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Who said: “Science without religion is lame; religion without science is blind.”
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Degree Quotes (82 quotes)

Je me rends parfaitement compte du desagreable effet que produit sur la majorite de l'humanité, tout ce qui se rapporte, même au plus faible dègré, á des calculs ou raisonnements mathematiques.
I am well aware of the disagreeable effect produced on the majority of humanity, by whatever relates, even at the slightest degree to calculations or mathematical reasonings.
From 'French Reply to Baron Czyllak' concerning the game at Monte Carlo, Monte Carlo Facts and Fallacies (1904), 290, originally published in L'Écho de la Mediterranée as a response to an earlier open letter by the Baron in the same magazine. Maxim defended his prior mathematical calculations about gambling games. At the end of his paper giving a cautionary mathematical analysis of 'The Gambler's Ruin', < a href="http://todayinsci.com/C/Coolidge_Julian/CoolidgeJulian-Quotations.htm">Julian Coolidge referenced this quotation, saying “it gives the best explanation which I have seen for the fact that the people continue to gamble.”
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Question: On freezing water in a glass tube, the tube sometimes breaks. Why is this? An iceberg floats with 1,000,000 tons of ice above the water line. About how many tons are below the water line?
Answer: The water breaks the tube because of capallarity. The iceberg floats on the top because it is lighter, hence no tons are below the water line. Another reason is that an iceberg cannot exceed 1,000,000 tons in weight: hence if this much is above water, none is below. Ice is exceptional to all other bodies except bismuth. All other bodies have 1090 feet below the surface and 2 feet extra for every degree centigrade. If it were not for this, all fish would die, and the earth be held in an iron grip.
P.S.—When I say 1090 feet, I mean 1090 feet per second.
Genuine student answer* to an Acoustics, Light and Heat paper (1880), Science and Art Department, South Kensington, London, collected by Prof. Oliver Lodge. Quoted in Henry B. Wheatley, Literary Blunders (1893), 179-80, Question 13. (*From a collection in which Answers are not given verbatim et literatim, and some instances may combine several students' blunders.)
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A graduate with a science degree asks: 'Why does it work?'
A graduate with an engineering degree asks: 'How does it work?'
A graduate with an accounting degree asks: 'How much will it cost?'
A graduate with an arts degree asks: 'Do you want fries with that?'
Anonymous
In Geoff Tibballs, The Mammoth Book of Humor (2000), 83.
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A great department of thought must have its own inner life, however transcendent may be the importance of its relations to the outside. No department of science, least of all one requiring so high a degree of mental concentration as Mathematics, can be developed entirely, or even mainly, with a view to applications outside its own range. The increased complexity and specialisation of all branches of knowledge makes it true in the present, however it may have been in former times, that important advances in such a department as Mathematics can be expected only from men who are interested in the subject for its own sake, and who, whilst keeping an open mind for suggestions from outside, allow their thought to range freely in those lines of advance which are indicated by the present state of their subject, untrammelled by any preoccupation as to applications to other departments of science. Even with a view to applications, if Mathematics is to be adequately equipped for the purpose of coping with the intricate problems which will be presented to it in the future by Physics, Chemistry and other branches of physical science, many of these problems probably of a character which we cannot at present forecast, it is essential that Mathematics should be allowed to develop freely on its own lines.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 286.
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A habit of basing convictions upon evidence, and of giving to them only that degree or certainty which the evidence warrants, would, if it became general, cure most of the ills from which the world suffers.
In Bertrand Russell and Paul Edwards (ed.), 'Preface', Why I Am Not a Christian: And Other Essays on Religion and Related Subjects (1957), vi.
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All that passes for knowledge can be arranged in a hierarchy of degrees of certainty, with arithmetic and the facts of perception at the top.
From 'Philosophy For Laymen', collected in Unpopular Essays (1950, 1996), 39.
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Archimedes … had stated that given the force, any given weight might be moved, and even boasted, we are told, relying on the strength of demonstration, that if there were another earth, by going into it he could remove this. Hiero being struck with amazement at this, and entreating him to make good this problem by actual experiment, and show some great weight moved by a small engine, he fixed accordingly upon a ship of burden out of the king’s arsenal, which could not be drawn out of the dock without great labor and many men; and, loading her with many passengers and a full freight, sitting himself the while far off with no great endeavor, but only holding the head of the pulley in his hand and drawing the cords by degrees, he drew the ship in a straight line, as smoothly and evenly, as if she had been in the sea. The king, astonished at this, and convinced of the power of the art, prevailed upon Archimedes to make him engines accommodated to all the purposes, offensive and defensive, of a siege. … the apparatus was, in most opportune time, ready at hand for the Syracusans, and with it also the engineer himself.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries—not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer. For my part I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conception only as cultural posits. The myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience.
From A Logical Point of View (1953), 44. [Note: “qua” means “in the character or role of,” thus “qua lay physicist” means “in the role of lay physicist,” or perhaps even (?) “putting on my lay physicist hat.” —Webmaster]
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At the planet’s very heart lies a solid rocky core, at least five times larger than Earth, seething with the appalling heat generated by the inexorable contraction of the stupendous mass of material pressing down to its centre. For more than four billion years Jupiter’s immense gravitational power has been squeezing the planet slowly, relentlessly, steadily, converting gravitational energy into heat, raising the temperature of that rocky core to thirty thousand degrees, spawning the heat flow that warms the planet from within. That hot, rocky core is the original protoplanet seed from the solar system’s primeval time, the nucleus around which those awesome layers of hydrogen and helium and ammonia, methane, sulphur compounds and water have wrapped themselves.
Ben Bova
Jupiter
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By the death of Mr. O. Chanute the world has lost one whose labors had to an unusual degree influenced the course of human progress. If he had not lived the entire history of progress in flying would have been other than it has been.
Writing in Aeronautics in Jan 1911 about Chanute's death, collected in Wilbur Wright and Orville Wright, The Papers of Wilbur and Orville Wright: Volume Two 1906-1948 (1953), 1013.
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Chemistry is the science or study of those effects and qualities of matter which are discovered by mixing bodies variously together, or applying them to one another with a view to mixture, and by exposing them to different degrees of heat, alone, or in mixture with one another, in order to enlarge our knowledge of nature, and to promote the useful arts.
From the first of a series of lectures on chemistry, collected in John Robison (ed.), Lectures on the Elements of Chemistry: Delivered in the University of Edinburgh (1807), Vol. 1, 11.
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Common sense in an uncommon degree is what the world calls wisdom.
In 'Hacket’s Life of Lord Keeper Williams', notes published in Henry Nelson Coleridge (ed.), The Literary Remains of Samuel Taylor Coleridge (1838), Vol. 3, 186.
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Consider the plight of a scientist of my age. I graduated from the University of California at Berkeley in 1940. In the 41 years since then the amount of biological information has increased 16 fold; during these 4 decades my capacity to absorb new information has declined at an accelerating rate and now is at least 50% less than when I was a graduate student. If one defines ignorance as the ratio of what is available to be known to what is known, there seems no alternative to the conclusion that my ignorance is at least 25 times as extensive as it was when I got my bachelor’s degree. Although I am sure that my unfortunate condition comes as no surprise to my students and younger colleagues, I personally find it somewhat depressing. My depression is tempered, however, by the fact that all biologists, young or old, developing or senescing, face the same melancholy situation because of an interlocking set of circumstances.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 228.
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Daniel Bernoulli used to tell two little adventures, which he said had given him more pleasure than all the other honours he had received. Travelling with a learned stranger, who, being pleased with his conversation, asked his name; “I am Daniel Bernoulli,” answered he with great modesty; “and I,” said the stranger (who thought he meant to laugh at him) “am Isaac Newton.” Another time, having to dine with the celebrated Koenig, the mathematician, who boasted, with some degree of self-complacency, of a difficult problem he had solved with much trouble, Bernoulli went on doing the honours of his table, and when they went to drink coffee he presented Koenig with a solution of the problem more elegant than his own.
In A Philosophical and Mathematical Dictionary (1815), 1, 226.
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Degree is much: the whole Atlantic might be lukewarm and never boil us a potato.
From chapter 'Jottings from a Note-book', in Canadian Stories (1918), 167.
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Embryology will often reveal to us the structure, in some degree obscured, of the prototype of each great class.
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Everybody can be great. Because anybody can serve. You don’t have to have a college degree to serve … You only need a heart full of grace. A soul generated by love.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 253
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I do not maintain that the chief value of the study of arithmetic consists in the lessons of morality that arise from this study. I claim only that, to be impressed from day to day, that there is something that is right as an answer to the questions with which one is able to grapple, and that there is a wrong answer—that there are ways in which the right answer can be established as right, that these ways automatically reject error and slovenliness, and that the learner is able himself to manipulate these ways and to arrive at the establishment of the true as opposed to the untrue, this relentless hewing to the line and stopping at the line, must color distinctly the thought life of the pupil with more than a tinge of morality. … To be neighborly with truth, to feel one’s self somewhat facile in ways of recognizing and establishing what is right, what is correct, to find the wrong persistently and unfailingly rejected as of no value, to feel that one can apply these ways for himself, that one can think and work independently, have a real, a positive, and a purifying effect upon moral character. They are the quiet, steady undertones of the work that always appeal to the learner for the sanction of his best judgment, and these are the really significant matters in school work. It is not the noise and bluster, not even the dramatics or the polemics from the teacher’s desk, that abide longest and leave the deepest and stablest imprint upon character. It is these still, small voices that speak unmistakably for the right and against the wrong and the erroneous that really form human character. When the school subjects are arranged on the basis of the degree to which they contribute to the moral upbuilding of human character good arithmetic will be well up the list.
In Arithmetic in Public Education (1909), 18. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 69.
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I read … that the celebrated Amontons, using a thermometer of his own invention, had discovered that water boils at a fixed degree of heat. I was at once inflamed with a great desire to make for myself a thermometer of the same sort, so that I might with my own eyes perceive this beautiful phenomenon of nature.
From 'Experimenta circa gradum caloris liquorum nonnullorum ebullientium instituta', Philosophical Transactions (1724), 33, 1, as translated in William Francis Magie, A Source Book in Physics (1935), 131.
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I refrained from writing another one, thinking to myself: Never mind, I will prove that I am able to become a greater scientist than some of you, even without the title of doctor.
Reaction when his thesis (1922) on rocket experiments was rejected as too cursory. In Astronautics (1959), 4, No. 6, 103.
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I studied for my degree in Calcium Anthropology: the study of milkmen.
Anonymous
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I will try to account for the degree of my aesthetic emotion. That, I conceive, is the function of the critic.
In Art (1913), 169.
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In destroying the predisposition to anger, science of all kind is useful; but the mathematics possess this property in the most eminent degree.
Quoted in Day, Collacon (no date).
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In order to comprehend and fully control arithmetical concepts and methods of proof, a high degree of abstraction is necessary, and this condition has at times been charged against arithmetic as a fault. I am of the opinion that all other fields of knowledge require at least an equally high degree of abstraction as mathematics,—provided, that in these fields the foundations are also everywhere examined with the rigour and completeness which is actually necessary.
In 'Die Theorie der algebraischen Zahlkorper', Vorwort, Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 4.
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In other branches of science, where quick publication seems to be so much desired, there may possibly be some excuse for giving to the world slovenly or ill-digested work, but there is no such excuse in mathematics. The form ought to be as perfect as the substance, and the demonstrations as rigorous as those of Euclid. The mathematician has to deal with the most exact facts of Nature, and he should spare no effort to render his interpretation worthy of his subject, and to give to his work its highest degree of perfection. “Pauca sed matura” was Gauss’s motto.
In Presidential Address British Association for the Advancement of Science, Section A, (1890), Nature, 42, 467. [The Latin motto translates as “Few, but ripe”. —Webmaster]
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In the 1940s when I did my natural sciences degree in zoology it was very much laboratory-based. … I was not keen on the idea of spending the rest of my life in the lab. I also don’t think I would have been particularly good at it. I don't think I have as analytical a mind or the degree of application that one would need to become a first-rate research scientist.
From interview with Michael Bond, 'It’s a Wonderful Life', New Scientist (14 Dec 2002), 176, No. 2373, 48.
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In the application of inductive logic to a given knowledge situation, the total evidence available must be used as a basis for determining the degree of confirmation.
In Logical Foundations of Probability (1950, 1962), 211.
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In the real changes which animals undergo during their embryonic growth, in those external transformations as well as in those structural modifications within the body, we have a natural scale to measure the degree or the gradation of those full grown animals which corresponds in their external form and in their structure, to those various degrees in the metamorphoses of animals, as illustrated by embryonic changes, a real foundation for zoological classification.
From Lecture 4, collected in Twelve Lectures on Comparative Embryology: Delivered Before the Lowell Institute in Boston: December and January 1848-9 (1849), 29.
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It is admitted by all that a finished or even a competent reasoner is not the work of nature alone; the experience of every day makes it evident that education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history, may be chosen for this purpose. Now of all these, it is desirable to choose the one which admits of the reasoning being verified, that is, in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. When the guiding property of the loadstone was first ascertained, and it was necessary to learn how to use this new discovery, and to find out how far it might be relied on, it would have been thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.
In On the Study and Difficulties of Mathematics (1898), chap. 1.
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It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
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It is now necessary to indicate more definitely the reason why mathematics not only carries conviction in itself, but also transmits conviction to the objects to which it is applied. The reason is found, first of all, in the perfect precision with which the elementary mathematical concepts are determined; in this respect each science must look to its own salvation .... But this is not all. As soon as human thought attempts long chains of conclusions, or difficult matters generally, there arises not only the danger of error but also the suspicion of error, because since all details cannot be surveyed with clearness at the same instant one must in the end be satisfied with a belief that nothing has been overlooked from the beginning. Every one knows how much this is the case even in arithmetic, the most elementary use of mathematics. No one would imagine that the higher parts of mathematics fare better in this respect; on the contrary, in more complicated conclusions the uncertainty and suspicion of hidden errors increases in rapid progression. How does mathematics manage to rid itself of this inconvenience which attaches to it in the highest degree? By making proofs more rigorous? By giving new rules according to which the old rules shall be applied? Not in the least. A very great uncertainty continues to attach to the result of each single computation. But there are checks. In the realm of mathematics each point may be reached by a hundred different ways; and if each of a hundred ways leads to the same point, one may be sure that the right point has been reached. A calculation without a check is as good as none. Just so it is with every isolated proof in any speculative science whatever; the proof may be ever so ingenious, and ever so perfectly true and correct, it will still fail to convince permanently. He will therefore be much deceived, who, in metaphysics, or in psychology which depends on metaphysics, hopes to see his greatest care in the precise determination of the concepts and in the logical conclusions rewarded by conviction, much less by success in transmitting conviction to others. Not only must the conclusions support each other, without coercion or suspicion of subreption, but in all matters originating in experience, or judging concerning experience, the results of speculation must be verified by experience, not only superficially, but in countless special cases.
In Werke [Kehrbach] (1890), Bd. 5, 105. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 19.
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It is still false to conclude that man is nothing but the highest animal, or the most progressive product of organic evolution. He is also a fundamentally new sort of animal and one in which, although organic evolution continues on its way, a fundamentally new sort of evolution has also appeared. The basis of this new sort of evolution is a new sort of heredity, the inheritance of learning. This sort of heredity appears modestly in other mammals and even lower in the animal kingdom, but in man it has incomparably fuller development and it combines with man's other characteristics unique in degree with a result that cannot be considered unique only in degree but must also be considered unique in kind.
In The Meaning of Evolution: A Study of the History of Life and of its Significance for Man (1949), 286.
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It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule. This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.
In Leibnitz (1884), 44-45. [The first sentence is reworded to better introduce the quotation. —Webmaster]
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Knowledge is invariably a matter of degree: you cannot put your finger upon even the simplest datum and say “this we know.”
From Knowledge and Experience in the Philosophy of F.H. Bradley (1964, 1989), 151.
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Look Nature thro’, ’tis neat Gradation all.
By what minute Degrees her Scale ascends!
Each middle Nature join’d at each Extreme,
To that above it join’d, to that beneath.
The Complaint: or, Night-Thoughts on Life, Death, and Immortality (1742, 1750), Night 6, 140.
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Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols—necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.
In 'Science as an Instrument of Education', Popular Science Monthly (1897), 253.
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Mathematics is indeed dangerous in that it absorbs students to such a degree that it dulls their senses to everything else.
While a student, an observation made about his teacher, Professor Karl Schellbach. Quoted, without citation, in Howard W. Eves, Mathematical Circles Adieu, (1977).
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Not long ago the head of what should be a strictly scientific department in one of the major universities commented on the odd (and ominous) phenomenon that persons who can claim to be scientists on the basis of the technical training that won them the degree of Ph.D. are now found certifying the authenticity of the painted rag that is called the “Turin Shroud” or adducing “scientific” arguments to support hoaxes about the “paranormal” or an antiquated religiosity. “You can hire a scientist [sic],” he said, “to prove anything.” He did not adduce himself as proof of his generalization, but he did boast of his cleverness in confining his own research to areas in which the results would not perturb the Establishment or any vociferous gang of shyster-led fanatics. If such is indeed the status of science and scholarship in our darkling age, Send not to ask for whom the bell tolls.
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Nothing in physics seems so hopeful to as the idea that it is possible for a theory to have a high degree of symmetry was hidden from us in everyday life. The physicist's task is to find this deeper symmetry.
In American Scientist (1977) (as cited in The Atlantic (1984), 254, 81.) As an epigraph in Crystal and Dragon: The Cosmic Dance of Symmetry and Chaos in Nature, Art and Consciousness (1993), 139.
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Now of the difficulties bound up with the public in which we doctors work, I hesitate to speak in a mixed audience. Common sense in matters medical is rare, and is usually in inverse ratio to the degree of education.
'Teaching and Thinking' (1894). In Aequanimitas with Other Addresses to Medical Students, Nurses and Practitioners of Medicine (1904), 131.
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One never finds fossil bones bearing no resemblance to human bones. Egyptian mummies, which are at least three thousand years old, show that men were the same then. The same applies to other mummified animals such as cats, dogs, crocodiles, falcons, vultures, oxen, ibises, etc. Species, therefore, do not change by degrees, but emerged after the new world was formed. Nor do we find intermediate species between those of the earlier world and those of today's. For example, there is no intermediate bear between our bear and the very different cave bear. To our knowledge, no spontaneous generation occurs in the present-day world. All organized beings owe their life to their fathers. Thus all records corroborate the globe's modernity. Negative proof: the barbaritY of the human species four thousand years ago. Positive proof: the great revolutions and the floods preserved in the traditions of all peoples.
'Note prese al Corso di Cuvier. Corso di Geologia all'Ateneo nel 1805', quoted in Pietro Corsi, The Age of Lamarck, trans. J. Mandelbaum (1988), 183.
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Owing to this struggle for life, any variation, however slight and from whatever cause proceeding, if it be in any degree profitable to an individual of any species, in its infinitely complex relationship to other organic beings and to external nature, will tend to the preservation of that individual, and will generally be inherited by its offspring.
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Science is a dynamic undertaking directed to lowering the degree of the empiricism involved in solving problems; or, if you prefer, science is a process of fabricating a web of interconnected concepts and conceptual schemes arising from experiments and ob
Modern Science and Modern Man, p. 62, New York (1952).
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Science is neither discontinuous nor monolithic. It is variously jointed, and loose in the joints in varying degrees.
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She has the sort of body you go to see in marble. She has golden hair. Quickly, deftly, she reaches with both hands behind her back and unclasps her top. Setting it on her lap, she swivels ninety degrees to face the towboat square. Shoulders back, cheeks high, she holds her pose without retreat. In her ample presentation there is defiance of gravity. There is no angle of repose. She is a siren and these are her songs.
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The American Cancer Society's position on the question of a possible cause-effect relationship between cigarette smoking and lung cancer is:
1. The evidence to date justifies suspicion that cigarette smoking does, to a degree as yet undetermined, increase the likelihood of developing cancer of the lung.
2. That available evidence does not constitute irrefutable proof that cigarette smoking is wholly or chiefly or partly responsible for lung cancer.
3. That the evidence at hand calls for the extension of statistical and laboratory studies designed to confirm or deny a causual relationship between cigarette smoking and lung cancer.
4. That the society is committed to furthering such intensified investigation as its resources will permit.
Conclusions of statement after a meeting of the ACS board of directors in San Francisco (17 Mar 1954). Quoted in 'Tobacco Industry Denies Cancer Tie'. New York Times (14 Apr 1954), 51.
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The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.
Aristotle
As translated in Book 13, 1078.a3, Aristotle’s Metaphysics, a Revised Text with Introduction and Commentary by W. D. Ross (1924), Vol. 2, 416.
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The computational formalism of mathematics is a thought process that is externalised to such a degree that for a time it becomes alien and is turned into a technological process. A mathematical concept is formed when this thought process, temporarily removed from its human vessel, is transplanted back into a human mold. To think ... means to calculate with critical awareness.
Mathematics and Physics (1981), Foreward. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 90.
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The degree of exactness of the intuition of space may be different in different individuals, perhaps even in different races. It would seem as if a strong naive space-intuition were an attribute pre-eminently of the Teutonic race, while the critical, purely logical sense is more fully developed in the Latin and Hebrew races. A full investigation of this subject, somewhat on the lines suggested by Francis Gallon in his researches on heredity, might be interesting.
In The Evanston Colloquium Lectures (1894), 46.
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The degree of one’s emotions varies inversely with one’s knowledge of the facts—the less you know the hotter you get.
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The general knowledge of our author [Leonhard Euler] was more extensive than could well be expected, in one who had pursued, with such unremitting ardor, mathematics and astronomy as his favorite studies. He had made a very considerable progress in medical, botanical, and chemical science. What was still more extraordinary, he was an excellent scholar, and possessed in a high degree what is generally called erudition. He had attentively read the most eminent writers of ancient Rome; the civil and literary history of all ages and all nations was familiar to him; and foreigners, who were only acquainted with his works, were astonished to find in the conversation of a man, whose long life seemed solely occupied in mathematical and physical researches and discoveries, such an extensive acquaintance with the most interesting branches of literature. In this respect, no doubt, he was much indebted to an uncommon memory, which seemed to retain every idea that was conveyed to it, either from reading or from meditation.
In Philosophical and Mathematical Dictionary (1815), 493-494.
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The great mathematician, like the great poet or naturalist or great administrator, is born. My contention shall be that where the mathematic endowment is found, there will usually be found associated with it, as essential implications in it, other endowments in generous measure, and that the appeal of the science is to the whole mind, direct no doubt to the central powers of thought, but indirectly through sympathy of all, rousing, enlarging, developing, emancipating all, so that the faculties of will, of intellect and feeling learn to respond, each in its appropriate order and degree, like the parts of an orchestra to the “urge and ardor” of its leader and lord.
In Lectures on Science, Philosophy and Art (1908), 22.
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The idea of winning a doctor’s degree gradually assumed the aspect of a great moral struggle, and the moral fight possessed immense attraction for me.
In Pioneer Work in Opening the Medical Profession to Women (1895), 29.
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The individual, if left alone from birth would remain primitive and beast-like in his thoughts and feelings to a degree that we can hardly conceive. The individual is what he is and has the significance that he has not so much in virtue of his individuality, but rather as a member of a great human society, which directs his material and spiritual existence from the cradle to the grave.
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The Johns Hopkins University certifies that John Wentworth Doe does not know anything but Biochemistry. Please pay no attention to any pronouncements he may make on any other subject, particularly when he joins with others of his kind to save the world from something or other. However, he worked hard for this degree and is potentially a most valuable citizen. Please treat him kindly.
[An imaginary academic diploma reworded to give a more realistic view of the value of the training of scientists.]
'Our Splintered Learning and the Nature of Scientists', Science (15 Apr 1955), 121, 516.
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The lives of scientists, considered as Lives, almost always make dull reading. For one thing, the careers of the famous and the merely ordinary fall into much the same pattern, give or take an honorary degree or two, or (in European countries) an honorific order. It could be hardly otherwise. Academics can only seldom lead lives that are spacious or exciting in a worldly sense. They need laboratories or libraries and the company of other academics. Their work is in no way made deeper or more cogent by privation, distress or worldly buffetings. Their private lives may be unhappy, strangely mixed up or comic, but not in ways that tell us anything special about the nature or direction of their work. Academics lie outside the devastation area of the literary convention according to which the lives of artists and men of letters are intrinsically interesting, a source of cultural insight in themselves. If a scientist were to cut his ear off, no one would take it as evidence of a heightened sensibility; if a historian were to fail (as Ruskin did) to consummate his marriage, we should not suppose that our understanding of historical scholarship had somehow been enriched.
'J.B.S: A Johnsonian Scientist', New York Review of Books (10 Oct 1968), reprinted in Pluto's Republic (1982), and inThe Strange Case of the Spotted Mice and Other Classic Essays on Science (1996), 86.
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The night spread out of the east in a great flood, quenching the red sunlight in a single minute. We wriggled by breathless degrees deep into our sleeping bags. Our sole thought was of comfort; we were not alive to the beauty or the grandeur of our position; we did not reflect on the splendor of our elevation. A regret I shall always have is that I did not muster up the energy to spend a minute or two stargazing. One peep I did make between the tent flaps into the night, and I remember dimly an appalling wealth of stars, not pale and remote as they appear when viewed through the moisture-laden air of lower levels, but brilliant points of electric blue fire standing out almost stereoscopically. It was a sight an astronomer would have given much to see, and here were we lying dully in our sleeping bags concerned only with the importance of keeping warm and comfortable.
…...
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The observer is not he who merely sees the thing which is before his eyes, but he who sees what parts the thing is composed of. To do this well is a rare talent. One person, from inattention, or attending only in the wrong place, overlooks half of what he sees; another sets down much more than he sees, confounding it with what he imagines, or with what he infers; another takes note of the kind of all the circumstances, but being inexpert in estimating their degree, leaves the quantity of each vague and uncertain; another sees indeed the whole, but makes such an awkward division of it into parts, throwing into one mass things which require to be separated, and separating others which might more conveniently be considered as one, that the result is much the same, sometimes even worse than if no analysis had been attempted at all.
In A System of Logic Ratiocinative and Inductive (1858), 216.
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The persons who have been employed on these problems of applying the properties of matter and the laws of motion to the explanation of the phenomena of the world, and who have brought to them the high and admirable qualities which such an office requires, have justly excited in a very eminent degree the admiration which mankind feels for great intellectual powers. Their names occupy a distinguished place in literary history; and probably there are no scientific reputations of the last century higher, and none more merited, than those earned by great mathematicians who have laboured with such wonderful success in unfolding the mechanism of the heavens; such for instance as D ’Alembert, Clairaut, Euler, Lagrange, Laplace.
In Astronomy and General Physics (1833), Bk. 3, chap. 4, 327.
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The qualities of bodies, which admit neither intension nor remission of degrees, and which are found to belong to fill bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.
From Isaac Newton, Rules of Reasoning in Philosophy, Rule 3, as translated by Andrew Motte in The Mathematical Principles of Natural Philosophy (1803), Vol. 2, 160.
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The rudest numerical scales, such as that by which the mineralogists distinguish different degrees of hardness, are found useful. The mere counting of pistils and stamens sufficed to bring botany out of total chaos into some kind of form. It is not, however, so much from counting as from measuring, not so much from the conception of number as from that of continuous quantity, that the advantage of mathematical treatment comes. Number, after all, only serves to pin us down to a precision in our thoughts which, however beneficial, can seldom lead to lofty conceptions, and frequently descend to pettiness.
On the Doctrine of Chances, with Later Reflections (1878), 61-2.
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The science of medicine is a barbarous jargon and the effects of our medicine on the human system are in the highest degree uncertain, except indeed that they have already destroyed more lives than war, pestilence, and famine combined.
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The sun is a mass of incandescent gas, a gigantic nuclear furnace,
Where hydrogen is built into helium at a temperature of millions of degrees.
Yo ho, it’s hot, the sun is not a place where we could live.
But here on earth there’d be no life without the light it gives.
We need its light, we need its heat, we need its energy.
Without the sun, without a doubt, there’d be no you and me.
Hy Zaret
From song 'Why Does the Sun Shine? (The Sun Is A Mass Of Incandescent Gas)' on LP record album Space Songs (1961), in the series Ballads for the Age of Science. Music by Louis Singer, and sung by Tom Glazer. Also recorded by the group They Might Be Giants (1998) who followed up with 'Why Does The Sun Really Shine? (The Sun is a Miasma of Incandescent Plasma)' on CD album Here Comes Science (2009), which corrects several scientific inaccuracies in the lyrics
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The Universe forces those who live in it to understand it. Those creatures who find everyday experience a muddled jumble of events with no predictability, no regularity, are in grave peril. The Universe belongs to those who, at least to some degree, have figured it out.
In Broca’s Brain: Reflections on the Romance of Science (1979, 1980), 19.
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The worth of a new idea is invariably determined, not by the degree of its intuitiveness—which incidentally, is to a major extent a matter of experience and habit—but by the scope and accuracy of the individual laws to the discovery of which it eventually leads.
In Scientific Autobiography and Other Papers (1968), 109-110.
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There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that… or: There is capitalism in so far as… The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.
From 'The Power of Words', collected in Siân Miles (ed.), Simone Weil: An Anthology (2000), 222-223.
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There must be some one quality without which a work of art cannot exist; possessing which, in the least degree, no work is altogether worthless.
In Art (1913), 7.
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This science, Geometry, is one of indispensable use and constant reference, for every student of the laws of nature; for the relations of space and number are the alphabet in which those laws are written. But besides the interest and importance of this kind which geometry possesses, it has a great and peculiar value for all who wish to understand the foundations of human knowledge, and the methods by which it is acquired. For the student of geometry acquires, with a degree of insight and clearness which the unmathematical reader can but feebly imagine, a conviction that there are necessary truths, many of them of a very complex and striking character; and that a few of the most simple and self-evident truths which it is possible for the mind of man to apprehend, may, by systematic deduction, lead to the most remote and unexpected results.
In The Philosophy of the Inductive Sciences Part 1, Bk. 2, chap. 4, sect. 8 (1868).
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Those who assert that the mathematical sciences make no affirmation about what is fair or good make a false assertion; for they do speak of these and frame demonstrations of them in the most eminent sense of the word. For if they do not actually employ these names, they do not exhibit even the results and the reasons of these, and therefore can be hardly said to make any assertion about them. Of what is fair, however, the most important species are order and symmetry, and that which is definite, which the mathematical sciences make manifest in a most eminent degree. And since, at least, these appear to be the causes of many things—now, I mean, for example, order, and that which is a definite thing, it is evident that they would assert, also, the existence of a cause of this description, and its subsistence after the same manner as that which is fair subsists in.
Aristotle
In Metaphysics [MacMahon] Bk. 12, chap. 3.
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We cannot observe external things without some degree of Thought; nor can we reflect upon our Thoughts, without being influenced in the course of our reflection by the Things which we have observed.
In The Elements of Morality (1845), Vol 1, 1.
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We know that the probability of well-established induction is great, but, when we are asked to name its degree we cannot. Common sense tells us that some inductive arguments are stronger than others, and that some are very strong. But how much stronger or how strong we cannot express.
In A Treatise on Probability (1921), Chap. 22, 259.
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We shall find everywhere, that the several Species are linked together, and differ but in almost insensible degrees. And when we consider the infinite Power and Wisdom of the Maker, we have reason to think, that it is suitable to the magnificent Harmony of the Universe, and the great Design and infinite Goodness of the Architect, that the Species of Creatures should also, by gentle degrees, ascend upward from us toward his infinite Perfection, as we see they gradually descend from us downwards.
In An Essay Concerning Humane Understanding (1689, 1706, 5th ed.), 381.
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When we have amassed a great store of such general facts, they become the objects of another and higher species of classification, and are themselves included in laws which, as they dispose of groups, not individuals have a far superior degree of generality, till at length, by continuing the process, we arrive at axioms of the highest degree of generality of which science is capable. This process is what we mean by induction.
In A Preliminary Discourse on the Study of Natural Philosophy (1830), 102.
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When we survey our lives and endeavours we soon observe that almost the whole of our actions and desires are bound up with the existence of other human beings. We see that our whole nature resembles that of the social animals. We eat food that others have grown, wear clothes that others have made, live in houses that others have built. The greater part of our knowledge and beliefs has been communicated to us by other people through the medium of a language which others have created. Without language our mental capacities would be poor indeed, comparable to those of the higher animals; we have, therefore, to admit that we owe our principal advantage over the beasts to the fact of living in human society. The individual, if left alone from birth would remain primitive and beast-like in his thoughts and feelings to a degree that we can hardly conceive. The individual is what he is and has the significance that he has not so much in virtue of his individuality, but rather as a member of a great human society, which directs his material and spiritual existence from the cradle to the grave.
…...
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Whether we like it or not, quantification in history is here to stay for reasons which the quantifiers themselves might not actively approve. We are becoming a numerate society: almost instinctively there seems now to be a greater degree of truth in evidence expressed numerically than in any literary evidence, no matter how shaky the statistical evidence, or acute the observing eye.
Is History Sick? (1973), 64.
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Who has studied the works of such men as Euler, Lagrange, Cauchy, Riemann, Sophus Lie, and Weierstrass, can doubt that a great mathematician is a great artist? The faculties possessed by such men, varying greatly in kind and degree with the individual, are analogous with those requisite for constructive art. Not every mathematician possesses in a specially high degree that critical faculty which finds its employment in the perfection of form, in conformity with the ideal of logical completeness; but every great mathematician possesses the rarer faculty of constructive imagination.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 290.
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Why then does science work? The answer is that nobody knows. It is a complete mystery—perhaps the complete mystery&mdashwhy the human mind should be able to understand anything at all about the wider universe. ... Perhaps it is because our brains evolved through the working of natural law that they somehow resonate with natural law. ... But the mystery, really, is not that we are at one with the universe, but that we are so to some degree at odds with it, different from it, and yet can understand something about it. Why is this so?
Coming of Age in the Milky Way (1988), 385. In Vinoth Ramachandra, Subverting Global Myths: Theology and the Public Issues Shaping our World (2008), 185.
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With highly civilised nations continued progress depends in a subordinate degree on natural selection; for such nations do not supplant and exterminate one another as do savage tribes. Nevertheless the more intelligent members within the same community will succeed better in the long run than the inferior, and leave a more numerous progeny, and this is a form of natural selection.
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[De Morgan relates that some person had made up 800 anagrams on his name, of which he had seen about 650. Commenting on these he says:]
Two of these I have joined in the title-page:
[Ut agendo surgamus arguendo gustamus.]
A few of the others are personal remarks.
Great gun! do us a sum!
is a sneer at my pursuit; but,
Go! great sum! [integral of a to the power u to the power n with respect to u] is more dignified. …
Adsum, nugator, suge!
is addressed to a student who continues talking after the lecture has commenced: …
Graduatus sum! nego
applies to one who declined to subscribe for an M.A. degree.
In Budget of Paradoxes (1872), 82. [The Latin phrases translate as, respectively, “Such action will start arguing with taste”, “Here babbler suck!” and “I graduate! I reject.” —Webmaster]
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[The famous attack of Sir William Hamilton on the tendency of mathematical studies] affords the most express evidence of those fatal lacunae in the circle of his knowledge, which unfitted him for taking a comprehensive or even an accurate view of the processes of the human mind in the establishment of truth. If there is any pre-requisite which all must see to be indispensable in one who attempts to give laws to the human intellect, it is a thorough acquaintance with the modes by which human intellect has proceeded, in the case where, by universal acknowledgment, grounded on subsequent direct verification, it has succeeded in ascertaining the greatest number of important and recondite truths. This requisite Sir W. Hamilton had not, in any tolerable degree, fulfilled. Even of pure mathematics he apparently knew little but the rudiments. Of mathematics as applied to investigating the laws of physical nature; of the mode in which the properties of number, extension, and figure, are made instrumental to the ascertainment of truths other than arithmetical or geometrical—it is too much to say that he had even a superficial knowledge: there is not a line in his works which shows him to have had any knowledge at all.
In Examination of Sir William Hamilton's Philosophy (1878), 607.
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~~[No known source]~~ Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.
Eine jede Wissenschaft fällt, hat sie erst eine gewisse Reife erreicht, automatisch der Mathematik anheim.
Webmaster has so far found no source for these verbatim words. (Can you help?) Expressed in totally different words, Hilbert expresses a similar idea in Address (11 Sep 1917), 'Axiomatisches Denken' delivered before the Swiss Mathematical Society in Zürich. See the quote that begins, “Anything at all that can be the object of scientific thought …”, on the David Hilbert Quotes page on this website.
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… on these expanded membranes [butterfly wings] Nature writes, as on a tablet, the story of the modifications of species, so truly do all changes of the organisation register themselves thereon. Moreover, the same colour-patterns of the wings generally show, with great regularity, the degrees of blood-relationship of the species. As the laws of nature must be the same for all beings, the conclusions furnished by this group of insects must be applicable to the whole world.
From The Naturalist on the River Amazons: A record of Adventures, Habits of Animals, Sketches of Brazilian and Indian life, and Aspects of Nature under the Equator, During Eleven Years of Travel (1864), 413.
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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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