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Home > Category Index for Science Quotations > Category Index C > Category: Constant

Constant Quotes (56 quotes)

Les causes primordiales ne nous sont point connues; mais elles sont assujetties à des lois simples et constantes, que l’on peut découvrir par l’observation, et dont l’étude est l’objet de la philosophie naturelle.
Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy.
Opening statement from 'Discours Préliminaire' to Théorie Analytique de la Chaleur (1822), i, translated by Alexander Freeman in The Analytical Theory of Heat (1878), 1.
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[Defining Life] The constant uniformity of phenomena under diversity of external influences.
Biologie (1802). As cited in translated form in George Henry Lewes, Physiology of Common Life (1875), Vol. 2, 356.
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A short, broad man of tremendous vitality, the physical type of Hereward, the last of the English, and his brother-in-arms, Winter, Sylvester’s capacious head was ever lost in the highest cloud-lands of pure mathematics. Often in the dead of night he would get his favorite pupil, that he might communicate the very last product of his creative thought. Everything he saw suggested to him something new in the higher algebra. This transmutation of everything into new mathematics was a revelation to those who knew him intimately. They began to do it themselves. His ease and fertility of invention proved a constant encouragement, while his contempt for provincial stupidities, such as the American hieroglyphics for π and e, which have even found their way into Webster’s Dictionary, made each young worker apply to himself the strictest tests.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 265.
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All parts of the material universe are in constant motion and though some of the changes may appear to be cyclical, nothing ever exactly returns, so far as human experience extends, to precisely the same condition.
Address (Jul 1874) at the grave of Joseph Priestley, in Joseph Henry and Arthur P. Molella, et al. (eds.), A Scientist in American Life: Essays and Lectures of Joseph Henry (1980), 119.
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Between men of different studies and professions, may be observed a constant reciprocation of reproaches. The collector of shells and stones derides the folly of him who pastes leaves and flowers upon paper, pleases himself with colours that are perceptibly fading, and amasses with care what cannot be preserved. The hunter of insects stands amazed that any man can waste his short time upon lifeless matter, while many tribes of animals yet want their history. Every one is inclined not only to promote his own study, but to exclude all others from regard, and having heated his imagination with some favourite pursuit, wonders that the rest of mankind are not seized with the same passion.
From 'Numb. 83, Tuesday, January 1, 1750', The Rambler (1756), Vol. 2, 150.
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Biological evolution is a system of constant divergence without subsequent joining of branches. Lineages, once distinct, are separate forever. In human history, transmission across lineages is, perhaps, the major source of cultural change. Europeans learned about corn and potatoes from Native Americans and gave them smallpox in return.
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By teaching us how to cultivate each ferment in its purity—in other words, by teaching us how to rear the individual organism apart from all others,—Pasteur has enabled us to avoid all these errors. And where this isolation of a particular organism has been duly effected it grows and multiplies indefinitely, but no change of it into another organism is ever observed. In Pasteur’s researches the Bacterium remained a Bacterium, the Vibrio a Vibrio, the Penicillium a Penicillium, and the Torula a Torula. Sow any of these in a state of purity in an appropriate liquid; you get it, and it alone, in the subsequent crop. In like manner, sow smallpox in the human body, your crop is smallpox. Sow there scarlatina, and your crop is scarlatina. Sow typhoid virus, your crop is typhoid—cholera, your crop is cholera. The disease bears as constant a relation to its contagium as the microscopic organisms just enumerated do to their germs, or indeed as a thistle does to its seed.
In 'Fermentation, and its Bearings on Surgery and Medicine', Essays on the Floating­Matter of the Air in Relation to Putrefaction and Infection (1881), 264.
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Computers and rocket ships are examples of invention, not of understanding. … All that is needed to build machines is the knowledge that when one thing happens, another thing happens as a result. It’s an accumulation of simple patterns. A dog can learn patterns. There is no “why” in those examples. We don’t understand why electricity travels. We don’t know why light travels at a constant speed forever. All we can do is observe and record patterns.
In God's Debris: A Thought Experiment (2004), 22.
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Everything around us is filled with mystery and magic. I find this no cause for despair, no reason to turn for solace to esoteric formulae or chariots of gods. On the contrary, our inability to find easy answers fills me with a fierce pride in our ambivalent biology ... with a constant sense of wonder and delight that we should be part of anything so profound.
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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 found out that the main ability to have was a visual, and also an almost tactile, way to imagine the physical situations, rather than a merely logical picture of the problems. … Very soon I discovered that if one gets a feeling for no more than a dozen … radiation and nuclear constants, one can imagine the subatomic world almost tangibly, and manipulate the picture dimensionally and qualitatively, before calculating more precise relationships.
In Adventures of a Mathematician (1976), 147.
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If a patient is poor he is committed to a public hospital as a 'psychotic.' If he can afford a sanitarium, the diagnosis is 'neurasthenia.' If he is wealthy enough to be in his own home under the constant watch of nurses and physicians, he is simply 'an indisposed eccentric.'
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In all works on Natural History, we constantly find details of the marvellous adaptation of animals to their food, their habits, and the localities in which they are found. But naturalists are now beginning to look beyond this, and to see that there must be some other principle regulating the infinitely varied forms of animal life. It must strike every one, that the numbers of birds and insects of different groups having scarcely any resemblance to each other, which yet feed on the same food and inhabit the same localities, cannot have been so differently constructed and adorned for that purpose alone. Thus the goat-suckers, the swallows, the tyrant fly-catchers, and the jacamars, all use the same kind ‘Of food, and procure it in the same manner: they all capture insects on the wing, yet how entirely different is the structure and the whole appearance of these birds!
In A Narrative of Travels on the Amazon and Rio Negro (1853), 83-84.
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In despair, I offer your readers their choice of the following definitions of entropy. My authorities are such books and journals as I have by me at the moment.
(a) Entropy is that portion of the intrinsic energy of a system which cannot be converted into work by even a perfect heat engine.—Clausius.
(b) Entropy is that portion of the intrinsic energy which can be converted into work by a perfect engine.—Maxwell, following Tait.
(c) Entropy is that portion of the intrinsic energy which is not converted into work by our imperfect engines.—Swinburne.
(d) Entropy (in a volume of gas) is that which remains constant when heat neither enters nor leaves the gas.—W. Robinson.
(e) Entropy may be called the ‘thermal weight’, temperature being called the ‘thermal height.’—Ibid.
(f) Entropy is one of the factors of heat, temperature being the other.—Engineering.
I set up these bald statement as so many Aunt Sallys, for any one to shy at.
[Lamenting a list of confused interpretations of the meaning of entropy, being hotly debated in journals at the time.]
In The Electrician (9 Jan 1903).
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In the center of everything rules the sun; for who in this most beautiful temple could place this luminary at another better place whence it can light up the whole at once? ... In this arrangement we thus find an admirable harmony of the world, and a constant harmonious connection between the motion and the size of the orbits as could not be found otherwise.
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It is easy to overlook this thought that life just is. As humans we are inclined to feel that life must have a point. We have plans and aspirations and desires. We want to take constant advantage of the intoxicating existence we’ve been endowed with. But what’s life to a lichen? Yet its impulse to exist, to be, is every bit as strong as ours-arguably even stronger. If I were told that I had to spend decades being a furry growth on a rock in the woods, I believe I would lose the will to go on. Lichens don’t. Like virtually all living things, they will suffer any hardship; endure any insult, for a moment’s additions existence. Life, in short just wants to be.
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It is hard to imagine while strenuously walking in the heart of an equatorial rain forest, gasping for every breath in a stifling humid sauna, how people could have ever adapted to life under these conditions. It is not just the oppressive climate - the tall forest itself is dark, little light reaching the floor from the canopy, and you do not see any animals. It is a complete contrast to the herbivore-rich dry savannahs of tropical Africa. Yet there are many animals here, evident by the loud, continual noise of large cryptic insects and the constant threat of stepping on a deadly king cobra. This was my first impression of the rain forest in Borneo.
The Humans Who Went Extinct
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It is the constant aim of the mathematician to reduce all his expressions to their lowest terms, to retrench every superfluous word and phrase, and to condense the Maximum of meaning into the Minimum of language.
In Address (22 Feb 1877) for Commemoration Day at Johns Hopkins University. Published as a pamphlet, and reprinted in The Collected Mathematical Papers of James Joseph Sylvester: (1870-1883) (1909), Vol. 3, 72-73.
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It is very remarkable that while the words Eternal, Eternity, Forever, are constantly in our mouths, and applied without hesitation, we yet experience considerable difficulty in contemplating any definite term which bears a very large proportion to the brief cycles of our petty chronicles. There are many minds that would not for an instant doubt the God of Nature to have existed from all Eternity, and would yet reject as preposterous the idea of going back a million of years in the History of His Works. Yet what is a million, or a million million, of solar revolutions to an Eternity?
Memoir on the Geology of Central France (1827), 165.
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It may be doubted whether any character can be named which is distinctive of a race and is constant.
…...
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It was cold. Space, the air we breathed, the yellow rocks, were deadly cold. There was something ultimate, passionless, and eternal in this cold. It came to us as a single constant note from the depths of space. We stood on the very boundary of life and death.
…...
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Just as the constant increase of entropy is the basic law of the universe, so it is the basic law of life to be ever more highly structured and to struggle against entropy.
In 'Letter to Dr. Gustáv Husák', Václav Havel: Or Living in Truth (1986), Pt. 1, 23.
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Much later, when I discussed the problem with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life. But this “blunder,” rejected by Einstein, is still sometimes used by cosmologists even today, and the cosmological constant denoted by the Greek letter Λ rears its ugly head again and again and again.
My World Line (1970). Cited in Edward Robert Harrison, Cosmology: the Science of the Universe (2000), 379, which adds: “The Λ force is referred to by various names, such as the cosmological constant, cosmological term, cosmical constant or cosmical term.”
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Nobody can be a good reasoner unless by constant practice he has realised the importance of getting hold of the big ideas and hanging on to them like grim death.
In 'Presidential Address to the London Branch of the Mathematical Association', Mathematical Gazette (Mar 1913), 7, No. 104, 92.
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One of the greatest gifts science has brought to the world is continuing elimination of the supernatural, and it was a lesson that my father passed on to me, that knowledge liberates mankind from superstition. We can live our lives without the constant fear that we have offended this or that deity who must be placated by incantation or sacrifice, or that we are at the mercy of devils or the Fates. With increasing knowledge, the intellectual darkness that surrounds us is illuminated and we learn more of the beauty and wonder of the natural world.
…...
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One of the most constant characteristics of beliefs is their intolerance. It is even more uncompromising as the belief is stronger. Men dominated by a certitude cannot tolerate those who do not accept it.
From Les Opinions et les Croyances: Genèse—Évolution (1911), 235. As translated in review of that book by: Samuel N. Reep, The American Journal of Sociology (1913), 18, No. 6, 814 (first and last sentences). Original French text: “Un des caractères généraux les plus constants des croyances est leur intolérance. Elle est d’autant plus intransigeante que la croyance est plus forte. Les hommes dominés par une certitude ne peuvent tolérer ceux qui ne l’acceptent pas.” The second sentence as translated by Webmaster from the original French. Also seen translated as, “The stronger the belief, the greater its intolerance.”
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One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts.
In Albert Einstein, translated by G.B. Jeffery and W. Perrett, 'Geometry and Experience',Sidelights on Relativity (1922), 27.
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One would have to have completely forgotten the history of science so as not to remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.
In Henri Poincaré and George Bruce Halsted (trans.), The Value of Science: Essential Writings of Henri Poincare (1907), 79.
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Pure Mathematics is the class of all propositions of the form “p implies q,” where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth.
In 'Definition of Pure Mathematics', Principles of Mathematics (1903), 3.
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Scientific theories need reconstruction every now and then. If they didn't need reconstruction they would be facts, not theories. The more facts we know, the less radical become the changes in our theories. Hence they are becoming more and more constant. But take the theory of gravitation; it has not been changed in four hundred years.
As quoted in 'Electricity Will Keep The World From Freezing Up', New York Times (12 Nov 1911), SM4.
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Suppose a number of equal waves of water to move upon the surface of a stagnant lake, with a certain constant velocity, and to enter a narrow channel leading out of the lake. Suppose then another similar cause to have excited another equal series of waves, which arrive at the same time, with the first. Neither series of waves will destroy the other, but their effects will be combined: if they enter the channel in such a manner that the elevations of one series coincide with those of the other, they must together produce a series of greater joint elevations; but if the elevations of one series are so situated as to correspond to the depressions of the other, they must exactly fill up those depressions. And the surface of the water must remain smooth; at least I can discover no alternative, either from theory or from experiment.
A Reply to the Animadversions of the Edinburgh Reviewers on Some Papers Published in the Philosophical Transactions (1804), 17-8.
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That which lies before the human race is a constant struggle to maintain and improve, in opposition to State of Nature, the State of Art of an organized polity; in which, and by which, man may develop a worthy civilization
'Prolegomena', Evolution and Ethics, and Other Essays (1897), 45.
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The balance of nature is not a status quo; it is fluid, ever shifting, in a constant state of adjustment.
In Silent Spring (1962), 246.
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The belief that mathematics, because it is abstract, because it is static and cold and gray, is detached from life, is a mistaken belief. Mathematics, even in its purest and most abstract estate, is not detached from life. It is just the ideal handling of the problems of life, as sculpture may idealize a human figure or as poetry or painting may idealize a figure or a scene. Mathematics is precisely the ideal handling of the problems of life, and the central ideas of the science, the great concepts about which its stately doctrines have been built up, are precisely the chief ideas with which life must always deal and which, as it tumbles and rolls about them through time and space, give it its interests and problems, and its order and rationality. That such is the case a few indications will suffice to show. The mathematical concepts of constant and variable are represented familiarly in life by the notions of fixedness and change. The concept of equation or that of an equational system, imposing restriction upon variability, is matched in life by the concept of natural and spiritual law, giving order to what were else chaotic change and providing partial freedom in lieu of none at all. What is known in mathematics under the name of limit is everywhere present in life in the guise of some ideal, some excellence high-dwelling among the rocks, an “ever flying perfect” as Emerson calls it, unto which we may approximate nearer and nearer, but which we can never quite attain, save in aspiration. The supreme concept of functionality finds its correlate in life in the all-pervasive sense of interdependence and mutual determination among the elements of the world. What is known in mathematics as transformation—that is, lawful transfer of attention, serving to match in orderly fashion the things of one system with those of another—is conceived in life as a process of transmutation by which, in the flux of the world, the content of the present has come out of the past and in its turn, in ceasing to be, gives birth to its successor, as the boy is father to the man and as things, in general, become what they are not. The mathematical concept of invariance and that of infinitude, especially the imposing doctrines that explain their meanings and bear their names—What are they but mathematicizations of that which has ever been the chief of life’s hopes and dreams, of that which has ever been the object of its deepest passion and of its dominant enterprise, I mean the finding of the worth that abides, the finding of permanence in the midst of change, and the discovery of a presence, in what has seemed to be a finite world, of being that is infinite? It is needless further to multiply examples of a correlation that is so abounding and complete as indeed to suggest a doubt whether it be juster to view mathematics as the abstract idealization of life than to regard life as the concrete realization of mathematics.
In 'The Humanization of Teaching of Mathematics', Science, New Series, 35, 645-46.
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The earth holds a silver treasure, cupped between ocean bed and tenting sky. Forever the heavens spend it, in the showers that refresh our temperate lands, the torrents that sluice the tropics. Every suckling root absorbs it, the very soil drains it down; the rivers run unceasing to the sea, the mountains yield it endlessly… Yet none is lost; in vast convection our water is returned, from soil to sky, and sky to soil, and back gain, to fall as pure as blessing. There was never less; there could never be more. A mighty mercy on which life depends, for all its glittering shifts, water is constant.
In A Cup of Sky (1950), 41.
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The establishment of the periodic law may truly be said to mark a line in chemical science, and we anticipate that its application and and extension will be fraught With the most important consequences. It reminds us how important above all things is the correct determination of the fundamental constants of our science—the atomic weights of the elements, about which in many cases great uncertainty prevails; it is much to be desired that this may not long remain the case. It also affords the strongest encouragement to the chemist to persevere in the search for new elements.
In The Encyclopaedia Britannica: Ninth Edition (1877), Vol. 5, 714.
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The fundamental characteristic of the scientific method is honesty. In dealing with any question, science asks no favors. ... I believe that constant use of the scientific method must in the end leave its impress upon him who uses it. ... A life spent in accordance with scientific teachings would be of a high order. It would practically conform to the teachings of the highest types of religion. The motives would be different, but so far as conduct is concerned the results would be practically identical.
Address as its retiring president, to the American Association for the Advancement of Science, St. Louis (28 Dec 1903). 'Scientific Investigation and Progress', Nature 928 Jan 1904), 69:1787, 309.
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The letter e may now no longer be used to denote anything other than this positive universal constant.
In Differential and Integral Calculus (1951), 44. This is Landau’s comment after he writes “Definition 13: “e is the solution of log y= 1”.
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The main sources of mathematical invention seem to be within man rather than outside of him: his own inveterate and insatiable curiosity, his constant itching for intellectual adventure; and likewise the main obstacles to mathematical progress seem to be also within himself; his scandalous inertia and laziness, his fear of adventure, his need of conformity to old standards, and his obsession by mathematical ghosts.
In The Study of the History of Mathematics (1936), 16.
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Thomas Robert Malthus quote The prodigious waste of human life
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The prodigious waste of human life occasioned by this perpetual struggle for room and food, was more than supplied by the mighty power of population, acting, in some degree, unshackled, from the constant habit of emigration.
An Essay on the Principle of Population (1798), 48.
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The responsibility for maintaining the composition of the blood in respect to other constituents devolves largely upon the kidneys. It is no exaggeration to say that the composition of the blood is determined not by what the mouth ingests but by what the kidneys keep; they are the master chemists of our internal environment, which, so to speak, they synthesize in reverse. When, among other duties, they excrete the ashes of our body fires, or remove from the blood the infinite variety of foreign substances which are constantly being absorbed from our indiscriminate gastrointestinal tracts, these excretory operations are incidental to the major task of keeping our internal environment in an ideal, balanced state. Our glands, our muscles, our bones, our tendons, even our brains, are called upon to do only one kind of physiological work, while our kidneys are called upon to perform an innumerable variety of operations. Bones can break, muscles can atrophy, glands can loaf, even the brain can go to sleep, without immediately endangering our survival, but when the kidneys fail to manufacture the proper kind of blood neither bone, muscle, gland nor brain can carry on.
'The Evolution of the Kidney', Lectures on the Kidney (1943), 3.
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The routine produces. But each day, nevertheless, when you try to get started you have to transmogrify, transpose yourself; you have to go through some kind of change from being a normal human being, into becoming some kind of slave.
I simply don’t want to break through that membrane. I’d do anything to avoid it. You have to get there and you don’t want to go there because there’s so much pressure and so much strain and you just want to stay on the outside and be yourself. And so the day is a constant struggle to get going.
And if somebody says to me, You’re a prolific writer—it seems so odd. It’s like the difference between geological time and human time. On a certain scale, it does look like I do a lot. But that’s my day, all day long, sitting there wondering when I’m going to be able to get started. And the routine of doing this six days a week puts a little drop in a bucket each day, and that’s the key. Because if you put a drop in a bucket every day, after three hundred and sixty-five days, the bucket’s going to have some water in it.
https://www.theparisreview.org/interviews/5997/john-mcphee-the-art-of-nonfiction-no-3-john-mcphee
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The theory is confirmed that pea hybrids form egg and pollen cells, which, in their constitution, represent in equal numbers all constant forms which result for the combination of the characters united in fertilization.
As collected in Forest Ray Moulton (ed.), The Autobiography of Science (1945), 586.
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The velocity of light is one of the most important of the fundamental constants of Nature. Its measurement by Foucault and Fizeau gave as the result a speed greater in air than in water, thus deciding in favor of the undulatory and against the corpuscular theory. Again, the comparison of the electrostatic and the electromagnetic units gives as an experimental result a value remarkably close to the velocity of light–a result which justified Maxwell in concluding that light is the propagation of an electromagnetic disturbance. Finally, the principle of relativity gives the velocity of light a still greater importance, since one of its fundamental postulates is the constancy of this velocity under all possible conditions.
Studies in Optics (1927), 120.
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There is a theory that creativity arises when individuals are out of sync with their environment. To put it simply, people who fit in with their communities have insufficient motivation to risk their psyches in creating something truly new, while those who are out of sync are driven by the constant need to prove their worth.
In 'Beyond the Soapsuds Universe', Discover Magazine (1997). The author explains (in a blog found online) that this “idea comes from a theory by Mihaly Csikszentmihalyi, who wrote a book called Flow: the Psychology of Optimal Experience. You do need someone to come in from outside. One of the theories about why mathematicians do their best work when they’re young is because they’re not yet educated enough to know what seems obviously wrong. So they try new things.”
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Things of all kinds are subject to a universal law which may be called the law of large numbers. It consists in the fact that, if one observes very considerable numbers of events of the same nature, dependent on constant causes and causes which vary irregularly, sometimes in one direction, sometimes in the other, it is to say without their variation being progressive in any definite direction, one shall find, between these numbers, relations which are almost constant.
Poisson’s Law of Large Numbers (16 Nov 1837), in Recherches sur la Probabilités (1837), 7. English version by Webmaster using Google Translate, from the original French, “Les choses de toutes natures sont soumises à une loi universelle qu’on) peut appeler la loi des grands nombres. Elle consiste en ce que, si l’on observe des nombres très considérables d’événements d’une même nature, dépendants de causes constantes et de causes qui varient irrégulièrement, tantôt dans un sens, tantôt daus l’autre, c’est-à-dire sans que leur variation soit progressive dans aucun sens déterminé, on trouvera, entre ces nombres, des rapports a très peu près constants.”
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This science, Geometry, is one of indispensable use and constant reference, for every student of the laws of nature; for the relations of space and number are the alphabet in which those laws are written. But besides the interest and importance of this kind which geometry possesses, it has a great and peculiar value for all who wish to understand the foundations of human knowledge, and the methods by which it is acquired. For the student of geometry acquires, with a degree of insight and clearness which the unmathematical reader can but feebly imagine, a conviction that there are necessary truths, many of them of a very complex and striking character; and that a few of the most simple and self-evident truths which it is possible for the mind of man to apprehend, may, by systematic deduction, lead to the most remote and unexpected results.
In The Philosophy of the Inductive Sciences Part 1, Bk. 2, chap. 4, sect. 8 (1868).
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Time was when all the parts of the subject were dissevered, when algebra, geometry, and arithmetic either lived apart or kept up cold relations of acquaintance confined to occasional calls upon one another; but that is now at an end; they are drawn together and are constantly becoming more and more intimately related and connected by a thousand fresh ties, and we may confidently look forward to a time when they shall form but one body with one soul.
In Presidential Address to British Association (19 Aug 1869), 'A Plea for the Mathematician', published in Nature (6 Jan 1870), 1, 262.
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To Nature nothing can be added; from Nature nothing can be taken away; the sum of her energies is constant, and the utmost man can do in the pursuit of physical truth, or in the applications of physical knowledge, is to shift the constituents of the never-varying total. The law of conservation rigidly excludes both creation and annihilation. Waves may change to ripples, and ripples to waves; magnitude may be substituted for number, and number for magnitude; asteroids may aggregate to suns, suns may resolve themselves into florae and faunae, and floras and faunas melt in air: the flux of power is eternally the same. It rolls in music through the ages, and all terrestrial energy—the manifestations of life as well as the display of phenomena—are but the modulations of its rhythm.
Conclusion of Heat Considered as a Mode of Motion: Being a Course of Twelve Lectures Delivered at the Royal Institution of Great Britain in the Season of 1862 (1863), 449.
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To the exact descriptions he gave of the crystalline forms, he added the measure of their angles, and, which was essential, showed that these angles were constant for each variety. In one word, his crystallography was the fruit of an immense work, almost entirely new and most precious in its usefulness.<[About Jean-Baptiste Romé de l’Isle.]
(1795). As quoted in André Authier, Early Days of X-ray Crystallography (2013), 313.
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We may be well be justified in saying that quantum theory is of greater importance to chemistry than physics. For where there are large fields of physics that can be discussed in a completely penetrating way without reference to Planck's constant and to quantum theory at all, there is no part of chemistry that does not depend, in its fundamental theory, upon quantum principles.
As quoted in Leonard W. Fine, Chemistry (1972), 537. Please contact Webmaster if you know the primary source.
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When Dr. Johnson felt, or fancied he felt, his fancy disordered, his constant recurrence was to the study of arithmetic.
In In Life of Johnson (1871), Vol. 2, 264.
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Why do the laws that govern [the universe] seem constant in time? One can imagine a Universe in which laws are not truly law-full. Talk of miracle does just this, invoking God to make things work. Physics aims to find the laws instead, and hopes that they will be uniquely constrained, as when Einstein wondered whether God had any choice when He made the Universe.
Gregory Benford, in John Brockman, What We Believe But Cannot Prove. In Clifford A. Pickover, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them (2008), 182-183.
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Winwood Reade … remarks that while a man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never foretell what any one man will do, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician.
Character Sherlock Holmes recommends Winwood Reade’s book The Martyrdom of Man to Dr. Watson in The Sign of the Four (1890), 196. Earlier in the novel, Holmes calls Reade’s book “one of the most remarkable ever penned.” Reade is a real person and his book was published in 1872. The actual statement in it reads: “As a single atom man is an enigma: as a whole he is a mathematical problem.”
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You can’t have a big ego and be a great inventor. You constantly have to be listening and evaluating.
Quoted in Timothy L. O’Brien, 'Not Invented here: Are U.S. Innovators Losing Their Competitive Edge?', New York Times (13 Nov 2005), B6.
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[A plant] does not change itself gradually, but remains unaffected during all succeeding generations. It only throws off new forms, which are sharply contrasted with the parent, and which are from the very beginning as perfect and as constant, as narrowly defined, and as pure of type as might be expected of any species.
In Species and Varieties: Their Origin and Mutation (1905), 28-9.
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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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