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Today in Science History - Quickie Quiz
Who said: “I seem to have been only like a boy playing on the seashore, ... finding a smoother pebble or a prettier shell ... whilst the great ocean of truth lay all undiscovered before me.”
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Home > Category Index for Science Quotations > Category Index C > Category: Certainly

Certainly Quotes (185 quotes)

[Certain students] suppose that because science has penetrated the structure of the atom it can solve all the problems of the universe. ... They are known in every ... college as the most insufferable, cocksure know-it-alls. If you want to talk to them about poetry, they are likely to reply that the "emotive response" to poetry is only a conditioned reflex .... If they go on to be professional scientists, their sharp corners are rubbed down, but they undergo no fundamental change. They most decidedly are not set apart from the others by their intellectual integrity and faith, and their patient humility in front of the facts of nature.... They are uneducated, in the fullest sense of the word, and they certainly are no advertisement for the claims of science teachers.
In Science is a Sacred Cow (1950), 18-19.
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[Consider] a fence or gate erected across a road] The more modern type of reformer goes gaily up to it and says, “I don't see the use of this; let us clear it away.” To which the more intelligent type of reformer will do well to answer: “If you don't see the use of it, I certainly won't let you clear it away. Go away and think. Then, when you can come back and tell me that you do see the use of it, I may allow you to destroy it.”
In The Thing (1929). Excerpt in Gilbert Keith Chesterton and Alvaro De Silva (ed.), Brave New Family: G.K. Chesterton on Men and Women, Children, Sex, Divorce (1990), 53. Note: This passage may be the source which John F. Kennedy had in mind when he wrote in his personal notebook, “Don't ever take a fence down until you know the reason why it was put up.” (see John F. Kennedy quotes on this site). The words in that terse paraphrase are those of Kennedy, and are neither those of Chesterton, or, as often attributed, Robert Frost (q.v.).
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[On the 11th day of November 1572], in the evening, after sunset, when, according to my habit, I was contemplating the stars in a clear sky, I noticed that a new and unusual star, surpassing all others in brilliancy, was shining almost directly over my head; and since I had, almost from boyhood, known all the stars of the heavens perfectly (there is no great difficulty in gaining that knowledge), it was quite evident to me that there had never before been any star in that place in the sky, even the smallest, to say nothing of a star so conspicuously bright as this. I was so astonished at this sight that I was not ashamed to doubt the trustworthiness of my own eyes. But when I observed that others, too, on having the place pointed out to them, could see that there was a star there, I had no further doubts. A miracle indeed, either the greatest of all that have occurred in the whole range of nature since the beginning of the world, or one certainly that is to be classed with those attested by the Holy Oracles.
De Stello. Nova (On the New Star) (1573). Quoted in H. Shapley and A. E. Howarth (eds.), Source Book in Astronomy (1929), 13.
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[Reply to a lady enquiring: “Have we lost faith?”] Certainly not, but we have only transferred it from God to the General Medical Council.
Invited to contribute to a series of article in a Manchester paper in reply to an enquiry [Have we lost faith?] the question, Shaws’s reply was the single sentence. In The Collected Works of Bernard Shaw (1930), Vol.22, 1.
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[T]he human desire to escape the flesh, which took one form in asceticism, might take another form in the creation of machines. Thus, the wish to rise above the bestial body manifested itself not only in angels but in mechanical creatures. Certainly, once machines existed, humans clearly attached to them feelings of escape from the flesh.
The Fourth Discontinuity: The Co-Evolution of Humans and Machines (1993), 218.
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[Almost certainly not by Einstein.] The more I study science, the more I believe in God.
No cited primary source has been found, so it is almost certainly falsely linked with Einstein. Also, it is not compatible with Einstein’s documented statements on his religious views. See, for example, the quote beginning “It was, of course, a lie what you read about my religious convictions….” The subject quote is included here so readers may find this disclaimer.
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Clarke's First Law: When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.
'Hazards of Prophecy: The Failure of Imagination'. In the collection. Profiles of the Future: An Enquiry into the Limits of the Possible (1962, rev. 1973), 14.
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Every teacher certainly should know something of non-euclidean geometry. Thus, it forms one of the few parts of mathematics which, at least in scattered catch-words, is talked about in wide circles, so that any teacher may be asked about it at any moment. … Imagine a teacher of physics who is unable to say anything about Röntgen rays, or about radium. A teacher of mathematics who could give no answer to questions about non-euclidean geometry would not make a better impression.
On the other hand, I should like to advise emphatically against bringing non-euclidean into regular school instruction (i.e., beyond occasional suggestions, upon inquiry by interested pupils), as enthusiasts are always recommending. Let us be satisfied if the preceding advice is followed and if the pupils learn to really understand euclidean geometry. After all, it is in order for the teacher to know a little more than the average pupil.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 72.
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L'homme est bien insensé. Il ne saurait forger un ciron, et forge des Dieux à douzaines.
Man is certainly crazy. He could not make a mite, and he makes gods by the dozen.
The Complete Essays of Montaigne, trans. Donald M. Frame (1958), 834.
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A fair number of people who go on to major in astronomy have decided on it certainly by the time they leave junior high, if not during junior high. I think it’s somewhat unusual that way. I think most children pick their field quite a bit later, but astronomy seems to catch early, and if it does, it sticks.
From interview by Rebecca Wright, 'Oral History Transcript' (15 Sep 2000), on NASA website.
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A study of Disease—of Pestilences methodically prepared and deliberately launched upon man and beast—is certainly being pursued in the laboratories of more than one great country. Blight to destroy crops, Anthrax to slay horses and cattle, Plague to poison not armies but whole districts—such are the lines along which military science is remorselessly advancing.
'Shall We All Commit Suicide?'. Pall Mall (Sep 1924). Reprinted in Thoughts and Adventures (1932), 250.
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A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.
In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.
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A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.
In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.
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All of our experience indicates that life can manifest itself only in a concrete form, and that it is bound to certain substantial loci. These loci are cells and cell formations. But we are far from seeking the last and highest level of understanding in the morphology of these loci of life. Anatomy does not exclude physiology, but physiology certainly presupposes anatomy. The phenomena that the physiologist investigates occur in special organs with quite characteristic anatomical arrangements; the various morphological parts disclosed by the anatomist are the bearers of properties or, if you will, of forces probed by the physiologist; when the physiologist has established a law, whether through physical or chemical investigation, the anatomist can still proudly state: This is the structure in which the law becomes manifest.
In 'Cellular-Pathologie', Archiv für pathologische Anatomie und Physiologie und fur klinische Medizin (1855), 8, 19, as translated in LellandJ. Rather, 'Cellular Pathology', Disease, Life, and Man: Selected Essays by Rudolf Virchow (1958), 84.
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And for rejecting such a Medium, we have the Authority of those the oldest and most celebrated Philosophers of Greece and Phoenicia, who made a Vacuum, and Atoms, and the Gravity of Atoms, the first Principles of their Philosophy; tacitly attributing Gravity to some other Cause than dense Matter. Later Philosophers banish the Consideration of such a Cause out of natural Philosophy, feigning Hypotheses for explaining all things mechanically, and referring other Causes to Metaphysicks: Whereas the main Business of natural Philosophy is to argue from Phaenomena without feigning Hypotheses, and to deduce Causes from Effects, till we come to the very first Cause, which certainly is not mechanical; and not only to unfold the Mechanism of the World, but chiefly to resolve these and such like Questions. What is there in places almost empty of Matter, and whence is it that the Sun and Planets gravitate towards one another, without dense Matter between them? Whence is it that Nature doth nothing in vain; and whence arises all that Order and Beauty which we see in the World? ... does it not appear from phaenomena that there is a Being incorporeal, living, intelligent, omnipresent, who in infinite space, as it were in his Sensory, sees the things themselves intimately, and thoroughly perceives them, and comprehends them wholly by their immediate presence to himself.
In Opticks, (1704, 2nd. Ed. 1718), Book 3, Query 28, 343-5. Newton’s reference to “Nature does nothing in vain” recalls the axiom from Aristotle, which may be seen as “Natura nihil agit frustra” in the Aristotle Quotes on this web site.
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Any one whose disposition leads him to attach more weight to unexplained difficulties than to the explanation of facts will certainly reject my theory.
The Origin of Species (1859), 482.
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Ardent desire for knowledge, in fact, is the one motive attracting and supporting investigators in their efforts; and just this knowledge, really grasped and yet always flying before them, becomes at once their sole torment and their sole happiness. Those who do not know the torment of the unknown cannot have the joy of discovery which is certainly the liveliest that the mind of man can ever feel.
From An Introduction to the Study of Experimental Medicine (1927, 1957), 221-222, as translated by Henry Copley Greene. From the original French by Claude Bernard: “Le désir ardent de la connaissance est l’unique mobile qui attire et soutient l’investigateur dans ses efforts; et c’est précisément cette connaissance qu’il saisit réellement et qui fuit cependant toujours devant lui, qui devient à la fois son seul tourment et son seul bonheur. Celui qui ne connaît pas les tourments de l’inconnu doit ignorer les joies de la découverte qui sont certainement les plus vives que l’esprit de l’homme puisse jamais ressentir.” (1865), 388. A Google translation gives: “The ardent desire for knowledge is the only motive which attracts and sustains the inquirer in his efforts; and it is precisely this knowledge which he really grasps and which nevertheless always flees before him, which becomes at the same time his only torment and his only happiness. He who does not know the torments of the unknown must ignore the joys of discovery which are certainly the most vivid that the mind of man can ever experience.”
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As mineralogy constitutes a part of chemistry, it is clear that this arrangement [of minerals] must derive its principles from chemistry. The most perfect mode of arrangement would certainly be to allow bodies to follow each other according to the order of their electro-chemical properties, from the most electro-negative, oxygen, to the most electro-positive, potassium; and to place every compound body according to its most electro-positive ingredient.
An Attempt to Establish a Pure Scientific System of Mineralogy (1814), trans. J. Black, 48.
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At some future period, not very distant as measured by centuries, the civilised races of man will almost certainly exterminate, and replace the savage races throughout the world.
In The Descent of Man and Selection in Relation to Sex (1871), Vol. 1, 193.
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At this point, however, I have no intention whatever of criticizing the false teachings of Galen, who is easily first among the professors of dissection, for I certainly do not wish to start off by gaining a reputation for impiety toward him, the author of all good things, or by seeming insubordinate to his authority. For I am well aware how upset the practitioners (unlike the followers of Aristotle) invariably become nowadays, when they discover in the course of a single dissection that Galen has departed on two hundred or more occasions from the true description of the harmony, function, and action of the human parts, and how grimly they examine the dissected portions as they strive with all the zeal at their command to defend him. Yet even they, drawn by their love of truth, are gradually calming down and placing more faith in their own not ineffective eyes and reason than in Galen’s writings.
From De Humani Corporis Fabrica Libri Septem: (1543), Book I, iv, as translated by William Frank Richardson, in On The Fabric of the Human Body: Book I: The Bones and Cartilages (1998), Preface, liv.
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Borel makes the amusing supposition of a million monkeys allowed to play upon the keys of a million typewriters. What is the chance that this wanton activity should reproduce exactly all of the volumes which are contained in the library of the British Museum? It certainly is not a large chance, but it may be roughly calculated, and proves in fact to be considerably larger than the chance that a mixture of oxygen and nitrogen will separate into the two pure constituents. After we have learned to estimate such minute chances, and after we have overcome our fear of numbers which are very much larger or very much smaller than those ordinarily employed, we might proceed to calculate the chance of still more extraordinary occurrences, and even have the boldness to regard the living cell as a result of random arrangement and rearrangement of its atoms. However, we cannot but feel that this would be carrying extrapolation too far. This feeling is due not merely to a recognition of the enormous complexity of living tissue but to the conviction that the whole trend of life, the whole process of building up more and more diverse and complex structures, which we call evolution, is the very opposite of that which we might expect from the laws of chance.
The Anatomy of Science (1926), 158-9.
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But although in theory physicists realize that their conclusions are ... not certainly true, this ... does not really sink into their consciousness. Nearly all the time ... they ... act as if Science were indisputably True, and what's more, as if only science were true.... Any information obtained otherwise than by the scientific method, although it may be true, the scientists will call “unscientific,” using this word as a smear word, by bringing in the connotation from its original [Greek] meaning, to imply that the information is false, or at any rate slightly phony.
In Science is a Sacred Cow (1950), 176-77.
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But I shall certainly admit a system as empirical or scientific only if it is capable of being tested by experience. These considerations suggest that not the verifiability but the falsifiability of a system is to be taken as a criterion of demarcation. In other words: I shall not require of a scientific system that it shall be capable of being singled out, once and for all, in a positive sense; but I shall require that its logical form shall be such that it can be singled out, by means of empirical tests, in a negative sense: it must be possible for an empirical scientific system to be refuted by experience. (1959)
The Logic of Scientific Discovery: Logik Der Forschung (1959, 2002), 18.
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But, further, no animal can live upon a mixture of pure protein, fat and carbohydrate, and even when the necessary inorganic material is carefully supplied, the animal still cannot flourish. The animal body is adjusted to live either upon plant tissues or the tissues of other animals, and these contain countless substances other than the proteins, carbohydrates and fats... In diseases such as rickets, and particularly in scurvy, we have had for long years knowledge of a dietetic factor; but though we know how to benefit these conditions empirically, the real errors in the diet are to this day quite obscure. They are, however, certainly of the kind which comprises these minimal qualitative factors that I am considering.
'The Analyst and the Medical Man', The Analyst (1906), 31, 395-6.
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But, you might say, “none of this shakes my belief that 2 and 2 are 4.” You are quite right, except in marginal cases—and it is only in marginal cases that you are doubtful whether a certain animal is a dog or a certain length is less than a meter. Two must be two of something, and the proposition “2 and 2 are 4” is useless unless it can be applied. Two dogs and two dogs are certainly four dogs, but cases arise in which you are doubtful whether two of them are dogs. “Well, at any rate there are four animals,” you may say. But there are microorganisms concerning which it is doubtful whether they are animals or plants. “Well, then living organisms,” you say. But there are things of which it is doubtful whether they are living organisms or not. You will be driven into saying: “Two entities and two entities are four entities.” When you have told me what you mean by “entity,” we will resume the argument.
In Basic Writings, 1903-1959 (1961), 108.
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Certainly it is by their signs and symptoms, that internal diseases are revealed to the physician.
Philosophy of Medical Science, Pt II, Ch. 10.
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Certainly Lord Byron has expressed in words some aspects of spiritual turmoil; but our immortal natural historian has reconstructed worlds from bleached bones.
From 'La Peau de Chagrin' (1831). As translated as The Wild Ass’s Skin (1906) trans. Herbert J. Hunt, The Wild Ass’s Skin (1977), 40-1.
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Certainly one of the most enthralling things about human life is the recognition that we live in what, for practical purposes, is a universe without bounds.
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Certainly the game is rigged. Don’t let that stop you; if you don’t bet, you can’t win.
In 'From the Notebooks of Lazarus Long', Time Enough for Love: The Lives of Lazarus Long (1973), 256.
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Certainly, it is heaven upon earth, to have a man's mind move in charity, rest in providence, and turn upon the poles of truth.
'Essays or Counsels: Civil and Moral. I. Of Truth'. In Francis Bacon, James Spedding, The Works of Francis Bacon (1864), Vol. 6, 378.
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Certainly, speaking for the United States of America, I pledge that, as we sign this treaty in an era of negotiation, we consider it only one step toward a greater goal: the control of nuclear weapons on earth and the reduction of the danger that hangs over all nations as long as those weapons are not controlled.
'Remarks at the Signing Ceremony of the Seabed Arms Control Treaty' (11 Feb 1971), Public Papers of the Presidents of the United States: Richard M. Nixon (1972), 150.
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Chemistry affords two general methods of determining the constituent principles of bodies, the method of analysis, and that of synthesis. When, for instance, by combining water with alkohol, we form the species of liquor called, in commercial language, brandy or spirit of wine, we certainly have a right to conclude, that brandy, or spirit of wine, is composed of alkohol combined with water. We can produce the same result by the analytical method; and in general it ought to be considered as a principle in chemical science, never to rest satisfied without both these species of proofs. We have this advantage in the analysis of atmospherical air, being able both to decompound it, and to form it a new in the most satisfactory manner.
Elements of Chemistry (1790), trans. R. Kerr, 33.
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Euler who could have been called almost without metaphor, and certainly without hyperbole, analysis incarnate.
In Oeuvres, t. 2 (1854), 443.
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Everything that can be invented, has been invented. [A myth, attributed - almost certainly falsely - to Duell.]
A classic example of a zombie-type quote. It should be long dead, but keeps living on as a myth, impossible to extirpate. For example, it is glibly recited and attributed (as always, without a valid primary source), to a Commissioner ("Director") of U.S. Patent Office, urging President McKinley to abolish his office, in Chris Morgan and David Langford, Facts and Fallacies (1981). (Duell held the office 1898-1901.) It has a long history of being debunked, for example, see Eber Jeffery, Journal of the Patent Office Society (July 1940), and Samuel Sass, 'A Patently False Patent Myth', Skeptical Inquirer (Spring 1989), 13, 310-313.
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Facts are certainly the solid and true foundation of all sectors of nature study ... Reasoning must never find itself contradicting definite facts; but reasoning must allow us to distinguish, among facts that have been reported, those that we can fully believe, those that are questionable, and those that are false. It will not allow us to lend faith to those that are directly contrary to others whose certainty is known to us; it will not allow us to accept as true those that fly in the face of unquestionable principles.
Memoires pour Servir a l'Histoire des Insectes (1736), Vol. 2, xxxiv. Quoted in Jacques Roger, The Life Sciences in Eighteenth-Century French Thought, ed. Keith R. Benson and trans. Robert Ellrich (1997), 165.
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Finally, since I thought that we could have all the same thoughts, while asleep, as we have while we are awake, although none of them is true at that time, I decided to pretend that nothing that ever entered my mind was any more true than the illusions of my dreams. But I noticed, immediately afterwards, that while I thus wished to think that everything was false, it was necessarily the case that I, who was thinking this, was something. When I noticed that this truth “I think, therefore I am” was so firm and certain that all the most extravagant assumptions of the sceptics were unable to shake it, I judged that I could accept it without scruple as the first principle of the philosophy for which I was searching. Then, when I was examining what I was, I realized that I could pretend that I had no body, and that there was no world nor any place in which I was present, but I could not pretend in the same way that I did not exist. On the contrary, from the very fact that I was thinking of doubting the truth of other things, it followed very evidently and very certainly that I existed; whereas if I merely ceased to think, even if all the rest of what I had ever imagined were true, I would have no reason to believe that I existed. I knew from this that I was a substance, the whole essence or nature of which was to think and which, in order to exist, has no need of any place and does not depend on anything material. Thus this self—that is, the soul by which I am what I am—is completely distinct from the body and is even easier to know than it, and even if the body did not exist the soul would still be everything that it is.
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 4, 24-5.
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For those who have seen the Earth from space, and for the hundreds and perhaps thousands more who will, the experience most certainly changes your perspective. The things that we share in our world are far more valuable than those which divide us.
As quoted, without citation, in Jeffrey O. Bennett, The Cosmic Perspective (1999), 24.
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Further, it will not be amiss to distinguish the three kinds and, as it were, grades of ambition in mankind. The first is of those who desire to extend their own power in their native country, a vulgar and degenerate kind. The second is of those who labor to extend the power and dominion of their country among men. This certainly has more dignity, though not less covetousness. But if a man endeavor to establish and extend the power and dominion of the human race itself over the universe, his ambition (if ambition it can be called) is without doubt both a more wholesome and a more noble thing than the other two. Now the empire of man over things depends wholly on the arts and sciences. For we cannot command nature except by obeying her.
From Novum Organum (1620), Book 1, Aphorism 129. Translated as The New Organon: Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man), collected in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 4, 114.
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Gentlemen and ladies, this is ordinary alcohol, sometimes called ethanol; it is found in all fermented beverages. As you well know, it is considered by many to be poisonous, a belief in which I do not concur. If we subtract from it one CH2-group we arrive at this colorless liquid, which you see in this bottle. It is sometimes called methanol or wood alcohol. It is certainly more toxic than the ethanol we have just seen. Its formula is CH3OH. If, from this, we subtract the CH2-group, we arrive at a third colorless liquid, the final member of this homologous series. This compound is hydrogen hydroxide, best known as water. It is the most poisonous of all.
In Ralph Oesper, The Human Side of Scientists (1975), 189.
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He [Robert Hooke] is but of midling stature, something crooked, pale faced, and his face but little belowe, but his head is lardge; his eie full and popping, and not quick; a grey eie. He haz a delicate head of haire, browne, and of an excellent moist curle. He is and ever was very temperate, and moderate in dyet, etc. As he is of prodigious inventive head, so is a person of great vertue and goodnes. Now when I have sayd his Inventive faculty is so great, you cannot imagine his Memory to be excellent, for they are like two Bucketts, as one goes up, the other goes downe. He is certainly the greatest Mechanick this day in the World.
Brief Lives (1680), edited by Oliver Lawson Dick (1949), 165.
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He [Samuel Johnson] bid me always remember this, that after a system is well settled upon positive evidence, a few objections ought not to shake it. “The human mind is so limited that it cannot take in all parts of a subject; so that there may be objections raised against anything. There are objections against a plenum, and objections against a vacuum. Yet one of them must certainly be true.”
Note: Whereas vacuum means devoid of matter, plenum regards a space with matter throughout.
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He [Winston Churchill] is rather like a layer cake. One layer was certainly seventeenth century. The eighteenth century in him is obvious. There was the nineteenth century, and a large slice, of course, of the twentieth century; and another, curious, layer which may possibly have been the twenty-first.
As quoted in Peter Stansky, Churchill: A Profile (1973), 197.
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Homo sapiens is a compulsive communicator. Look at the number of people you see walking around talking on mobile phones. We seem to have an infinite capacity for communicating and being communicated with. I’m not sure how admirable it is, but it certainly demonstrates that we are social organisms.
From interview with Michael Bond, 'It’s a Wonderful Life', New Scientist (14 Dec 2002), 176, No. 2373, 48.
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However improbable we regard [the spontaneous origin of life],… it will almost certainly happen at least once…. The time… is of the order of two billion years.… Given so much time, the “impossible” becomes possible, the possible probable, and the probable virtually certain. One only has to wait: time itself performs the miracles.
In 'The Origin of Life', Scientific American (Aug 1954), 191, No. 2, 46. Note that the quoted time of 2 billion years is rejected as impossibly short by such authors as H. J. Morowitz, in Energy Flow in Biology (1968), 317.
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Humanity certainly needs practical men, who get the most out of their work, and, without forgetting the general good, safeguard their own interests. But humanity also needs dreamers, for whom the disinterested development of an enterprise is so captivating that it becomes impossible for them to devote their care to their own material profit. Without the slightest doubt, these dreamers do not deserve wealth, because they do not desire it. Even so, a well-organised society should assure to such workers the efficient means of accomplishing their task, in a life freed from material care and freely consecrated to research.
In Eve Curie, Madame Curie: A Biography by Eve Curie (1938, 2007), 344.
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I believe myself to possess a most singular combination of qualities exactly fitted to make me pre-eminently a discoverer of the hidden realities of nature… the belief has been forced upon me…
Firstly: Owing to some peculiarity in my nervous system, I have perceptions of some things, which no one else has… and intuitive perception of… things hidden from eyes, ears, & ordinary senses…
Secondly: my sense reasoning faculties;
Thirdly: my concentration faculty, by which I mean the power not only of throwing my whole energy & existence into whatever I choose, but also of bringing to bear on anyone subject or idea, a vast apparatus from all sorts of apparently irrelevant & extraneous sources…
Well, here I have written what most people would call a remarkably mad letter; & yet certainly one of the most logical, sober-minded, cool, pieces of composition, (I believe), that I ever framed.
Lovelace Papers, Bodleian Library, Oxford University, 42, folio 12 (6 Feb 1841). As quoted and cited in Dorothy Stein (ed.), 'This First Child of Mine', Ada: A Life and a Legacy (1985), 86.
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I can certainly wish for new, large, and properly constructed instruments, and enough of them, but to state where and by what means they are to be procured, this I cannot do. Tycho Brahe has given Mastlin an instrument of metal as a present, which would be very useful if Mastlin could afford the cost of transporting it from the Baltic, and if he could hope that it would travel such a long way undamaged… . One can really ask for nothing better for the observation of the sun than an opening in a tower and a protected place underneath.
As quoted in James Bruce Ross and Mary Martin McLaughlin, The Portable Renaissance Reader (1968), 605.
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I do not intend to go deeply into the question how far mathematical studies, as the representatives of conscious logical reasoning, should take a more important place in school education. But it is, in reality, one of the questions of the day. In proportion as the range of science extends, its system and organization must be improved, and it must inevitably come about that individual students will find themselves compelled to go through a stricter course of training than grammar is in a position to supply. What strikes me in my own experience with students who pass from our classical schools to scientific and medical studies, is first, a certain laxity in the application of strictly universal laws. The grammatical rules, in which they have been exercised, are for the most part followed by long lists of exceptions; accordingly they are not in the habit of relying implicitly on the certainty of a legitimate deduction from a strictly universal law. Secondly, I find them for the most part too much inclined to trust to authority, even in cases where they might form an independent judgment. In fact, in philological studies, inasmuch as it is seldom possible to take in the whole of the premises at a glance, and inasmuch as the decision of disputed questions often depends on an aesthetic feeling for beauty of expression, or for the genius of the language, attainable only by long training, it must often happen that the student is referred to authorities even by the best teachers. Both faults are traceable to certain indolence and vagueness of thought, the sad effects of which are not confined to subsequent scientific studies. But certainly the best remedy for both is to be found in mathematics, where there is absolute certainty in the reasoning, and no authority is recognized but that of one’s own intelligence.
In 'On the Relation of Natural Science to Science in general', Popular Lectures on Scientific Subjects, translated by E. Atkinson (1900), 25-26.
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I have from my childhood, in conformity with the precepts of a mother void of all imaginary fear, been in the constant habit of taking toads in my hand, and applying them to my nose and face as it may happen. My motive for doing this very frequently is to inculcate the opinion I have held, since I was told by my mother, that the toad is actually a harmless animal; and to whose manner of life man is certainly under some obligation as its food is chiefly those insects which devour his crops and annoy him in various ways.
Letter to an unknown correspondent, quoted by Bowdler Sharpe, The Natural History and Antiquities of Selborne (1900), Vol. 1, 69. In Averil M. Lysaght, Joseph Banks in Newfoundland and Labrador, 1766: his Diary, Manuscripts, and Collections (1971), 44.
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I have indeed lived and worked to my taste either in art or science. What more could a man desire? Knowledge has always been my goal. There is much that I shall leave behind undone…but something at least I was privileged to leave for the world to use, if it so intends…As the Latin poet said I will leave the table of the living like a guest who has eaten his fill. Yes, if I had another life to spend, I certainly would not waste it. But that cannot be, so why complain?
Letter to R. C. Craw, quoted in Tuatara (1984) Vol. 27 (1): 5-7
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I have long since come to see that no one deserves either praise or blame for the ideas that come to him, but only for the actions resulting therefrom. Ideas and beliefs are certainly not voluntary acts. They come to us—we hardly know how or whence, and once they have got possession of us we can not reject or change them at will. It is for the common good that the promulgation of ideas should be free—uninfluenced by either praise or blame, reward or punishment. But the actions which result from our ideas may properly be so treated, because it is only by patient thought and work, that new ideas, if good and true, become adopted and utilized; while, if untrue or if not adequately presented to the world, they are rejected or forgotten.
In 'The Origin of the Theory of Natural Selection', Popular Science Monthly (1909), 74, 400.
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I have no doubt that certain learned men, now that the novelty of the hypotheses in this work has been widely reported—for it establishes that the Earth moves, and indeed that the Sun is motionless in the middle of the universe—are extremely shocked, and think that the scholarly disciplines, rightly established once and for all, should not be upset. But if they are willing to judge the matter thoroughly, they will find that the author of this work has committed nothing which deserves censure. For it is proper for an astronomer to establish a record of the motions of the heavens with diligent and skilful observations, and then to think out and construct laws for them, or rather hypotheses, whatever their nature may be, since the true laws cannot be reached by the use of reason; and from those assumptions the motions can be correctly calculated, both for the future and for the past. Our author has shown himself outstandingly skilful in both these respects. Nor is it necessary that these hypotheses should be true, nor indeed even probable, but it is sufficient if they merely produce calculations which agree with the observations. … For it is clear enough that this subject is completely and simply ignorant of the laws which produce apparently irregular motions. And if it does work out any laws—as certainly it does work out very many—it does not do so in any way with the aim of persuading anyone that they are valid, but only to provide a correct basis for calculation. Since different hypotheses are sometimes available to explain one and the same motion (for instance eccentricity or an epicycle for the motion of the Sun) an astronomer will prefer to seize on the one which is easiest to grasp; a philosopher will perhaps look more for probability; but neither will grasp or convey anything certain, unless it has been divinely revealed to him. Let us therefore allow these new hypotheses also to become known beside the older, which are no more probable, especially since they are remarkable and easy; and let them bring with them the vast treasury of highly learned observations. And let no one expect from astronomy, as far as hypotheses are concerned, anything certain, since it cannot produce any such thing, in case if he seizes on things constructed for another other purpose as true, he departs from this discipline more foolish than he came to it.
Although this preface would have been assumed by contemporary readers to be written by Copernicus, it was unsigned. It is now believed to have been written and added at press time by Andreas Osiander (who was then overseeing the printing of the book). It suggests the earth’s motion as described was merely a mathematical device, and not to be taken as absolute reality. Text as given in 'To the Reader on the Hypotheses in this Work', Copernicus: On the Revolutions of the Heavenly Spheres (1543), translated by ‎Alistair Matheson Duncan (1976), 22-3. By adding this preface, Osiander wished to stave off criticism by theologians. See also the Andreas Osiander Quotes page of this website.
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I have no patience with attempts to identify science with measurement, which is but one of its tools, or with any definition of the scientist which would exclude a Darwin, a Pasteur or a Kekulé. The scientist is a practical man and his are practical aims. He does not seek the ultimate but the proximate. He does not speak of the last analysis but rather of the next approximation. His are not those beautiful structures so delicately designed that a single flaw may cause the collapse of the whole. The scientist builds slowly and with a gross but solid kind of masonry. If dissatisfied with any of his work, even if it be near the very foundations, he can replace that part without damage to the remainder. On the whole, he is satisfied with his work, for while science may never be wholly right it certainly is never wholly wrong; and it seems to be improving from decade to decade.
The Anatomy of Science (1926), 6-7.
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I suppose that the first chemists seemed to be very hard-hearted and unpoetical persons when they scouted the glorious dream of the alchemists that there must be some process for turning base metals into gold. I suppose that the men who first said, in plain, cold assertion, there is no fountain of eternal youth, seemed to be the most cruel and cold-hearted adversaries of human happiness. I know that the economists who say that if we could transmute lead into gold, it would certainly do us no good and might do great harm, are still regarded as unworthy of belief. Do not the money articles of the newspapers yet ring with the doctrine that we are getting rich when we give cotton and wheat for gold rather than when we give cotton and wheat for iron?
'The Forgotten Man' (1883). In The Forgotten Man and Other Essays (1918), 468.
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I then shouted into M [the mouthpiece] the following sentence: “Mr. Watson—Come here—I want to see you.” To my delight he came and declared that he had heard and understood what I said. I asked him to repeat the words. He answered “You said—‘Mr. Watson—-come here—I want to see you.’” We then changed places and I listened at S [the reed receiver] while Mr. Watson read a few passages from a book into the mouth piece M. It was certainly the case that articulate sounds proceeded from S. The effect was loud but indistinct and muffled. If I had read beforehand the passage given by Mr. Watson I should have recognized every word. As it was I could not make out the sense—but an occasional word here and there was quite distinct. I made out “to” and “out” and “further”; and finally the sentence “Mr. Bell do you understand what I say? Do—you—un—der—stand—what—I—say” came quite clearly and intelligibly. No sound was audible when the armature S was removed.
Notebook, 'Experiments made by A. Graham Bell, vol. I'. Entry for 10 March 1876. Quoted in Robert V. Bruce, Bell: Alexander Graham Bell and the Conquest of Solitude (1973), 181.
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I think she [Rosalind Franklin] was a good experimentalist but certainly not of the first rank. She was simply not in the same class as Eigen or Bragg or Pauling, nor was she as good as Dorothy Hodgkin. She did not even select DNA to study. It was given to her. Her theoretical crystallography was very average.
Letter to Charlotte Friend (18 Sep 1979). In Francis Harry Compton Crick Papers, Wellcome Library for the History and Understanding of Medicine.
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I thought that the wisdom of our City had certainly designed the laudable practice of taking and distributing these accompts [parish records of christenings and deaths] for other and greater uses than [merely casual comments], or, at least, that some other uses might be made of them; and thereupon I ... could, and (to be short) to furnish myself with as much matter of that kind ... the which when I had reduced into tables ... so as to have a view of the whole together, in order to the more ready comparing of one Year, Season, Parish, or other Division of the City, with another, in respect of all Burials and Christnings, and of all the Diseases and Casualties happening in each of them respectively...
Moreover, finding some Truths and not-commonly-believed opinions to arise from my meditations upon these neglected Papers, I proceeded further to consider what benefit the knowledge of the same would bring to the world, ... with some real fruit from those ayrie blossoms.
From Natural and Political Observations Mentioned in a Following Index and Made upon Bills of Mortality (1662), Preface. Reproduced in Cornelius Walford, The Insurance Cyclopaedia (1871), Vol. 1, 286-287.
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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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I took this view of the subject. The medulla spinalis has a central division, and also a distinction into anterior and posterior fasciculi, corresponding with the anterior and posterior portions of the brain. Further we can trace down the crura of the cerebrum into the anterior fasciculus of the spinal marrow, and the crura of the cerebellum into the posterior fasciculus. I thought that here I might have an opportunity of touching the cerebellum, as it were, through the posterior portion of the spinal marrow, and the cerebrum by the anterior portion. To this end I made experiments which, though they were not conclusive, encouraged me in the view I had taken. I found that injury done to the anterior portion of the spinal marrow, convulsed the animal more certainly than injury done to the posterior portion; but I found it difficult to make the experiment without injuring both portions.
Idea of a New Anatomy of the Brain (1811), 21-22.
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I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. That would be claiming too much. But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming-and a little mad. Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings.
In Science and the Modern World (1926), 31.
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I would not have it inferred ... that I am, as yet, an advocate for the hypothesis of chemical life. The doctrine of the vitality of the blood, stands in no need of aid from that speculative source. If it did, I would certainly abandon it. For, notwithstanding the fashionableness of the hypothesis in Europe, and the ascendancy it has gained over some minds in this country [USA], it will require stubborn facts to convince me that man with all his corporeal and intellectual attributes is nothing but hydro-phosphorated oxyde of azote ... When the chemist declares, that the same laws which direct the crystallization of spars, nitre and Glauber's salts, direct also the crystallization of man, he must pardon me if I neither understand him, nor believe him.
Medical Theses (1805), 391-2, footnote.
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If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero. To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages, where we shall explain this calculus.
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If any layman were to ask a number of archaeologists to give, on the spur of the moment, a definition of archaeology, I suspect that such a person might find the answers rather confusing. He would, perhaps, sympathize with Socrates who, when he hoped to learn from the poets and artisans something about the arts they practised, was forced to go away with the conviction that, though they might themselves be able to accomplish something, they certainly could give no clear account to others of what they were trying to do.
Opening statement in lecture at Columbia University (8 Jan 1908), 'Archaeology'. Published by the Columbia University Press (1908).
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If any philosopher had been asked for a definition of infinity, he might have produced some unintelligible rigmarole, but he would certainly not have been able to give a definition that had any meaning at all.
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If God didn't create life this way, He certainly missed a good bet.
Remark he made after experiments simulating electric discharges in the primitive atmosphere of the earth produced amino acids molecules (the first step- toward life). As quoted by Carl Sagan in Henry S.F. Cooper Jr., 'A Resonance with Something Alive', collected in Carl Sagan and Tom Head (ed.), Conversations with Carl Sagan (2006), 30. Reprinted from The Search for Life on Mars (1979).
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If our intention had been merely to bring back a handful of soil and rocks from the lunar gravel pit and then forget the whole thing, we would certainly be history's biggest fools. But that is not our intention now—it never will be. What we are seeking in tomorrow's [Apollo 11] trip is indeed that key to our future on earth. We are expanding the mind of man. We are extending this God-given brain and these God-given hands to their outermost limits and in so doing all mankind will benefit. All mankind will reap the harvest…. What we will have attained when Neil Armstrong steps down upon the moon is a completely new step in the evolution of man.
Banquet speech on the eve of the Apollo 11 launch, Royal Oaks Country Club, Titusville (15 Jul 1969). In "Of a Fire on the Moon", Life (29 Aug 1969), 67, No. 9, 34.
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If the finding of Coines, Medals, Urnes, and other Monuments of famous Persons, or Towns, or Utensils, be admitted for unquestionable Proofs, that such Persons or things have, in former Times, had a being, certainly those Petrifactions may be allowed to be of equal Validity and Evidence, that there have been formerly such Vegetables or Animals. These are truly Authentick Antiquity not to be counterfeited, the Stamps, and Impressions, and Characters of Nature that are beyond the Reach and Power of Humane Wit and Invention, and are true universal Characters legible to all rational Men.
Lectures and Discourses of Earthquakes (1668). In The Posthumous Works of Robert Hooke, containing his Cutlerian Lectures and other Discourses read at the Meetings of the Illustrious Royal Society (1705), 449.
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If the love of surgery is a proof of a person’s being adapted for it, then certainly I am fitted to he a surgeon; for thou can’st hardly conceive what a high degree of enjoyment I am from day to day experiencing in this bloody and butchering department of the healing art. I am more and more delighted with my profession.
Letter to his father (1853). In John Vaughan, 'Lord Lister', The Living Age (1918), 297, 361. Reprinted from The Fortnightly Review (1918), 109, 417- .
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If you know how to make chemical or electrical energy out of solar energy the way plants do it—without going through a heat engine—that is certainly a trick. And I’m sure we can do it. It’s just a question of how long it will take to solve the technical question.
As quoted in 'Melvin Calvin and Photosynthesis', Science Matters@Berkeley, 2, No. 11.
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In a randomly infinite Universe, any event occurring here and now with finite probability must be occurring simultaneously at an infinite number of other sites in the Universe. It is hard to evaluate this idea any further, but one thing is certain: if it is true then it is certainly not original!
With co-author Frank Tipler, The Anthropic Cosmological Principle (1986).
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In my considered opinion the peer review system, in which proposals rather than proposers are reviewed, is the greatest disaster visited upon the scientific community in this century. No group of peers would have approved my building the 72-inch bubble chamber. Even Ernest Lawrence told me he thought I was making a big mistake. He supported me because he knew my track record was good. I believe that U.S. science could recover from the stultifying effects of decades of misguided peer reviewing if we returned to the tried-and-true method of evaluating experimenters rather than experimental proposals. Many people will say that my ideas are elitist, and I certainly agree. The alternative is the egalitarianism that we now practice and I’ve seen nearly kill basic science in the USSR and in the People's Republic of China.
Alvarez: Adventures of a Physicist (1987), 200-1.
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In my work I now have the comfortable feeling that I am so to speak on my own ground and territory and almost certainly not competing in an anxious race and that I shall not suddenly read in the literature that someone else had done it all long ago. It is really at this point that the pleasure of research begins, when one is, so to speak, alone with nature and no longer worries about human opinions, views and demands. To put it in a way that is more learned than clear: the philological aspect drops out and only the philosophical remains.
In Davis Baird, R.I.G. Hughes and Alfred Nordmann, Heinrich Hertz: Classical Physicist, Modern Philosopher (1998), 157.
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In science, each of us knows that what he has accomplished will be antiquated in ten, twenty, fifty years. That is the fate to which science is subjected; it is the very meaning of scientific work, to which it is devoted in a quite specific sense, as compared with other spheres of culture for which in general the same holds. Every scientific “fulfilment” raises new “questions”; it asks to be “surpassed” and outdated. Whoever wishes to serve science has to resign himself to this fact. Scientific works certainly can last as “gratifications” because of their artistic quality, or they may remain important as a means of training. Yet they will be surpassed scientifically—let that be repeated—for it is our common fate and, more our common goal. We cannot work without hoping that others will advance further than we have. In principle, this progress goes on ad infinitum.
Max Weber
From a Speech (1918) presented at Munich University, published in 1919, and collected in 'Wissenschaft als Beruf', Gessammelte Aufsätze zur Wissenschaftslehre (1922), 524-525. As given in H.H. Gerth and C. Wright-Mills (translators and eds.), 'Science as a Vocation', Max Weber: Essays in Sociology (1946), 138. A different translation of a shorter excerpt from this quote, beginning “[In] the realm of science, …” is also on the Max Weber Quotes web page on this site.
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In scientific thought we adopt the simplest theory which will explain all the facts under consideration and enable us to predict new facts of the same kind. The catch in this criterion lies in the world “simplest.” It is really an aesthetic canon such as we find implicit in our criticisms of poetry or painting. The layman finds such a law as dx/dt = κ(d²x/dy²) much less simple than “it oozes,” of which it is the mathematical statement. The physicist reverses this judgment, and his statement is certainly the more fruitful of the two, so far as prediction is concerned. It is, however, a statement about something very unfamiliar to the plain man, namely the rate of change of a rate of change.
In 'Science and Theology as Art-Forms', Possible Worlds (1927), 227.
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In the world’s history certain inventions and discoveries occurred of peculiar value, on account of their great efficiency in facilitating all other inventions and discoveries. Of these were the art of writing and of printing, the discovery of America, and the introduction of patent laws. The date of the first … is unknown; but it certainly was as much as fifteen hundred years before the Christian era; the second—printing—came in 1436, or nearly three thousand years after the first. The others followed more rapidly—the discovery of America in 1492, and the first patent laws in 1624.
Lecture 'Discoveries, Inventions and Improvements' (22 Feb 1860) in John George Nicolay and John Hay (eds.), Complete Works of Abraham Lincoln (1894), Vol. 5, 109-10.
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Is pure science to be considered as something potentially harmful? Answer: Most certainly! Every child knows that it is potentially exceedingly harmful. … The menace of blowing ourselves up by atom bombs, doing ourselves in by chemical or biological warfare, or by population explosion, is certainly with us. I consider the environment thing a trivial question, by comparison—like housekeeping. In any home, the dishes have to be washed, the floors swept, the beds made, and there must be rules as to who is allowed to produce how much stink and noise, and where in the house: When the garbage piles up, these questions become pressing. But they are momentary problems. Once the house is in order, you still want to live in it, not just sit around enjoying its orderliness. I would be sorry to see Caltech move heavily into this type of applied research. … SCIENCE POTENTIALLY HARMFUL? DEFINITELY.
In 'Homo Scientificus According to Beckett," collected in William Beranek, Jr. (ed.)Science, Scientists, and Society, (1972), 135. Excerpted in Ann E. Kammer, Science, Sex, and Society (1979), 277.
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It certainly strikes the beholder with astonishment, to perceive what vast difficulties can be overcome by the pigmy arms of little mortal man, aided by science and directed by superior skill.
About his visit to Lockport on the Erie Canal, in Letter IX, to a friend in England from Lockport, New York (25 Jul 1831), collected in Narrative of a Tour in North America (1834), Vol. 1, 233-234,
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It has been asserted … that the power of observation is not developed by mathematical studies; while the truth is, that; from the most elementary mathematical notion that arises in the mind of a child to the farthest verge to which mathematical investigation has been pushed and applied, this power is in constant exercise. By observation, as here used, can only be meant the fixing of the attention upon objects (physical or mental) so as to note distinctive peculiarities—to recognize resemblances, differences, and other relations. Now the first mental act of the child recognizing the distinction between one and more than one, between one and two, two and three, etc., is exactly this. So, again, the first geometrical notions are as pure an exercise of this power as can be given. To know a straight line, to distinguish it from a curve; to recognize a triangle and distinguish the several forms—what are these, and all perception of form, but a series of observations? Nor is it alone in securing these fundamental conceptions of number and form that observation plays so important a part. The very genius of the common geometry as a method of reasoning—a system of investigation—is, that it is but a series of observations. The figure being before the eye in actual representation, or before the mind in conception, is so closely scrutinized, that all its distinctive features are perceived; auxiliary lines are drawn (the imagination leading in this), and a new series of inspections is made; and thus, by means of direct, simple observations, the investigation proceeds. So characteristic of common geometry is this method of investigation, that Comte, perhaps the ablest of all writers upon the philosophy of mathematics, is disposed to class geometry, as to its method, with the natural sciences, being based upon observation. Moreover, when we consider applied mathematics, we need only to notice that the exercise of this faculty is so essential, that the basis of all such reasoning, the very material with which we build, have received the name observations. Thus we might proceed to consider the whole range of the human faculties, and find for the most of them ample scope for exercise in mathematical studies. Certainly, the memory will not be found to be neglected. The very first steps in number—counting, the multiplication table, etc., make heavy demands on this power; while the higher branches require the memorizing of formulas which are simply appalling to the uninitiated. So the imagination, the creative faculty of the mind, has constant exercise in all original mathematical investigations, from the solution of the simplest problems to the discovery of the most recondite principle; for it is not by sure, consecutive steps, as many suppose, that we advance from the known to the unknown. The imagination, not the logical faculty, leads in this advance. In fact, practical observation is often in advance of logical exposition. Thus, in the discovery of truth, the imagination habitually presents hypotheses, and observation supplies facts, which it may require ages for the tardy reason to connect logically with the known. Of this truth, mathematics, as well as all other sciences, affords abundant illustrations. So remarkably true is this, that today it is seriously questioned by the majority of thinkers, whether the sublimest branch of mathematics,—the infinitesimal calculus—has anything more than an empirical foundation, mathematicians themselves not being agreed as to its logical basis. That the imagination, and not the logical faculty, leads in all original investigation, no one who has ever succeeded in producing an original demonstration of one of the simpler propositions of geometry, can have any doubt. Nor are induction, analogy, the scrutinization of premises or the search for them, or the balancing of probabilities, spheres of mental operations foreign to mathematics. No one, indeed, can claim preeminence for mathematical studies in all these departments of intellectual culture, but it may, perhaps, be claimed that scarcely any department of science affords discipline to so great a number of faculties, and that none presents so complete a gradation in the exercise of these faculties, from the first principles of the science to the farthest extent of its applications, as mathematics.
In 'Mathematics', in Henry Kiddle and Alexander J. Schem, The Cyclopedia of Education, (1877.) As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 27-29.
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It has been demonstrated that a species of penicillium produces in culture a very powerful antibacterial substance which affects different bacteria in different degrees. Generally speaking it may be said that the least sensitive bacteria are the Gram-negative bacilli, and the most susceptible are the pyogenic cocci ... In addition to its possible use in the treatment of bacterial infections penicillin is certainly useful... for its power of inhibiting unwanted microbes in bacterial cultures so that penicillin insensitive bacteria can readily be isolated.
'On the Antibacterial Action of Cultures of a Penicillium, with Special Reference to their Use in the Isolation of B. Influenzae', British Journal of Experimental Pathology, 1929, 10, 235-6.
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It has been just so in all my inventions. The first step is an intuition—and comes with a burst, then difficulties arise. This thing that gives out and then that—“Bugs” as such little faults and difficulties are called show themselves and months of anxious watching, study and labor are requisite before commercial success—or failure—is certainly reached.
Describing his invention of a storage battery that involved 10,296 experiments. Note Edison’s use of the term “Bug” in the engineering research field for a mechanical defect greatly predates the use of the term as applied by Admiral Grace Murray Hopper to a computing defect upon finding a moth in the electronic mainframe.] Letter to Theodore Puskas (18 Nov 1878). In The Yale Book of Quotations (2006), 226.
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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 often been said, and certainly not without justification, that the man of science is a poor philosopher. Why then should it not be the right thing for the physicist to let the philosopher do the philosophising? Such might indeed be the right thing to do a time when the physicist believes he has at his disposal a rigid system of fundamental laws which are so well that waves of doubt can't reach them; but it cannot be right at a time when the very foundations of physics itself have become problematic as they are now … when experience forces us to seek a newer and more solid foundation.
‘Physics and Reality’, Franklin Institute Journal (Mar 1936). Collected in Out of My Later Years (1950), 58.
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It is certainly true in the United States that there is an uneasiness about certain aspects of science, particularly evolution, because it conflicts, in some people’s minds, with their sense of how we all came to be. But you know, if you are a believer in God, it’s hard to imagine that God would somehow put this incontrovertible evidence in front of us about our relationship to other living organisms and expect us to disbelieve it. I mean, that doesn't make sense at all.
From video of interview with Huffington post reporter at the 2014 Davos Annual Meeting, World Economic Forum (25 Jan 2014). On web page 'Dr. Francis Collins: “There Is An Uneasiness” About Evolution'
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It is certainly true that all physical phenomena are subject to strictly mathematical conditions, and mathematical processes are unassailable in themselves. The trouble arises from the data employed. Most phenomena are so highly complex that one can never be quite sure that he is dealing with all the factors until the experiment proves it. So that experiment is rather the criterion of mathematical conclusions and must lead the way.
In Matter, Ether, Motion (1894), 89.
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It is certainly true that principles cannot be more securely founded than on experience and consciously clear thinking.
'The Goal' lecture at Princeton University (1939), quoted in Philipp Frank and George Rosen, Einstein (2002), 287.
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It is for such inquiries the modern naturalist collects his materials; it is for this that he still wants to add to the apparently boundless treasures of our national museums, and will never rest satisfied as long as the native country, the geographical distribution, and the amount of variation of any living thing remains imperfectly known. He looks upon every species of animal and plant now living as the individual letters which go to make up one of the volumes of our earth’s history; and, as a few lost letters may make a sentence unintelligible, so the extinction of the numerous forms of life which the progress of cultivation invariably entails will necessarily render obscure this invaluable record of the past. It is, therefore, an important object, which governments and scientific institutions should immediately take steps to secure, that in all tropical countries colonised by Europeans the most perfect collections possible in every branch of natural history should be made and deposited in national museums, where they may be available for study and interpretation. If this is not done, future ages will certainly look back upon us as a people so immersed in the pursuit of wealth as to be blind to higher considerations. They will charge us with having culpably allowed the destruction of some of those records of Creation which we had it in our power to preserve; and while professing to regard every living thing as the direct handiwork and best evidence of a Creator, yet, with a strange inconsistency, seeing many of them perish irrecoverably from the face of the earth, uncared for and unknown.
In 'On the Physical Geography of the Malay Archipelago', Journal of the Royal Geographical Society (1863), 33, 234.
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It is impossible to travel faster than light, and certainly not desirable, as one’s hat keeps blowing off.
Side Effects (1981), 36.
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It is inconceivable that anything should be existing. It is not inconceivable that a lot of people should also be existing who are not interested in the fact that they exist. But it is certainly very odd.
In The Decline and Fall of Science (1976), 2.
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It is usual to say that the two sources of experience are Observation and Experiment. When we merely note and record the phenomena which occur around us in the ordinary course of nature we are said to observe. When we change the course of nature by the intervention of our will and muscular powers, and thus produce unusual combinations and conditions of phenomena, we are said to experiment. [Sir John] Herschel has justly remarked that we might properly call these two modes of experience passive and active observation. In both cases we must certainly employ our senses to observe, and an experiment differs from a mere observation in the fact that we more or less influence the character of the events which we observe. Experiment is thus observation plus alteration of conditions.
Principles of Science: A Treatise on Logic and Scientific Method (1874, 2nd ed., 1913), 400.
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It makes me feel both proud and rather humble that it shall be called Lonsdaleite. Certainly the name seems appropriate since the mineral only occurs in very small quantities (perhaps rare would be too flattering) and it is generally rather mixed up!
From Letter to Clifford Frondel, who had named a meteoritic form of diamond after Lonsdale (a petite person). As quoted in Maureen M. Julian, 'Women in Crystallography', in G. Kass-Simon and P. Farnes (eds.), Women of Science: Righting the Record (1990), 356.
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It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation. So there are mere philologists, mere jurists, mere soldiers, mere merchants, etc. To such idle talk it might further be added: that whenever a certain exclusive occupation is coupled with specific shortcomings, it is likewise almost certainly divorced from certain other shortcomings.
In Gauss-Schumacher Briefwechsel, Bd. 4, (1862), 387.
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It may not always be profitable at first for businesses to be online, but it is certainly going to be unprofitable not to be online.
…...
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It must be conceded that a theory has an important advantage if its basic concepts and fundamental hypotheses are 'close to experience,' and greater confidence in such a theory is certainly justified. There is less danger of going completely astray, particularly since it takes so much less time and effort to disprove such theories by experience. Yet more and more, as the depth of our knowledge increases, we must give up this advantage in our quest for logical simplicity in the foundations of physical theory...
'On the Generalized Theory of Gravitation', Scientific American (Apr 1950), 13. In David H. Levy (Ed.), The Scientific American Book of the Cosmos (2000), 19.
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It must not be forgotten that although a high standard of morality gives a slight or no advantage to each individual man and his children over the other men of the same tribe, yet an advancement in the standard of morality will certainly give an immense advantage to one tribe over another.
…...
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It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained. … I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject.
In Presidential Address British Association for the Advancement of Science, Section A., (1890), Nature, 42, 466.
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Kurt Gödel’s achievement in modern logic is singular and monumental—indeed it is more than a monument, it is a landmark which will remain visible far in space and time. … The subject of logic has certainly completely changed its nature and possibilities with Gödel's achievement.
From remarks at the Presentation (Mar 1951) of the Albert Einstein Award to Dr. Gödel, as quoted in 'Tribute to Dr. Gödel', in Jack J. Bulloff, ‎Thomas C. Holyok (eds.), Foundations of Mathematics: Symposium Papers Commemorating the Sixtieth Birthday of Kurt Gödel (1969), ix. https://books.google.com/books?id=irZLAAAAMAAJ Kurt Gödel, ‎Jack J. Bulloff, ‎Thomas C. Holyoke - 1969 -
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Let us sum up the three possible explanations of the decision to drop the bomb and its timing. The first that it was a clever and highly successful move in the field of power politics, is almost certainly correct; the second, that the timing was coincidental, convicts the American government of a hardly credible tactlessness [towards the Soviet Union]; and the third, the Roman holiday theory [a spectacular event to justify the cost of the Manhattan Project], convicts them of an equally incredible irresponsibility.
In The Political and Military Consequences of Atomic Energy (1948), 126. As cited by Maurice W. Kirby and Jonathan Rosenhead, 'Patrick Blackett (1897)' in Arjang A. Assad (ed.) and Saul I. Gass (ed.),Profiles in Operations Research: Pioneers and Innovators (2011), 17. Blackett regarded the dropping of the atomic bombs on Japan as unnecessary because a Japanese surrender was inevitable.
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Man is not a machine, ... although man most certainly processes information, he does not necessarily process it in the way computers do. Computers and men are not species of the same genus. .... No other organism, and certainly no computer, can be made to confront genuine human problems in human terms. ... However much intelligence computers may attain, now or in the future, theirs must always be an intelligence alien to genuine human problems and concerns.
Computer Power and Human Reason: From Judgment to Calculation, (1976) 203 and 223. Also excerpted in Ronald Chrisley (ed.), Artificial Intelligence: Critical Concepts (2000), Vol. 3, 313 and 321. Note that the second ellipsis spans 8 pages.
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Many people are shrinking from the future and from participation in the movement toward a new, expanded reality. And, like homesick travelers abroad, they are focusing their anxieties on home. The reasons are not far to seek. We are at a turning point in human history. … We could turn our attention to the problems that going to the moon certainly will not solve … But I think this would be fatal to our future. … A society that no longer moves forward does not merely stagnate; it begins to die.
In 'Man On the Moon' (1969) collected in Margaret Mead and Robert B. Textor (ed.), The World Ahead: An Anthropologist Anticipates the Future (2005), 248. The original magazine article was written shortly before the first Moon landing for the lay public, in Redbook (Jun 1969). It was later reprinted in the Congressional Record—Senate (30 Jun 1969), 17725-17726.
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Mathematics … certainly would never have come into existence if mankind had known from the beginning that in all nature there is no perfectly straight line, no true circle, no standard of measurement.
From 'Of the First and Last Things', All Too Human: A Book For Free Spirits (1878, 1908), Part 1, section 11, 31.
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Mere numbers cannot bring out … the intimate essence of the experiment. This conviction comes naturally when one watches a subject at work. … What things can happen! What reflections, what remarks, what feelings, or, on the other hand, what blind automatism, what absence of ideas! … The experimenter judges what may be going on in [the subject’s] mind, and certainly feels difficulty in expressing all the oscillations of a thought in a simple, brutal number, which can have only a deceptive precision. How, in fact, could it sum up what would need several pages of description!
In La Suggestibilité (1900), 119-20.
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Most of the crackpot papers which are submitted to The Physical Review are rejected, not because it is impossible to understand them, but because it is possible. Those which are impossible to understand are usually published. When the great innovation appears, it will almost certainly be in a muddled, incomplete and confusing form. To the discoverer himself it will be only half-understood; to everybody else it will be a mystery. For any speculation which does not at first glance look crazy, there is no hope.
In 'Innovation in Physics', Scientific American (Sep 1958), 199. Collected in From Eros to Gaia (1993).
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My attitude was: “Just look at all the interesting atoms in that region of the periodic table; certainly the reason that carbon dominates chemistry is our own ignorance.”
Recollection of being unimpressed in high school when taught that carbon, being the basic building block of life, was the most important element in the periodic table. In Chappell Brown, 'A Carbon Copy of the Real Thing', Electronic Engineering Times (28 Dec 1998), 50.
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My view, the skeptical one, holds that we may be as far away from an understanding of elementary particles as Newton's successors were from quantum mechanics. Like them, we have two tremendous tasks ahead of us. One is to study and explore the mathematics of the existing theories. The existing quantum field-theories may or may not be correct, but they certainly conceal mathematical depths which will take the genius of an Euler or a Hamilton to plumb. Our second task is to press on with the exploration of the wide range of physical phenomena of which the existing theories take no account. This means pressing on with experiments in the fashionable area of particle physics. Outstanding among the areas of physics which have been left out of recent theories of elementary particles are gravitation and cosmology
In Scientific American (Sep 1958). As cited in '50, 100 & 150 years ago', Scientific American (Sep 2008), 299, No. 3, 14.
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Nature, the parent of all things, designed the human backbone to be like a keel or foundation. It is because we have a backbone that we can walk upright and stand erect. But this was not the only purpose for which Nature provided it; here, as elsewhere, she displayed great skill in turning the construction of a single member to a variety of different uses.
It Provides a Path for the Spinal Marrow, Yet is Flexible.
Firstly, she bored a hole through the posterior region of the bodies of all the vertebrae, thus fashioning a suitable pathway for the spinal marrow which would descend through them.
Secondly, she did not make the backbone out of one single bone with no joints. Such a unified construction would have afforded greater stability and a safer seat for the spinal marrow since, not having joints, the column could not have suffered dislocations, displacements, or distortions. If the Creator of the world had paid such attention to resistance to injury and had subordinated the value and importance of all other aims in the fabric of parts of the body to this one, he would certainly have made a single backbone with no joints, as when someone constructing an animal of wood or stone forms the backbone of one single and continuous component. Even if man were destined only to bend and straighten his back, it would not have been appropriate to construct the whole from one single bone. And in fact, since it was necessary that man, by virtue of his backbone, be able to perform a great variety of movements, it was better that it be constructed from many bones, even though as a result of this it was rendered more liable to injury.
From De Humani Corporis Fabrica Libri Septem: (1543), Book I, 57-58, as translated by William Frank Richardson, in 'Nature’s Skill in Creating a Backbone to Hold Us Erect', On The Fabric of the Human Body: Book I: The Bones and Cartilages (1998), 138.
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Richard M. Nixon quote: Because of what you have done, the heavens have become a part of
Neil and Buzz, I am talking to you by telephone from the Oval Office at the White House, and this certainly has to be the most historic telephone call ever made. Because of what you have done, the heavens have become a part of man’s world. As you talk to us from the Sea of Tranquility, it inspires us to redouble our efforts to bring peace and tranquility to Earth.
Speaking to the first astronauts while they were standing on the Moon (20 Jul 1969).
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No doubt, a scientist isn’t necessarily penalized for being a complex, versatile, eccentric individual with lots of extra-scientific interests. But it certainly doesn't help him a bit.
'The Historical Background to the Anti-Science Movement'. In Gordon Ethelbert Ward Wolstenholme, Civilization & Science in Conflict or Collaboration? (1972), 29.
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Nobody, certainly, will deny that the idea of the existence of an omnipotent, just, and omnibeneficent personal God is able to accord man solace, help, and guidance; also, by virtue of its simplicity it is accessible to the most undeveloped mind. But, on the other hand, there are decisive weaknesses attached to this idea in its elf, which have been painfully felt since the beginning of history. That is, if this being is omnipotent, then every occurrence, including every human action, every human thought, and every human feeling and aspiration is also His work; how is it possible to think of holding men responsible for their deeds and thoughts before such an almighty Being? In giving out punishment and rewards He would to a certain extent be passing judgment on Himself. How can this be combined with the goodness and righteousness ascribed to Him?
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Not only is science fiction an idea of tremendous import, but it is to be an important factor in making the world a better place to live in, through educating the public to the possibilities of science and the influence of science on life which, even today, are not appreciated byu the man on the street. ... If every man, woman, boy and girl, could be induced to read science fiction right along, there would certainly be a great resulting benefit to the community, in that the educational standards of its people would be raised tremendously. Science fiction would make people happier, give them a broader understanding of the world, make tham more tolerant.
Editorial, Science Fiction Week (1930). In Gary Westfahl, Hugo Gernsback and the Century of Science Fiction (2007), 166.
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Once it happened that all the other members of a man mutinied against the stomach, which they accused as the single, idle, uncontributing part in the entire body, while the rest were put to hardships and the expense of much labor to supply and minister to its appetites. However, the stomach merely ridiculed the fatuity of the members, who appeared not to be aware that the stomach certainly does receive the general nourishment, but only to return it again and distribute it amongst the rest.
Fable related by Menenius Agrippa to resolve a grievance of plebeians against the social hierarchy, described in 'Life of Coriolanus', collected in A.H. Clough (ed.), Plutarch’s Lives of Illustrious Men (1859, 1881), 155.
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One day we shall certainly 'reduce' thought experimentally to molecular and chemical motions in the brain; but does that exhaust the essence of thought?
Dialectics of Nature (1925), trans. Clemens Dutt (1940), 175.
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One of the most successful physicians I have ever known, has assured me, that he used more bread pills, drops of colored water, and powders of hickory ashes, than of all other medicines put together. It was certainly a pious fraud.
In letter to Caspar Wistar (21 Jun 1807), collected in Thomas Jefferson Randolph (ed.), Memoir, Correspondence, And Miscellanies, From The Papers Of Thomas Jefferson (1829), Vol. 4, 93.
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One thought [spectra are] marvellous, but it is not possible to make progress there. Just as if you have the wing of a butterfly then certainly it is very regular with the colors and so on, but nobody thought one could get the basis of biology from the coloring of the wing of a butterfly.
Quoted from Interviews (I, 7) in 'The Genesis of the Bohr Atom', J.L. Heilbron and T.S. Kuhn, Historical Studies in the Physical Sciences (1969), 257, reprinted in J. L. Heilbron, Historical Studies in the Theory of Atomic Structure (1981), 195.
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Our federal income tax law defines the tax y to be paid in terms of the income x; it does so in a clumsy enough way by pasting several linear functions together, each valid in another interval or bracket of income. An archaeologist who, five thousand years from now, shall unearth some of our income tax returns together with relics of engineering works and mathematical books, will probably date them a couple of centuries earlier, certainly before Galileo and Vieta.
From Address (1940), given at the Bicentennial Conference at the University of Pennsylvania, 'The Mathematical Way of Thinking'. Collected in Hermann Weyl and Peter Pesic (ed.), Levels of Infinity: Selected Writings on Mathematics and Philosophy (2012), 67.
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People have wracked their brains for an explanation of benzene and how the celebrated man [Kekulé] managed to come up with the concept of the benzene theory. With regard to the last point especially, a friend of mine who is a farmer and has a lively interest in chemistry has asked me a question which I would like to share with you. My “agricultural friend” apparently believes he has traced the origins of the benzene theory. “Has Kekulé,” so ran the question, “once been a bee-keeper? You certainly know that bees too build hexagons; they know well that they can store the greatest amount of honey that way with the least amount of wax. I always liked it,” my agricultural friend went on, “When I received a new issue of the Berichte; admittedly, I don't read the articles, but I like the pictures very much. The patterns of benzene, naphthalene and especially anthracene are indeed wonderful. When I look at the pictures I always have to think of the honeycombs of my bee hives.”
A. W. Hofmann, after-dinner speech at Kekulé Benzolfest (Mar 1890). Trans. in W. H. Brock, O. Theodor Benfrey and Susanne Stark, 'Hofmann's Benzene Tree at the Kekulé Festivities', Journal of Chemical Education (1991), 68, 888.
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People were pretty well spellbound by what Bohr said… While I was very much impressed by [him], his arguments were mainly of a qualitative nature, and I was not able to really pinpoint the facts behind them. What I wanted was statements which could be expressed in terms of equations, and Bohr's work very seldom provided such statements. I am really not sure how much later my work was influenced by these lectures of Bohr's... He certainly did not have a direct influence because he did not stimulate one to think of new equations.
Recalling the occasion in May 1925 (a year before receiving his Ph.D.) when he met Niels Bohr who was in Cambridge to give a talk on the fundamental difficulties of the quantum theory.
In History of Twentieth Century Physics (1977), 109. In A. Pais, 'Playing With Equations, the Dirac Way'. Behram N. Kursunoglu (Ed.) and Eugene Paul Wigner (Ed.), Paul Adrien Maurice Dirac: Reminiscences about a Great Physicist (1990), 94.
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Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. In our endeavour to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way of opening the case. If he is ingenious he may form some picture of a mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility or the meaning of such a comparison. But he certainly believes that, as his knowledge increases, his picture of reality will become simpler and simpler and will explain a wider and wider range of his sensuous impressions. He may also believe in the existence of the ideal limit of knowledge and that it is approached by the human mind. He may call this ideal limit the objective truth.
Albert Einstein and Leopold Infeld, The Evolution of Physics (1938), 33.
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Probably if half a kilogram [of radium] were in a bottle on that table it would kill us all. It would almost certainly destroy our sight and burn our skins to such an extent that we could not survive. The smallest bit placed on one’s arm would produce a blister which it would need months to heal.
As quoted in 'Radium', New York Times (22 Feb 1903), 6. Note that X-rays were discovered only a few years before, in 1895, radioactivity in 1896, and the electron in 1897. Full knowledge of the harmful radiation did not exist at the time. Nevertheless, Crookes’ remark, in the words of the reporter, “would seem to indicate that it [radium] emits something more than light. Heat and actinic energy must make up a large part of its radiation. It also emits electrons with [great] velocity…”
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Psychoanalysis is a science conducted by lunatics for lunatics. They are generally concerned with proving that people are irresponsible; and they certainly succeed in proving that some people are.
From Illustrated London News (23 Jun 1928). In Dale Ahlquist (ed.) The Universe According to G.K. Chesterton: A Dictionary of the Mad, Mundane and Metaphysical (2013), 93.
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Psychotherapy–the theory that the patient will probably get well anyhow, and is certainly a damn fool.
In A Mencken Chrestomathy (1949, 1956), 626.
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Quantum mechanics is certainly imposing. But an inner voice tells me that this is not yet the real thing. The theory says a lot, but does not bring us any closer to the secrets of the “Old One.” I, at any rate, am convinced that He is not playing at dice.
Letter to Max Born (4 Dec 1926). Collected in The Born-Einstein Letters: Correspondence between Albert Einstein and Max and Hedwig Born from 1916-1955 (1971), 91. Also seen as “God does not play dice [with the universe].”
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Science has hitherto been proceeding without the guidance of any rational theory of logic, and has certainly made good progress. It is like a computer who is pursuing some method of arithmetical approximation. Even if he occasionally makes mistakes in his ciphering, yet if the process is a good one they will rectify themselves. But then he would approximate much more rapidly if he did not commit these errors; and in my opinion, the time has come when science ought to be provided with a logic. My theory satisfies me; I can see no flaw in it. According to that theory universality, necessity, exactitude, in the absolute sense of these words, are unattainable by us, and do not exist in nature. There is an ideal law to which nature approximates; but to express it would require an endless series of modifications, like the decimals expressing surd. Only when you have asked a question in so crude a shape that continuity is not involved, is a perfectly true answer attainable.
Letter to G. F. Becker, 11 June 1893. Merrill Collection, Library of Congress. Quoted in Nathan Reingold, Science in Nineteenth-Century America: A Documentary History (1966), 231-2.
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Science is knowledge certain and evident in itself, or by the principles from which it is deducted, or with which it is certainly connected. It is subjective, as existing in the mind; objective, as embodied in truths; speculative, as leading to do something, as in practical science.
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Science is not gadgetry. The desirable adjuncts of modern living, although in many instances made possible by science, certainly do not constitute science. Basic scientific knowledge often (but not always) is a prerequisite to such developments, but technology primarily deserves the credit for having the financial courage, the ingenuity, and the driving energy to see to it that so-called ‘pure knowledge’ is in fact brought to the practical service of man. And it should also be recognized that those who have the urge to apply knowledge usefully have themselves often made significant contribution to pure knowledge and have even more often served as a stimulation to the activities of a pure researcher.
Warren Weaver (1894–1978), U.S. mathematician, scientist, educator. Science and Imagination, ch. 1, Basic Books (1967).
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So in regard to mental qualities, their transmission is manifest in our dogs, horses and other domestic animals. Besides special tastes and habits, general intelligence, courage, bad and good tempers. etc., are certainly transmitted.
The Descent of Man
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So, Fabricius, I already have this: that the most true path of the planet [Mars] is an ellipse, which Dürer also calls an oval, or certainly so close to an ellipse that the difference is insensible.
Letter to David Fabricius (11 Oct 1605). Johannes Kepler Gesammelte Werke (1937- ), Vol. 15, letter 358, l. 390-92, p. 249.
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The analogies between science and art are very good as long as you are talking about the creation and the performance. The creation is certainly very analogous. The aesthetic pleasure of the craftsmanship of performance is also very strong in science.
As quoted in Robert S. Root-Bernstein, Michele M. Root-Bernstein, Sparks of Genius: The Thirteen Thinking Tools of the World's Most Creative People (2013), 11.
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The automatic computing engine now being designed at N.P.L. [National Physics Laboratory] is atypical large scale electronic digital computing machine. In a single lecture it will not be possible to give much technical detail of this machine, and most of what I shall say will apply equally to any other machine of this type now being planned. From the point of view of the mathematician the property of being digital should be of greater interest than that of being electronic. That it is electronic is certainly important because these machines owe their high speed to this, and without the speed it is doubtful if financial support for their construction would be forthcoming. But this is virtually all that there is to be said on that subject. That the machine is digital however has more subtle significance. It means firstly that numbers are represented by sequences of digits which can be as long as one wishes. One can therefore work to any desired degree of accuracy. This accuracy is not obtained by more careful machining of parts, control of temperature variations, and such means, but by a slight increase in the amount of equipment in the machine.
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), 106.
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The chemical differences among various species and genera of animals and plants are certainly as significant for the history of their origins as the differences in form. If we could define clearly the differences in molecular constitution and functions of different kinds of organisms, there would be possible a more illuminating and deeper understanding of question of the evolutionary reactions of organisms than could ever be expected from morphological considerations.
'Uber das Vorkommen von Haemoglobin in den Muskeln der Mollusken und die Verbreitung desselben in den lebenden Organismen', Pflügers Archiv für die gesamte Physiologie des Menschen und der Tiere, 1871, 4, 318-9. Trans. Joseph S. Fruton, Proteins, Enzymes, Genes: The Interplay of Chemistry and Biology (1999), 270.
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The concepts of ‘soul’ or ‘life’ do not occur in atomic physics, and they could not, even indirectly, be derived as complicated consequences of some natural law. Their existence certainly does not indicate the presence of any fundamental substance other than energy, but it shows only the action of other kinds of forms which we cannot match with the mathematical forms of modern atomic physics ... If we want to describe living or mental processes, we shall have to broaden these structures. It may be that we shall have to introduce yet other concepts.
…...
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The construction of the universe is certainly very much easier to explain than is that of the plant.
Aphorism 4 in Notebook J (1789-1793), as translated by R. J. Hollingdale in Aphorisms (1990), 119. Reprinted as The Waste Books (2000), 128.
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The Designe of the Royall Society being the Improvement of Naturall knowledge all ways and meanes that tend thereunto ought to be made use of in the prosecution thereof. Naturall knowledge then being the thing sought for, we are to consider by what meanes it may soonest easiest and most certainly attaind. These meanes we shall the sooner find if we consider where tis to be had to wit in three places. first in bookes, 2dly in men. 3ly in the things themselves. and these three point us out the search of books. the converse & correspondence with men the Experimenting and Examining the things themselves under each of these there is a multitude of businesse to be done but the first hath the Least [and is] the most easily attained, the 2d hath a great Deal and requires much en[deavour] and Industry; and the 3d is infinite and the difficultest of all.
'Proposals for advancement of the R[oyal] S[ociety]' (c.1700), quoted in Michael Hunter, Establishing the New Science: The Experience of the Early Royal Society (1989), 232.
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The experience was more fulfilling than I could have ever imagined. I have a newfound sense of wonder seeing the Earth and stars from such an incredible perspective. Certainly, through my training I was prepared for the technical aspects, but I had no idea that I would be flooded with such amazement and joy after seeing my first sunrise and sunset from space.
…...
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The great mathematicians have acted on the principle “Divinez avant de demontrer”, and it is certainly true that almost all important discoveries are made in this fashion.
In 'The Present Problems in Geometry', Bulletin American Mathematical Society, 11, 285. [The French phrase has the sense of “Guess before proving”. —Webmaster]
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The late Alan Gregg pointed out that human population growth within the ecosystem was closely analogous to the growth of malignant tumor cells within an organism: that man was acting like a cancer on the biosphere. The multiplication of human numbers certainly seems wild and uncontrolled… Four million a month—the equivalent of the population of Chicago… We seem to be doing all right at the moment; but if you could ask cancer cells, I suspect they would think they were doing fine. But when the organism dies, so do they; and for our own, selfish, practical, utilitarian reasons, I think we should be careful about how we influence the rest of the ecosystem.
From Horace M. Albright Conservation Lectureship Berkeley, California (23 Apr 1962), 'The Human Environment', collected in Conservators of Hope: the Horace M. Albright Conservation Lectures (1988), 44.
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The main Business of Natural Philosophy is to argue from Phænomena without feigning Hypotheses, and to deduce Causes from Effects till we come to the very first Cause, which certainly is not mechanical; and not only to unfold the Mechanism of the World, but chiefly to resolve these, and to such like Questions.
From 'Query 31', Opticks (1704, 2nd ed., 1718), 344.
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The main thing that induces me to question the safeness of the vulgar methodus medendi in many cases is the consideration of the nature of those Helps they usually employ, and some of which are honoured with the title of Generous Remedies. These helps are Bleeding, Vomiting, Purging, Sweating, and Spitting, of which I briefly observe in General, that they are sure to weaken or discompose when they are imployed, but do not certainly cure afterwards.
RSMS 199, Folio 177v. Michael Hunter identfies as passages or a suppressed work, Considerations and Doubts Touching the Vulgar Method of Physick. Quoted In Barbara Kaplan (ed.), Divulging of Useful Truths in Physick: The Medical Agenda of Robert Boyle (1993), 138.
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The method of inquiry which all our ingenious Theorists of the Earth have pursued is certainly erroneous. They first form an hypothesis to solve the phenomena, but in fact the Phenomena are always used as a prop to the hypothesis.
Instead therefore of attempting to cut the gordian knot by Hypothetical analysis, we shall follow the synthetic method of inquiry and content ourselves with endeavouring to establish facts rather than attempt solutions and try by experiments how far that method may leave us thro' the mazes of this subject
Introduction to his lecture course. In Robert Jameson, edited by H. W. Scott, Lectures on Geology, (1966), 27. In Patrick Wyse Jackson, Four Centuries of Geological Travel (2007), 33.
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The mystery of life is certainly the most persistent problem ever placed before the thought of man. There is no doubt that from the time humanity began to think it has occupied itself with the problem of its origin and its future which undoubtedly is the problem of life. The inability of science to solve it is absolute. This would be truly frightening were it not for faith.
Address (10 Sep 1934) to the International Congress of Electro-Radio Biology, Venice. In Associated Press, 'Life a Closed Book, Declares Marconi', New York Times (11 Sep 1934), 15.
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The novelties in the fish line this week are two—brook trout and California salmon. … Long Island cultivated trout, alive, sell for $1.50 a pound; killed $1 a pound; trout from other portions of the state, 75 cents; wild trout from the Adirondacks, 50 cents; Canada trout 25 to 35 cents. … Certainly ten times as many trout are eaten in New-York as in former years. California salmon … brought 45 cents a pound. … This is rather a high price for California fish, but the catch is very light, caused by overfishing. (1879)
In 'Features of the Markets', New York Times (6 Apr 1879), 9.
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The other experiment (which I shall hardly, I confess, make again, because it was cruel) was with a dog, which, by means of a pair of bellows, wherewith I filled his lungs, and suffered them to empty again, I was able to preserve alive as long as I could desire, after I had wholly opened the thorax, and cut off all the ribs, and opened the belly. Nay, I kept him alive above an hour after I had cut off the pericardium and the mediastinum, and had handled and turned his lungs and heart and all the other parts of its body, as I pleased. My design was to make some enquiries into the nature of respiration. But though I made some considerable discovery of the necessity of fresh air, and the motion of the lungs for the continuance of the animal life, yet I could not make the least discovery in this of what I longed for, which was, to see, if I could by any means discover a passage of the air of the lungs into either the vessels or the heart; and I shall hardly be induced to make any further trials of this kind, because of the torture of this creature: but certainly the enquiry would be very noble, if we could any way find a way so to stupify the creature, as that it might not be sensible.
Letter from Robert Hooke to Robert Boyle (10 Nov 1664). In M. Hunter, A. Clericuzio and L. M. Principe (eds.), The Correspondence of Robert Boyle (2001), Vol. 2, 399.
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The outlook seems grim. Natural selection under civilized conditions may lead mankind to evolve towards a state of genetic overspecialization for living in gadget-ridden environments. It is certainly up to man to decide whether this direction of his evolution is or is not desirable. If it is not, man has, or soon will have, the knowledge requisite to redirect the evolution of his species pretty much as he sees fit. Perhaps we should not be too dogmatic about this choice of direction. We may be awfully soft compared to paleolithic men when it comes to struggling, unaided by gadgets, with climatic difficulties and wild beasts. Most of us feel most of the time that this is not a very great loss. If our remote descendants grow to be even more effete than we are, they may conceivably be compensated by acquiring genotypes conducive to kindlier dispositions and greater intellectual capacities than those prevalent in mankind today.
[Co-author with American statistician Gordon Allen.]
Theodosius Dobzhansky and Gordon Allen, 'Does Natural Selection Continue to Operate in Modern Mankind?', American Anthropologist, 1956, 58 599.
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The planned and orderly development and conservation of our natural resources is the first duty of the United States. It is the only form of insurance that will certainly protect us against disasters that lack of foresight has repeatedly brought down on nations since passed away.
In 'The Conservation of Natural Resources', The Outlook (12 Oct 1907), 87, 294.
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The powerful notion of entropy, which comes from a very special branch of physics … is certainly useful in the study of communication and quite helpful when applied in the theory of language.
From 'The Growth of Science and the Structure of Culture', Daedalus (Winter 1958), 87, No. 1, 67.
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The present lack of a definitely acceptable account of the origin of life should certainly not be taken as a stumbling block for the whole Darwinian world view.
In The Blind Watchmaker (1991), 166.
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The publication of the Darwin and Wallace papers in 1858, and still more that of the 'Origin' in 1859, had the effect upon them of the flash of light, which to a man who has lost himself in a dark night, suddenly reveals a road which, whether it takes him straight home or not, certainly goes his way. That which we were looking for, and could not find, was a hypothesis respecting the origin of known organic forms, which assumed the operation of no causes but such as could be proved to be actually at work. We wanted, not to pin our faith to that or any other speculation, but to get hold of clear and definite conceptions which could be brought face to face with facts and have their validity tested. The 'Origin' provided us with the working hypothesis we sought.
'On the Reception of the Origin of Species'. In F. Darwin (ed.), The Life and Letters of Charles Darwin, Including an Autobiographical Chapter (1888), Vol 2, 197.
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The results have exhibited one striking feature which has been frequently emphasized, namely that at high pressures all twelve liquids become more nearly like each other. This suggests that it might be useful in developing a theory of liquids to arbitrarily construct a 'perfect liquid' and to discuss its properties. Certainly the conception of a 'perfect gas' has been of great service in the kinetic theory of gases; and the reason is that all actual gases approximate closely to the 'perfect gas.' In the same way, at high pressures all liquids approximate to one and the same thing, which may be called by analogy the 'perfect liquid.' It seems to offer at least a promising line of attack to discuss the properties of this 'perfect liquid,' and then to invent the simplest possible mechanism to explain them.
'Thermodynamic Properties of Twelve Liquids Between 200 and 800 and up to 1200 KGM. Per Sq. Cm.', Memoirs of the American Academy of Arts and Sciences, 1913, 49, 113.
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The scientist who yields anything to theology, however slight, is yielding to ignorance and false pretenses, and as certainly as if he granted that a horse-hair put into a bottle of water will turn into a snake.
Minority Report (1956), 33.
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The stories of Whitney’s love for experimenting are legion. At one time he received a letter asking if insects could live in a vacuum. Whitney took the letter to one of the members of his staff and asked the man if he cared to run an experiment on the subject. The man replied that there was no point in it, since it was well established that life could not exist without a supply of oxygen. Whitney, who was an inveterate student of wild life, replied that on his farm he had seen turtles bury themselves in mud each fall, and, although the mud was covered with ice and snow for months, emerge again in the spring. The man exclaimed, “Oh, you mean hibernation!” Whitney answered, “I don’t know what I mean, but I want to know if bugs can live in a vacuum.”
He proceeded down the hall and broached the subject to another member of the staff. Faced with the same lack of enthusiasm for pursuing the matter further, Whitney tried another illustration. “I’ve been told that you can freeze a goldfish solidly in a cake of ice, where he certainly can’t get much oxygen, and can keep him there for a month or two. But if you thaw him out carefully he seems none the worse for his experience.” The second scientist replied, “Oh, you mean suspended animation.” Whitney once again explained that his interest was not in the terms but in finding an answer to the question.
Finally Whitney returned to his own laboratory and set to work. He placed a fly and a cockroach in a bell jar and removed the air. The two insects promptly keeled over. After approximately two hours, however, when he gradually admitted air again, the cockroach waved its feelers and staggered to its feet. Before long, both the cockroach and the fly were back in action.
'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 357-358.
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The theory of numbers is particularly liable to the accusation that some of its problems are the wrong sort of questions to ask. I do not myself think the danger is serious; either a reasonable amount of concentration leads to new ideas or methods of obvious interest, or else one just leaves the problem alone. “Perfect numbers” certainly never did any good, but then they never did any particular harm.
In A Mathematician’s Miscellany (1953). Reissued as Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 74.
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The word, “Vitamine,” served as a catchword which meant something even to the uninitiated, and it was not by mere accident that just at that time, research developed so markedly in this direction. Our view as to the fortunate choice of this name is strengthened, on the one hand, because it has become popular (and a badly chosen catchword, like a folksong without feeling, can never become popular), and on the other, because of the untiring efforts of other workers to introduce a varied nomenclature, for example, “accessory food factors, food hormones, water-soluble B and fat-soluble A, nutramine, and auximone” (for plants). Some of these designations are certainly not better, while others are much worse than “Vitamine.”
The Vitamines translated by Harry Ennis Dubin (1922), 18.
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The world is a construct of our sensations, perceptions, memories. It is convenient to regard it as existing objectively on its own. But it certainly does not become manifest by its mere existence.
Opening remark in first Tarner Lecture, at Trinity College, Cambridge (Oct 1956), 'The Physical Basis of Consciousness', printed in Mind and Matter (1958), 1. Also collected in What is Life?: With Mind and Matter and Autobiographical Sketches (1992, 2012).
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The world is full of signals that we don’t perceive. Tiny creatures live in a different world of unfamiliar forces. Many animals of our scale greatly exceed our range of perception for sensations familiar to us ... What an imperceptive lot we are. Surrounded by so much, so fascinating and so real, that we do not see (hear, smell, touch, taste) in nature, yet so gullible and so seduced by claims for novel power that we mistake the tricks of mediocre magicians for glimpses of a psychic world beyond our ken. The paranormal may be a fantasy; it is certainly a haven for charlatans. But ‘parahuman’ powers of perception lie all about us in birds, bees, and bacteria.
…...
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There are many points in the history of an invention which the inventor himself is apt to overlook as trifling, but in which posterity never fail to take a deep interest. The progress of the human mind is never traced with such a lively interest as through the steps by which it perfects a great invention; and there is certainly no invention respecting which this minute information will be more eagerly sought after, than in the case of the steam-engine.
Quoted in The Origin and Progress of the Mechanical Inventions of James Watt (1854), Vol.1, 4.
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There is certainly no absolute standard of beauty. That precisely is what makes its pursuit so interesting.
In 'For Public and Potent Building', The New York Times Magazine (9 Oct 1960), M34.
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There once was a brainy baboon,
Who always breathed down a bassoon,
For he said, “It appears
That in billions of years
I shall certainly hit on a tune”.
New Pathways in Science (1935), 62.
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There’s very good news from the asteroids. It appears that a large fraction of them, including the big ones, are actually very rich in H2O. Nobody imagined that. They thought they were just big rocks … It’s easier to get to an asteroid than to Mars, because the gravity is lower and landing is easier. Certainly the asteroids are much more practical, right now. If we start space colonies in, say, the next 20 years, I would put my money on the asteroids.
As quoted in Kenneth Brower, 'The Danger of Cosmic Genius', The Atlantic (Dec 2010).
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Those who have taken upon them to lay down the law of nature as a thing already searched out and understood, whether they have spoken in simple assurance or professional affectation, have therein done philosophy and the sciences great injury. For as they have been successful in inducing belief, so they have been effective in quenching and stopping inquiry; and have done more harm by spoiling and putting an end to other men's efforts than good by their own. Those on the other hand who have taken a contrary course, and asserted that absolutely nothing can be known — whether it were from hatred of the ancient sophists, or from uncertainty and fluctuation of mind, or even from a kind of fullness of learning, that they fell upon this opinion — have certainly advanced reasons for it that are not to be despised; but yet they have neither started from true principles nor rested in the just conclusion, zeal and affectation having carried them much too far...
Now my method, though hard to practice, is easy to explain; and it is this. I propose to establish progressive stages of certainty. The evidence of the sense, helped and guarded by a certain process of correction, I retain. But the mental operation which follows the act of sense I for the most part reject; and instead of it I open and lay out a new and certain path for the mind to proceed in, starting directly from the simple sensuous perception.
Novum Organum (1620)
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To be creative, scientists need libraries and laboratories and the company of other scientists; certainly a quiet and untroubled life is a help. A scientist's work is in no way deepened or made more cogent by privation, anxiety, distress, or emotional harassment. To be sure, the private lives of scientists may be strangely and even comically mixed up, but not in ways that have any special bearing on the nature and quality of their work. If a scientist were to cut off an ear, no one would interpret such an action as evidence of an unhappy torment of creativity; nor will a scientist be excused any bizarrerie, however extravagant, on the grounds that he is a scientist, however brilliant.
In Advice to a Young Scientist (1979), 40.
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To cross the seas, to traverse the roads, and to work machinery by galvanism, or rather electro-magnetism, will certainly, if executed, be the most noble achievement ever performed by man.
In Elements of Electro-Metallurgy: or The Art of Working in Metals by the Galvanic Fluid (1841), 147.
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To day we made the grand experiment of burning the diamond and certainly the phenomena presented were extremely beautiful and interesting… The Duke’s burning glass was the instrument used to apply heat to the diamond. It consists of two double convex lenses … The instrument was placed in an upper room of the museum and having arranged it at the window the diamond was placed in the focus and anxiously watched. The heat was thus continued for 3/4 of an hour (it being necessary to cool the globe at times) and during that time it was thought that the diamond was slowly diminishing and becoming opaque … On a sudden Sir H Davy observed the diamond to burn visibly, and when removed from the focus it was found to be in a state of active and rapid combustion. The diamond glowed brilliantly with a scarlet light, inclining to purple and, when placed in the dark, continued to burn for about four minutes. After cooling the glass heat was again applied to the diamond and it burned again though not for nearly so long as before. This was repeated twice more and soon after the diamond became all consumed. This phenomenon of actual and vivid combustion, which has never been observed before, was attributed by Sir H Davy to be the free access of air; it became more dull as carbonic acid gas formed and did not last so long.
Entry (Florence, 27 Mar 1814) in his foreign journal kept whilst on a continental tour with Sir Humphry Davy. In Michael Faraday, Bence Jones (ed.), The Life and Letters of Faraday (1870), Vol. 1, 119. Silvanus Phillips Thompson identifies the Duke as the Grand Duke of Tuscany, in Michael Faraday, His Life and Work (1901), 21.
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To emphasize this opinion that mathematicians would be unwise to accept practical issues as the sole guide or the chief guide in the current of their investigations, ... let me take one more instance, by choosing a subject in which the purely mathematical interest is deemed supreme, the theory of functions of a complex variable. That at least is a theory in pure mathematics, initiated in that region, and developed in that region; it is built up in scores of papers, and its plan certainly has not been, and is not now, dominated or guided by considerations of applicability to natural phenomena. Yet what has turned out to be its relation to practical issues? The investigations of Lagrange and others upon the construction of maps appear as a portion of the general property of conformal representation; which is merely the general geometrical method of regarding functional relations in that theory. Again, the interesting and important investigations upon discontinuous two-dimensional fluid motion in hydrodynamics, made in the last twenty years, can all be, and now are all, I believe, deduced from similar considerations by interpreting functional relations between complex variables. In the dynamics of a rotating heavy body, the only substantial extension of our knowledge since the time of Lagrange has accrued from associating the general properties of functions with the discussion of the equations of motion. Further, under the title of conjugate functions, the theory has been applied to various questions in electrostatics, particularly in connection with condensers and electrometers. And, lastly, in the domain of physical astronomy, some of the most conspicuous advances made in the last few years have been achieved by introducing into the discussion the ideas, the principles, the methods, and the results of the theory of functions. … the refined and extremely difficult work of Poincare and others in physical astronomy has been possible only by the use of the most elaborate developments of some purely mathematical subjects, developments which were made without a thought of such applications.
In Presidential Address British Association for the Advancement of Science, Section A, (1897), Nature, 56, 377.
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To me there never has been a higher source of earthly honour or distinction than that connected with advances in science. I have not possessed enough of the eagle in my character to make a direct flight to the loftiest altitudes in the social world; and I certainly never endeavored to reach those heights by using the creeping powers of the reptile, who, in ascending, generally chooses the dirtiest path, because it is the easiest.
In Maturin Murray Ballou, Treasury of Thought (1894), 459.
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To me there never has been a higher source of honour or distinction than that connected with advances in science. I have not possessed enough of the eagle in my character to make a direct flight to the loftiest altitudes in the social world; and I certainly never endeavored to reach those heights by using the creeping powers of the reptile, who in ascending, generally chooses the dirtiest path, because it is the easiest.
Consolations in Travel (1830), Dialogue 5, The Chemical Philosopher, 225.
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To suppose that the eye, with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest possible degree. When it was first said that the sun stood still and the world turned round, the common sense of mankind declared the doctrine false; but the old saying of Vox populi, vox Dei, as every philosopher knows, cannot be trusted in science. Reason tells me, that if numerous gradations from a perfect and complex eye to one very imperfect and simple, each grade being useful to its possessor, can be shown to exist; if further, the eye does vary ever so slightly, and the variations be inherited, which is certainly the case; and if any variation or modification in the organ be ever useful to an animal under changing conditions of life, then the difficulty of believing that a perfect and complex eye could be formed by natural selection, though insuperable by our imagination, can hardly be considered real.
On The Origin of Species by Means of Natural Selection (1859, 1882), 143-144.
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To teach doubt and Experiment Certainly was not what Christ meant.
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True, no one can absolutely control the direction of his life; but each person can certainly influence it. The armchair explorers who complain that they never got their “one lucky shot” were never really infected by the incurable drive to explore. Those who have the bug—go.
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 32.
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Truth, like Gold, is not the less so, for being newly brought out of the Mine. ’Tis Trial and Examination must give it price, and not any antick Fashion: And though it be not yet current by the publick stamp; yet it may, for all that, be as old as Nature, and is certainly not the less genuine.
In 'The Epistle Dedicatory', Essay Concerning Human Understanding (1690), second unnumbered page.
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Very few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languages of the world than to master all mathematics at present known. The languages could, I imagine, be learnt in a lifetime; mathematics certainly could not. Nor is the subject static.
In 'The Extent of Mathematics', Prelude to Mathematics (1955), 11.
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Very few people, including authors willing to commit to paper, ever really read primary sources–certainly not in necessary depth and contemplation, and often not at all ... When writers close themselves off to the documents of scholarship, and then rely only on seeing or asking, they become conduits and sieves rather than thinkers. When, on the other hand, you study the great works of predecessors engaged in the same struggle, you enter a dialogue with human history and the rich variety of our own intellectual traditions. You insert yourself, and your own organizing powers, into this history–and you become an active agent, not merely a ‘reporter.’
…...
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We are going to die, and that makes us the lucky ones. Most people are never going to die because they are never going to be born. The potential people who could have been here in my place but who will in fact never see the light of day outnumber the sand grains of Arabia. Certainly those unborn ghosts include greater poets than Keats, scientists greater than Newton. We know this because the set of possible people allowed by our DNA so massively outnumbers the set of actual people. In the teeth of these stupefying odds it is you and I, in our ordinariness, that are here.
Unweaving the Rainbow (1998), 1.
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We know that there is an infinite, and we know not its nature. As we know it to be false that numbers are finite, it is therefore true that there is a numerical infinity. But we know not of what kind; it is untrue that it is even, untrue that it is odd; for the addition of a unit does not change its nature; yet it is a number, and every number is odd or even (this certainly holds of every finite number). Thus we may quite well know that there is a God without knowing what He is.
Pensées (1670), Section 1, aphorism 223. In H. F. Stewart (ed.), Pascal's Pensées (1950), 117.
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What is mathematics? What is it for? What are mathematicians doing nowadays? Wasn't it all finished long ago? How many new numbers can you invent anyway? Is today’s mathematics just a matter of huge calculations, with the mathematician as a kind of zookeeper, making sure the precious computers are fed and watered? If it’s not, what is it other than the incomprehensible outpourings of superpowered brainboxes with their heads in the clouds and their feet dangling from the lofty balconies of their ivory towers?
Mathematics is all of these, and none. Mostly, it’s just different. It’s not what you expect it to be, you turn your back for a moment and it's changed. It's certainly not just a fixed body of knowledge, its growth is not confined to inventing new numbers, and its hidden tendrils pervade every aspect of modern life.
Opening paragraphs of 'Preface', From Here to Infinity (1996), vii.
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What of the future of this adventure? What will happen ultimately? We are going along guessing the laws; how many laws are we going to have to guess? I do not know. Some of my colleagues say that this fundamental aspect of our science will go on; but I think there will certainly not be perpetual novelty, say for a thousand years. This thing cannot keep on going so that we are always going to discover more and more new laws … It is like the discovery of America—you only discover it once. The age in which we live is the age in which we are discovering the fundamental laws of nature, and that day will never come again. Of course in the future there will be other interests … but there will not be the same things that we are doing now … There will be a degeneration of ideas, just like the degeneration that great explorers feel is occurring when tourists begin moving in on a territory.
In The Character of Physical Law (1965, 1994), 166.
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What opposite discoveries we have seen!
(Signs of true genius, and of empty pockets.)
One makes new noses, one a guillotine,
One breaks your bones, one sets them in their sockets;
But vaccination certainly has been
A kind antithesis to Congreve's rockets, ...
Don Juan (1819, 1858), Canto I, CCXXIX, 35. Referring to Edward Jenner's work on vaccination (started 14 May 1796), later applied by Napoleon who caused his soldiers to be vaccinated. Sir William Congreve's shells, invented in 1804, proved very effective at the battle of Leipzig (1813).
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What to-day is to be believed is to-morrow to be cast aside, certainly has been the law of advancement, and seemingly must continue to be so. With what a babel of discordant voices does it [medicine] celebrate its two thousand years of experience!
…...
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When autumn returns with its long anticipated holidays, and preparations are made for a scamper in some distant locality, hammer and notebook will not occupy much room in the portmanteau, and will certainly be found most entertaining company.
In The Story of a Boulder: or, Gleanings from the Note-book of a Field Geologist (1858), viii.
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Where we reach the sphere of mathematics we are among processes which seem to some the most inhuman of all human activities and the most remote from poetry. Yet it is just here that the artist has the fullest scope for his imagination. … We are in the imaginative sphere of art, and the mathematician is engaged in a work of creation which resembles music in its orderliness, … It is not surprising that the greatest mathematicians have again and again appealed to the arts in order to find some analogy to their own work. They have indeed found it in the most varied arts, in poetry, in painting, and in sculpture, although it would certainly seem that it is in music, the most abstract of all the arts, the art of number and time, that we find the closest analogy.
In The Dance of Life (1923), 138-139.
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While DNA could be claimed to be both simple and elegant, it must be remembered that DNA almost certainly originated fairly close to the origin of life when things were necessarily simple or they would not have got going.
In What Mad Pursuit: A Personal View of Scientific Discovery (1988), 138.
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Why then be concerned about the conservation of wildlife when for all practical purposes we would be much better off if humans and their domestic animals and pets were the only living creatures on the face of the earth? There is no obvious and demolishing answer to this rather doubtful logic although in practice the destruction of all wild animals would certainly bring devastating changes to our existence on this planet as we know it today… The trouble is that everything in nature is completely interdependent. Tinker with one part of it and the repercussions ripple out in all directions… Wildlife—and that includes everything from microbes to blue whales and from a fungus to a redwood tree—has been so much part of life on the earth that we are inclined to take its continued existence for granted… Yet the wildlife of the world is disappearing, not because of a malicious and deliberate policy of slaughter and extermination, but simply because of a general and widespread ignorance and neglect.
World Wildlife Fund Dinner, York, (1969). As quoted and cited in 'The Mirror of a Duke', The Dorset Eye on dorseteye.com website
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With crystals we are in a situation similar to an attempt to investigate an optical grating merely from the spectra it produces... But a knowledge of the positions and intensities of the spectra does not suffice for the determination of the structure. The phases with which the diffracted waves vibrate relative to one another enter in an essential way. To determine a crystal structure on the atomic scale, one must know the phase differences between the different interference spots on the photographic plate, and this task may certainly prove to be rather difficult.
Physikalische Zeitschrift (1913), 14. Translated in Walter Moore, Schrödinger. Life and Thought (1989), 73.
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Yet man does recognise himself [as an animal]. But I ask you and the whole world for a generic differentia between man and ape which conforms to the principles of natural history, I certainly know of none... If I were to call man ape or vice versa, I should bring down all the theologians on my head. But perhaps I should still do it according to the rules of science.
Letter to Johann Gmelon (14 Jan 1747), quoted in Mary Gribbin, Flower Hunters (2008), 56.
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You can certainly destroy enough of humanity so that only the greatest act of faith can persuade you that what’s left will be human.
…...
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You have read my writings, and from them you have certainly understood which was the true and real motive that caused, under the lying mask of religion, this war against me that continually restrains and undercuts me in all directions, so that neither can help come to me from outside nor can I go forth to defend myself, there having been issued an express order to all Inquisitors that they should not allow any of my works to be reprinted which had been printed many years ago or grant permission to any new work that I would print. … a most rigorous and general order, I say, against all my works, omnia et edenda; so that it is left to me only to succumb in silence under the flood of attacks, exposures, derision, and insult coming from all sides.
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You have read my writings, and from them you have certainly understood which was the true and real motive that caused, under the lying mask of religion, this war against me that continually restrains and undercuts me in all directions, so that neither can help come to me from outside nor can I go forth to defend myself, there having been issued an express order to all Inquisitors that they should not allow any of my works to be reprinted which had been printed many years ago or grant permission to any new work that I would print. … a most rigorous and general order, I say, against all my works, omnia et edenda; so that it is left to me only to succumb in silence under the flood of attacks, exposures, derision, and insult coming from all sides.
In Letter to Nicolas-Claude Fabri de Peiresc (16 Mar 1635). As quoted in translation in Giorgio de Santillana, The Crime of Galileo (1976), 324, with footnote that “he had known about the reserved orders to the provincial Inquisitors from Micanzio in Venice. On September 8, 1633, the Pope had further reprimanded the Inquisitor of Florence for giving permission to reprint some past works.”
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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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