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Home > Category Index for Science Quotations > Category Index C > Category: Characteristic

Characteristic Quotes (94 quotes)

Bei solchen chemischen Untersuchungen, die man zersetzende oder zergliedernde nennt, kommt es zunächst darauf an, zu ermitteln, mit welchen Stoffen man es zu thun hat, oder um chemisch zu reden, welche Stoffe in einem bestimmten Gemenge oder Gemisch enthalten sind. Hierzu bedient man sich sogenannter gegenwirkender Mittel, d. h. Stoffe, die bestimmte Eigenschaften und Eigenthümlichkeiten besitzen und die man aus Ueberlieferung oder eigner Erfahrung genau kennt, so daß die Veränderungen, welche sie bewirken oder erleiden, gleichsam die Sprache sind, mit der sie reden und dadurch dem Forscher anzeigen, daß der und der bestimmte Stoff in der fraglichen Mischung enthalten sei.
In the case of chemical investigations known as decompositions or analyses, it is first important to determine exactly what ingredients you are dealing with, or chemically speaking, what substances are contained in a given mixture or composite. For this purpose we use reagents, i.e., substances that possess certain properties and characteristics, which we well know from references or personal experience, such that the changes which they bring about or undergo, so to say the language that they speak thereby inform the researcher that this or that specific substance is present in the mixture in question.
From Zur Farben-Chemie Musterbilder für Freunde des Schönen und zum Gebrauch für Zeichner, Maler, Verzierer und Zeugdrucker [On Colour Chemistry...] (1850), Introduction. Translation tweaked by Webmaster from version in Herbert and W. Roesky and Klaud Möckel, translated from the original German by T.N. Mitchell and W.E. Russey, Chemical Curiosities: Spectacular Experiments and Inspired Quotes (1996), 1.
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Neumann, to a physicist seeking help with a difficult problem: Simple. This can be solved by using the method of characteristics.
Physicist: I'm afraid I don’t understand the method of characteristics.
Neumann: In mathematics you don't understand things. You just get used to them.
Attributed, as related by Dr. Felix Smith (Head of Molecular Physics, Stanford Research Institute) to author Gary Zukav, who quoted it in The Dancing Wu Li Masters: An Overview of the New Physics (1979, 2001), 208, footnote. The physicist (a friend of Dr. Smith) worked at Los Alamos after WW II. It should be noted that although the author uses quotation marks around the spoken remarks, that they represent the author's memory of Dr. Smith's recollection, who heard it from the physicist. Therefore the fourth-hand wording is very likely not verbatim. Webmaster finds Zukav's book seems to be the only source for this quote.
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Surtout l’astronomie et l’anatomie sont les deux sciences qui nous offrent le plus sensiblement deux grands caractères du Créateur; l’une, son immensité, par les distances, la grandeur, et le nombre des corps célestes; l’autre, son intelligence infinie, par la méchanique des animaux.
Above all, astronomy and anatomy are the two sciences which present to our minds most significantly the two grand characteristics of the Creator; the one, His immensity, by the distances, size, and number of the heavenly bodies; the other, His infinite intelligence, by the mechanism of animate beings.
Original French and translation in Craufurd Tait Ramage (ed.) Beautiful Thoughts from French and Italian Authors (1866), 119-120.
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The classification of facts, the recognition of their sequence and relative significance is the function of science, and the habit of forming a judgment upon these facts unbiassed by personal feeling is characteristic of what may be termed the scientific frame of mind.
From The Grammar of Science (1892), 8.
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Wenn sich für ein neues Fossil kein, auf eigenthümliche Eigenschaften desselben hinweisender, Name auffinden lassen Will; als in welchem Falle ich mich bei dem gegenwärtigen zu befinden gestehe; so halte ich es für besser, eine solche Benennung auszuwählen, die an sich gar nichts sagt, und folglich auch zu keinen unrichtigen Begriffen Anlass geben kann. Diesem zufolge will ich den Namen für die gegenwärtige metallische Substanz, gleichergestalt wie bei dem Uranium geschehen, aus der Mythologie, und zwar von den Ursöhnen der Erde, den Titanen, entlehnen, und benenne also dieses neue Metallgeschlecht: Titanium.
Wherefore no name can be found for a new fossil [element] which indicates its peculiar and characteristic properties (in which position I find myself at present), I think it is best to choose such a denomination as means nothing of itself and thus can give no rise to any erroneous ideas. In consequence of this, as I did in the case of Uranium, I shall borrow the name for this metallic substance from mythology, and in particular from the Titans, the first sons of the earth. I therefore call this metallic genus TITANIUM.
Martin Heinrich Klaproth. Original German edition, Beiträge Zur Chemischen Kenntniss Der Mineralkörper (1795), Vol. 1 , 244. English edition, translator not named, Analytical Essays Towards Promoting the Chemical Knowledge of Mineral Substances (1801), Vol. 1, 210. Klaproth's use of the term fossil associates his knowledge of the metal as from ore samples dug out of a mine.
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A black hole has no hair.
[Summarizing the simplicity of a black hole, which shows only three characteristics to the outside world (mass, charge, spin) and comparing the situation to a room full of bald-pated people who had one characteristic in common, but no differences in hair length, style or color for individual variations.]
In Geons, Black Holes, and Quantum Foam (2000), 297. Quote introduced previously as the No-Hair Theorem in Charles W. Misner, Kip S. Thorne and John Wheeler, Gravitation (1973).
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A new species develops if a population which has become geographically isolated from its parental species acquires during this period of isolation characters which promote or guarantee reproductive isolation when the external barriers break down.
Systematics and the Origin of Species: From the Viewpoint of a Zoologist (1942), 155.
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Acceptance without proof is the fundamental characteristic of Western religion, rejection without proof is the fundamental characteristic of Western science.
In The dancing Wu Li Masters: an Overview of the New Physics (1979), 88.
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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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Although the ocean’s surface seems at first to be completely homogeneous, after half a month we began to differentiate various seas and even different parts of oceans by their characteristic shades. We were astonished to discover that, during an flight, you have to learn anew not only to look, but also to see. At first the finest nuances of color elude you, but gradually your vision sharpens and your color perception becomes richer, and the planet spreads out before you with all its indescribable beauty.
…...
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Among the minor, yet striking characteristics of mathematics, may be mentioned the fleshless and skeletal build of its propositions; the peculiar difficulty, complication, and stress of its reasonings; the perfect exactitude of its results; their broad universality; their practical infallibility.
In Charles S. Peirce, ‎Charles Hartshorne (ed.), ‎Paul Weiss (ed.), Collected Papers of Charles Sanders Peirce (1931), Vol. 4, 197.
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Another characteristic of mathematical thought is that it can have no success where it cannot generalize.
In Eberhard Zeidler, Applied Functional Analysis: main principles and their applications (1995), 282.
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Anthropology is the study of human beings as creatures of society. It fastens its attention upon those physical characteristics and industrial techniques, those conventions and values, which distinguish one community from all others that belong to a different tradition.
In 'The Science of Custom', Patterns of Culture (1934, 2005), 1.
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As soon as matter took over, the force of Newtonian gravity, which represents one of the most important characteristics of “ponderable” matter, came into play.
In Conclusion of The Creation of the Universe (1952, 2012), 136.
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At times the [radio telescope] records exhibited a feature characteristic of interference, occurring some time later than the passage of the two known sources. This intermittent feature was curious, and I recall saying once that we would have to investigate the origin of that interference some day. We joked that it was probably due to the faulty ignition of some farm hand returning from a date.
From address to the 101st Meeting of the American Astronomical Society, Gainesville, Florida (27 Dec 1958). Printed in 'An Account of the Discovery of Jupiter as a Radio Source', The Astronomical Journal (Mar 1959), 64, No. 2, 37.
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But no pursuit at Cambridge was followed with nearly so much eagerness or gave me so much pleasure as collecting beetles. It was the mere passion for collecting, for I did not dissect them, and rarely compared their external characters with published descriptions, but got them named anyhow. I will give a proof of my zeal: one day, on tearing off some old bark, I saw two rare beetles, and seized one in each hand; then I saw a third and new kind, which I could not bear to lose, so that I popped the one which I held in my right hand into my mouth. Alas! it ejected some intensely acrid fluid, which burnt my tongue so that I was forced to spit the beetle out, which was lost, as was the third one.
In Charles Darwin and Francis Darwin (ed.), Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of His Published Letters (1892), 20.
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Curves that have no tangents are the rule. … Those who hear of curves without tangents, or of functions without derivatives, often think at first that Nature presents no such complications. … The contrary however is true. … Consider, for instance, one of the white flakes that are obtained by salting a solution of soap. At a distance its contour may appear sharply defined, but as we draw nearer its sharpness disappears. The eye can no longer draw a tangent at any point. … The use of a magnifying glass or microscope leaves us just as uncertain, for fresh irregularities appear every time we increase the magnification. … An essential characteristic of our flake … is that we suspect … that any scale involves details that absolutely prohibit the fixing of a tangent.
(1906). As quoted “in free translation” in Benoit B. Mandelbrot, The Fractal Geometry of Nature (1977, 1983), 7.
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Darwin grasped the philosophical bleakness with his characteristic courage. He argued that hope and morality cannot, and should not, be passively read in the construction of nature. Aesthetic and moral truths, as human concepts, must be shaped in human terms, not ‘discovered’ in nature. We must formulate these answers for ourselves and then approach nature as a partner who can answer other kinds of questions for us–questions about the factual state of the universe, not about the meaning of human life. If we grant nature the independence of her own domain–her answers unframed in human terms–then we can grasp her exquisite beauty in a free and humble way. For then we become liberated to approach nature without the burden of an inappropriate and impossible quest for moral messages to assuage our hopes and fears. We can pay our proper respect to nature’s independence and read her own ways as beauty or inspiration in our different terms.
…...
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Darwinian fitness is compounded of a mutual relationship between the organism and the environment. Of this, fitness of environment is quite as essential a component as the fitness which arises in the process of organic evolution; and in fundamental characteristics the actual environment is the fittest possible abode of life.
His thesis for the book stated at the beginning of The Fitness of the Environment (1913), Preface, v.
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Dissection ... teaches us that the body of man is made up of certain kinds of material, so differing from each other in optical and other physical characters and so built up together as to give the body certain structural features. Chemical examination further teaches us that these kinds of material are composed of various chemical substances, a large number of which have this characteristic that they possess a considerable amount of potential energy capable of being set free, rendered actual, by oxidation or some other chemical change. Thus the body as a whole may, from a chemical point of view, be considered as a mass of various chemical substances, representing altogether a considerable capital of potential energy.
From Introduction to A Text Book of Physiology (1876, 1891), Book 1, 1.
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Doubtless the reasoning faculty, the mind, is the leading and characteristic attribute of the human race. By the exercise of this, man arrives at the properties of the natural bodies. This is science, properly and emphatically so called. It is the science of pure mathematics; and in the high branches of this science lies the truly sublime of human acquisition. If any attainment deserves that epithet, it is the knowledge, which, from the mensuration of the minutest dust of the balance, proceeds on the rising scale of material bodies, everywhere weighing, everywhere measuring, everywhere detecting and explaining the laws of force and motion, penetrating into the secret principles which hold the universe of God together, and balancing worlds against worlds, and system against system. When we seek to accompany those who pursue studies at once so high, so vast, and so exact; when we arrive at the discoveries of Newton, which pour in day on the works of God, as if a second fiat had gone forth from his own mouth; when, further, we attempt to follow those who set out where Newton paused, making his goal their starting-place, and, proceeding with demonstration upon demonstration, and discovery upon discovery, bring new worlds and new systems of worlds within the limits of the known universe, failing to learn all only because all is infinite; however we may say of man, in admiration of his physical structure, that “in form and moving he is express and admirable,” it is here, and here without irreverence, we may exclaim, “In apprehension how like a god!” The study of the pure mathematics will of course not be extensively pursued in an institution, which, like this [Boston Mechanics’ Institute], has a direct practical tendency and aim. But it is still to be remembered, that pure mathematics lie at the foundation of mechanical philosophy, and that it is ignorance only which can speak or think of that sublime science as useless research or barren speculation.
In Works (1872), Vol. 1, 180.
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Euclid always contemplates a straight line as drawn between two definite points, and is very careful to mention when it is to be produced beyond this segment. He never thinks of the line as an entity given once for all as a whole. This careful definition and limitation, so as to exclude an infinity not immediately apparent to the senses, was very characteristic of the Greeks in all their many activities. It is enshrined in the difference between Greek architecture and Gothic architecture, and between Greek religion and modern religion. The spire of a Gothic cathedral and the importance of the unbounded straight line in modern Geometry are both emblematic of the transformation of the modern world.
In Introduction to Mathematics (1911), 119.
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Louis Pasteur quote: Every chemical substance, whether natural or artificial, falls into one of two major categories, according
Every chemical substance, whether natural or artificial, falls into one of two major categories, according to the spatial characteristic of its form. The distinction is between those substances that have a plane of symmetry and those that do not. The former belong to the mineral, the latter to the living world.
Pasteur Vallery-Radot (ed.), Oeuvres de Pasteur (1922-1939), Vol. I, 331. Quoted in Patrice Debré, Louis Pasteur, trans. Elborg Forster (1994), 261.
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For nearly twelve years I travelled and lived mostly among uncivilised or completely savage races, and I became convinced that they all possessed good qualities, some of them in a very remarkable degree, and that in all the great characteristics of humanity they are wonderfully like ourselves. Some, indeed, among the brown Polynesians especially, are declared by numerous independent and unprejudiced observers, to be physically, mentally, and intellectually our equals, if not our superiors; and it has always seemed to me one of the disgraces of our civilisation that these fine people have not in a single case been protected from contamination by the vices and follies of our more degraded classes, and allowed to develope their own social and political organislll under the advice of some of our best and wisest men and the protection of our world-wide power. That would have been indeed a worthy trophy of our civilisation. What we have actually done, and left undone, resulting in the degradation and lingering extermination of so fine a people, is one of the most pathetic of its tragedies.
In 'The Native Problem in South Africa and Elsewhere', Independent Review (1906), 11, 182.
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Fractals are patterns which occur on many levels. This concept can be applied to any musical parameter. I make melodic fractals, where the pitches of a theme I dream up are used to determine a melodic shape on several levels, in space and time. I make rhythmic fractals, where a set of durations associated with a motive get stretched and compressed and maybe layered on top of each other. I make loudness fractals, where the characteristic loudness of a sound, its envelope shape, is found on several time scales. I even make fractals with the form of a piece, its instrumentation, density, range, and so on. Here I’ve separated the parameters of music, but in a real piece, all of these things are combined, so you might call it a fractal of fractals.
Interview (1999) on The Discovery Channel. As quoted by Benoit B. Manelbrot and Richard Hudson in The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward (2010), 133.
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Genetics was, I would say, the first part of biology to become a pretty good theoretical subject, based on the theory of the gene and patterns of inheritance of characteristics.
From interview with Neil A. Campbell, in 'Crossing the Boundaries of Science', BioScience (Dec 1986), 36, No. 11, 738.
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However, all scientific statements and laws have one characteristic in common: they are “true or false” (adequate or inadequate). Roughly speaking, our reaction to them is “yes” or “no.” The scientific way of thinking has a further characteristic. The concepts which it uses to build up its coherent systems are not expressing emotions. For the scientist, there is only “being,” but no wishing, no valuing, no good, no evil; no goal. As long as we remain within the realm of science proper, we can never meet with a sentence of the type: “Thou shalt not lie.” There is something like a Puritan's restraint in the scientist who seeks truth: he keeps away from everything voluntaristic or emotional.
Essays in Physics (1950), 68.
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However, if we consider that all the characteristics which have been cited are only differences in degree of structure, may we not suppose that this special condition of organization of man has been gradually acquired at the close of a long period of time, with the aid of circumstances which have proved favorable? What a subject for reflection for those who have the courage to enter into it!
In Recherches sur l'Organization des corps vivans (1802), as translated in Alpheus Spring Packard, Lamarck, the Founder of Evolution: His Life and Work (1901), 363. Packard's italics.
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Human societies are glued together with conversation and friendship. Conversation is the natural and characteristic activity of human beings. Friendship is the milieu within which we function.
In From Eros to Gaia (1992), 197.
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I definitely deny that any pathological process, i.e. any life-process taking place under unfavourable circumstances, is able to call forth qualitatively new formations lying beyond the customary range of forms characteristic of the species. All pathological formations are either degenerations, transformations, or repetitions of typical physiological structures.
In 'Cellular-Pathologie', Archiv für pathologische Anatomie und Physiologie und fur klinische Medizin (1855), 8, 13-14, as translated in LellandJ. Rather, 'Cellular Pathology', Disease, Life, and Man: Selected Essays by Rudolf Virchow (1958), 81.
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I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my previous researches. Disgusted at my want of success, I went away to spend a few days at the seaside, and thought of entirely different things. One day, as I was walking on the cliff, the idea came to me, again with the same characteristics of conciseness, suddenness, and immediate certainty, that arithmetical transformations of indefinite ternary quadratic forms are identical with those of non-Euclidian geometry.
Science and Method (1908), trans. Francis Maitland (1914), 53-4.
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In science its main worth is temporary, as a stepping-stone to something beyond. Even the Principia, as Newton with characteristic modesty entitled his great work, is truly but the beginning of a natural philosophy, and no more an ultimate work, than Watt’s steam-engine, or Arkwright's spinning-machine.
Co-author with his brother Augustus William Hare Guesses At Truth, By Two Brothers: Second Edition: With Large Additions (1848), Second Series, 46. (The volume is introduced as “more than three fourths new.” This quote is identified as by Julius; Augustus had died in 1833.)
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In this generation, along with the dominating traits, the recessive ones also reappear, their individuality fully revealed, and they do so in the decisively expressed average proportion of 3:1, so that among each four plants of this generation three receive the dominating and one the recessive characteristic.
'Experiments on Plant Hybrids' (1865). In Curt Stern and Eva R. Sherwood (eds.), The Origin of Genetics: A Mendel Source Book (1966), 10.
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Indeed the modern developments of mathematics constitute not only one of the most impressive, but one of the most characteristic, phenomena of our age. It is a phenomenon, however, of which the boasted intelligence of a “universalized” daily press seems strangely unaware; and there is no other great human interest, whether of science or of art, regarding which the mind of the educated public is permitted to hold so many fallacious opinions and inferior estimates.
In Lectures on Science, Philosophy and Arts (1908), 8.
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Induction and analogy are the special characteristics of modern mathematics, in which theorems have given place to theories and no truth is regarded otherwise than as a link in an infinite chain. “Omne exit in infinitum” is their favorite motto and accepted axiom.
In 'A Plea for the Mathematician', Nature, Vol. 1, 861. [The Latin phrase “Omne exit in infinitum” means “Everything goes to infinity”.
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Iron and coal dominated everywhere, from grey to black: the black boots, the black stove-pipe hat, the black coach or carriage, the black iron frame of the hearth, the black cooking pots and pans and stoves. Was it a mourning? Was it protective coloration? Was it mere depression of the senses? No matter what the original color of the paleotechnic milieu might be it was soon reduced by reason of the soot and cinders that accompanied its activities, to its characteristic tones, grey, dirty-brown, black.
Technics and Civilisation (1934), 163.
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Isolating mechanisms are biological properties of individuals that prevent the interbreeding of populations that are actually or potentially sympatric.
Animal Species and Evolution (1963), 91.
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It is a strange fact, characteristic of the incomplete state of our present knowledge, that totally opposing conclusions are drawn about prehistoric conditions on our planet, depending on whether the problem is approached from the biological or the geophysical viewpoint.
In The Origins of Continents and Oceans (4th ed. 1929), trans. John Biram (1966), 5.
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It is as true now, as it was in the days when Werner first drew his far-reaching inferences before his charmed listeners, that on the characteristic phenomena and varying distribution of the grand mineral masses of the rock-formations, almost all that concerns the relative habitability of a land depends.
In 'The Relations of Geology', Scottish Geographical Magazine (Aug 1902), 19, No. 8, 409.
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It is characteristic of experimental science that it opens ever-widening horizons to our vision.
As translated in René J. Dubos, Louis Pasteur, Free Lance of Science (1950, 1986), 329.
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It is characteristic of science that the full explanations are often seized in their essence by the percipient scientist long in advance of any possible proof.
The Origin of Life, 1967
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It is characteristic of the unlearned that they are forever proposing something which is old, and because it has recently come to their own attention, supposing it to be new.
Address at Holy Cross College (25 Jun 1919), collected in Have Faith In Massachusetts: A Collection of Speeches and Messages (1919, 2nd Ed.), 231. (This speech was not included in the period covered by the first edition.)
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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.
[* This sentence has been reworded for the purpose of this quotation.]
In Leibnitz (1884), 44-45.
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Just as a tree constitutes a mass arranged in a definite manner, in which, in every single part, in the leaves as in the root, in the trunk as in the blossom, cells are discovered to be the ultimate elements, so is it also with the forms of animal life. Every animal presents itself as a sum of vital unities, every one of which manifests all the characteristics of life. The characteristics and unity of life cannot be limited to anyone particular spot in a highly developed organism (for example, to the brain of man), but are to be found only in the definite, constantly recurring structure, which every individual element displays. Hence it follows that the structural composition of a body of considerable size, a so-called individual, always represents a kind of social arrangement of parts, an arrangement of a social kind, in which a number of individual existences are mutually dependent, but in such a way, that every element has its own special action, and, even though it derive its stimulus to activity from other parts, yet alone effects the actual performance of its duties.
In Lecture I, 'Cells and the Cellular Theory' (1858), Rudolf Virchow and Frank Chance (trans.) ,Cellular Pathology (1860), 13-14.
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Knowledge of the laws of nature offers humankind the only chance of survival in a changing environment. … The search for knowledge gives expression to a basic curiosity which appears to be the salient defining characteristic of human beings.
From opening paragraph of Preface, Quasars, Redshifts and Controversies (1987).
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Looking back over the last thousand years, one can divide the development of the machine and the machine civilization into three successive but over-lapping and interpenetrating phases: eotechnic, paleotechnic, neotechnic … Speaking in terms of power and characteristic materials, the eotechnic phase is a water-and-wood complex: the paleotechnic phase is a coal-and-wood complex… The dawn-age of our modern technics stretches roughly from the year 1000 to 1750. It did not, of course, come suddenly to an end in the middle of the eighteenth century. A new movement appeared in industrial society which had been gathering headway almost unnoticed from the fifteenth century on: after 1750 industry passed into a new phase, with a different source of power, different materials, different objectives.
Technics and Civilisation (1934), 109.
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Man has never been a particularly modest or self-deprecatory animal, and physical theory bears witness to this no less than many other important activities. The idea that thought is the measure of all things, that there is such a thing as utter logical rigor, that conclusions can be drawn endowed with an inescapable necessity, that mathematics has an absolute validity and controls experience—these are not the ideas of a modest animal. Not only do our theories betray these somewhat bumptious traits of self-appreciation, but especially obvious through them all is the thread of incorrigible optimism so characteristic of human beings.
In The Nature of Physical Theory (1936), 135-136.
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Man’s respect for knowledge is one of his most peculiar characteristics. Knowledge in Latin is scientia, and science came to be the name of the most respectable kind of knowledge.
In Radio Lecture (30 Jun 1973) broadcast by the Open University, collected in Imre Lakatos, John Worrall (ed.) and Gregory Currie (ed.), 'Introduction: Science and Pseudoscience', The Methodology of Scientific Research Programmes (1978, 1980), Vol. 1, 1.
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Mars is the next frontier, what the Wild West was, what America was 500 years ago. It’s time to strike out anew. Mars is where the action is for the next thousand years. The characteristic of human nature, and perhaps our simian branch of the family, is curiosity and exploration. When we stop doing that, we won’t be humans anymore. I’ve seen far more in my lifetime than I ever dreamed. Many of our problems on Earth can only be solved by space technology. The next step is in space. It’s inevitable.
…...
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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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May we attribute to the color of the herbage and plants, which no doubt clothe the plains of Mars, the characteristic hue of that planet, which is noticeable by the naked eye, and which led the ancients to personify it as a warrior?
In 'Mars, by the Latest Observations', Popular Science (Dec 1873), 4, 190.
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One feature which will probably most impress the mathematician accustomed to the rapidity and directness secured by the generality of modern methods is the deliberation with which Archimedes approaches the solution of any one of his main problems. Yet this very characteristic, with its incidental effects, is calculated to excite the more admiration because the method suggests the tactics of some great strategist who foresees everything, eliminates everything not immediately conducive to the execution of his plan, masters every position in its order, and then suddenly (when the very elaboration of the scheme has almost obscured, in the mind of the spectator, its ultimate object) strikes the final blow. Thus we read in Archimedes proposition after proposition the bearing of which is not immediately obvious but which we find infallibly used later on; and we are led by such easy stages that the difficulties of the original problem, as presented at the outset, are scarcely appreciated. As Plutarch says: “It is not possible to find in geometry more difficult and troublesome questions, or more simple and lucid explanations.” But it is decidedly a rhetorical exaggeration when Plutarch goes on to say that we are deceived by the easiness of the successive steps into the belief that anyone could have discovered them for himself. On the contrary, the studied simplicity and the perfect finish of the treatises involve at the same time an element of mystery. Though each step depends on the preceding ones, we are left in the dark as to how they were suggested to Archimedes. There is, in fact, much truth in a remark by Wallis to the effect that he seems “as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results.” Wallis adds with equal reason that not only Archimedes but nearly all the ancients so hid away from posterity their method of Analysis (though it is certain that they had one) that more modern mathematicians found it easier to invent a new Analysis than to seek out the old.
In The Works of Archimedes (1897), Preface, vi.
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One of the most constant characteristics of beliefs is their intolerance. It is even more uncompromising as the belief is stronger. Men dominated by a certitude cannot tolerate those who do not accept it.
From Les Opinions et les Croyances: Genèse—Évolution (1911), 235. As translated in review of that book by: Samuel N. Reep, The American Journal of Sociology (1913), 18, No. 6, 814 (first and last sentences). Original French text: “Un des caractères généraux les plus constants des croyances est leur intolérance. Elle est d’autant plus intransigeante que la croyance est plus forte. Les hommes dominés par une certitude ne peuvent tolérer ceux qui ne l’acceptent pas.” The second sentence as translated by Webmaster from the original French. Also seen translated as, “The stronger the belief, the greater its intolerance.”
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Professor Bethe … is a man who has this characteristic: If there’s a good experimental number you’ve got to figure it out from theory. So, he forced the quantum electrodynamics of the day to give him an answer [for the experimentally measured Lamb-shift of hydrogen], … and thus, made the most important discovery in the history of the theory of quantum electrodynamics. He worked this out on the train from Ithaca, New York to Schenectady.
Bethe calculated, what Lamb had experimentally just measured, for the separation of the 2S½ and 2P½ of hydrogen. Both theory and measurement yielded about one thousand megacycles for the Lamb-shift. Feynman was at the time associated with Bethe at Cornell. In Feynman’s Nobel Prize Lecture (11 Dec 1965), 'The Development of the Space-Time View of Quantum Electrodynamics'. Collected in Stig Lundqvist, Nobel Lectures: Physics, 1963-1970 (1998), 170.
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Sooner or later for good or ill, a united mankind, equipped with science and power, will probably turn its attention to the other planets, not only for economic exploitation, but also as possible homes for man... The goal for the solar system would seem to be that it should become an interplanetary community of very diverse worlds... each contributing to the common experience its characteristic view of the universe. Through the pooling of this wealth of experience, through this “commonwealth of worlds,” new levels of mental and spiritual development should become possible, levels at present quite inconceivable to man.
…...
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Take the living human brain endowed with mind and thought. …. The physicist brings his tools and commences systematic exploration. All that he discovers is a collection of atoms and electrons and fields of force arranged in space and time, apparently similar to those found in inorganic objects. He may trace other physical characteristics, energy, temperature, entropy. None of these is identical with thought. … How can this collection of ordinary atoms be a thinking machine? … The Victorian physicist felt that he knew just what he was talking about when he used such terms as matter and atoms. … But now we realize that science has nothing to say as to the intrinsic nature of the atom. The physical atom is, like everything else in physics, a schedule of pointer readings.
From a Gifford Lecture, University of Edinburgh (1927), published in 'Pointer Readings: Limits of Physical Knowledge', The Nature of the Physical World (1929), 258-259.
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The activity characteristic of professional engineering is the design of structures, machines, circuits, or processes, or of combinations of these elements into systems or plants and the analysis and prediction of their performance and costs under specified working conditions.
1954
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The apodictic quality of mathematical thought, the certainty and correctness of its conclusions, are due, not to a special mode of ratiocination, but to the character of the concepts with which it deals. What is that distinctive characteristic? I answer: precision, sharpness, completeness,* of definition. But how comes your mathematician by such completeness? There is no mysterious trick involved; some ideas admit of such precision, others do not; and the mathematician is one who deals with those that do.
In 'The Universe and Beyond', Hibbert Journal (1904-1905), 3, 309. An editorial footnote indicates “precision, sharpness, completeness” — i.e., in terms of the absolutely clear and indefinable.
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The assumptions of population thinking are diametrically opposed to those of the typologist. The populationist stresses the uniqueness of everything in the organic world. What is true for the human species,–that no two individuals are alike, is equally true for all other species of animals and plants ... All organisms and organic phenomena are composed of unique features and can be described collectively only in statistical terms. Individuals, or any kind of organic entities, form populations of which we can determine the arithmetic mean and the statistics of variation. Averages are merely statistical abstractions, only the individuals of which the populations are composed have reality. The ultimate conclusions of the population thinker and of the typologist are precisely the opposite. For the typologist, the type (eidos) is real and the variation. an illusion, while for the populationist the type (average) is an abstraction and only the variation is real. No two ways of looking at nature could be more different.
Darwin and the Evolutionary Theory in Biology (1959), 2.
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The basic thesis of gestalt theory might be formulated thus: there are contexts in which what is happening in the whole cannot be deduced from the characteristics of the separate pieces, but conversely; what happens to a part of the whole is, in clearcut cases, determined by the laws of the inner structure of its whole.
Lecture at the Kantgesellschaft (Kant Society), Berlin (17 Dec 1924), 'Über Gestalttheorie', as taken down in shorthand. Translated by N. Nairn-Allison in Social Research (1944), 11, 84.
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The chemists work with inaccurate and poor measuring services, but they employ very good materials. The physicists, on the other hand, use excellent methods and accurate instruments, but they apply these to very inferior materials. The physical chemists combine both these characteristics in that they apply imprecise methods to impure materials.
Quoted in Ralph Oesper, The Human Side of Scientists (1975), 116.
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The dreadful cocksureness that is characteristic of scientists in bulk is not only quite foreign to the spirit of true science, it is not even justified by a superficial view.
In Science is a Sacred Cow (1950), 31.
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The fundamental characteristic of the scientific method is honesty. In dealing with any question, science asks no favors. ... I believe that constant use of the scientific method must in the end leave its impress upon him who uses it. ... A life spent in accordance with scientific teachings would be of a high order. It would practically conform to the teachings of the highest types of religion. The motives would be different, but so far as conduct is concerned the results would be practically identical.
Address as its retiring president, to the American Association for the Advancement of Science, St. Louis (28 Dec 1903). 'Scientific Investigation and Progress', Nature 928 Jan 1904), 69:1787, 309.
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The idea that the bumps or depressions on a man's head indicate the presence or absence of certain moral characteristics in his mental equipment is one of the absurdities developed from studies in this field that has long since been discarded by science. The ideas of the phrenologist Gall, however ridiculous they may now seem in the light of a century's progress, were nevertheless destined to become metamorphosed into the modern principles of cerebral localization.
From 'Looking for "The Face Within the Face" in Man', in the New York Times, 4 Mar 1906, SM page 3.
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The laws and conditions of the production of wealth partake of the character of physical truths. There is nothing optional or arbitrary in them ... It is not so with the Distribution of Wealth. That is a matter of human institution solely. The things once there, mankind, individually or collectively, can do with them as they like.
Principles of Political Economy (1848), Book 2, 199.
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The majority of evolutive movements are degenerative. Progressive cases are exceptional. Characters appear suddenly that have no meaning in the atavistic series. Evolution in no way shows a general tendency toward progress… . The only thing that could be accomplished by slow changes would be the accumulation of neutral characteristics without value for survival. Only important and sudden mutations can furnish the material which can be utilized by selection.
As quoted in Isaac Asimov's Book of Science and Nature Quotations (1988), 91. Please contact Webmaster if you know the primary source.
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The most distinctive characteristic which differentiates mathematics from the various branches of empirical science, and which accounts for its fame as the queen of the sciences, is no doubt the peculiar certainty and necessity of its results.
First sentence of 'Geometry and Empirical Science', collected in Carl Hempel and James H. Fetzer (ed.), The Philosophy of Carl G. Hempel: Studies in Science, Explanation, and Rationality (2001), Chap. 2, 18. Also Carl Hempel, 'Geometry and Empirical Science', collected in J.R. Newman (ed.), The World of Mathematics (1956), Vol. 3, 1635.
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The process of natural selection has been summed up in the phrase “survival of the fittest.” This, however, tells only part of the story. “Survival of the existing” in many cases covers more of the truth. For in hosts of cases the survival of characters rests not on any special usefulness or fitness, but on the fact that individuals possessing these characters have inhabited or invaded a certain area. The principle of utility explains survivals among competing structures. It rarely accounts for qualities associated with geographic distribution.
The nature of animals which first colonize a district must determine what the future fauna will be. From their specific characters, which are neither useful nor harmful, will be derived for the most part the specific characters of their successors.
It is not essential to the meadow lark that he should have a black blotch on the breast or the outer tail-feather white. Yet all meadow larks have these characters just as all shore larks have the tiny plume behind the ear. Those characters of the parent stock, which may be harmful in the new relations, will be eliminated by natural selection. Those especially helpful will be intensified and modified, but the great body of characters, the marks by which we know the species, will be neither helpful nor hurtful. These will be meaningless streaks and spots, variations in size of parts, peculiar relations of scales or hair or feathers, little matters which can neither help nor hurt, but which have all the persistence heredity can give.
Foot-notes to Evolution. A Series of Popular Addresses on the Evolution of Life (1898), 218.
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The specific character of the greater part of the toxins which are known to us (I need only instance such toxins as those of tetanus and diphtheria) would suggest that the substances produced for effecting the correlation of organs within the body, through the intermediation of the blood stream, might also belong to this class, since here also specificity of action must be a distinguishing characteristic. These chemical messengers, however, or 'hormones' (from όρμάω, I excite or arouse), as we might call them, have to be carried from the organ where they are produced to the organ which they affect by means of the blood stream and the continually recurring physiological needs of the organism must determine their repeated production and circulation through the body.
'The Chemical Correlation of the Functions of the Body', The Lancet (1905), ii, 340.
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The work of the inventor consists of conceptualizing, combining, and ordering what is possible according to the laws of nature. This inner working out which precedes the external has a twofold characteristic: the participation of the subconscious in the inventing subject; and that encounter with an external power which demands and obtains complete subjugation, so that the way to the solution is experienced as the fitting of one's own imagination to this power.
Philosophie der Technik (1927). 'Technology in Its Proper Sphere' translated by William Carroll. In Carl Mitcham (ed.) and Robert Mackey (ed.), Philosophy and Technology: Readings in the Philosophical Problems of Technology, (1972), Vol. 14, 321. In David Lovekin, Technique, Discourse, and Consciousness (1991), 73.
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This brings me to the final point of my remarks, the relation between creativity and aging, a topic with which I have had substantial experience. Scientific research, until it has gone through the grueling and sometimes painful process of publication, is just play, and play is characteristic of young vertebrates, particularly young mammals. In some ways, scientific creativity is related to the exuberant behavior of young mammals. Indeed, creativity seems to be a natural characteristic of young humans. If one is fortunate enough to be associated with a university, even as one ages, teaching allows one to contribute to, and vicariously share, in the creativity of youth.”
In 'Integrative Biology: An Organismic Biologist’s Point of View', Integrative and Comparative Biology (2005), 45, 331.
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This characteristic of modern experiments–that they consist principally of measurements,–is so prominent, that the opinion seems to have got abroad, that in a few years all the great physical constants will have been approximately estimated, and that the only occupation which will then be left to men of science will be to carry these measurements to another place of decimals … But we have no right to think thus of the unsearchable riches of creation, or of the untried fertility of those fresh minds into which these riches will continue to be poured.
Maxwell strongly disagreed with the prominent opinion, and was attacking it. Thus, he was saying he did not believe in such a future of merely making “measurements to another place of decimals.” In 'Introductory Lecture on Experimental Physics', (Oct 1871). In W.D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 244. Note that his reference to making measurements to another place of decimals is often seen extracted as a short quote without the context showing - obscuring the fact that he actually despised that opinion.
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Those who consider James Watt only as a great practical mechanic form a very erroneous idea of his character: he was equally distinguished as a natural philosopher and a chemist, and his inventions demonstrate his profound knowledge of those sciences, and that peculiar characteristic of genius, the union of them for practical application.
As reported in Proceedings of the Public Meeting held at Preemasons' Hall, on the 18th June, 1824, for Erecting a Monument to the Late James Watt (1824), 8.
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To ask what qualities distinguish good from routine scientific research is to address a question that should be of central concern to every scientist. We can make the question more tractable by rephrasing it, “What attributes are shared by the scientific works which have contributed importantly to our understanding of the physical world—in this case the world of living things?” Two of the most widely accepted characteristics of good scientific work are generality of application and originality of conception. . These qualities are easy to point out in the works of others and, of course extremely difficult to achieve in one’s own research. At first hearing novelty and generality appear to be mutually exclusive, but they really are not. They just have different frames of reference. Novelty has a human frame of reference; generality has a biological frame of reference. Consider, for example, Darwinian Natural Selection. It offers a mechanism so widely applicable as to be almost coexistent with reproduction, so universal as to be almost axiomatic, and so innovative that it shook, and continues to shake, man’s perception of causality.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 230.
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To characterize the import of pure geometry, we might use the standard form of a movie-disclaimer: No portrayal of the characteristics of geometrical figures or of the spatial properties of relationships of actual bodies is intended, and any similarities between the primitive concepts and their customary geometrical connotations are purely coincidental.
From 'Geometry and Empirical Science', collected in Carl Hempel and James H. Fetzer (ed.), The Philosophy of Carl G. Hempel: Studies in Science, Explanation, and Rationality (2001), Chap. 2, 24. Also Carl Hempel, 'Geometry and Empirical Science', collected in J.R. Newman (ed.), The World of Mathematics (1956), Vol. 3, 1641.
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To study men, we must look close by; to study man, we must learn to look afar; if we are to discover essential characteristics, we must first observe differences.
Essai sur l'origine des langues (1781), 384
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To the extent that remaining old-growth Douglas fir ecosystems possess unique structural and functional characteristics distinct from surrounding managed forests, the analogy between forest habitat islands and oceanic islands applies. Forest planning decision variables such as total acreage to be maintained, patch size frequency distribution, spatial distribution of patches, specific locations, and protective measures all need to be addressed.
In The Fragmented Forest: Island Biogeography Theory and the Preservation of Biotic Diversity (1984), 6.
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Two important characteristics of maps should be noticed. A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness. ... If we reflect upon our languages, we find at best they must be considered only as maps.
Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics (1958), 58.
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Under certain given circumstances, and only under those circumstances, an agglomeration of men presents new characteristics very different from those of the individuals composing it. The sentiments and ideas of all the persons in the gathering take one and the same direction, and their conscious personality vanishes. A collective mind is formed, doubtless transitory, but presenting very clearly defined characteristics. The gathering has thus become what, in the absence of a better expression, I will call an organized crowd, or, if the term is considered preferable, a psychological crowd. It forms a single being and is subject to the law of the mental unity of crowds.
From Psychologie des Foules (1895), 12. English text in The Crowd: A Study of the Popular Mind (1897), Book 1, Chap. 1, 1-2. The original French text is, “Dans certaines circonstances données, et seulement dans ces circonstances, une agglomération d’hommes possède des caractères nouveaux fort différents de ceux des individus composant cette agglomération. La personnalité consciente s’évanouit, les sentiments et les idées de toutes les unités sont orientés dans une même direction. Il se forme une âme collective, transitoire sans doute, mais présentant des caractères très nets. La collectivité est alors devenue ce que, faute d’une expression meilleure, j’appellerai une foule organisée, ou, si l’on préfère, une foule psychologique. Elle forme un seul être et se trouve soumise à la loi de l'unité mentale des foules.”
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We are accustomed to say that every human being displays both male and female instinctual impulses, needs, and attributes, but the characteristics of what is male and female can only be demonstrated in anatomy, and not in psychology.
In Sigmund Freud and Joan Riviere (trans.), Civilization and Its Discontents (1930, 1994), 35.
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We may assume the existence of an aether; only we must give up ascribing a definite state of motion to it, I.e. we must by abstraction take from it the last mechanical characteristic which Lorentz had still left it.
…...
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We may regard [Scheele] not only as having given the first indication of the rich harvest to be reaped by the investigation of the compounds of organic chemistry, but as having been the first to discover and make use of characteristic reactions by which closely allied substances can be detected and separated, so that he must be considered one of the chief founders of analytical chemistry.
In Treatise on Chemistry (1877, 1890), Vol. 1, 23.
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We may summarize … the fundamental characteristics and limitations of mathematics as follows: mathematics is ultimately an experimental science, for freedom from contradiction cannot be proved, but only postulated and checked by observation, and similarly existence can only be postulated and checked by observation. Furthermore, mathematics requires the fundamental device of all thought, of analyzing experience into static bits with static meanings.
In The Nature of Physical Theory (1936), 58.
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We see, then, that the disappearance of the conscious personality, the predominance of the unconscious personality, the turning by means of suggestion and contagion of feelings and ideas in an identical direction, the tendency to immediately transform the suggested ideas into acts; these, we see, are the principal characteristics of the individual forming part of a crowd. He is no longer himself, but has become an automaton who has ceased to be guided by his will.
From Psychologie des Foules (1895), 20. English text in The Crowd: A Study of the Popular Mind (1897), Book 1, Chap. 1, 12. Original French text: “Donc, évanouissement de la personnalité consciente, prédominance de la personnalité inconsciente, orientation par voie de suggestion et de contagion des sentiments et des idées dans un même sens, tendance a transformer immédiatement en actes les idée suggérées, tels sont les principaux caractères de l’individu en foule. II n’est plus lui-même, il est devenu un automate que sa volonté ne guide plus.”
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What is this subject, which may be called indifferently either mathematics or logic? Is there any way in which we can define it? Certain characteristics of the subject are clear. To begin with, we do not, in this subject, deal with particular things or particular properties: we deal formally with what can be said about any thing or any property. We are prepared to say that one and one are two, but not that Socrates and Plato are two, because, in our capacity of logicians or pure mathematicians, we have never heard of Socrates or Plato. A world in which there were no such individuals would still be a world in which one and one are two. It is not open to us, as pure mathematicians or logicians, to mention anything at all, because, if we do so we introduce something irrelevant and not formal.
In Introduction to Mathematical Philosophy (1920), 196-197.
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When the late Sophus Lie … was asked to name the characteristic endowment of the mathematician, his answer was the following quaternion: Phantasie, Energie, Selbstvertrauen, Selbstkritik.
In Lectures on Philosophy, Science and Art (1908), 31. [“Quaternion” is used here in its meaning of a set of four people or things. The last four words, given in German, translate as “Imagination, Energy, Self-confidence, Self-criticism.” —Webmaster]
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Within the nucleus [of a cell] is a network of fibers, a sap fills the interstices of the network. The network resolves itself into a definite number of threads at each division of the cell. These threads we call chromosomes. Each species of animals and plants possesses a characteristic number of these threads which have definite size and sometimes a specific shape and even characteristic granules at different levels. Beyond this point our strongest microscopes fail to penetrate.
In A Critique of the Theory of Evolution (1916), 91.
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Without doubt one of the most characteristic features of mathematics in the last century is the systematic and universal use of the complex variable. Most of its great theories received invaluable aid from it, and many owe their very existence to it.
In 'History of Mathematics in the Nineteenth Century', Congress of Arts and Sciences (1905), Vol. 1, 474. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 115.
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[The enigmatical motto of Marischal College, Aberdeen: They say; what say they; let them say.] It expresses the three stages of an undergraduate’s career. “They say”—in his first year he accepts everything he is told as if it were inspired. “What say they”—in his second year he is skeptical and asks that question. “Let them say” expresses the attitude of contempt characteristic of his third year.
As quoted, without citation, in Alexander Macfarlane, 'Henry John Stephen Smith', Lectures on Ten British Mathematicians of the Nineteenth Century (1916), 100-101.
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[The] subjective [historical] element in geologic studies accounts for two characteristic types that can be distinguished among geologists: one considering geology as a creative art, the other regarding geology as an exact science.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 453.
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[To a man expecting a scientific proof of the impossibility of flying saucers] I might have said to him: “Listen, I mean that from my knowledge of the world that I see around me, I think that it is much more likely that the reports of flying saucers are the results of the known irrational characteristics of terrestrial intelligence than of the unknown rational efforts of extra-terrestrial intelligence.” It is just more likely, that is all. It is a good guess. And we always try to guess the most likely explanation, keeping in the back of the mind the fact that if it does not work we must discuss the other possibilities.
In The Character of Physical Law (1965, 2001), 166.
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… the reasoning process [employed in mathematics] is not different from that of any other branch of knowledge, … but there is required, and in a great degree, that attention of mind which is in some part necessary for the acquisition of all knowledge, and in this branch is indispensably necessary. This must be given in its fullest intensity; … the other elements especially characteristic of a mathematical mind are quickness in perceiving logical sequence, love of order, methodical arrangement and harmony, distinctness of conception.
In Treatise on Infinitesimal Calculus (1868), Vol. 8, 6.
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… the three positive characteristics that distinguish mathematical knowledge from other knowledge … may be briefly expressed as follows: first, mathematical knowledge bears more distinctly the imprint of truth on all its results than any other kind of knowledge; secondly, it is always a sure preliminary step to the attainment of other correct knowledge; thirdly, it has no need of other knowledge.
In Mathematical Essays and Recreations (1898), 35.
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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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