to hazard many conjectures, as I have no desire of teaching what I am ignorant of myself. For the vanity of attempting to guide others in paths where we find ourselves in the dark, shews, in my humble opinion, the last degree of arrogance and ignorance.
'A Treatise on the Sensible and Irritable Parts of Animals' (Read 1752). Trans. 1755 and reprinted in Bulletin of the Institute of the History of Medicine, 1936, 4(2), 657-8.
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The ridge of the Lammer-muir hills... consists of primary micaceous schistus, and extends from St Abb's head westward... The sea-coast affords a transverse section of this alpine tract at its eastern extremity, and exhibits the change from the primary to the secondary strata... Dr HUTTON wished particularly to examine the latter of these, and on this occasion Sir JAMES HALL and I had the pleasure to accompany him. We sailed in a boat from Dunglass ... We made for a high rocky point or head-land, the SICCAR ... On landing at this point, we found that we actually trode [sic] on the primeval rock... It is here a micaceous schistus, in beds nearly vertical, highly indurated, and stretching from S.E. to N. W. The surface of this rock... has thin covering of red horizontal sandstone laid over it, ... Here, therefore, the immediate contact of the two rocks is not only visible, but is curiously dissected and laid open by the action of the waves... On us who saw these phenomena for the first time, the impression will not easily be forgotten. The palpable evidence presented to us, of one of the most extraordinary and important facts in the natural history of the earth, gave a reality and substance to those theoretical speculations, which, however probable had never till now been directly authenticated by the testimony of the senses... What clearer evidence could we have had of the different formation of these rocks, and of the long interval which separated their formation, had we actually seen them emerging from the bosom of the deep? ... The mind seemed to grow giddy by looking so far into the abyss of time; and while we listened with earnestness and admiration to the philosopher who was now unfolding to us the order and series of these wonderful events, we became sensible how much farther reason may sometimes go than imagination can venture to follow.
'Biographical Account of the Late Dr James Hutton, F.R.S. Edin.' (read 1803), Transactions of the Royal Society of Edinburgh (1805), 5, 71-3.
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The roads of science are narrow, so that they who travel them, must wither follow or meet one another…
In Samuel Johnson and W. Jackson Bate (Ed.), ',The Rambler, No. 121, Tuesday, 14 May 1751.' The Selected Essays from the Rambler, Adventurer, and Idler (1968), 172.
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The ruthless destruction of their forests by the Chinese is one of the reasons why famine and plague today hold this nation in their sinister grasp. Denudation, wherever practiced, leaves naked soil; floods and erosion follow, and when the soil is gone men must also go—and the process does not take long. The great plains of Eastern China were centuries ago transformed from forest into agricultural land. The mountain plateau of Central China have also within a few hundred years been utterly devastated of tree growth, and no attempt made at either natural or artificial reforestation. As a result, the water rushes off the naked slopes in veritable floods, gullying away the mountain sides, causing rivers to run muddy with yellow soil, and carrying enormous masses of fertile earth to the sea. Water courses have also changed; rivers become uncontrollable, and the water level of the country is lowered perceptibly. In consequence, the unfortunate people see their crops wither and die for lack of water when it is most needed.
Statement (11 May 1921) by United States Department of Agriculture (USDA) concerning the famine in China in seven out of every ten years. Reported in 'Blames Deforestation: Department of Agriculture Ascribes Chinese Famine to it', New York Times (12 May 1921), 12.
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The saying of Protagoras is like the views we have mentioned; he said that man is the measure of all things, meaning simply that that which seems to each man assuredly is. If this is so, it follows that the same thing both is and is not, and is bad and good, and that the contents of all other opposite statements are true, because often a particular thing appears beautiful to some and ugly to others, and that which appears to each man is the measure
Aristotle
Metaphysics, 1062b, 12- I 9. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. 2, 1678.
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The science of calculation … is indispensable as far as the extraction of the square and cube roots: Algebra as far as the quadratic equation and the use of logarithms are often of value in ordinary cases: but all beyond these is but a luxury; a delicious luxury indeed; but not to be indulged in by one who is to have a profession to follow for his subsistence.
In Letter (18 Jun 1799) to William G. Munford. On founders.archives.gov website.
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The sciences are like a beautiful river, of which the course is easy to follow, when it has acquired a certain regularity; but if one wants to go back to the source, one will find it nowhere, because it is everywhere; it is spread so much [as to be] over all the surface of the earth; it is the same if one wants to go back to the origin of the sciences, one will find only obscurity, vague ideas, vicious circles; and one loses oneself in the primitive ideas.
In Essai sur les machines en général (1783), conclusion, as translated in Ivor Grattan-Guinness, Convolutions in French Mathematics, 1800-1840 (1990), Vol. 1, 32.
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The sciences have sworn among themselves an inviolable partnership; it is almost impossible to separate them, for they would rather suffer than be torn apart; and if anyone persists in doing so, he gets for his trouble only imperfect and confused fragments. Yet they do not arrive all together, but they hold each other by the hand so that they follow one another in a natural order which it is dangerous to change, because they refuse to enter in any other way where they are called. ...
Les Préludes de l'Harmonie Universelle (1634), 135-139. In Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 316.
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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 Struggle for Existence amongst all organic beings throughout the world, which inevitably follows from their high geometrical powers of increase ... This is the doctrine of Malthus, applied to the whole animal and vegetable kingdoms. As many more individuals of each species are born than can possibly survive; and as, consequently, there is a frequently recurring struggle for existence, it follows that any being, if it vary however slightly in any manner profitable to itself, under the complex and sometimes varying conditions of life, will have a better chance of surviving, and thus be naturally selected. From the strong principle of inheritance, any selected variety will tend to propagate its new and modified form.
From On the Origin of Species by Means of Natural Selection; or, The Preservation of Favoured Races in the Struggle for Life (1861), 12.
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The study of … simple cases would, I think, often be of advantage even to students whose mathematical attainments are sufficient to enable them to follow the solution of the more general cases. For in these simple cases the absence of analytical difficulties allows attention to be more easily concentrated on the physical aspects of the question, and thus gives the student a more vivid idea and a more manageable grasp of the subject than he would be likely to attain if he merely regarded electrical phenomena through a cloud of analytical symbols.
Elements of the Mathematical Theory of Electricity and Magnetism (189S), v-vi.
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The sun’s rays proceed from the sun along straight lines and are reflected from every polished object at equal angles, i.e. the reflected ray subtends, together with the line tangential to the polished object which is in the plane of the reflected ray, two equal angles. Hence it follows that the ray reflected from the spherical surface, together with the circumference of the circle which is in the plane of the ray, subtends two equal angles. From this it also follows that the reflected ray, together with the diameter of the circle, subtends two equal angles. And every ray which is reflected from a polished object to a point produces a certain heating at that point, so that if numerous rays are collected at one point, the heating at that point is multiplied: and if the number of rays increases, the effect of the heat increases accordingly.
Alhazan
In H.J.J. Winter, 'A Discourse of the Concave Spherical Mirror by Ibn Al-Haitham', Journal of the Royal Asiatic Society of Bengal, 1950, 16, 2.
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The theory that gravitational attraction is inversely proportional to the square of the distance leads by remorseless logic to the conclusion that the path of a planet should be an ellipse, … It is this logical thinking that is the real meat of the physical sciences. The social scientist keeps the skin and throws away the meat. … His theorems no more follow from his postulates than the hunches of a horse player follow logically from the latest racing news. The result is guesswork clad in long flowing robes of gobbledygook.
In Science is a Sacred Cow (1950), 149-150.
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The third [argument of motion is] to the effect that the flying arrow is at rest, which result follows from the assumption that time is composed of moments: if this assumption is not granted, the conclusion will not follow.Arrow paradox
Zeno
Aristotle, Physics, 239b, 30-1. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. 1, 405.
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The two great components of the critical movement, though distinct in origin and following separate paths, are found to converge at last in the thesis: Symbolic Logic is Mathematics, Mathematics is Symbolic Logic, the twain are one.
In Lecture delivered at Columbia University (16 Oct 1907), 'Mathematics', the first of a series published as Lectures on Science, Philosophy and Art (1908), 19.
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The two revolutions, I mean the annual revolutions of the declination and of the centre of the Earth, are not completely equal; that is the return of the declination to its original value is slightly ahead of the period of the centre. Hence it necessarily follows that the equinoxes and solstices seem to anticipate their timing, not because the sphere of the fixed stars moves to the east, but rather the equatorial circle moves to the west, being at an angle to the plane of the ecliptic in proportion to the declination of the axis of the terrestrial globe.
'Book Three. Chapter I. The Precession of the equinoxes and solstices', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A. M. Duncan (1976), 141.
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The vast outpourings of publications by Professor Djerassi and his cohorts marks him as one of the most prolific scientific writers of our day... a plot of N, the papers published by Professor Djerassi in a given year, against T, the year (starting with 1945, T = 0) gives a good straight-line relationship. This line follows the equation N = 2.413T + 1.690 ... Assuming that the inevitable inflection point on the logistic curve is still some 10 years away, this equation predicts (a) a total of about 444 papers by the end of this year, (b) the average production of one paper per week or more every year beginning in 1966, and (c) the winning of the all-time productivity world championship in 10 years from now, in 1973. In that year Professor Djerassi should surpass the record of 995 items held by ...
Steroids Made it Possible (1990), 11-12.
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The well-marked path to knowledge is open to anyone willing to make the effort to follow it, though no one will ever quite reach its end.
In 'Prologue', Conversation with the Earth (1954), 4. As translated by E.B. Garside from Gespräch mit der Erde (1947).
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The world goes up and the world goes down,
And the sunshine follows the rain;
And yesterday’s sneer and yesterday’s frown
can never come over again.
…...
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The year 1896 … marked the beginning of what has been aptly termed the heroic age of Physical Science. Never before in the history of physics has there been witnessed such a period of intense activity when discoveries of fundamental importance have followed one another with such bewildering rapidity.
In 'The Electrical Structure of Matter', Reports of the British Association for the Advancement of Science (1924), C2.
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The young specialist in English Lit, having quoted me, went on to lecture me severely on the fact that in every century people have thought they understood the Universe at last, and in every century they were proved to be wrong. It follows that the one thing we can say about our modern “knowledge” is that it is wrong.
The young man then quoted with approval what Socrates had said on learning that the Delphic oracle had proclaimed him the wisest man in Greece. “If I am the wisest man,” said Socrates, “it is because I alone know that I know nothing.” The implication was that I was very foolish because I was under the impression I knew a great deal.
Alas, none of this was new to me. (There is very little that is new to me; I wish my correspondents would realize this.) This particular theme was addressed to me a quarter of a century ago by John Campbell, who specialized in irritating me. He also told me that all theories are proven wrong in time.
My answer to him was, “John, when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical, they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together.”
In The Relativity of Wrong (1989), 214.
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Then if the first argument remains secure (for nobody will produce a neater one, than the length of the periodic time is a measure of the size of the spheres), the order of the orbits follows this sequence, beginning from the highest: The first and highest of all is the sphere of the fixed stars, which contains itself and all things, and is therefore motionless. It is the location of the universe, to which the motion and position of all the remaining stars is referred. For though some consider that it also changes in some respect, we shall assign another cause for its appearing to do so in our deduction of the Earth’s motion. There follows Saturn, the first of the wandering stars, which completes its circuit in thirty years. After it comes Jupiter which moves in a twelve-year long revolution. Next is Mars, which goes round biennially. An annual revolution holds the fourth place, in which as we have said is contained the Earth along with the lunar sphere which is like an epicycle. In fifth place Venus returns every nine months. Lastly, Mercury holds the sixth place, making a circuit in the space of eighty days. In the middle of all is the seat of the Sun. For who in this most beautiful of temples would put this lamp in any other or better place than the one from which it can illuminate everything at the same time? Aptly indeed is he named by some the lantern of the universe, by others the mind, by others the ruler. Trismegistus called him the visible God, Sophocles' Electra, the watcher over all things. Thus indeed the Sun as if seated on a royal throne governs his household of Stars as they circle around him. Earth also is by no means cheated of the Moon’s attendance, but as Aristotle says in his book On Animals the Moon has the closest affinity with the Earth. Meanwhile the Earth conceives from the Sun, and is made pregnant with annual offspring. We find, then, in this arrangement the marvellous symmetry of the universe, and a sure linking together in harmony of the motion and size of the spheres, such as could be perceived in no other way. For here one may understand, by attentive observation, why Jupiter appears to have a larger progression and retrogression than Saturn, and smaller than Mars, and again why Venus has larger ones than Mercury; why such a doubling back appears more frequently in Saturn than in Jupiter, and still more rarely in Mars and Venus than in Mercury; and furthermore why Saturn, Jupiter and Mars are nearer to the Earth when in opposition than in the region of their occultation by the Sun and re-appearance. Indeed Mars in particular at the time when it is visible throughout the night seems to equal Jupiter in size, though marked out by its reddish colour; yet it is scarcely distinguishable among stars of the second magnitude, though recognized by those who track it with careful attention. All these phenomena proceed from the same course, which lies in the motion of the Earth. But the fact that none of these phenomena appears in the fixed stars shows their immense elevation, which makes even the circle of their annual motion, or apparent motion, vanish from our eyes.
'Book One. Chapter X. The Order of the Heavenly Spheres', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A. M. Duncan (1976), 49-51.
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Then one day Lagrange took out of his pocket a paper which he read at the Académe, and which contained a demonstration of the famous Postulatum of Euclid, relative to the theory of parallels. This demonstration rested on an obvious paralogism, which appeared as such to everybody; and probably Lagrange also recognised it such during his lecture. For, when he had finished, he put the paper back in his pocket, and spoke no more of it. A moment of universal silence followed, and one passed immediately to other concerns.
Quoting Lagrange at a meeting of the class of mathematical and physical sciences at the Institut de France (3 Feb 1806) in Journal des Savants (1837), 84, trans. Ivor Grattan-Guinness.
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There appears to be a total absence of place names [in southern Sudan]; there are indeed names for regions, areas, but all hamlets (there are scarcely any villages) bear the name of their headman or district head…, which is as ephemeral as the existence of the bearer himself in this unquiet country. Furthermore, residences are shifted every few years, in order to have fresh farmland; added to this the frequent wars, many deaths etc. In contrast, all bodies of water, even the most insignificant ditches, are permanently named. These will be the only guides if future travelers follow my path in this country or wish to trace it.
On the diffuse difficulties and contradictions in placing permanent names on the maps was making. In August Petermann, Petermann’s Geographische Mittheilungen (1871), 137. As quoted and cited in Kathrin Fritsch, '"You Have Everything Confused And Mixed Up…!" Georg Schweinfurth, Knowledge And Cartography Of Africa In The 19th Century', History in Africa (2009), 36, 91.
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There are many arts and sciences of which a miner should not be ignorant. First there is Philosophy, that he may discern the origin, cause, and nature of subterranean things; for then he will be able to dig out the veins easily and advantageously, and to obtain more abundant results from his mining. Secondly there is Medicine, that he may be able to look after his diggers and other workman ... Thirdly follows astronomy, that he may know the divisions of the heavens and from them judge the directions of the veins. Fourthly, there is the science of Surveying that he may be able to estimate how deep a shaft should be sunk … Fifthly, his knowledge of Arithmetical Science should be such that he may calculate the cost to be incurred in the machinery and the working of the mine. Sixthly, his learning must comprise Architecture, that he himself may construct the various machines and timber work required underground … Next, he must have knowledge of Drawing, that he can draw plans of his machinery. Lastly, there is the Law, especially that dealing with metals, that he may claim his own rights, that he may undertake the duty of giving others his opinion on legal matters, that he may not take another man’s property and so make trouble for himself, and that he may fulfil his obligations to others according to the law.
In De Re Metallica (1556), trans. H.C. and L.H. Hoover (1950), 3-4.
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There is only one subject matter for education, and that is Life in all its manifestations. Instead of this single unity, we offer children—Algebra, from which nothing follows; Geometry, from which nothing follows; Science, from which nothing follows; History, from which nothing follows; a Couple of Languages, never mastered; and lastly, most dreary of all, Literature, represented by plays of Shakespeare, with philological notes and short analyses of plot and character to be in substance committed to memory.
In 'The Aims of Education', The Aims of Education: & Other Essays (1917), 10.
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There is something sublime in the secrecy in which the really great deeds of the mathematician are done. No popular applause follows the act; neither contemporary nor succeeding generations of the people understand it. The geometer must be tried by his peers, and those who truly deserve the title of geometer or analyst have usually been unable to find so many as twelve living peers to form a jury. Archimedes so far outstripped his competitors in the race, that more than a thousand years elapsed before any man appeared, able to sit in judgment on his work, and to say how far he had really gone. And in judging of those men whose names are worthy of being mentioned in connection with his,—Galileo, Descartes, Leibnitz, Newton, and the mathematicians created by Leibnitz and Newton’s calculus,—we are forced to depend upon their testimony of one another. They are too far above our reach for us to judge of them.
In 'Imagination in Mathematics', North American Review, 86, 223.
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There may be instances of mere accidental discovery; but, setting these aside, the great advances made in the inductive sciences are, for the most part, preceded by a more or less probable hypothesis. The imagination, having some small light to guide it, goes first. Further observation, experiment, and reason follow.
Presidential Address to Anniversary meeting of the Royal Society (30 Nov 1859), Proceedings of the Royal Society of London (1860), 10, 166.
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These principles have given me a way of explaining naturally the union or rather the mutual agreement [conformité] of the soul and the organic body. The soul follows its own laws, and the body likewise follows its own laws; and they agree with each other in virtue of the pre-established harmony between all substances, since they are all representations of one and the same universe.
The Monadology and Other Philosophical Writings (1714), trans. Robert Latta (1898), 262.
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Thirty seconds after the explosion came, first the air blast pressing hard against people and things, to be followed almost immediately by the strong, sustained awesome roar which warned of doomsday and made us feel that we puny things were blasphemous to dare tamper with the forces heretofore reserved to the Almighty.
official report on the first atom bomb test, Alamogordo, New Mexico, July 16, 1945 [See Kenneth Tompkins Bainbridge and J. Robert Oppenheimer].
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This is the excellent foppery of the world: that when we are sick in fortune—often the surfeits of our own behaviour—we make guilty of our disasters the sun, the moon, and stars, as if we were villains on necessity, fools by heavenly compulsion, knaves, thieves, and treachers by spherical predominance, drunkards, liars, and adulterers, by an enforced obedience of planetary influence, and all that we are evil in, by a divine thrusting on. An admirable evasion of whoremaster man, to lay his goatish disposition on the charge of a star! My father compounded with my mother under the Dragon's tail and my nativity was under Ursa Major, so that it follows that I am rough and lecherous. Fut! I should have been that I am had the maidenliest star in the firmament twinkled on my bastardizing.
King Lear (1605-6), I, ii.
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This nation has tossed its cap over the wall of space, and we have no choice but to follow it.
Remarks in San Antonio at the Dedication of the Aerospace Medical Health Center, San Antonio (21 Nov 1963), Collected in Public Papers of the Presidents: John F. Kennedy (1964), 883. According to the JFK Library web site, the original anecdote from which Kennedy derived this comparison is in Frank O’Connor, An Only Child, (1961), 180, which reads, “I had tossed my cap over the wall of life, and I knew I must follow it, wherever it had fallen.”
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Those who have taken upon them to lay down the law of nature as a thing already searched out and understood, whether they have spoken in simple assurance or professional affectation, have therein done philosophy and the sciences great injury. For as they have been successful in inducing belief, so they have been effective in quenching and stopping inquiry; and have done more harm by spoiling and putting an end to other men's efforts than good by their own. Those on the other hand who have taken a contrary course, and asserted that absolutely nothing can be known — whether it were from hatred of the ancient sophists, or from uncertainty and fluctuation of mind, or even from a kind of fullness of learning, that they fell upon this opinion — have certainly advanced reasons for it that are not to be despised; but yet they have neither started from true principles nor rested in the just conclusion, zeal and affectation having carried them much too far...
Now my method, though hard to practice, is easy to explain; and it is this. I propose to establish progressive stages of certainty. The evidence of the sense, helped and guarded by a certain process of correction, I retain. But the mental operation which follows the act of sense I for the most part reject; and instead of it I open and lay out a new and certain path for the mind to proceed in, starting directly from the simple sensuous perception.
Novum Organum (1620)
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Those who knew that the judgements of many centuries had reinforced the opinion that the Earth is placed motionless in the middle of heaven, as though at its centre, if I on the contrary asserted that the Earth moves, I hesitated for a long time whether to bring my treatise, written to demonstrate its motion, into the light of day, or whether it would not be better to follow the example of the Pythagoreans and certain others, who used to pass on the mysteries of their philosophy merely to their relatives and friends, not in writing but by personal contact, as the letter of Lysis to Hipparchus bears witness. And indeed they seem to me to have done so, not as some think from a certain jealousy of communicating their doctrines, but so that their greatest splendours, discovered by the devoted research of great men, should not be exposed to the contempt of those who either find it irksome to waste effort on anything learned, unless it is profitable, or if they are stirred by the exhortations and examples of others to a high-minded enthusiasm for philosophy, are nevertheless so dull-witted that among philosophers they are like drones among bees.
'To His Holiness Pope Paul III', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A. M. Duncan (1976), 24.
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Thought and science follow their own law of development; they are slowly elaborated in the growth and forward pressure of humanity, in what Shakespeare calls
...The prophetic soul,
Of the wide world dreaming on things to come.
St. Paul and Protestantism (1875), 155.
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Throughout his career, [Richard] Drew tried to create an environment where people were encouraged to follow their instincts. He was known at 3M as a consummate mentor, encouraging and helping to train many of the company’s young scientists, who went on to develop successful products of their own, paving the way for 3M’s culture of innovation.
In Press Release (7 May 2007) on 3M Company website.
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Thus it might be said, that the vegetable is only the sketch, nor rather the ground-work of the animal; that for the formation of the latter, it has only been requisite to clothe the former with an apparatus of external organs, by which it might be connected with external objects.
From hence it follows, that the functions of the animal are of two very different classes. By the one (which is composed of an habitual succession of assimilation and excretion) it lives within itself, transforms into its proper substance the particles of other bodies, and afterwards rejects them when they are become heterogeneous to its nature. By the other, it lives externally, is the inhabitant of the world, and not as the vegetable of a spot only; it feels, it perceives, it reflects on its sensations, it moves according to their influence, and frequently is enabled to communicate by its voice its desires, and its fears, its pleasures, and its pains.
The aggregate of the functions of the first order, I shall name the organic life, because all organized beings, whether animal or vegetable, enjoy it more or less, because organic texture is the sole condition necessary to its existence. The sum of the functions of the second class, because it is exclusively the property of the animal, I shall denominate the animal life.
Physiological Researches on Life and Death (1815), trans. P. Gold, 22-3.
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To derive two or three general Principles of Motion from Phænomena, and afterwards to tell us how the Properties and Actions of all corporeal Things follow from those manifest Principles, would be a very great step in Philosophy.
From 'Query 31', Opticks (1704, 2nd ed., 1718), 377.
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To fully understand the mathematical genius of Sophus Lie, one must not turn to books recently published by him in collaboration with Dr. Engel, but to his earlier memoirs, written during the first years of his scientific career. There Lie shows himself the true geometer that he is, while in his later publications, finding that he was but imperfectly understood by the mathematicians accustomed to the analytic point of view, he adopted a very general analytic form of treatment that is not always easy to follow.
In Lectures on Mathematics (1911), 9.
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To me, spirituality means “no matter what.” One stays on the path, one commits to love, one does one’s work; one follows one’s dream...no matter what.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 20
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To prove that tuberculosis is caused by the invasion of bacilli, and that it is a parasitic disease primarily caused by the growth and multiplication of bacilli, it is necessary to isolate the bacilli from the body, to grow them in pure culture until they are freed from every disease product of the animal organism, and, by introducing isolated bacilli into animals, to reproduce the same morbid condition that is known to follow from inoculation with spontaneously developed tuberculous material.
'The Etiology of Tuberculosis' (1882), Essays of Robert Koch (1987), trans. K. Codell Carter, 87.
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To prove to an indignant questioner on the spur of the moment that the work I do was useful seemed a thankless task and I gave it up. I turned to him with a smile and finished, “To tell you the truth we don’t do it because it is useful but because it’s amusing.” The answer was thought of and given in a moment: it came from deep down in my soul, and the results were as admirable from my point of view as unexpected. My audience was clearly on my side. Prolonged and hearty applause greeted my confession. My questioner retired shaking his head over my wickedness and the newspapers next day, with obvious approval, came out with headlines “Scientist Does It Because It’s Amusing!” And if that is not the best reason why a scientist should do his work, I want to know what is. Would it be any good to ask a mother what practical use her baby is? That, as I say, was the first evening I ever spent in the United States and from that moment I felt at home. I realised that all talk about science purely for its practical and wealth-producing results is as idle in this country as in England. Practical results will follow right enough. No real knowledge is sterile. The most useless investigation may prove to have the most startling practical importance: Wireless telegraphy might not yet have come if Clerk Maxwell had been drawn away from his obviously “useless” equations to do something of more practical importance. Large branches of chemistry would have remained obscure had Willard Gibbs not spent his time at mathematical calculations which only about two men of his generation could understand. With this faith in the ultimate usefulness of all real knowledge a man may proceed to devote himself to a study of first causes without apology, and without hope of immediate return.
A.V. Hill
From lecture to a scientific society in Philadelphia on “The Mechanism of the Muscle” given by invitation after he received a Nobel Prize for that work. The quote is Hill’s response to a post-talk audience question asking disapprovingly what practical use the speaker thought there was in his research. The above quoted answer, in brief, is—for the intellectual curiosity. As quoted about Hill by Bernard Katz in his own autobiographical chapter, 'Sir Bernard Katz', collected in Larry R. Squire (ed.), The History of Neuroscience in Autobiography (1996), Vol. 1, 350-351. Two excerpts from the above have been highlighted as standalone quotes here in this same quote collection for A. V. Hill. They begin “All talk about science…” and “The most useless investigation may prove…”.
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To stop short in any research that bids fair to widen the gates of knowledge, to recoil from fear of difficulty or adverse criticism, is to bring reproach on science. There is nothing for the investigator to do but go straight on, 'to explore up and down, inch by inch, with the taper his reason;' to follow the light wherever it may lead, even should it at times resemble a will-o'-the-wisp.
Referring to his interest in psychical (spiritual) research.
Presidential address to the British Association (1898). Quoted in Harold Begbie in Pall Mall magazine (Jan 1903). In Albert Shaw, The American Monthly Review of Reviews (1903), 27, 232.
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To write the true natural history of the world, we should need to be able to follow it from within. It would thus appear no longer as an interlocking succession of structural types replacing one another, but as an ascension of inner sap spreading out in a forest of consolidated instincts. Right at its base, the living world is constituted by conscious clothes in flesh and bone.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 151. Originally published in French as Le Phénomene Humain (1955).
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To-day, science has withdrawn into realms that are hardly understanded of the people. Biology means very largely histology, the study of the cell by difficult and elaborate microscopical processes. Chemistry has passed from the mixing of simple substances with ascertained reactions, to an experimentation of these processes under varying conditions of temperature, pressure, and electrification—all requiring complicated apparatus and the most delicate measurement and manipulation. Similarly, physics has outgrown the old formulas of gravity, magnetism, and pressure; has discarded the molecule and atom for the ion, and may in its recent generalizations be followed only by an expert in the higher, not to say the transcendental mathematics.
Anonymous
‘Exit the Amateur Scientist.’ Editorial, The Nation, 23 August 1906, 83, 160.
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Today, nothing is unusual about a scientific discovery's being followed soon after by a technical application: The discovery of electrons led to electronics; fission led to nuclear energy. But before the 1880's, science played almost no role in the advances of technology. For example, James Watt developed the first efficient steam engine long before science established the equivalence between mechanical heat and energy.
Edward Teller with Judith L. Shoolery, Memoirs: A Twentieth-Century Journey in Science and Politics (2001), 42.
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Very few, even among those who have taken the keenest interest in the progress of the revolution in natural knowledge set afoot by the publication of the “Origin of Species”; and who have watched, not without astonishment, the rapid and complete change which has been effected both inside and outside the boundaries of the scientific world in the attitude of men’s minds towards the doctrines which are expounded in that great work, can have been prepared for the extraordinary manifestation of affectionate regard for the man, and of profound reverence for the philosopher, which followed the announcement, on Thursday last, of the death of Mr Darwin.
'Obituary [of Charles Darwin]' (1882). In Collected Essays (1893), Vol. 2, 244.
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Very old and wide-spread is the opinion that forests have an important impact on rainfall. ... If forests enhance the amount and frequency of precipitation simply by being there, deforestation as part of agricultural expansion everywhere, must necessarily result in less rainfall and more frequent droughts. This view is most poignantly expressed by the saying: Man walks the earth and desert follows his steps! ... It is not surprising that under such circumstances the issue of a link between forests and climate has ... been addressed by governments. Lately, the Italian government has been paying special attention to reforestation in Italy and its expected improvement of the climate. ... It must be prevented that periods of heavy rainfall alternate with droughts. ...In the Unites States deforestation plays an important role as well and is seen as the cause for a reduction in rainfall. ... committee chairman of the American Association for Advancement of Science demands decisive steps to extend woodland in order to counteract the increasing drought. ... some serious concerns. In 1873, in Vienna, the congress for agriculture and forestry discussed the problem in detail; and when the Prussian house of representatives ordered a special commission to examine a proposed law pertaining to the preservation and implementation of forests for safeguarding, it pointed out that the steady decrease in the water levels of Prussian rivers was one of the most serious consequences of deforestation only to be rectified by reforestation programs. It is worth mentioning that ... the same concerns were raised in Russia as well and governmental circles reconsidered the issue of deforestation.
as quoted in Eduard Brückner - The Sources and Consequences of Climate Change and Climate Variability in Historical Times editted by N. Stehr and H. von Storch (2000)
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We are not afraid to follow truth wherever it may lead, nor to tolerate any error so long as reason is left free to combat it.
Letter to William Roscoe (27 Dec 1820).
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We believe that interest in nature leads to knowledge,
which is followed by understanding,
and later, appreciation.
Once respect is gained
it is a short step to responsibility,
and ultimately action
to preserve our Earth.
…...
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We come back then to our records of nervous messages with a reasonable assurance that they do tell us what the message is like. It is a succession of brief waves of surface breakdown, each allowing a momentary leakage of ions from the nerve fibre. The waves can be set up so that they follow one another in rapid or in slow succession, and this is the only form of gradation of which the message is capable. Essentially the same kind of activity is found in all sorts of nerve fibres from all sorts of animals and there is no evidence to suggest that any other kind of nervous transmission is possible. In fact we may conclude that the electrical method can tell us how the nerve fibre carries out its function as the conducting unit of the nervous system, and that it does so by reactions of a fairly simple type.
The Mechanism of Nervous Action (1932), 21.
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We do not draw conclusions with our eyes, but with our reasoning powers, and if the whole of the rest of living nature proclaims with one accord from all sides the evolution of the world of organisms, we cannot assume that the process stopped short of Man. But it follows also that the factors which brought about the development of Man from his Simian ancestry must be the same as those which have brought about the whole of evolution.
Translation of Weismann's work in German, by John Arthur Thomson and Margaret R. Thomson, The Evolution Theory (1904), Vol. 2, 393.
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We do not know what is disease, how remedies act, and still less how diseases are cured. We must abandon the way which has thus far been followed
…...
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We have also here an acting cause to account for that balance so often observed in nature,—a deficiency in one set of organs always being compensated by an increased development of some others—powerful wings accompanying weak feet, or great velocity making up for the absence of defensive weapons; for it has been shown that all varieties in which an unbalanced deficiency occurred could not long continue their existen The action of this principle is exactly like that of the centrifugal governor of the steam engine, which checks and corrects any irregularities almost before they become evident; and in like manner no unbalanced deficiency in the animal kingdom can ever reach any conspicuous magnitude, because it would make itself felt at the very first step, by rendering existence difficult and extinction almost sure soon to follow.
In 'On the Tendency of Varieties to Depart Indefinitely from the Original Type', Journal of the Proceedings of the Linnean Society, Zoology (1858), 3, 61-62.
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We may safely say, that the whole form of modern mathematical thinking was created by Euler. It is only with the greatest difficulty that one is able to follow the writings of any author immediately preceding Euler, because it was not yet known how to let the formulas speak for themselves. This art Euler was the first one to teach.
As quoted in W. Ahrens Scherz und Ernst in der Mathematik (1904), 251. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 183.
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We may summarize … the fundamental characteristics and limitations of mathematics as follows: mathematics is ultimately an experimental science, for freedom from contradiction cannot be proved, but only postulated and checked by observation, and similarly existence can only be postulated and checked by observation. Furthermore, mathematics requires the fundamental device of all thought, of analyzing experience into static bits with static meanings.
In The Nature of Physical Theory (1936), 58.
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We must examine the moral alchemy through which the in-group readily transmutes virtue into vice and vice into virtue, as the occasion may demand. … We begin with the engagingly simple formula of moral alchemy: the same behavior must be differently evaluated according to the person who exhibits it. For example, the proficient alchemist will at once know that the word “firm” is properly declined as follows:
I am firm,
Thou art obstinate,
He is pig-headed.
There are some, unversed in the skills of this science, who will tell you that one and the same term should be applied to all three instances of identical behavior.
In article, 'The Self-Fulfilling Prophecy', The Antioch Review (Summer 1948), 8, No. 2, 195-196. Included as Chap. 7 of Social Theory and Social Structure (1949), 201.
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We must make the following remark: a proof, that after a certain time t1, the spheres must necessarily be mixed uniformly, whatever may be the initial distribution of states, cannot be given. This is in fact a consequence of probability theory, for any non-uniform distribution of states, no matter how improbable it may be, is still not absolutely impossible. Indeed it is clear that any individual uniform distribution, which might arise after a certain time from some particular initial state, is just as improbable as an individual non-uniform distribution; just as in the game of Lotto, any individual set of five numbers is as improbable as the set 1, 2, 3, 4, 5. It is only because there are many more uniform distributions than non-uniform ones that the distribution of states will become uniform in the course of time. One therefore cannot prove that, whatever may be the positions and velocities of the spheres at the beginning, the distributions must become uniform after a long time; rather one can only prove that infinitely many more initial states will lead to a uniform one after a definite length of time than to a non-uniform one. Loschmidt's theorem tells us only about initial states which actually lead to a very non-uniform distribution of states after a certain time t1; but it does not prove that there are not infinitely many more initial conditions that will lead to a uniform distribution after the same time. On the contrary, it follows from the theorem itself that, since there are infinitely many more uniform distributions, the number of states which lead to uniform distributions after a certain time t1, is much greater than the number that leads to non-uniform ones, and the latter are the ones that must be chosen, according to Loschmidt, in order to obtain a non-uniform distribution at t1.
From 'On the Relation of a General Mechanical Theorem to the Second Law of Thermodynamics' (1877), in Stephen G. Brush (ed.), Selected Readings in Physics (1966), Vol. 2, Irreversible Processes, 191-2.
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We ought then to consider the present state of the universe as the effect of its previous state and as the cause of that which is to follow. An intelligence that, at a given instant, could comprehend all the forces by which nature is animated and the respective situation of the beings that make it up, if moreover it were vast enough to submit these data to analysis, would encompass in the same formula the movements of the greatest bodies of the universe and those of the lightest atoms. For such an intelligence nothing would be uncertain, and the future, like the past, would be open to its eyes.
Philosophical Essay on Probabilities (1814), 5th edition (1825), trans. Andrew I. Dale (1995), 2.
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We try never to forget that medicine is for the people. It is not for the profits. The profits follow, and if we have remembered that, they have never failed to appear. The better we have remembered it, the larger they have been.
Address to the Medical College of Virginia, Richmond (1 Dec 1950). Quoted in James C. Collins and Jerry I. Porras, Built to Last (1994, 1997), 48.
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Weierstrass related … that he followed Sylvester’s papers on the theory of algebraic forms very attentively until Sylvester began to employ Hebrew characters. That was more than he could stand and after that he quit him.
From Naturwissenschaftliche Rundschau (1897), 12 (1897), 361. As cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 180.
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What we do see depends mainly on what we look for. ... In the same field the farmer will notice the crop, the geologists the fossils, botanists the flowers, artists the colouring, sportmen the cover for the game. Though we may all look at the same things, it does not all follow that we should see them.
The Beauties of Nature (1893, 2009), 12.
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What you learn from others you can use to follow.
What you learn for yourself you can use to lead.
In The Art of Doing Science and Engineering: Learning to Learn (1975, 2005), 160.
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Whatever things are not derived from objects themselves, whether by the external senses or by the sensation of internal thoughts, are to be taken as hypotheses…. Those things which follow from the phenomena neither by demonstration nor by the argument of induction, I hold as hypotheses.
As quoted in Ernan McMullin, 'The Principia: Significance For Empiricism', collected in Margaret J. Osler and Paul Lawrence Farber (eds.), Religion, Science, and Worldview: Essays in Honor of Richard S. Westfall (2002), 38.
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When a doctor arrives to attend some patient of the working class...let him condescend to sit down...if not on a gilded chair...one a three-legged stool... He should question the patient carefully... So says Hippocrates in his work 'Affections.' I may venture to add one more question: What occupation does he follow?
De Morbis Artificum Diatriba (1713) Trans. by W.C. Wright in A.L. Birmingham, Classics of Medicine Library (1983). Quoted in Edward J. Huth and T. J. Murray. Medicine in Quotations: Views of Health and Disease Through the Ages (2006), 276.
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When April wind wakes the call for the soil, I hold the plough as my only hold upon the earth, and, as I follow through the fresh and fragrant furrow, I am planted with every foot-step, growing, budding, blooming in a spirit of spring.
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When the difficulty of a problem lies only in finding out what follows from certain fixed premises, mathematical methods furnish invaluable wings for flying over intermediate obstructions.
From The Economic Theory of the Location of Railways (1887, 1914), viii.
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When the late Sophus Lie … was asked to name the characteristic endowment of the mathematician, his answer was the following quaternion: Phantasie, Energie, Selbstvertrauen, Selbstkritik.
In Lectures on Philosophy, Science and Art (1908), 31. [“Quaternion” is used here in its meaning of a set of four people or things. The last four words, given in German, translate as “Imagination, Energy, Self-confidence, Self-criticism.” —Webmaster]
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When the seagulls follow the trawler, it is because they think sardines will be thrown into the sea.
Only utterance at press conference, directed at the media, after he won his appeal at Croydon Magistrates Court against a prison sentence for his conviction of assault on a hostile fan. Quoted in Simon Midgley, 'When the seagulls follow the trawler, it is because they think sardines will be thrown into the sea', The Independent (31 Mar 1995). According to Maurice Watkins (legal director of Manchester United) the statement was prepared by Cantona before facing the press, though the reporters may have taken it to be spontaneous. In Simon Stone, 'Maurice Watkins reveals role in Eric Cantona’s “seagulls” speech', The Independent (27 Nov 2012).
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While playing the part of the detective the investigator follows clues, but having captured his alleged fact, he turns judge and examines the case by means of logically arranged evidence. Both functions are equally essential but they are different.
In The Art of Scientific Investigation (1950, 1957), 92.
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Who … is not familiar with Maxwell’s memoirs on his dynamical theory of gases? … from one side enter the equations of state; from the other side, the equations of motion in a central field. Ever higher soars the chaos of formulae. Suddenly we hear, as from kettle drums, the four beats “put n=5.” The evil spirit v vanishes; and … that which had seemed insuperable has been overcome as if by a stroke of magic … One result after another follows in quick succession till at last … we arrive at the conditions for thermal equilibrium together with expressions for the transport coefficients.
In Ceremonial Speech (15 Nov 1887) celebrating the 301st anniversary of the Karl-Franzens-University Graz. Published as Gustav Robert Kirchhoff: Festrede zur Feier des 301. Gründungstages der Karl-Franzens-Universität zu Graz (1888), 29, as translated in Michael Dudley Sturge, Statistical and Thermal Physics (2003), 343. A more complete alternate translation also appears on the Ludwig Boltzmann Quotes page of this website.
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Why does man regret, even though he may endeavour to banish any such regret, that he has followed the one natural impulse, rather than the other; and why does he further feel that he ought to regret his conduct? Man in this respect differs profoundly from the lower animals.
Descent of Man
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With NMR we don’t touch the cell at all. We can follow it through time, watch its development.
Describing the benefits of the newly developed nuclear magnetic resonance imaging microscope. As quoted in L. Davis, 'Seeing the Cell and Letting it Live', Science News (19 Jul 1986), 130, No. 3, 39. Reference to Letter, James B. Aguayo, et al.,'Nuclear Magnetic Resonance Imaging of a Single Cell', Nature (10 Jul 1986), 322, 190–191, which announced the first NMR images of a single cell.
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Without the cultivation of the earth, [man] is, in all countries, a savage. Until he gives up the chase, and fixes himself in some place and seeks a living from the earth, he is a roaming barbarian. When tillage begins, other arts follow. The farmers, therefore, are the founders of human civilization.
Address to the Legislature of Massachussetts, Boston, On the Agriculture of England (13 Jan 1840). Collected in The Works of Daniel Webster (1851), Vol. 1, 457.
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Would you have a man reason well, you must use him to it betimes; exercise his mind in observing the connection between ideas, and following them in train. Nothing does this better than mathematics, which therefore, I think should be taught to all who have the time and opportunity, not so much to make them mathematicians, as to make them reasonable creatures; for though we all call ourselves so, because we are born to it if we please, yet we may truly say that nature gives us but the seeds of it, and we are carried no farther than industry and application have carried us.
In Conduct of the Understanding, Sect. 6.
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You have to have a lot of ideas. First, if you want to make discoveries, it’s a good thing to have good ideas. And second, you have to have a sort of sixth sense—the result of judgment and experience—which ideas are worth following up. I seem to have the first thing, a lot of ideas, and I also seem to have good judgment as to which are the bad ideas that I should just ignore, and the good ones, that I’d better follow up.
As quoted by Nancy Rouchette, The Journal of NIH Research (Jul 1990), 2, 63. Reprinted in Linus Pauling, Barclay Kamb, Linus Pauling: Selected Scientific Papers, Vol. 2, Biomolecular Sciences (2001), 1101.
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You see, if the height of the mercury [barometer] column is less on the top of a mountain than at the foot of it (as I have many reasons for believing, although everyone who has so far written about it is of the contrary opinion), it follows that the weight of the air must be the sole cause of the phenomenon, and not that abhorrence of a vacuum, since it is obvious that at the foot of the mountain there is more air to have weight than at the summit, and we cannot possibly say that the air at the foot of the mountain has a greater aversion to empty space than at the top.
In letter to brother-in-law Perier (Nov 1647) as given in Daniel Webster Hering, Physics: the Science of the Forces of Nature (1922), 114. As also stated by Hering, Perier conducted an experiment on 19 Sep 1648 comparing readings on two barometers, one at the foot, and another at the top of 4,000-ft Puy-de-Dôme neighboring mountain.
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Your mind works very simply: you are either trying to find out what are God’s laws in order to follow them; or you are trying to outsmart Him.
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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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