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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Nevertheless Quotes (90 quotes)

A man of science rises ever, in seeking truth; and if he never finds it in its wholeness, he discovers nevertheless very significant fragments; and these fragments of universal truth are precisely what constitutes science.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 222.
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Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena.
…...
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Aristotle, in spite of his reputation, is full of absurdities. He says that children should be conceived in the Winter, when the wind is in the North, and that if people marry too young the children will be female. He tells us that the blood of females is blacker then that of males; that the pig is the only animal liable to measles; that an elephant suffering from insomnia should have its shoulders rubbed with salt, olive-oil, and warm water; that women have fewer teeth than men, and so on. Nevertheless, he is considered by the great majority of philosophers a paragon of wisdom.
From An Outline of Intellectual Rubbish (1937, 1943), 19. Collected in The Basic Writings of Bertrand Russell (2009), 63.
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At first sight nothing seems more obvious than that everything has a beginning and an end, and that everything can be subdivided into smaller parts. Nevertheless, for entirely speculative reasons the philosophers of Antiquity, especially the Stoics, concluded this concept to be quite unnecessary. The prodigious development of physics has now reached the same conclusion as those philosophers, Empedocles and Democritus in particular, who lived around 500 B.C. and for whom even ancient man had a lively admiration.
'Development of the Theory of Electrolytic Dissociation', Nobel Lecture, 11 December 1903. In Nobel Lectures: Chemistry 1901-1921 (1966), 45.
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At this stage you must admit that whatever is seen to be sentient is nevertheless composed of atoms that are insentient. The phenomena open to our observation so not contradict this conclusion or conflict with it. Rather they lead us by the hand and compel us to believe that the animate is born, as I maintain, of the insentient.
In On the Nature of the Universe, translated by R. E. Latham (1951, 1994), 59.
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But having considered everything which has been said, one could by this believe that the earth and not the heavens is so moved, and there is no evidence to the contrary. Nevertheless, this seems prima facie as much, or more, against natural reason as are all or several articles of our faith. Thus, that which I have said by way of diversion (esbatement) in this manner can be valuable to refute and check those who would impugn our faith by argument.
On the Book of the Heavens and the World of Aristotle [1377], bk. II, ch. 25, sect. 10, trans. A. D. Menut and A. J. Denomy, quoted in Marshall Clagett, The Science of Mechanics in the Middle Ages (1959), 606.
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But there is another alchemy, operative and practical, which teaches how to make the noble metals and colours and many other things better and more abundantly by art than they are made in nature. And science of this kind is greater than all those preceding because it produces greater utilities. For not only can it yield wealth and very many other things for the public welfare, but it also teaches how to discover such things as are capable of prolonging human life for much longer periods than can be accomplished by nature … Therefore this science has special utilities of that nature, while nevertheless it confirms theoretical alchemy through its works.
Opus Tertium [1266-1268], chapter 12, quoted in A. C. Crombie, Augustine to Galileo (1959), Vol. I, 69.
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Circumstantial evidence can be overwhelming. We have never seen an atom, but we nevertheless know that it must exist.
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 31.
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Consider now the Milky Way. Here also we see an innumerable dust, only the grains of this dust are no longer atoms but stars; these grains also move with great velocities, they act at a distance one upon another, but this action is so slight at great distances that their trajectories are rectilineal; nevertheless, from time to time, two of them may come near enough together to be deviated from their course, like a comet that passed too close to Jupiter. In a word, in the eyes of a giant, to whom our Suns were what our atoms are to us, the Milky Way would only look like a bubble of gas.
Science and Method (1908), trans. Francis Maitland (1914), 254-5.
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Copernicus, the most learned man whom we are able to name other than Atlas and Ptolemy, even though he taught in a most learned manner the demonstrations and causes of motion based on observation, nevertheless fled from the job of constructing tables, so that if anyone computes from his tables, the computation is not even in agreement with his observations on which the foundation of the work rests. Therefore first I have compared the observations of Copernicus with those of Ptolemy and others as to which are the most accurate, but besides the bare observations, I have taken from Copernicus nothing other than traces of demonstrations. As for the tables of mean motion, and of prosthaphaereses and all the rest, I have constructed these anew, following absolutely no other reasoning than that which I have judged to be of maximum harmony.
Dedication to the Duke of Prussia, Prutenicae Tabulae (1551), 1585 edition, as quoted in Owen Gingerich, The Eye of Heaven: Ptolemy, Copernicus, Kepler (1993), 227.
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Ecology has not yet explicitly developed the kind of cohesive, simplifying generalizations exemplified by, say, the laws of physics. Nevertheless there are a number of generalizations that are already evident in what we now know about the ecosphere and that can be organized into a kind of informal set of laws of ecology.
In The Closing Circle: Nature, Man, and Technology (2014).
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Even though the realms of religion and science in themselves are clearly marked off from each other, nevertheless there exist between the two strong reciprocal relationships and dependencies. Though religion may be that which determines the goal, it has, nevertheless, learned from science, in the broadest sense, what means will contribute to the attainment of the goals it has set up. But science can only be created by those who are thoroughly imbued with the aspiration toward truth and understanding. This source of feeling, however, springs from the sphere of religion. To this there also belongs the faith in the possibility that the regulations valid for the world of existence are rational, that is, comprehensible to reason. I cannot conceive of a genuine scientist without that profound faith. The situation may be expressed by an image: science without religion is lame, religion without science is blind.
From paper 'Science, Philosophy and Religion', prepared for initial meeting of the Conference on Science, Philosophy and Religion in Their Relation to the Democratic Way of Life, at the Jewish Theological Seminary of America, New York City (9-11 Sep 1940). Collected in Albert Einstein: In His Own Words (2000), 212.
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Extinction has only separated groups: it has by no means made them; for if every form which has ever lived on this earth were suddenly to reappear, though it would be quite impossible to give definitions by which each group could be distinguished from other groups, as all would blend together by steps as fine as those between the finest existing varieties, nevertheless a natural classification, or at least a natural arrangement, would be possible.
From On the Origin of Species by Means of Natural Selection; or, The Preservation of Favoured Races in the Struggle for Life (1860), 431.
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For FRICTION is inevitable because the Universe is FULL of God's works.
For the PERPETUAL MOTION is in all works of Almighty GOD.
For it is not so in the engines of man, which are made of dead materials, neither indeed can be.
For the Moment of bodies, as it is used, is a false term—bless God ye Speakers on the Fifth of November.
For Time and Weight are by their several estimates.
For I bless GOD in the discovery of the LONGITUDE direct by the means of GLADWICK.
For the motion of the PENDULUM is the longest in that it parries resistance.
For the WEDDING GARMENTS of all men are prepared in the SUN against the day of acceptation.
For the wedding Garments of all women are prepared in the MOON against the day of their purification.
For CHASTITY is the key of knowledge as in Esdras, Sir Isaac Newton & now, God be praised, in me.
For Newton nevertheless is more of error than of the truth, but I am of the WORD of GOD.
From 'Jubilate Agno' (c.1758-1763), in N. Callan (ed.), The Collected Poems of Christopher Smart (1949), Vol. 1, 276.
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Genetics is the first biological science which got in the position in which physics has been in for many years. One can justifiably speak about such a thing as theoretical mathematical genetics, and experimental genetics, just as in physics. There are some mathematical geniuses who work out what to an ordinary person seems a fantastic kind of theory. This fantastic kind of theory nevertheless leads to experimentally verifiable prediction, which an experimental physicist then has to test the validity of. Since the times of Wright, Haldane, and Fisher, evolutionary genetics has been in a similar position.
Oral history memoir. Columbia University, Oral History Research Office, New York, 1962. Quoted in William B. Provine, Sewall Wright and Evolutionary Biology (1989), 277.
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I am an organic chemist, albeit one who adheres to the definition of organic chemistry given by the great Swedish chemist Berzelius, namely, the chemistry of substances found in living matter, and my science is one of the more abstruse insofar as it rests on concepts and employs a jargon neither of which is a part of everyday experience. Nevertheless, organic chemistry deals with matters of truly vital Importance and in some of its aspects with which I myself have been particularly concerned it may prove to hold the keys to Life itself.
In 'Synthesis in the Study of Nucleotides', Nobel Lecture, 11 December 1957. In Nobel Lectures: Chemistry 1942-1962 (1964), 522.
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I cannot let the year run out without sending you a sign of my continued existence and to extend my sincere wishes for the well-being of you and your dear ones in the New Year. We will not be able to send New Year greetings much longer; but even when we have passed away and have long since decomposed, the bonds that united us in life will remain and we shall be remembered as a not too common example of two men, who truly without envy and jealousy, contended and struggled in the same field, yet nevertheless remained always closely bound in friendship.
Letter from Liebig to Wohler (31 Dec 1871). Quoted in Ralph Oesper, The Human Side of Scientists (1975), 206.
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I myself consider that gravity is merely a certain natural inclination with which parts are imbued by the architect of all things for gathering themselves together into a unity and completeness by assembling into the form of a globe. It is easy to believe that the Sun, Moon and other luminaries among the wandering stars have this tendency also, so that by its agency they retain the rounded shape in which they reveal themselves, but nevertheless go round their orbits in various ways. If then the Earth also performs other motions, as for example the one about the centre, they must necessarily be like those which are similarly apparent in many external bodies in which we find an annual orbit.
'Book One. Chapter IX. Whether several motions can be attributed to the Earth, and on the centre of the universe', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A. M. Duncan (1976), 46.
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I therefore took this opportunity and also began to consider the possibility that the Earth moved. Although it seemed an absurd opinion, nevertheless, because I knew that others before me had been granted the liberty of imagining whatever circles they wished to represent the phenomena of the stars, I thought that I likewise would readily be allowed to test whether, by assuming some motion of the Earth's, more dependable representations than theirs could be found for the revolutions of the heavenly spheres.
'To His Holiness Pope Paul III', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A. M. Duncan (1976), 26.
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I think it is a duty I owe to my profession and to my sex to show that a woman has a right to the practice of her profession and cannot be condemned to abandon it merely because she marries. I cannot conceive how women’s colleges, inviting and encouraging women to enter professions can be justly founded or maintained denying such a principle.
(From a letter Brooks wrote to her dean, knowing that she would be told to resign if she married, she asked to keep her job. Nevertheless, she lost her teaching position at Barnard College in 1906. Dean Gill wrote that “The dignity of women’s place in the home demands that your marriage shall be a resignation.”)
As quoted by Margaret W. Rossiter in Women Scientists in America: Struggles and Strategies to 1940. Baltimore: Johns Hopkins University Press (1982).
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I would be the last to deny that the greatest scientific pioneers belonged to an aristocracy of the spirit and were exceptionally intelligent, something that we as modest investigators will never attain, no matter how much we exert ourselves. Nevertheless … I continue to believe that there is always room for anyone with average intelligence … to utilize his energy and … any man could, if he were so inclined, be the sculptor of his own brain, and that even the least gifted may, like the poorest land that has been well-cultivated and fertilized, produce an abundant harvest..
From Preface to the second edition, Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad. (1897), as translated by Neely and Larry W. Swanson, in Advice for a Young Investigator (1999), xv.
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If it were possible for us to have so deep an insight into a man's character as shown both in inner and in outer actions, that every, even the least, incentive to these actions and all external occasions which affect them were so known to us that his future conduct could be predicted with as great a certainty as the occurrence of a solar or lunar eclipse, we could nevertheless still assert that the man is free.
Critique of Practical Reason (1788). In L. W. Beck (ed. & trans.), Critique of Practical Reason and Other Writings in Moral Philosophy (1949), 204-5.
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If the words of a wise man are few, they are nevertheless worth listening to.
Aphorism as given by the fictional character Dezhnev Senior, in Fantastic Voyage II: Destination Brain (1987), 242.
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If we view mathematical speculations with reference to their use, it appears that they should be divided into two classes. To the first belong those which furnish some marked advantage either to common life or to some art, and the value of such is usually determined by the magnitude of this advantage. The other class embraces those speculations which, though offering no direct advantage, are nevertheless valuable in that they extend the boundaries of analysis and increase our resources and skill. Now since many investigations, from which great advantage may be expected, must be abandoned solely because of the imperfection of analysis, no small value should be assigned to those speculations which promise to enlarge the field of anaylsis.
In Novi Comm. Petr., Vol. 4, Preface.
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In man, then, let us take the amount that is extruded by the individual beats, and that cannot return into the heart because of the barrier set in its way by the valves, as half an ounce, or three drachms, or at least one drachm. In half an hour the heart makes over a thousand beats; indeed, in some individuals, and on occasion, two, three, or four thousand. If you multiply the drachms per beat by the number of beats you will see that in half an hour either a thousand times three drachms or times two drachms, or five hundred ounces, or other such proportionate quantity of blood has been passed through the heart into the arteries, that is, in all cases blood in greater amount than can be found in the whole of the body. Similarly in the sheep or the dog. Let us take it that one scruple passes in a single contraction of the heart; then in half an hour a thousand scruples, or three and a half pounds of blood, do so. In a body of this size, as I have found in the sheep, there is often not more than four pounds of blood.
In the above sort of way, by calculating the amount of blood transmitted [at each heart beat] and by making a count of the beats, let us convince ourselves that the whole amount of the blood mass goes through the heart from the veins to the arteries and similarly makes the pulmonary transit.
Even if this may take more than half an hour or an hour or a day for its accomplishment, it does nevertheless show that the beat of the heart is continuously driving through that organ more blood than the ingested food can supply, or all the veins together at any time contain.
De Motu Cordis (1628), The Circulation of the Blood and Other Writings, trans. Kenneth J. Franklin (1957), Chapter 9, 62-3.
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In my youth I often asked what could be the use and necessity of smelting by putting powdered charcoal at the bottom of the furnace. Nobody could give me any other reason except that the metal and especially lead, could bury itself in the charcoal and so be protected against the action of the bellows which would calcine or dissipate it. Nevertheless it is evident that this does not answer the question. I accordingly examined the operation of a metallurgical furnace and how it was used. In assaying some litharge [lead oxide], I noticed each time a little charcoal fell into the crucible, I always obtained a bit of lead … I do not think up to the present time foundry-men ever surmised that in the operation of founding with charcoal there was something [phlogiston] which became corporeally united with the metal.
Traité de Soufre (1766), 64. French translation published 1766, first published in German in 1718.
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It appears, nevertheless, that all such simple solutions of the problem of vertebrate ancestry are without warrant. They arise from a very common tendency of the mind, against which the naturalist has to guard himself,—a tendency which finds expression in the very widespread notion that the existing anthropoid apes, and more especially the gorilla, must be looked upon as the ancestors of mankind, if once the doctrine of the descent of man from ape-like forefathers is admitted. A little reflexion suffices to show that any given living form, such as the gorilla, cannot possibly be the ancestral form from which man was derived, since ex-hypothesi that ancestral form underwent modification and development, and in so doing, ceased to exist.
'Vertebrata', entry in Encyclopaedia Britannica, 9th edition (1899), Vol. 24, 180.
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It has been said that computing machines can only carry out the processes that they are instructed to do. This is certainly true in the sense that if they do something other than what they were instructed then they have just made some mistake. It is also true that the intention in constructing these machines in the first instance is to treat them as slaves, giving them only jobs which have been thought out in detail, jobs such that the user of the machine fully understands what in principle is going on all the time. Up till the present machines have only been used in this way. But is it necessary that they should always be used in such a manner? Let us suppose we have set up a machine with certain initial instruction tables, so constructed that these tables might on occasion, if good reason arose, modify those tables. One can imagine that after the machine had been operating for some time, the instructions would have altered out of all recognition, but nevertheless still be such that one would have to admit that the machine was still doing very worthwhile calculations. Possibly it might still be getting results of the type desired when the machine was first set up, but in a much more efficient manner. In such a case one would have to admit that the progress of the machine had not been foreseen when its original instructions were put in. It would be like a pupil who had learnt much from his master, but had added much more by his own work. When this happens I feel that one is obliged to regard the machine as showing intelligence.
Lecture to the London Mathematical Society, 20 February 1947. Quoted in B. E. Carpenter and R. W. Doran (eds.), A. M. Turing's Ace Report of 1946 and Other Papers (1986), 122-3.
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It has come to pass, I know not how, that Mathematics and Logic, which ought to be but the handmaids of Physic, nevertheless presume on the strength of the certainty which they possess to exercise dominion over it.
From De Augmentis Scientiaurum as translated in Francis Guy Selby, The Advancement of Learning (1893), Vol. 2, 73.
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It has often been said that, to make discoveries, one must be ignorant. This opinion, mistaken in itself, nevertheless conceals a truth. It means that it is better to know nothing than to keep in mind fixed ideas based on theories whose confirmation we constantly seek, neglecting meanwhile everything that fails to agree with them.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 37.
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It is clear, then, that though there may be countless instances of the perishing of unmoved movers, and though many things that move themselves perish and are succeeded by others that come into being, and though one thing that is unmoved moves one thing while another moves another, nevertheless there is something that comprehends them all, and that as something apart from each one of them, and this it is that is the cause of the fact that some things are and others are not and of the continuous process of change; and this causes the motion of the other movers, while they are the causes of the motion of other things. Motion, then, being eternal, the first mover, if there is but one, will be eternal also; if there are more than one, there will be a plurality of such eternal movers.
Aristotle
Physics, 258b, 32-259a, 8. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. 1, 432.
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It is profitable nevertheless to permit ourselves to talk about 'meaningless' terms in the narrow sense if the preconditions to which all profitable operations are subject are so intuitive and so universally accepted as to form an almost unconscious part of the background of the public using the term. Physicists of the present day do constitute a homogenous public of this character; it is in the air that certain sorts of operation are valueless for achieving certain sorts of result. If one wants to know how many planets there are one counts them but does not ask a philosopher what is the perfect number.
Reflections of a Physicist (1950), 6.
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It [mathematics] is in the inner world of pure thought, where all entia dwell, where is every type of order and manner of correlation and variety of relationship, it is in this infinite ensemble of eternal verities whence, if there be one cosmos or many of them, each derives its character and mode of being,—it is there that the spirit of mathesis has its home and its life.
Is it a restricted home, a narrow life, static and cold and grey with logic, without artistic interest, devoid of emotion and mood and sentiment? That world, it is true, is not a world of solar light, not clad in the colours that liven and glorify the things of sense, but it is an illuminated world, and over it all and everywhere throughout are hues and tints transcending sense, painted there by radiant pencils of psychic light, the light in which it lies. It is a silent world, and, nevertheless, in respect to the highest principle of art—the interpenetration of content and form, the perfect fusion of mode and meaning—it even surpasses music. In a sense, it is a static world, but so, too, are the worlds of the sculptor and the architect. The figures, however, which reason constructs and the mathematic vision beholds, transcend the temple and the statue, alike in simplicity and in intricacy, in delicacy and in grace, in symmetry and in poise. Not only are this home and this life thus rich in aesthetic interests, really controlled and sustained by motives of a sublimed and supersensuous art, but the religious aspiration, too, finds there, especially in the beautiful doctrine of invariants, the most perfect symbols of what it seeks—the changeless in the midst of change, abiding things hi a world of flux, configurations that remain the same despite the swirl and stress of countless hosts of curious transformations.
In 'The Universe and Beyond', Hibbert Journal (1904-1906), 3, 314.
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Just as, in civil History, one consults title-deeds, one studies coins, one deciphers ancient inscriptions, in order to determine the epochs of human revolutions and to fix the dates of moral [i.e. human] events; so, in Natural History, one must excavate the archives of the world, recover ancient monuments from the depths of the earth, collect their remains, and assemble in one body of proofs all the evidence of physical changes that enable us to reach back to the different ages of Nature. This, then, is the order of the times indicated by facts and monuments: these are six epochs in the succession of the first ages of Nature; six spaces of duration, the limits of which although indeterminate are not less real; for these epochs are not like those of civil History ... that we can count and measure exactly; nevertheless we can compare them with each other and estimate their relative duration.
'Des Époques de la Nature', Histoire Naturelle, Générale et Particulière contenant les Époques de la Nature (1778), Supplement Vol. 9, 1-2, 41. Trans. Martin J. Rudwick.
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Let us hope that the advent of a successful flying machine, now only dimly foreseen and nevertheless thought to be possible, will bring nothing but good into the world; that it shall abridge distance, make all parts of the globe accessible, bring men into closer relation with each other, advance civilization, and hasten the promised era in which there shall be nothing but peace and goodwill among all men.
Concluding paragraph, Progress in Flying Machines (1894), 269.
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Let us now declare the means whereby our understanding can rise to knowledge without fear of error. There are two such means: intuition and deduction. By intuition I mean not the varying testimony of the senses, nor the deductive judgment of imagination naturally extravagant, but the conception of an attentive mind so distinct and so clear that no doubt remains to it with regard to that which it comprehends; or, what amounts to the same thing, the self-evidencing conception of a sound and attentive mind, a conception which springs from the light of reason alone, and is more certain, because more simple, than deduction itself. …
It may perhaps be asked why to intuition we add this other mode of knowing, by deduction, that is to say, the process which, from something of which we have certain knowledge, draws consequences which necessarily follow therefrom. But we are obliged to admit this second step; for there are a great many things which, without being evident of themselves, nevertheless bear the marks of certainty if only they are deduced from true and incontestable principles by a continuous and uninterrupted movement of thought, with distinct intuition of each thing; just as we know that the last link of a long chain holds to the first, although we can not take in with one glance of the eye the intermediate links, provided that, after having run over them in succession, we can recall them all, each as being joined to its fellows, from the first up to the last. Thus we distinguish intuition from deduction, inasmuch as in the latter case there is conceived a certain progress or succession, while it is not so in the former; … whence it follows that primary propositions, derived immediately from principles, may be said to be known, according to the way we view them, now by intuition, now by deduction; although the principles themselves can be known only by intuition, the remote consequences only by deduction.
In Rules for the Direction of the Mind, Philosophy of Descartes. [Torrey] (1892), 64-65.
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Many will, no doubt, prefer to retain old unsystematic names as far as possible, but it is easy to see that the desire to avoid change may carry us too far in this direction; it will undoubtedly be very inconvenient to the present generation of chemists to abandon familiar and cherished names, but nevertheless it may be a wise course to boldly face the difficulty, rather than inflict on coming generations a partially illogical and unsystematic nomenclature.
'International Conference on Chemical Nomenclature', Nature (19 May 1892), 46, 57.
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Mathematics may be compared to a mill of exquisite workmanship, which grinds you stuff of any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat-flour from peascods, so pages of formulae will not get a definite result out of loose data.
From Anniversary Address of the President to the Geological Society, Quarterly Journal of the Geological Society (1869), l. In 'Geological Reform', Collected Essays: Discourses, Biological and Geological (1894), Vol. 8, 333.
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Matter, though divisible in an extreme degree, is nevertheless not infinitely divisible. That is, there must be some point beyond which we cannot go in the division of matter. ... I have chosen the word “atom” to signify these ultimate particles.
Dalton's Manuscript Notes, Royal Institution Lecture 18 (30 Jan 1810). In Ida Freund, The Study of Chemical Composition: An Account of its Method and Historical Development (1910), 288.
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Maybe we have to accept that after reaching the deepest possible level of understanding science can offer, there will nevertheless be aspects of the universe that remain unexplained. Maybe we will have to accept that certain features of the universe are the way they are because of happenstance, accident, or divine choice.
In The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (2000), 385.
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Medicine, likewise, because it deals with things, has always been for our serener circles a Cinderella, blooming maid as happily as she has grown nevertheless.
In Fielding Hudson Garrison, An Introduction to the History of Medicine (1929), 16.
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Men of science belong to two different types—the logical and the intuitive. Science owes its progress to both forms of minds. Mathematics, although a purely logical structure, nevertheless makes use of intuition. Among the mathematicians there are intuitives and logicians, analysts and geometricians. Hermite and Weierstrass were intuitives. Riemann and Bertrand, logicians. The discoveries of intuition have always to be developed by logic.
In Man the Unknown (1935), 123.
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Metaphysical ghosts cannot be killed, because they cannot be touched; but they may be dispelled by dispelling the twilight in which shadows and solidities are easily confounded. The Vital Principle is an entity of this ghostly kind; and although the daylight has dissipated it, and positive Biology is no longer vexed with its visitations, it nevertheless reappears in another shape in the shadowy region of mystery which surrounds biological and all other questions.
The History of Philosophy from Thales to Comte (1867), lxxxiv.
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Nevertheless if any skillful Servant of Nature shall bring force to bear on matter, and shall vex it and drive it to extremities as if with the purpose of reducing it to nothing, then will matter (since annihilation or true destruction is not possible except by the omnipotence of God) finding itself in these straits, turn and transform itself into strange shapes, passing from one change to another till it has gone through the whole circle and finished the period.
From 'Proteus; or Matter', De Sapientia Veterum (1609), Sec. 13. As translated in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 6, 726.
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Nevertheless most of the evergreen forests of the north must always remain the home of wild animals and trappers, a backward region in which it is easy for a great fur company to maintain a practical monopoly.
The Red Man's Continent: A Chronicle of Aboriginal America (1919), 94.
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Nevertheless, his [Dostoyevsky’s] personality retained sadistic traits in plenty, which show themselves in his irritability, his love of tormenting, and his intolerance even towards people he loved, and which appear also in the way in which, as an author, he treats his readers. Thus in little things he was a sadist towards others, and in bigger things a sadist towards himself, in fact a masochist—that is to say the mildest, kindliest, most helpful person possible.
In James Strachey (ed.), 'Dostoyevsky and Parricide', The Standard Edition of the Complete Psychological Works of Sigmund Freud (1953-74), Vol. 21, 178-179. Reprinted in Writings on Art and Literature (1997), 236
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Nevertheless, it is even harder for the average ape to believe that he has descended from man.
In a collection of his own work, which he selected, A Mencken Chrestomathy (1949, 1956), 618. He specifies the epigrams are his work, on p. 615. First appeared as a page-bottom filler, without attribution (there), in George Jean Nathan and H.L. Mencken (eds.), The Smart Set: A Magazine of Cleverness (1916), 48, No. 1, 200.
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Nevertheless, it is necessary to remember that a planned economy is not yet socialism. A planned economy as such may be accompanied by the complete enslavement of the individual. The achievement of socialism requires the solution of some extremely difficult socio-political problems: how is it possible, in view of the far-reaching centralisation of political and economic power, to prevent bureaucracy from becoming all-powerful and overweening? How can the rights of the individual be protected and therewith a democratic counterweight to the power of bureaucracy be assured?
…...
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Nevertheless, paradigm changes do cause scientists to see the world of their research engagements differently. Insofar as their only recourse to that world is through what they see and do, we may want to say that after a revolution scientists are responding to a different world.
In The Structure of Scientific Revolutions (1962), 110.
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Nevertheless, scientific method is not the same as the scientific spirit. The scientific spirit does not rest content with applying that which is already known, but is a restless spirit, ever pressing forward towards the regions of the unknown, and endeavouring to lay under contribution for the special purpose in hand the knowledge acquired in all portions of the wide field of exact science. Lastly, it acts as a check, as well as a stimulus, sifting the value of the evidence, and rejecting that which is worthless, and restraining too eager flights of the imagination and too hasty conclusions.
'The Scientific Spirit in Medicine: Inaugural Sessional Address to the Abernethian Society', St. Bartholomew's Hospital Journal, 1912, 20, 19.
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Nothing is more humbling than to look with a strong magnifying glass at an insect so tiny that the naked eye sees only the barest speck and to discover that nevertheless it is sculpted and articulated and striped with the same care and imagination as a zebra. Apparently it does not occur to nature whether or not a creature is within our range of vision, and the suspicion arises that even the zebra was not designed for our benefit.
…...
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Now this circumscribed power, which we have scarcely examined, scarcely studied, this power to whose actions we nearly always attribute an intention and a goal, this power, finally, that always does necessarily the same things in the same circumstances and nevertheless does so many and such admirable ones, is what we call 'nature' .
Histoire Naturelle des Animaux sans Vertèbres (1815), Vol. 1, 312, trans. M. H. Shank and quoted in Madeleine Barthélemy-Madaule, Lamarck the Mythical Precursor: A Study of the Relations between Science and Ideology (1982), 28-9.
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Objections … inspired Kronecker and others to attack Weierstrass’ “sequential” definition of irrationals. Nevertheless, right or wrong, Weierstrass and his school made the theory work. The most useful results they obtained have not yet been questioned, at least on the ground of their great utility in mathematical analysis and its implications, by any competent judge in his right mind. This does not mean that objections cannot be well taken: it merely calls attention to the fact that in mathematics, as in everything else, this earth is not yet to be confused with the Kingdom of Heaven, that perfection is a chimaera, and that, in the words of Crelle, we can only hope for closer and closer approximations to mathematical truth—whatever that may be, if anything—precisely as in the Weierstrassian theory of convergent sequences of rationals defining irrationals.
In Men of Mathematics (1937), 431-432.
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On our planet, all objects are subject to continual and inevitable changes which arise from the essential order of things. These changes take place at a variable rate according to the nature, condition, or situation of the objects involved, but are nevertheless accomplished within a certain period of time. Time is insignificant and never a difficulty for Nature. It is always at her disposal and represents an unlimited power with which she accomplishes her greatest and smallest tasks.
Hydrogéologie (1802), trans. A. V. Carozzi (1964), 61.
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Our earth is very old, an old warrior that has lived through many battles. Nevertheless, the face of it is still changing, and science sees no certain limit of time for its stately evolution. Our solid earth, apparently so stable, inert, and finished, is changing, mobile, and still evolving. Its major quakings are largely the echoes of that divine far-off event, the building of our noble mountains. The lava floods and intriguing volcanoes tell us of the plasticity, mobility, of the deep interior of the globe. The slow coming and going of ancient shallow seas on the continental plateaus tell us of the rhythmic distortion of the deep interior-deep-seated flow and changes of volume. Mountain chains prove the earth’s solid crust itself to be mobile in high degree. And the secret of it all—the secret of the earthquake, the secret of the “temple of fire,” the secret of the ocean basin, the secret of the highland—is in the heart of the earth, forever invisible to human eyes.
In Our Mobile Earth (1926), 320.
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Penetrating so many secrets, we cease to believe in the Unknowable. But there it sits, nevertheless, calmly licking its chops.
John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren't There More Happy People?: Smart Quotes for Dumb Times (2009), 217.
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Several times every day I observed the portions of the polyp with a magnifying glass. On the 4th December, that is to say on the ninth day after having cut the polyp, I seemed in the morning to be able to perceive, on the edges of the anterior end of the second part (the part that had neither head nor arms), three little points arising from those edges. They immediately made me think of the horns that serve as the legs and arms of the polyp. Nevertheless I did not want to decide at once that these were actually arms that were beginning to grow. Throughout the next day I continually observed these points: this excited me extremely, and awaited with impatience the moment when I should know with certainty what they were. At last, on the following day, they were so big that there was no longer any room for doubt that they were actually arms growing at the anterior extremity of this second part. The next day two more arms started to grow out, and a few days later three more. The second part thus had eight of them, and they were all in a short time as long as those of the first part, that is to say as long as those the polyp possessed before it was cut. I then no longer found any difference between the second part and a polyp that had never been cut. I had remarked the same thing about the first part since the day after the operation. When I observed them with the magnifying glass with all the attention of which I was capable, each of the two appeared perceptibly to be a complete polyp, and they performed all the functions that were known to me: they extended, contracted, and walked.
Mémoires, pour servir à l'histoire d'un genre de polyps d'eau douce à bras en forme de cornes (1744), 7-16. Trans. John R. Baker, in Abraham Trembley of Geneva: Scientist and Philosopher 1710-1784 (1952), 32.
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That our knowledge only illuminates a small corner of the Universe, that it is incomplete, approximate, tentative and merely probable need not concert us. It is genuine nevertheless. Physical science stands as one of the great achievements of the human spirit.
Scientific Method: An Inquiry into the Character and Validy of Natural Law (1923), 201-202.
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The advances of biology during the past 20 years have been breathtaking, particularly in cracking the mystery of heredity. Nevertheless, the greatest and most difficult problems still lie ahead. The discoveries of the 1970‘s about the chemical roots of memory in nerve cells or the basis of learning, about the complex behavior of man and animals, the nature of growth, development, disease and aging will be at least as fundamental and spectacular as those of the recent past.
As quoted in 'H. Bentley Glass', New York Times (12 Jan 1970), 96.
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The chemists who uphold dualism are far from being agreed among themselves; nevertheless, all of them in maintaining their opinion, rely upon the phenomena of chemical reactions. For a long time the uncertainty of this method has been pointed out: it has been shown repeatedly, that the atoms put into movement during a reaction take at that time a new arrangement, and that it is impossible to deduce the old arrangement from the new one. It is as if, in the middle of a game of chess, after the disarrangement of all the pieces, one of the players should wish, from the inspection of the new place occupied by each piece, to determine that which it originally occupied.
Chemical Method (1855), 18.
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The concept of an independent system is a pure creation of the imagination. For no material system is or can ever be perfectly isolated from the rest of the world. Nevertheless it completes the mathematician’s “blank form of a universe” without which his investigations are impossible. It enables him to introduce into his geometrical space, not only masses and configurations, but also physical structure and chemical composition. Just as Newton first conclusively showed that this is a world of masses, so Willard Gibbs first revealed it as a world of systems.
The Order of Nature: An Essay (1917), 126.
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The demand for certainty is one which is natural to man, but is nevertheless an intellectual vice. If you take your children for a picnic on a doubtful day, they will demand a dogmatic answer as to whether it will be fine or wet, and be disappointed in you when you cannot be sure.
From 'Philosophy For Laymen', collected in Unpopular Essays (1950, 1996), 38. This idea may be summarized as “What men want is not knowledge, but certainty” — a widely circulated aphorism attributed to Russell, but for which Webmaster has so far found no citation. (Perhaps it is a summary, never expressed in those exact words, but if you know the primary source, please contact Webmaster.)
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The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it. But when a woman, who because of her sex and our prejudices encounters infinitely more obstacles that an man in familiarizing herself with complicated problems, succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of them, without doubt she must have the noblest courage, quite extraordinary talents and superior genius.
in a letter to Sophie Germain (c.April 1807)
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The epoch of intense cold which preceded the present creation has been only a temporary oscillation of the earth’s temperature, more important than the century-long phases of cooling undergone by the Alpine valleys. It was associated with the disappearance of the animals of the diluvial epoch of the geologists, as still demonstrated by the Siberian mammoths; it preceded the uplifting of the Alps and the appearance of the present-day living organisms, as demonstrated by the moraines and the existence of fishes in our lakes. Consequently, there is complete separation between the present creation and the preceding ones, and if living species are sometimes almost identical to those buried inside the earth, we nevertheless cannot assume that the former are direct descendants of the latter or, in other words, that they represent identical species.
From Discours de Neuchâtel (1837), as translated by Albert V. Carozzi in Studies on Glaciers: Preceded by the Discourse of Neuchâtel (1967), lviii.
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The genius of Laplace was a perfect sledge hammer in bursting purely mathematical obstacles; but, like that useful instrument, it gave neither finish nor beauty to the results. In truth, in truism if the reader please, Laplace was neither Lagrange nor Euler, as every student is made to feel. The second is power and symmetry, the third power and simplicity; the first is power without either symmetry or simplicity. But, nevertheless, Laplace never attempted investigation of a subject without leaving upon it the marks of difficulties conquered: sometimes clumsily, sometimes indirectly, always without minuteness of design or arrangement of detail; but still, his end is obtained and the difficulty is conquered.
In 'Review of “Théorie Analytique des Probabilites” par M. le Marquis de Laplace, 3eme edition. Paris. 1820', Dublin Review (1837), 2, 348.
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The golden age of mathematics—that was not the age of Euclid, it is ours. Ours is the age when no less than six international congresses have been held in the course of nine years. It is in our day that more than a dozen mathematical societies contain a growing membership of more than two thousand men representing the centers of scientific light throughout the great culture nations of the world. It is in our time that over five hundred scientific journals are each devoted in part, while more than two score others are devoted exclusively, to the publication of mathematics. It is in our time that the Jahrbuch über die Fortschritte der Mathematik, though admitting only condensed abstracts with titles, and not reporting on all the journals, has, nevertheless, grown to nearly forty huge volumes in as many years. It is in our time that as many as two thousand books and memoirs drop from the mathematical press of the world in a single year, the estimated number mounting up to fifty thousand in the last generation. Finally, to adduce yet another evidence of a similar kind, it requires not less than seven ponderous tomes of the forthcoming Encyclopaedie der Mathematischen Wissenschaften to contain, not expositions, not demonstrations, but merely compact reports and bibliographic notices sketching developments that have taken place since the beginning of the nineteenth century.
In Lectures on Science, Philosophy and Art (1908), 8.
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The idea that the bumps or depressions on a man's head indicate the presence or absence of certain moral characteristics in his mental equipment is one of the absurdities developed from studies in this field that has long since been discarded by science. The ideas of the phrenologist Gall, however ridiculous they may now seem in the light of a century's progress, were nevertheless destined to become metamorphosed into the modern principles of cerebral localization.
From 'Looking for "The Face Within the Face" in Man', in the New York Times, 4 Mar 1906, SM page 3.
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The ingenious but nevertheless somewhat artificial assumptions of [Bohr’s model of the atom], … are replaced by a much more natural assumption in de Broglie’s wave phenomena. The wave phenomenon forms the real “body” of the atom. It replaces the individual punctiform electrons, which in Bohr’s model swarm around the nucleus.
From 'Our Image of Matter', collected in Werner Heisenberg, Max Born, Erwin Schrödinger, Pierre Auger, On Modern Physics (1961), 50. Webmaster note: “punctiform” means composed of points.
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The line separating investment and speculation, which is never bright and clear, becomes blurred still further when most market participants have recently enjoyed triumphs. Nothing sedates rationality like large doses of effortless money. After a heady experience of that kind, normally sensible people drift into behavior akin to that of Cinderella at the ball. They know that overstaying the festivities—that is, continuing to speculate in companies that have gigantic valuations relative to the cash they are likely to generate in the future—will eventually bring on pumpkins and mice. But they nevertheless hate to miss a single minute of what is one helluva party. Therefore, the giddy participants all plan to leave just seconds before midnight. There’s a problem, though: They are dancing in a room in which the clocks have no hands.
…...
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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 open society, the unrestricted access to knowledge, the unplanned and uninhibited association of men for its furtherance—these are what may make a vast, complex, ever growing, ever changing, ever more specialized and expert technological world, nevertheless a world of human community.
'Science and the Common Understanding' (1954), 95. Reprinted in John Dewey and Julius A. Sigler, Classical Selections On Great Issues, Vol. 8, Science, Technology, and Society (1997), 35.
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The original question, “Can machines think?,” I believe too meaningless to deserve discussion. Nevertheless I believe that at the end of the century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted.
(1950) As quoted in The World of Mathematics (1956), 2083.
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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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There have, however, always been men of high and disciplined spirituality who have insisted on their direct experience of something greater than themselves. Their conviction of the reality of a spiritual life apart from and transcending the life of the body may not lend itself to scientific proof or disproof; nevertheless the remarkable transformation in personality seen in those who rightfully lay claim to such experience is as objective as tomorrow's sunrise. Millions of lesser men draw strength from the contacts they can make through prayer and meditation with this aspect of the inner life.
at a convention of scientists in 1967 at the University of Notre Dame
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There is a noble vision of the great Castle of Mathematics, towering somewhere in the Platonic World of Ideas, which we humbly and devotedly discover (rather than invent). The greatest mathematicians manage to grasp outlines of the Grand Design, but even those to whom only a pattern on a small kitchen tile is revealed, can be blissfully happy. … Mathematics is a proto-text whose existence is only postulated but which nevertheless underlies all corrupted and fragmentary copies we are bound to deal with. The identity of the writer of this proto-text (or of the builder of the Castle) is anybody’s guess. …
In 'Mathematical Knowledge: Internal, Social, and Cultural Aspects', Mathematics As Metaphor: Selected Essays (2007), 4.
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There is not wholly unexpected surprise, but surprise nevertheless, that mathematics has direct application to the physical world about us.
In The American Mathematical Monthly (1949), 56, 19. Excerpted in John Ewing (ed,), A Century of Mathematics: Through the Eyes of the Monthly (1996), 186.
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Those who knew that the judgements of many centuries had reinforced the opinion that the Earth is placed motionless in the middle of heaven, as though at its centre, if I on the contrary asserted that the Earth moves, I hesitated for a long time whether to bring my treatise, written to demonstrate its motion, into the light of day, or whether it would not be better to follow the example of the Pythagoreans and certain others, who used to pass on the mysteries of their philosophy merely to their relatives and friends, not in writing but by personal contact, as the letter of Lysis to Hipparchus bears witness. And indeed they seem to me to have done so, not as some think from a certain jealousy of communicating their doctrines, but so that their greatest splendours, discovered by the devoted research of great men, should not be exposed to the contempt of those who either find it irksome to waste effort on anything learned, unless it is profitable, or if they are stirred by the exhortations and examples of others to a high-minded enthusiasm for philosophy, are nevertheless so dull-witted that among philosophers they are like drones among bees.
'To His Holiness Pope Paul III', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A. M. Duncan (1976), 24.
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Though we must not without further consideration condemn a body of reasoning merely because it is easy, nevertheless we must not allow ourselves to be lured on merely by easiness; and we should take care that every problem which we choose for attack, whether it be easy or difficult, shall have a useful purpose, that it shall contribute in some measure to the up-building of the great edifice.
From 'On Some Recent Tendencies in Geometric Investigation', Rivista di Matematica (1891), 63. In Bulletin American Mathematical Society (1904), 465.
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Vulnerable, like all men, to the temptations of arrogance, of which intellectual pride is the worst, he [the scientist] must nevertheless remain sincere and modest, if only because his studies constantly bring home to him that, compared with the gigantic aims of science, his own contribution, no matter how important, is only a drop in the ocean of truth.
New Perspectives in Physics (1962), 215.
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We may also draw a very important additional conclusion from the gradual dissolution of the milky way; for the state into which the incessant action of the clustering power [presumably, gravity] has brought it at present, is a kind of chronometer that may be used to measure the time of its past and future existence; and although we do not know the rate of going of this mysterious chronometer, it is nevertheless certain, that since the breaking up of the parts of the milky way affords a proof that it cannot last for ever, it equally bears witness that its past duration cannot be admitted to the infinite.
'Astronomical Observations... ' Philosophical Transactions (1814), 104, 284.
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What remains to be learned may indeed dwarf imagination. Nevertheless, the universe itself is closed and finite. … The uniformity of nature and the general applicability of natural laws set limits to knowledge. If there are just 100, or 105, or 110 ways in which atoms may form, then when one has identified the full range of properties of these, singly and in combination, chemical knowledge will be complete.
Presidential Address (28 Dec 1970) to the American Association for the Advancement of Science. 'Science: Endless Horizons or Golden Age?', Science (8 Jan 1971), 171, No. 3866, 24.
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What these two sciences of recognition, evolution and immunology, have in common is not found in nonbiological systems such as 'evolving' stars. Such physical systems can be explained in terms of energy transfer, dynamics, causes, and even 'information transfer'. But they do not exhibit repertoires of variants ready for interaction by selection to give a population response according to a hereditary principle. The application of a selective principle in a recognition system, by the way, does not necessarily mean that genes must be involved—it simply means that any state resulting after selection is highly correlated in structure with the one that gave rise to it and that the correlation continues to be propagated. Nor is it the case that selection cannot itself introduce variation. But a constancy or 'memory' of selected events is necessary. If changes occurred so fast that what was selected could not emerge in the population or was destroyed, a recognition system would not survive. Physics proper does not deal with recognition systems, which are by their nature biological and historical systems. But all the laws of physics nevertheless apply to recognition systems.
Bright and Brilliant Fire, On the Matters of the Mind (1992), 79.
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When I observe the luminous progress and expansion of natural science in modern times, I seem to myself like a traveller going eastwards at dawn, and gazing at the growing light with joy, but also with impatience; looking forward with longing to the advent of the full and final light, but, nevertheless, having to turn away his eyes when the sun appeared, unable to bear the splendour he had awaited with so much desire.
In The Maxims and Reflections of Goethe (1906), 197-198.
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When one ponders on the tremendous journey of evolution over the past three billion years or so, the prodigious wealth of structures it has engendered, and the extraordinarily effective teleonomic performances of living beings from bacteria to man, one may well find oneself beginning to doubt again whether all this could conceiveably be the product of an enormous lottery presided over by natural selection, blindly picking the rare winners from among numbers drawn at random. [Nevertheless,] a detailed review of the accumulated modern evidence [shows] that this conception alone is compatible with the facts.
In Jacques Monod and Austryn Wainhouse (trans.), Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology (1971), 138.
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When the number of factors coming into play in a phenomenological complex is too large, scientific method in most cases fails us. One need only think of the weather, in which case prediction even for a few days ahead is impossible. Nevertheless no one doubts that we are confronted with a causal connection whose causal components are in the main known to us.
Out of My Later Years (1995), 28.
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Where a cell arises, there a cell must have previously existed (omnis cellula e cellula), just as an animal can spring only from an animal, a plant only from a plant. In this manner, although there are still a few spots in the body where absolute demonstration has not yet been afforded, the principle is nevertheless established, that in the whole series of living things, whether they be entire plants or animal organisms, or essential constituents of the same, an eternal law of continuous development prevails.
In Lecture II 'Physiological Tissues' (17 Feb 1858), as translated by Frank Chance in Cellular Pathology: As Based Upon Physiological and Pathological Histology. Twenty Lectures Delivered in the Pathological Institute of Berlin During the Months of February, March and April, 1858 (1860), 27-28.
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While electric railroading is perhaps the most important branch of electrical engineering, at least as regards commercial importance, considering the amount capital invested therein, nevertheless it is a remarkable fact that while most other branches of electrical engineering had been developed to a very high degree of perfection, even a few years ago theoretical investigation of electric railroading was still conspicuous by its almost entire absence.
All the work was done by some kind of empirical experimenting, that is, some kind of motor was fitted up with some gearing or some sort of railway car, and then run, and if the motor burned out frequently it was replaced with a larger motor, and if it did not burn out, a trailer was put on the car, and perhaps a second trailer, until the increase of the expense account in burn-outs of the motors balanced the increased carrying capacity of the train.
'The Electric Railway', Transactions of the American Institute of Electrical Engineers (1902), 125.
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With highly civilised nations continued progress depends in a subordinate degree on natural selection; for such nations do not supplant and exterminate one another as do savage tribes. Nevertheless the more intelligent members within the same community will succeed better in the long run than the inferior, and leave a more numerous progeny, and this is a form of natural selection.
…...
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[F. Werner, while a student in Princeton,] came to me and expressed his bewilderment with the fact that we make a rather narrow selection when choosing the data on which we test our theories. “How do we know that, if we made a theory which focuses its attention on phenomena we disregard and disregards some of the phenomena now commanding our attention, that we could not build another theory which has little in common with the present one but which, nevertheless, explains just as many phenomena as the present theory?” It has to be admitted that we have no definite evidence that there is no such theory.
In 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences,' Communications in Pure and Applied Mathematics (Feb 1960), 13, No. 1 (February 1960). Collected in Eugene Paul Wigner, A.S. Wightman (ed.), Jagdish Mehra (ed.), The Collected Works of Eugene Paul Wigner (1955), Vol. 6, 535.
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[There is] some mathematical quality in Nature, a quality which the casual observer of Nature would not suspect, but which nevertheless plays an important role in Nature’s scheme.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 122.
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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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