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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Home > Category Index for Science Quotations > Category Index E > Category: Exceedingly

Exceedingly Quotes (28 quotes)

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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Against filling the Heavens with fluid Mediums, unless they be exceeding rare, a great Objection arises from the regular and very lasting Motions of the Planets and Comets in all manner of Courses through the Heavens.
From Opticks: Or, A Treatise of the Reflections, Refractions, Inflections and Colours of Light (1718), 339.
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Being also in accord with Goethe that discoveries are made by the age and not by the individual, I should consider the instances to be exceedingly rare of men who can be said to be living before their age, and to be the repository of knowledge quite foreign to the thought of the time. The rule is that a number of persons are employed at a particular piece of work, but one being a few steps in advance of the others is able to crown the edifice with his name, or, having the ability to generalise already known facts, may become in time to be regarded as their originator. Therefore it is that one name is remembered whilst those of coequals have long been buried in obscurity.
In Historical Notes on Bright's Disease, Addison's Disease, and Hodgkin's Disease', Guy's Hospital Reports (1877), 22, 259-260.
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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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First, by what means it is that a Plant, or any Part of it, comes to Grow, a Seed to put forth a Root and Trunk... How the Aliment by which a Plant is fed, is duly prepared in its several Parts ... How not only their Sizes, but also their Shapes are so exceedingly various ... Then to inquire, What should be the reason of their various Motions; that the Root should descend; that its descent should sometimes be perpendicular, sometimes more level: That the Trunk doth ascend, and that the ascent thereof, as to the space of Time wherein it is made, is of different measures... Further, what may be the Causes as of the Seasons of their Growth; so of the Periods of their Lives; some being Annual, others Biennial, others Perennial ... what manner the Seed is prepared, formed and fitted for Propagation.
'An Idea of a Philosophical History of Plants', in The Anatomy of Plants With an Idea of a Philosophical History of Plants and Several Other Lectures Read Before the Royal Society (1682), 3-4.
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For if there is any truth in the dynamical theory of gases the different molecules in a gas at uniform temperature are moving with very different velocities. Put such a gas into a vessel with two compartments [A and B] and make a small hole in the wall about the right size to let one molecule through. Provide a lid or stopper for this hole and appoint a doorkeeper, very intelligent and exceedingly quick, with microscopic eyes but still an essentially finite being.
Whenever he sees a molecule of great velocity coming against the door from A into B he is to let it through, but if the molecule happens to be going slow he is to keep the door shut. He is also to let slow molecules pass from B to A but not fast ones ... In this way the temperature of B may be raised and that of A lowered without any expenditure of work, but only by the intelligent action of a mere guiding agent (like a pointsman on a railway with perfectly acting switches who should send the express along one line and the goods along another).
I do not see why even intelligence might not be dispensed with and the thing be made self-acting.
Moral The 2nd law of Thermodynamics has the same degree of truth as the statement that if you throw a tumblerful of water into the sea you cannot get the same tumblerful of water out again.
Letter to John William Strutt (6 Dec 1870). In P. M. Hannan (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 582-3.
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I am a misanthrope, but exceedingly benevolent; I am very cranky, and am a super-idealist. ... I can digest philosophy better than food.
In Ake Erlandsson, 'The Nobel Library of the Swediah Academy', Libri (1999), 167.
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I have enjoyed the trees and scenery of Kentucky exceedingly. How shall I ever tell of the miles and miles of beauty that have been flowing into me in such measure? These lofty curving ranks of lobing, swelling hills, these concealed valleys of fathomless verdure, and these lordly trees with the nursing sunlight glancing in their leaves upon the outlines of the magnificent masses of shade embosomed among their wide branches—these are cut into my memory to go with me forever.
John Muir
Letter, written “among the hills of Bear Creek, seven miles southeast of Burkesville, Kentucky” (Sep 1867). In John Muir and William Frederick Badé (Ed.), A Thousand-Mile Walk to the Gulf (1916), xix. This was by far Muir's longest botanical excursion made in his earlier years.
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I took a good clear piece of Cork and with a Pen-knife sharpen'd as keen as a Razor, I cut a piece of it off, and thereby left the surface of it exceeding smooth, then examining it very diligently with a Microscope, me thought I could perceive it to appear a little porous; but I could not so plainly distinguish them, as to be sure that they were pores, much less what Figure they were of: But judging from the lightness and yielding quality of the Cork, that certainly the texture could not be so curious, but that possibly, if I could use some further diligence, I might find it to be discernable with a Microscope, I with the same sharp Penknife, cut off from the former smooth surface an exceeding thin piece of it with a deep plano-convex Glass, I could exceedingly plainly perceive it to be all perforated and porous, much like a Honey-comb, but that the pores of it were not regular; yet it was not unlike a Honey-comb in these particulars.
First, in that it had a very little solid substance, in comparison of the empty cavity that was contain'd between, ... for the Interstitia or walls (as I may so call them) or partitions of those pores were neer as thin in proportion to their pores as those thin films of Wax in a Honey-comb (which enclose and constitute the sexangular cells) are to theirs.
Next, in that these pores, or cells, were not very deep, but constituted of a great many little Boxes, separated out of one continued long pore, by certain Diaphragms...
I no sooner discerned these (which were indeed the first microscopical pores I ever saw, and perhaps, that were ever seen, for I had not met with any Writer or Person, that had made any mention of them before this) but me thought I had with the discovery of them, presently hinted to me the true and intelligible reason of all the Phænomena of Cork.
Micrographia, or some Physiological Descriptions of Minute Bodies made by Magnifying Glasses with Observations and Inquiries thereupon (1665), 112-6.
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If we take a survey of our own world … our portion in the immense system of creation, we find every part of it, the earth, the waters, and the air that surround it, filled, and as it were crouded with life, down from the largest animals that we know of to the smallest insects the naked eye can behold, and from thence to others still smaller, and totally invisible without the assistance of the microscope. Every tree, every plant, every leaf, serves not only as an habitation, but as a world to some numerous race, till animal existence becomes so exceedingly refined, that the effluvia of a blade of grass would be food for thousands.
In The Age of Reason: Being an Investigation of True and Fabulous Theology (27 Jan O.S. 1794), 60. The word “crouded” is as it appears in the original.
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In every true searcher of Nature there is a kind of religious reverence, for he finds it impossible to imagine that he is the first to have thought out the exceedingly delicate threads that connect his perceptions.
1920, in Conversations with Einstein by Alexander Moszkowski (1970).
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Indeed, while Nature is wonderfully inventive of new structures, her conservatism in holding on to old ones is still more remarkable. In the ascending line of development she tries an experiment once exceedingly thorough, and then the question is solved for all time. For she always takes time enough to try the experiment exhaustively. It took ages to find how to build a spinal column or brain, but when the experiment was finished she had reason to be, and was, satisfied.
In The Whence and Whither of Man; a Brief History of his Origin and Development through Conformity to Environment; being the Morse Lectures of 1895. (1896), 173. The Morse lectureship was founded by Prof. Samuel F.B. Morse in 1865 at Union Theological Seminary, the lectures to deal with “the relation of the Bible to any of the sciences.”
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It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consists only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory—which seems entirely adequate for the treatment of atomic processes; for visualization, however, we must content ourselves with two incomplete analogies—the wave picture and the corpuscular picture.
The Physical Principles of the Quantum Theory, trans. Carl Eckart and Frank C. Hoyt (1949), 11.
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Mathematics has beauties of its own—a symmetry and proportion in its results, a lack of superfluity, an exact adaptation of means to ends, which is exceedingly remarkable and to be found only in the works of the greatest beauty. … When this subject is properly and concretely presented, the mental emotion should be that of enjoyment of beauty, not that of repulsion from the ugly and the unpleasant.
In The Teaching of Mathematics in the Elementary and the Secondary School (1906), 44-45.
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Natural selection is a mechanism for generating an exceedingly high degree of improbability.
This is not a verbatim quote, but it is a summary of Fisher’s idea, as appearing without quotation marks in the words of the editor, Julian Huxley, in J.S. Huxley, A.C. Hardy and E.B. Ford (eds.), Evolution as a Process (1954), 5. The lengthier quote is from Fisher’s full essay 'Retrospect of the Criticisms of the Theory of Natural Selection' which appears in the same book on p.91. See it elsewhere in this site’s collection, as the Fisher quote that begins: “It was Darwin’s chief contribution…”.
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On the whole, I cannot help saying that it appears to me not a little extraordinary, that a theory so new, and of such importance, overturning every thing that was thought to be the best established in chemistry, should rest on so very narrow and precarious a foundation, the experiments adduced in support of it being not only ambiguous or explicable on either hypothesis, but exceedingly few. I think I have recited them all, and that on which the greatest stress is laid, viz. That of the formation of water from the decomposition of the two kinds of air, has not been sufficiently repeated. Indeed it required so difficult and expensive an apparatus, and so many precautions in the use of it, that the frequent repetition of the experiment cannot be expected; and in these circumstances the practised experimenter cannot help suspecting the accuracy of the result and consequently the certainty of the conclusion.
Considerations on the Doctrine of Phlogiston (1796), 57-8.
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The ancients devoted a lifetime to the study of arithmetic; it required days to extract a square root or to multiply two numbers together. Is there any harm in skipping all that, in letting the school boy learn multiplication sums, and in starting his more abstract reasoning at a more advanced point? Where would be the harm in letting the boy assume the truth of many propositions of the first four books of Euclid, letting him assume their truth partly by faith, partly by trial? Giving him the whole fifth book of Euclid by simple algebra? Letting him assume the sixth as axiomatic? Letting him, in fact, begin his severer studies where he is now in the habit of leaving off? We do much less orthodox things. Every here and there in one’s mathematical studies one makes exceedingly large assumptions, because the methodical study would be ridiculous even in the eyes of the most pedantic of teachers. I can imagine a whole year devoted to the philosophical study of many things that a student now takes in his stride without trouble. The present method of training the mind of a mathematical teacher causes it to strain at gnats and to swallow camels. Such gnats are most of the propositions of the sixth book of Euclid; propositions generally about incommensurables; the use of arithmetic in geometry; the parallelogram of forces, etc., decimals.
In Teaching of Mathematics (1904), 12.
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The embryos of mammals, of birds, lizards, and snakes are, in their earliest states, exceedingly like one another, both as a whole and in the mode of development of their parts, indeed we can often distinguish such embryos only by their size. I have two little embryos in spirit [alcohol] to which I have omitted to attach the names. I am now quite unable to say to what class they belong.
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The following story (here a little softened from the vernacular) was narrated by Lord Kelvin himself when dining at Trinity Hall:
A certain rough Highland lad at the university had done exceedingly well, and at the close of the session gained prizes both in mathematics and in metaphysics. His old father came up from the farm to see his son receive the prizes, and visited the College. Thomson was deputed to show him round the place. “Weel, Mr. Thomson,” asked the old man, “and what may these mathematics be, for which my son has getten a prize?” “I told him,” replied Thomson, “that mathematics meant reckoning with figures, and calculating.” “Oo ay,” said the old man, “he’ll ha’ getten that fra’ me: I were ever a braw hand at the countin’.” After a pause he resumed: “And what, Mr. Thomson, might these metapheesics be?” “I endeavoured,” replied Thomson, “to explain how metaphysics was the attempt to express in language the indefinite.” The old Highlander stood still and scratched his head. “Oo ay: may be he’ll ha’ getten that fra’ his mither. She were aye a bletherin’ body."
As given in Life of Lord Kelvin (1910), Vol. 2, 1124, footnote. [Note: William Thomson, later became Lord Kelvin. —Webmaster]
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The heart is an exceedingly strong muscle. … It contains two separate cavities.
As translated by E.T. Withington in 'The Heart', Hippocratic Writings (1978), 348.
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The interior parts of the earth and its internal depths are a region totally impervious to the eye of mortal man, and can least of all be approached by those ordinary paths of hypothesis adopted by naturalists and geologists. The region designed for the existence of man, and of every other creature endowed with organic life, as well as the sphere opened to the perception of man's senses, is confined to a limited space between the upper and lower parts of the earth, exceedingly small in proportion to the diameter, or even semi-diameter of the earth, and forming only the exterior surface, or outer skin, of the great body of the earth.
In Friedrich von Schlegel and James Burton Robertson (trans.), The Philosophy of History (1835), 20.
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The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote.
In Light Waves and Their Uses (1903), 23-4.
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The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. Nevertheless, it has been found that there are apparent exceptions to most of these laws, and this is particularly true when the observations are pushed to a limit, i.e., whenever the circumstances of experiment are such that extreme cases can be examined. Such examination almost surely leads, not to the overthrow of the law, but to the discovery of other facts and laws whose action produces the apparent exceptions. As instances of such discoveries, which are in most cases due to the increasing order of accuracy made possible by improvements in measuring instruments, may be mentioned: first, the departure of actual gases from the simple laws of the so-called perfect gas, one of the practical results being the liquefaction of air and all known gases; second, the discovery of the velocity of light by astronomical means, depending on the accuracy of telescopes and of astronomical clocks; third, the determination of distances of stars and the orbits of double stars, which depend on measurements of the order of accuracy of one-tenth of a second-an angle which may be represented as that which a pin's head subtends at a distance of a mile. But perhaps the most striking of such instances are the discovery of a new planet or observations of the small irregularities noticed by Leverrier in the motions of the planet Uranus, and the more recent brilliant discovery by Lord Rayleigh of a new element in the atmosphere through the minute but unexplained anomalies found in weighing a given volume of nitrogen. Many other instances might be cited, but these will suffice to justify the statement that “our future discoveries must be looked for in the sixth place of decimals.”
In Light Waves and Their Uses (1903), 23-4. Michelson had some years earlier referenced “an eminent physicist” that he did not name who had “remarked that the future truths of physical science are to be looked for in the sixth place of decimals,” near the end of his Convocation Address at the Dedication of the Ryerson Physical Laboratory at the University of Chicago, 'Some of the Objects and Methods of Physical Science' (4 Jul 1894), published in University of Chicago Quarterly Calendar (Aug 1894), 3, No.2, 15. Also
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The oppressive weight of disaster and tragedy in our lives does not arise from a high percentage of evil among the summed total of all acts, but from the extraordinary power of exceedingly rare incidents of depravity to inflict catastrophic damage, especially in our technological age when airplanes can become powerful bombs. (An even more evil man, armed only with a longbow, could not have wreaked such havoc at the Battle of Agincourt in 1415.)
…...
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The science of alchemy I like very well. I like it not only for the profits it brings in melting metals, in decocting, preparing, extracting, and distilling herbs, roots; I like it also for the sake of the allegory and secret signification, which is exceedingly fine, touching the resurrection of the dead at the last day.
In The Table Talk (1569).
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This example illustrates the differences in the effects which may be produced by research in pure or applied science. A research on the lines of applied science would doubtless have led to improvement and development of the older methods—the research in pure science has given us an entirely new and much more powerful method. In fact, research in applied science leads to reforms, research in pure science leads to revolutions, and revolutions, whether political or industrial, are exceedingly profitable things if you are on the winning side.
In Lord Rayleigh, The Life of Sir J. J. Thomson (1943), 199
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When external objects are impressed on the sensory nerves, they excite vibrations in the aether residing in the pores of these nerves... Thus it seems that light affects both the optic nerve and the aether and ... the affections of the aether are communicated to the optic nerve, and vice versa. And the same may be observed of frictions of the skin, taste, smells and sounds... Vibrations in the aether will agitate the small particles of the medullary substance of the sensory nerves with synchronous vibrations... up to the brain... These vibrations are motions backwards and forwards of small particles, of the same kind with the oscillations of pendulums, and the tremblings of the particles of the sounding bodies (but) exceedingly short and small, so as not to have the least efficacy to disturb or move the whole bodies of the nerves... That the nerves themselves should vibrate like musical strings is highly absurd.
Observations on Man, His Frame, His Duty, and His Expectations (1749), part 1, 11-22.
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[Other than fossils,] the most important of these other records of creation is, without doubt, ontogeny, that is, the history of the developmment of the organic individual (embryology and motamorphology). It briefly repeats in great and marked features the series of forms which the ancestors of the respective individuals have passed through from the beginning of their tribe. We have designated the palaeontological history of the development of the ancestors of a living form as the history of a tribe, or phylogeny, and we may therefore thus enunciate this exceedingly important biogenetic fundamental principle: “Ontogeny is a short and quick repetition, or recapitulation, of Phylogeny, determined by the laws of Inheritance and Adaptation.”
In Ernst Haeckel and E. Ray Lankester (trans.), The History of Creation (1876), Vol. 2, 33. Seen shortened to “Ontogeny recapitulates phylogeny.” This was Haeckel's (incorrect) answer to the vexing question of his time: what is the relationship between individual development (ontogeny) and the evolution of species and lineages (phylogeny)?
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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- 80 -
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- 70 -
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- 60 -
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- 50 -
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Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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