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Who said: “I have no satisfaction in formulas unless I feel their arithmetical magnitude.”
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Home > Category Index for Science Quotations > Category Index A > Category: Appreciate

Appreciate Quotes (63 quotes)

To Wheeler's comment, If you haven't found something strange during the day, it hasn't been much of a day, a student responded, I can't believe that space is that crummy. Wheeler replied: To disagree leads to study, to study leads to understanding, to understand is to appreciate, to appreciate is to love. So maybe I'll end up loving your theory.
Quoted in Charles Birch, Biology and the Riddle of Life (1999), 10.
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A good work of visual art carries a person who is capable of appreciating it out of life into ecstasy.
In Art (1913), 29-30
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Biodiversity is our most valuable but least appreciated resource.
In 'Unmined Riches', The Diversity of Life (1992), 281.
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Difficulties [in defining mathematics with full generality, yet simplicity] are but consequences of our refusal to see that mathematics cannot be defined without acknowledging its most obvious feature: namely, that it is interesting. Nowhere is intellectual beauty so deeply felt and fastidiously appreciated.
In Personal Knowledge (1958, 2012), 200,
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Do you remember what Darwin says about music? He claims that the power of producing and appreciating it existed among the human race long before the power of speech was arrived at. Perhaps that is why we are so subtly influenced by it. There are vague memories in our souls of those misty centuries when the world was in its childhood.
Spoken by character, Sherlock Holmes, in A Study in Scarlet (1887), Chap. 5. Collected in Works of Arthur Conan Doyle (1902), Vol. 11, 68-69.
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Etna presents us not merely with an image of the power of subterranean heat, but a record also of the vast period of time during which that power has been exerted. A majestic mountain has been produced by volcanic action, yet the time of which the volcanic forms the register, however vast, is found by the geologist to be of inconsiderable amount, even in the modern annals of the earth's history. In like manner, the Falls of Niagara teach us not merely to appreciate the power of moving water, but furnish us at the same time with data for estimating the enormous lapse of ages during which that force has operated. A deep and long ravine has been excavated, and the river has required ages to accomplish the task, yet the same region affords evidence that the sum of these ages is as nothing, and as the work of yesterday, when compared to the antecedent periods, of which there are monuments in the same district.
Travels in North America (1845), Vol. 1, 28-9.
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He [Lord Bacon] appears to have been utterly ignorant of the discoveries which had just been made by Kepler’s calculations … he does not say a word about Napier’s Logarithms, which had been published only nine years before and reprinted more than once in the interval. He complained that no considerable advance had been made in Geometry beyond Euclid, without taking any notice of what had been done by Archimedes and Apollonius. He saw the importance of determining accurately the specific gravities of different substances, and himself attempted to form a table of them by a rude process of his own, without knowing of the more scientific though still imperfect methods previously employed by Archimedes, Ghetaldus and Porta. He speaks of the εὕρηκα of Archimedes in a manner which implies that he did not clearly appreciate either the problem to be solved or the principles upon which the solution depended. In reviewing the progress of Mechanics, he makes no mention either of Archimedes, or Stevinus, Galileo, Guldinus, or Ghetaldus. He makes no allusion to the theory of Equilibrium. He observes that a ball of one pound weight will fall nearly as fast through the air as a ball of two, without alluding to the theory of acceleration of falling bodies, which had been made known by Galileo more than thirty years before. He proposed an inquiry with regard to the lever,—namely, whether in a balance with arms of different length but equal weight the distance from the fulcrum has any effect upon the inclination—though the theory of the lever was as well understood in his own time as it is now. … He speaks of the poles of the earth as fixed, in a manner which seems to imply that he was not acquainted with the precession of the equinoxes; and in another place, of the north pole being above and the south pole below, as a reason why in our hemisphere the north winds predominate over the south.
From Spedding’s 'Preface' to De Interpretations Naturae Proœmium, in The Works of Francis Bacon (1857), Vol. 3, 511-512. [Note: the Greek word “εὕρηκα” is “Eureka” —Webmaster.]
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Here are a few things to keep in mind the next time ants show up in the potato salad. The 8,800 known species of the family Formicidae make up from 10% to 15% of the world's animal biomass, the total weight of all fauna. They are the most dominant social insect in the world, found almost everywhere except in the polar regions. Ants turn more soil than earthworms; they prune, weed and police most of the earth's carrion. Among the most gregarious of creatures, they are equipped with a sophisticated chemical communications system. To appreciate the strength and speed of this pesky invertebrate, consider that a leaf cutter the size of a man could run repeated four-minute miles while carrying 750 lbs. of potato salad.
From book review, 'Nature: Splendor in The Grass', Time (3 Sep 1990).
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Histology is an exotic meal, but can be as repulsive as a dose of medicine for students who are obliged to study it, and little loved by doctors who have finished their study of it all too hastily. Taken compulsorily in large doses it is impossible to digest, but after repeated tastings in small draughts it becomes completely agreeable and even addictive. Whoever possesses a refined sensitivity for artistic manifestations will appreciate that, in the science of histology, there exists an inherent focus of aesthetic emotions.
Opening remarks of paper, 'Art and Artifice in the Science of Histology' (1933), reprinted in Histopathology (1993), 22, 515-525. Quoted in Ross, Pawlina and Barnash, Atlas of Descriptive Histology (2009).
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I believe it to be of particular importance that the scientist have an articulate and adequate social philosophy, even more important than the average man should have a philosophy. For there are certain aspects of the relation between science and society that the scientist can appreciate better than anyone else, and if he does not insist on this significance no one else will, with the result that the relation of science to society will become warped, to the detriment of everybody.
Reflections of a Physicist (1950), 287.
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I can well appreciate, Holy Father, that as soon as certain people realise that in these books which I have written about the Revolutions of the spheres of the universe I attribute certain motions to the globe of the Earth, they will at once clamour for me to be hooted off the stage with such an opinion.
'To His Holiness Pope Paul III', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A.M. Duncan (1976), 23.
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I took biology in high school and didn't like it at all. It was focused on memorization. ... I didn't appreciate that biology also had principles and logic ... [rather than dealing with a] messy thing called life. It just wasn't organized, and I wanted to stick with the nice pristine sciences of chemistry and physics, where everything made sense. I wish I had learned sooner that biology could be fun as well.
Interview (23 May 1998), 'Creating the Code to Life', Academy of Achievement web site.
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If, unwarned by my example, any man shall undertake and shall succeed in really constructing an engine embodying in itself the whole of the executive department of mathematical analysis upon different principles or by simpler mechanical means, I have no fear of leaving my reputation in his charge, for he alone will be fully able to appreciate the nature of my efforts and the value of their results.
In Passages from the Life of a Philosopher (1864), 450.
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In a sense, genetics grew up as an orphan. In the beginning botanists and zoologists were often indifferent and sometimes hostile toward it. 'Genetics deals only with superficial characters', it was often said. Biochemists likewise paid it little heed in its early days. They, especially medical biochemists, knew of Garrod's inborn errors of metabolism and no doubt appreciated them in the biochemical sense and as diseases; but the biological world was inadequately prepared to appreciate fully the significance of his investigations and his thinking. Geneticists, it should be said, tended to be preoccupied mainly with the mechanisms by which genetic material is transmitted from one generation to, the next.
'Genes and chemical reactions In Neurospora', Nobel Lecture, 11 December 1958. In Nobel Lectures: Physiology or Medicine 1942-1962 (1964), 598.
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In October 1838, that is, fifteen months after I had begun my systematic enquiry, I happened to read for amusement Malthus on Population, and being well prepared to appreciate the struggle for existence which everywhere goes on from long-continued observation of the habits of animals and plants, it at once struck me that under these circumstances favourable variations would tend to be, preserved, and unfavourable ones to be destroyed. The result of this would be the formation of new species. Here, then, I had at last got a theory by which to work; but I was so anxious to avoid prejudice, that I determined not for some time to write even the briefest sketch of it.
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), 40.
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It did not cause anxiety that Maxwell’s equations did not apply to gravitation, since nobody expected to find any link between electricity and gravitation at that particular level. But now physics was faced with an entirely new situation. The same entity, light, was at once a wave and a particle. How could one possibly imagine its proper size and shape? To produce interference it must be spread out, but to bounce off electrons it must be minutely localized. This was a fundamental dilemma, and the stalemate in the wave-photon battle meant that it must remain an enigma to trouble the soul of every true physicist. It was intolerable that light should be two such contradictory things. It was against all the ideals and traditions of science to harbor such an unresolved dualism gnawing at its vital parts. Yet the evidence on either side could not be denied, and much water was to flow beneath the bridges before a way out of the quandary was to be found. The way out came as a result of a brilliant counterattack initiated by the wave theory, but to tell of this now would spoil the whole story. It is well that the reader should appreciate through personal experience the agony of the physicists of the period. They could but make the best of it, and went around with woebegone faces sadly complaining that on Mondays, Wednesdays, and Fridays they must look on light as a wave; on Tuesdays, Thursdays, and Saturdays, as a particle. On Sundays they simply prayed.
The Strange Story of the Quantum (1947), 42.
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It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.
Quoted in Return to Mathematical Circles H. Eves (Boston 1988).
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It is known that the mathematics prescribed for the high school [Gymnasien] is essentially Euclidean, while it is modern mathematics, the theory of functions and the infinitesimal calculus, which has secured for us an insight into the mechanism and laws of nature. Euclidean mathematics is indeed, a prerequisite for the theory of functions, but just as one, though he has learned the inflections of Latin nouns and verbs, will not thereby be enabled to read a Latin author much less to appreciate the beauties of a Horace, so Euclidean mathematics, that is the mathematics of the high school, is unable to unlock nature and her laws.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 37-38. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112.
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It’s a case of many oceans around the world being degraded by negligence. The ocean is the lifeblood of our world. If we were to lose our fish that we appreciate so much by overfishing; or if we were to lose some of our favorite beaches to overbuilding and pollution, then how would we feel? It’s become a case of not knowing what you’ve got until it’s gone. But by no means is it too late.
From transcript of interview, 'Olympic swimmer: Oceans need our help', NBC News Today web site (14 Nov 2008).
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I’ve come to appreciate the planet we live on. It’s a small ball in a large universe. It’s a very fragile ball but also very beautiful. You don’t recognize that until you see it from a little farther off.
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Modern cytological work involves an intricacy of detail, the significance of which can be appreciated by the specialist alone; but Miss Stevens had a share in a discovery of importance, and her work will be remembered for this, when the minutiae of detailed investigations that she carried out have become incorporated in the general body of the subject.
In obituary, 'The Scientific Work of Miss N.M. Steves', Science (11 Oct 1912), 36, No. 928, 468.
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Most of the arts, as painting, sculpture, and music, have emotional appeal to the general public. This is because these arts can be experienced by some one or more of our senses. Such is not true of the art of mathematics; this art can be appreciated only by mathematicians, and to become a mathematician requires a long period of intensive training. The community of mathematicians is similar to an imaginary community of musical composers whose only satisfaction is obtained by the interchange among themselves of the musical scores they compose.
In Anton Z. Capri, Quips, Quotes and Quanta: An Anecdotal History of Physics (2007), 151. The author described Lanczos invited up on the platform at the Trieste Conference to celebrate Dirac’s 70th birthday, and gave an impromptu quote by Lanczos speaking about Pauli. The author followed that unrelated topic with another beginning, “Here is a comment by Lanczos…” followed by the subject quote above.
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Ohm (a distinguished mathematician, be it noted) brought into order a host of puzzling facts connecting electromotive force and electric current in conductors, which all previous electricians had only succeeded in loosely binding together qualitatively under some rather vague statements. Even as late as 20 years ago, “quantity” and “tension” were much used by men who did not fully appreciate Ohm's law. (Is it not rather remarkable that some of Germany's best men of genius should have been, perhaps, unfairly treated? Ohm; Mayer; Reis; even von Helmholtz has mentioned the difficulty he had in getting recognised. But perhaps it is the same all the world over.)
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One feature which will probably most impress the mathematician accustomed to the rapidity and directness secured by the generality of modern methods is the deliberation with which Archimedes approaches the solution of any one of his main problems. Yet this very characteristic, with its incidental effects, is calculated to excite the more admiration because the method suggests the tactics of some great strategist who foresees everything, eliminates everything not immediately conducive to the execution of his plan, masters every position in its order, and then suddenly (when the very elaboration of the scheme has almost obscured, in the mind of the spectator, its ultimate object) strikes the final blow. Thus we read in Archimedes proposition after proposition the bearing of which is not immediately obvious but which we find infallibly used later on; and we are led by such easy stages that the difficulties of the original problem, as presented at the outset, are scarcely appreciated. As Plutarch says: “It is not possible to find in geometry more difficult and troublesome questions, or more simple and lucid explanations.” But it is decidedly a rhetorical exaggeration when Plutarch goes on to say that we are deceived by the easiness of the successive steps into the belief that anyone could have discovered them for himself. On the contrary, the studied simplicity and the perfect finish of the treatises involve at the same time an element of mystery. Though each step depends on the preceding ones, we are left in the dark as to how they were suggested to Archimedes. There is, in fact, much truth in a remark by Wallis to the effect that he seems “as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results.” Wallis adds with equal reason that not only Archimedes but nearly all the ancients so hid away from posterity their method of Analysis (though it is certain that they had one) that more modern mathematicians found it easier to invent a new Analysis than to seek out the old.
In The Works of Archimedes (1897), Preface, vi.
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One looks back with appreciation to the brilliant teachers, but with gratitude to those who touched our human feelings. The curriculum is so much necessary raw material, but warmth is the vital element for the growing plant and for the soul of the child.
Carl Jung
From The Gifted Child collected in Collected Works (1954, 1971), Vol. 17, 144. Translated from 'Der Begabt', Psychologie und Erziehung (1946).
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One ought to be ashamed to make use of the wonders of science embodied in a radio set, while appreciating them as little as a cow appreciates the botanical marvels in the plant she munches.
…...
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Only a few years ago, it was generally supposed that by crossing two somewhat different species or varieties a mongrel might be produced which might, or more likely might not, surpass its parents. The fact that crossing was only the first step and that selection from the numerous variations secured in the second and a few succeeding generations was the real work of new plant creation had never been appreciated; and to-day its significance is not fully understood either by breeders or even by many scientific investigators along these very lines.
From Paper read at the Annual Meeting of the American Breeders’ Association, at Columbia, Mo. (5-8 January 1909). In 'Another Mode of Species Forming', Popular Science Monthly (Sep 1909), 75, 264-265.
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Our exploration of the planets represents a triumph of imagination and will for the human race. The events of the last twenty years are perhaps too recent for us to adequately appreciate their proper historical significance.
We can, however, appraise the scientific significance of these voyages of exploration: They have been nothing less than revolutionary both in providing a new picture of the nature of the solar system, its likely origin and evolution, and in giving us a new perspective on our own planet Earth.
NASA
NASA Advisory Committee, report of Solar System Exploration Committee, Planetary Exploration Through Year 2000: A Core Program (1983).
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Physiology, in its analysis of the physiological functions of the sense organs, must use the results of subjective observation of sensations; and psychology, in its turn, needs to know the physiological aspects of sensory function, in order rightly to appreciate the psychological.
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Quite often, when an idea that could be helpful presents itself, we do not appreciate it, for it is so inconspicuous. The expert has, perhaps, no more ideas than the inexperienced, but appreciates more what he has and uses it better.
How to Solve it: A New Aspect of Mathematical Method (1957), 223.
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Science develops best when its concepts and conclusions are integrated into the broader human culture and its concerns for ultimate meaning and value. Scientists cannot, therefore, hold themselves entirely aloof from the sorts of issues dealt with by philosophers and theologians. By devoting to these issues something of the energy and care they give to their research in science, they can help others realize more fully the human potentialities of their discoveries. They can also come to appreciate for themselves that these discoveries cannot be a genuine substitute for knowledge of the truly ultimate.
In Letter (1 Jun 1988) to Father George V. Coyne, Director of the Vatican Observatory. On vatican.va website.
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Science gains from it [the pendulum] more than one can expect. With its huge dimensions, the apparatus presents qualities that one would try in vain to communicate by constructing it on a small [scale], no matter how carefully. Already the regularity of its motion promises the most conclusive results. One collects numbers that, compared with the predictions of theory, permit one to appreciate how far the true pendulum approximates or differs from the abstract system called 'the simple pendulum'.
In 'Demonstration Experimentale du Movement de Rotation de la Terre' (31 May 1851). In C.M. Gariel (ed.), J. Bertrand (ed.) and Harold Burstyn (trans.), Recueil des Travaux Scientifiques de Lion Foucault (1878), Vol. 2, 527.
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Since the seventeenth century, physical intuition has served as a vital source for mathematical porblems and methods. Recent trends and fashions have, however, weakened the connection between mathematics and physics; mathematicians, turning away from their roots of mathematics in intuition, have concentrated on refinement and emphasized the postulated side of mathematics, and at other times have overlooked the unity of their science with physics and other fields. In many cases, physicists have ceased to appreciate the attitudes of mathematicians. This rift is unquestionably a serious threat to science as a whole; the broad stream of scientific development may split into smaller and smaller rivulets and dry out. It seems therefore important to direct our efforts towards reuniting divergent trends by classifying the common features and interconnections of many distinct and diverse scientific facts.
As co-author with David Hilbert, in Methods of Mathematical Physics (1937, 1989), Preface, v.
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That no generally applicable law of the formulation and development of hybrids has yet been successfully formulated can hardly astonish anyone who is acquainted with the extent of the task and who can appreciate the difficulties with which experiments of this kind have to contend.
'Experiments on Plant Hybrids' (1865). In Curt Stern and Eva R. Sherwood (eds.), The Origin of Genetics: A Mendel Source Book (1966), 2.
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The Earth reminded us of a Christmas tree ornament hanging in the blackness of space. As we got farther and farther away it diminished in size. Finally it shrank to the size of a marble, the most beautiful marble you can imagine. That beautiful, warm, living object looked so fragile, so delicate, that if you touched it with a finger it would crumble and fall apart. Seeing this has to change a man, has to make a man appreciate the creation of God and the love of God.
…...
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The engineer is the key figure in the material progress of the world. It is his engineering that makes a reality of the potential value of science by translating scientific knowledge into tools, resources, energy and labor to bring them to the service of man ... To make contribution of this kind the engineer requires the imagination to visualize the needs of society and to appreciate what is possible as well as the technological and broad social age understanding to bring his vision to reality.
In Philip Sporn, Foundations of Engineering: Cornell College of Engineering Lectures, Spring 1963 (1964), 22.
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The existence of an extensive Science of Mathematics, requiring the highest scientific genius in those who contributed to its creation, and calling for the most continued and vigorous exertion of intellect in order to appreciate it when created, etc.
In System of Logic, Bk. 2, chap. 4, sect. 4.
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The eye which can appreciate the naked and absolute beauty of a scientific truth is far more rare than that which is attracted by a moral one.
In A Week on the Concord and Merrimack Rivers (1862), 381.
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The eye, the window of the soul, is the chief means whereby the understanding can most fully and abundantly appreciate the infinite works of Nature; and the ear is second.
As quoted in Daniel J. Boorstin, The Discoverers (1983), 350.
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The force of gravity—though it is the first force with which we are acquainted, and though it is always with us, and though it is the one with a strength we most thoroughly appreciate—is by far the weakest known force in nature. It is first and rearmost.
In Asimov On Physics (1976, 1988), 56. Also in Isaac Asimov’s Book of Science and Nature Quotations (1988), 113.
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The laws of thermodynamics, as empirically determined, express the approximate and probable behavior of systems of a great number of particles, or, more precisely, they express the laws of mechanics for such systems as they appear to beings who have not the fineness of perception to enable them to appreciate quantities of the order of magnitude of those which relate to single particles, and who cannot repeat their experiments often enough to obtain any but the most probable results.
Elementary Principles in Statististical Mechanics (1902), Preface, viii.
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The other book you may have heard of and perhaps read, but it is not one perusal which will enable any man to appreciate it. I have read it through five or six times, each time with increasing admiration. It will live as long as the ‘Principia’ of Newton. It shows that nature is, as I before remarked to you, a study that yields to none in grandeur and immensity. The cycles of astronomy or even the periods of geology will alone enable us to appreciate the vast depths of time we have to contemplate in the endeavour to understand the slow growth of life upon the earth. The most intricate effects of the law of gravitation, the mutual disturbances of all the bodies of the solar system, are simplicity itself compared with the intricate relations and complicated struggle which have determined what forms of life shall exist and in what proportions. Mr. Darwin has given the world a new science, and his name should, in my opinion, stand above that of every philosopher of ancient or modem times. The force of admiration can no further go!!!
Letter to George Silk (1 Sep 1860), in My Life (1905), Vol. I, 372-373.
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The overwhelming astonishment, the queerest structure we know about so far in the whole universe, the greatest of all cosmological scientific puzzles, confounding all our efforts to comprehend it, is the earth. We are only now beginning to appreciate how strange and splendid it is, how it catches the breath, the loveliest object afloat around the sun, enclosed in its own blue bubble of atmosphere, manufacturing and breathing its own oxygen, fixing its own nitrogen from the air into its own soil, generating its own weather at the surface of its rain forests, constructing its own carapace from living parts: chalk cliffs, coral reefs, old fossils from earlier forms of life now covered by layers of new life meshed together around the globe, Troy upon Troy.
In Late Night Thoughts on Listening to Mahler’s Ninth Symphony (1984), 22-23.
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The present rate of progress [in X-ray crystallography] is determined, not so much by the lack of problems to investigate or the limited power of X-ray analysis, as by the restricted number of investigators who have had a training in the technique of the new science, and by the time it naturally takes for its scientific and technical importance to become widely appreciated.
Concluding remark in Lecture (1936) on 'Forty Years of Crystal Physics', collected in Needham and Pagel (eds.) in Background to Modern Science: Ten Lectures at Cambridge Arranged by the History of Science Committee, (1938), 89.
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The present state of electrical science seems peculiarly unfavorable to speculation … to appreciate the requirements of the science, the student must make himself familiar with a considerable body of most intricate mathematics, the mere retention of which in the memory materially interferes with further progress. The first process therefore in the effectual study of the science, must be one of simplification and reduction of the results of previous investigation to a form in which the mind can grasp them.
First sentence of Maxwell’s first paper (read 10 Dec 1855), 'On Faraday’s Lines of Force', Transactions of the Cambridge Philosophical Society (1857), Vol. X, part I. Collected in William Davidson Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 1, 155.
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The public blabbers about preventative medicine, but will neither appreciate nor pay for it. You get paid for what you cure.
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The situation with regard to insulin is particularly clear. In many parts of the world diabetic children still die from lack of this hormone. ... [T]hose of us who search for new biological facts and for new and better therapeutic weapons should appreciate that one of the central problems of the world is the more equitable distribution and use of the medical and nutritional advances which have already been established. The observations which I have recently made in parts of Africa and South America have brought this fact very forcible to my attention.
'Studies on Diabetes and Cirrhosis', Proceedings, American Philosophical Society (1952) 96, No. 1, 29.
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The theory of probabilities is at bottom nothing but common sense reduced to calculus; it enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which of times they are unable to account.
Introduction to Théorie Analytique des Probabilitiés
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The theory of probabilities is at bottom only common sense reduced to calculation; it makes us appreciate with exactitude what reasonable minds feel by a sort of instinct, often without being able to account for it. … It is remarkable that [this] science, which originated in the consideration of games of chance, should have become the most important object of human knowledge.
From A Philosophical Essay on Probabilities. As given in epigraph, E.T. Bell, Men of Mathematics (2014), 71.
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The world is so full of wonderful things we should all, if we were taught how to appreciate it, be far richer than kings.
In Growing Young (1989), 120.
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To appreciate a work of art we need bring with us nothing but a sense of form and colour and a knowledge of three-dimensional space.
In Art (1913), 27.
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To appreciate a work of art we need bring with us nothing from life, no knowledge of its ideas and affairs, no familiarity with its emotions. Art transports us from the world of man’s activity to a world of æsthetic exaltation. For a moment we are shut off from human interests; our anticipations and memories are arrested; we are lifted above the stream of life. The pure mathematician rapt in his studies knows a state of mind which I take to be similar, if not identical. He feels an emotion for his speculations which arises from no perceived relation between them and the lives of men, but springs, inhuman or super-human, from the heart of an abstract science. I wonder, sometimes, whether the appreciators of art and of mathematical solutions are not even more closely allied.
In Art (1913), 25.
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Use in the aim of Science; this the end
The wise appreciate, and the good commend.
From poem, 'An Essay on Mind' (1826). In Elizabeth Barrett Browning and Harriet Waters Preston (ed.), 'Appendix: Juvenilia', The Complete Poetical Works of Mrs. Browning (1900), 505.
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We are concerned to understand the motivation for the development of pure mathematics, and it will not do simply to point to aesthetic qualities in the subject and leave it at that. It must be remembered that there is far more excitement to be had from creating something than from appreciating it after it has been created. Let there be no mistake about it, the fact that the mathematician is bound down by the rules of logic can no more prevent him from being creative than the properties of paint can prevent the artist. … We must remember that the mathematician not only finds the solutions to his problems, he creates the problems themselves.
In A Signpost to Mathematics (1951), 19. As quoted and cited in William L. Schaaf, 'Memorabilia Mathematica', The Mathematics Teacher (Mar 1957), 50, No. 3, 230. Note that this paper incorrectly attributes “A.H. Head”.
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We can see our forests vanishing, our water-powers going to waste, our soil being carried by floods into the sea; and the end of our coal and our iron is in sight. But our larger wastes of human effort, which go on every day through such of our acts as are blundering, ill-directed, or inefficient, … are less visible, less tangible, and are but vaguely appreciated.
In The Principles of Scientific Management (1911), 5.
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We receive it as a fact, that some minds are so constituted as absolutely to require for their nurture the severe logic of the abstract sciences; that rigorous sequence of ideas which leads from the premises to the conclusion, by a path, arduous and narrow, it may be, and which the youthful reason may find it hard to mount, but where it cannot stray; and on which, if it move at all, it must move onward and upward… . Even for intellects of a different character, whose natural aptitude is for moral evidence and those relations of ideas which are perceived and appreciated by taste, the study of the exact sciences may be recommended as the best protection against the errors into which they are most likely to fall. Although the study of language is in many respects no mean exercise in logic, yet it must be admitted that an eminently practical mind is hardly to be formed without mathematical training.
In Orations and Speeches (1870), Vol. 8, 510.
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What progress individuals could make, and what progress the world would make, if thinking were given proper consideration! It seems to me that not one man in a thousand appreciates what can be accomplished by training the mind to think.
As quoted from an interview by B.C. Forbes in The American Magazine (Jan 1921), 10.
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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.
…...
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Yet I also appreciate that we cannot win this battle to save species and environments without forging an emotional bond between ourselves and nature as well–for we will not fight to save what we do not love (but only appreciate in some abstract sense). So let them all continue–the films, the books, the television programs, the zoos, the little half acre of ecological preserve in any community, the primary school lessons, the museum demonstrations, even ... the 6:00 A.M. bird walks. Let them continue and expand because we must have visceral contact in order to love. We really must make room for nature in our hearts.
…...
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You almost wish you could turn off the COMM and just appreciate the deafening quiet.
As quoted in Neil Armstrong, Michael Collins and Edwin E. Aldrin, First on the Moon: The Astronauts’ Own Story (1970), 99.
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You will be able to appreciate the influence of such an Engine on the future progress of science. I live in a country which is incapable of estimating it.
To an unidentified American, Burndy Library, as quoted inAnthony Hyman, Charles Babbage: Pioneer of the Computer (1985), 135.
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You will be able to appreciate the influence of such an Engine on the future progress of science. I live in a country which is incapable of estimating it.
To an unidentified American, Burndy Library, as quoted inAnthony Hyman, Charles Babbage: Pioneer of the Computer (1985), 135.
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[The teaching of Nature] is harsh and wasteful in its operation. Ignorance is visited as sharply as wilful disobedience—incapacity meets with the same punishment as crime. Nature’s discipline is not even a word and a blow, and the blow first; but the blow without the word. It is left to you to find out why your ears are boxed.
The object of what we commonly call education—that education in which man intervenes, and which I shall distinguish as artificial education—is to make good these defects in Nature’s methods; to prepare the child to receive Nature’s education, neither incapably, nor ignorantly, nor with wilful disobedience; and to understand the preliminary symptoms of her displeasure, without waiting for the box on the ear. In short, all artificial education ought to he an anticipation of natural education. And a liberal education is an artificial education, which has not only prepared a man to escape the great evils of disobedience to natural laws, but has trained him to appreciate and to seize upon the rewards, which Nature scatters with as free a hand as her penalties.
From Inaugural Address as Principal, South London Working Men’s College, in 'A Liberal Education; and Where to Find it', Macmillan's Magazine (Mar 1868), 17, 370.
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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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