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Quantitative Quotes (29 quotes)

A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.
In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.
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A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.
In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.
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According to my views, aiming at quantitative investigations, that is at establishing relations between measurements of phenomena, should take first place in the experimental practice of physics. By measurement to knowledge [door meten tot weten] I should like to write as a motto above the entrance to every physics laboratory.
'The Significance of Quantitative Research in Physics', Inaugural Address at the University of Leiden (1882). In Hendrik Casimir, Haphazard Reality: Half a Century of Science (1983), 160-1.
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Almost all the greatest discoveries in astronomy have resulted from what we have elsewhere termed Residual Phenomena, of a qualitative or numerical kind, of such portions of the numerical or quantitative results of observation as remain outstanding and unaccounted for, after subducting and allowing for all that would result from the strict application of known principles.
Outlines of Astronomy (1876), 626.
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At the beginning of its existence as a science, biology was forced to take cognizance of the seemingly boundless variety of living things, for no exact study of life phenomena was possible until the apparent chaos of the distinct kinds of organisms had been reduced to a rational system. Systematics and morphology, two predominantly descriptive and observational disciplines, took precedence among biological sciences during the eighteenth and nineteenth centuries. More recently physiology has come to the foreground, accompanied by the introduction of quantitative methods and by a shift from the observationalism of the past to a predominance of experimentation.
In Genetics and the Origin of Species (1937, 1982), 6.
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Chemistry works with an enormous number of substances, but cares only for some few of their properties; it is an extensive science. Physics on the other hand works with rather few substances, such as mercury, water, alcohol, glass, air, but analyses the experimental results very thoroughly; it is an intensive science. Physical chemistry is the child of these two sciences; it has inherited the extensive character from chemistry. Upon this depends its all-embracing feature, which has attracted so great admiration. But on the other hand it has its profound quantitative character from the science of physics.
In Theories of Solutions (1912), xix.
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Dalton transformed the atomic concept from a philosophical speculation into a scientific theory—framed to explain quantitative observations, suggesting new tests and experiments, and capable of being given quantitative form through the establishment of relative masses of atomic particles.
Development of Concepts of Physics. In Clifford A. Pickover, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them (2008), 175.
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Experiments may be of two kinds: experiments of simple fact, and experiments of quantity. ...[In the latter] the conditions will ... vary, not in quality, but quantity, and the effect will also vary in quantity, so that the result of quantitative induction is also to arrive at some mathematical expression involving the quantity of each condition, and expressing the quantity of the result. In other words, we wish to know what function the effect is of its conditions. We shall find that it is one thing to obtain the numerical results, and quite another thing to detect the law obeyed by those results, the latter being an operation of an inverse and tentative character.
Principles of Science: A Treatise on Logic and Scientific Method (1874, 1892), 439.
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I beg this committee to recognize that knowledge is not simply another commodity. On the contrary. Knowledge is never used up, it increases by diffusion, and grows by dispersion. Knowledge and information cannot be quantitatively assessed, as a percentage of the G.N.P. Any willful cut in our resources of knowledge is an act of self-destruction.
While Librarian of Congress, asking a House Appropriations subcommittee to restore money cut from the library’s budget. As reported in New York Times (23 Feb 1986).
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It seems to me that the view toward which we are tending is that the specificity in gene action is always a chemical specificity, probably the production of enzymes which guide metabolic processes along particular channels. A given array of genes thus determines the production of a particular kind of protoplasm with particular properties—such, for example, as that of responding to surface forces by the formation of a special sort of semipermeable membrane, and that of responding to trivial asymmetries in the play of external stimuli by polarization, with consequent orderly quantitative gradients in all physiologic processes. Different genes may now be called into play at different points in this simple pattern, either through the local formation of their specific substrates for action, or by activation of a mutational nature. In either case the pattern becomes more complex and qualitatively differentiated. Successive interactions of differentiated regions and the calling into play of additional genes may lead to any degree of complexity of pattern in the organism as a largely self-contained system. The array of genes, assembled in the course of evolution, must of course be one which determines a highly self­regulatory system of reactions. On this view the genes are highly specific chemically, and thus called into play only under very specific conditions; but their morphological effects, if any, rest on quantitative influences of immediate or remote products on growth gradients, which are resultants of all that has gone on before in the organism.
In 'Genetics of Abnormal Growth in the Guinea Pig', Cold Spring Harbor Symposia on Quantitative Biology (1934), 2, 142.
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John [H.] Van Vleck, who was a leading young theoretical physicist when I was also a leading young theoretical physicist, said to me one day, “I never have made a contribution to physics that I didn’t get by fiddling with the equations,” and I said, “I’ve never made a contribution that I didn’t get by just having a new idea. Then I would fiddle with the equations to help support the new idea.” Van Vleck was essentially a mathematical physicist, you might say, and I was essentially a person of ideas. I don’t think I’m primarily mathematical. … I have a great curiosity about the nature of the world as a whole, and most of my ideas are qualitative rather than quantitative.
Interview with George B. Kauffman and Laurie M. Kauffman, in 'Linus Pauling: Reflections', American Scientist (Nov-Dec 1994), 82, No. 6, 523.
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Mathematics in its pure form, as arithmetic, algebra, geometry, and the applications of the analytic method, as well as mathematics applied to matter and force, or statics and dynamics, furnishes the peculiar study that gives to us, whether as children or as men, the command of nature in this its quantitative aspect; mathematics furnishes the instrument, the tool of thought, which we wield in this realm.
In Psychologic Foundations of Education (1898), 325.
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Mathematics, or the science of magnitudes, is that system which studies the quantitative relations between things; logic, or the science of concepts, is that system which studies the qualitative (categorical) relations between things.
In 'The Axioms of Logic', Tertium Organum: The Third Canon of Thought; a Key to the Enigmas of the World (1922), 246.
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Nor can it be supposed that the diversity of chemical structure and process stops at the boundary of the species, and that within that boundary, which has no real finality, rigid uniformity reigns. Such a conception is at variance with any evolutionary conception of the nature and origin of species. The existence of chemical individuality follows of necessity from that of chemical specificity, but we should expect the differences between individuals to be still more subtle and difficult of detection. Indications of their existence are seen, even in man, in the various tints of skin, hair, and eyes, and in the quantitative differences in those portions of the end-products of metabolism which are endogenous and are not affected by diet, such as recent researches have revealed in increasing numbers. Even those idiosyncrasies with regard to drugs and articles of food which are summed up in the proverbial saying that what is one man's meat is another man's poison presumably have a chemical basis.
Inborn Errors of Metabolism. The Croonian Lectures delivered before the Royal College of Physicians of London, in June, 1908 (1909), 2-3.
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Not enough of our society is trained how to understand and interpret quantitative information. This activity is a centerpiece of science literacy to which we should all strive—the future health, wealth, and security of our democracy depend on it. Until that is achieved, we are at risk of making under-informed decisions that affect ourselves, our communities, our country, and even the world.
From email message, as published on Huffington Post website (5 Feb 2015).
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One may summarize by saying that by a combination of behavior and physiology mammals can successfully occupy all but the most extreme environments on earth without anything more than quantitative shifts in the basic physiological pattern common to all.
From 'The role of physiology in the distribution of terrestrial vertebrates', collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 87.
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Quantitative work shows clearly that natural selection is a reality, and that, among other things, it selects Mendelian genes, which are known to be distributed at random through wild populations, and to follow the laws of chance in their distribution to offspring. In other words, they are an agency producing variation of the kind which Darwin postulated as the raw material on which selection acts.
'Natural Selection', Nature, 1929, 124, 444.
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Statistics are the triumph of the quantitative method, and the quantitative method is the victory of sterility and death.
'On Statistics'. In On the Silence of the Sea and Other Essays (1941),199-200.
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That all plants immediately and substantially stem from the element water alone I have learnt from the following experiment. I took an earthern vessel in which I placed two hundred pounds of earth dried in an oven, and watered with rain water. I planted in it a willow tree weighing five pounds. Five years later it had developed a tree weighing one hundred and sixty-nine pounds and about three ounces. Nothing but rain (or distilled water) had been added. The large vessel was placed in earth and covered by an iron lid with a tin-surface that was pierced with many holes. I have not weighed the leaves that came off in the four autumn seasons. Finally I dried the earth in the vessel again and found the same two hundred pounds of it diminished by about two ounces. Hence one hundred and sixty-four pounds of wood, bark and roots had come up from water alone. (1648)
A diligent experiment that was quantitatively correct only as far as it goes. He overlooked the essential role of air and photosynthesis in the growth process.
Complex. atque mist. elem. fig., 30, Opp. pp. 104-5; Aufgang, 148. In Walter Pagel, Joan Baptista Van Helmont (2002) , 53.
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The foundations of population genetics were laid chiefly by mathematical deduction from basic premises contained in the works of Mendel and Morgan and their followers. Haldane, Wright, and Fisher are the pioneers of population genetics whose main research equipment was paper and ink rather than microscopes, experimental fields, Drosophila bottles, or mouse cages. Theirs is theoretical biology at its best, and it has provided a guiding light for rigorous quantitative experimentation and observation.
'A Review of Some Fundamental Concepts and Problems of Population Genetics', Cold Spring Harbor Symposia on Quantitative Biology, 1955, 20, 13-14.
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The metaphysical philosopher from his point of view recognizes mathematics as an instrument of education, which strengthens the power of attention, develops the sense of order and the faculty of construction, and enables the mind to grasp under the simple formulae the quantitative differences of physical phenomena.
In Dialogues of Plato (1897), Vol. 2, 78.
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The physiological combustion theory takes as its starting point the fundamental principle that the amount of heat that arises from the combustion of a given substance is an invariable quantity–i.e., one independent of the circumstances accompanying the combustion–from which it is more specifically concluded that the chemical effect of the combustible materials undergoes no quantitative change even as a result of the vital process, or that the living organism, with all its mysteries and marvels, is not capable of generating heat out of nothing.
Bemerkungen über das mechanische Aequivalent der Wärme [Remarks on the Mechanical Equivalent of Heat] (1851), 17-9. Trans. Kenneth L. Caneva, Robert Mayer and the Conservation of Energy (1993), 240.
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The role of inhibition in the working of the central nervous system has proved to be more and more extensive and more and more fundamental as experiment has advanced in examining it. Reflex inhibition can no longer be regarded merely as a factor specially developed for dealing with the antagonism of opponent muscles acting at various hinge-joints. Its role as a coordinative factor comprises that, and goes beyond that. In the working of the central nervous machinery inhibition seems as ubiquitous and as frequent as is excitation itself. The whole quantitative grading of the operations of the spinal cord and brain appears to rest upon mutual interaction between the two central processes 'excitation' and 'inhibition', the one no less important than the other. For example, no operation can be more important as a basis of coordination for a motor act than adjustment of the quantity of contraction, e.g. of the number of motor units employed and the intensity of their individual tetanic activity. This now appears as the outcome of nice co-adjustment of excitation and inhibition upon each of all the individual units which cooperate in the act.
Inhibition as a Coordinative Factor', Nobel Lecture (12 Dec 1932). Nobel Lectures: Physiology or Medicine 1922-1941 (1965), 288.
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The saying often quoted from Lord Kelvin… that “where you cannot measure your knowledge is meagre and unsatisfactory,” as applied in mental and social science, is misleading and pernicious. This is another way of saying that these sciences are not science in the sense of physical science and cannot attempt to be such without forfeiting their proper nature and function. Insistence on a concretely quantitative economics means the use of statistics of physical magnitudes, whose economic meaning and significance is uncertain and dubious. (Even wheat is approximately homogeneous only if measured in economic terms.) And a similar statement would even apply more to other social sciences. In this field, the Kelvin dictum very largely means in practice, “if you cannot measure, measure anyhow!”
'What is Truth' in Economics? (1956), 166.
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There is no sharp boundary line separating the reactions of the immune bodies from chemical processes between crystalloids, just as in nature there exists every stage between crystalloid and colloid. The nearer the colloid particle approximates to the normal electrolyte, the nearer its compounds must obviously come to conforming to the law of simple stoichiometric proportions, and the compounds themselves to simple chemical compounds. At this point, it should be recalled that Arrhenius has shown that the quantitative relationship between toxin and antitoxin is very similar to that between acid and base.
Landsteiner and Nicholas von Jagic, 'Uber Reaktionen anorganischer Kolloide und Immunkorper', Münchener medizinischer Wochenschrift (1904), 51, 1185-1189. Trans. Pauline M. H. Mazumdar.
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To us … the only acceptable point of view appears to be the one that recognizes both sides of reality—the quantitative and the qualitative, the physical and the psychical—as compatible with each other, and can embrace them simultaneously … It would be most satisfactory of all if physis and psyche (i.e., matter and mind) could be seen as complementary aspects of the same reality.
From Lecture at the Psychological Club of Zurich (1948), 'The Influence of Archetypal Ideas on the Scientific Theories of Kepler', collected in Writings on Physics and Philosophy (1994), 260, as translated by Robert Schlapp.
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When experimental results are found to be in conflict with those of an earlier investigator, the matter is often taken too easily and disposed of for an instance by pointing out a possible source of error in the experiments of the predessessor, but without enquiring whether the error, if present, would be quantitatively sufficient to explain the discrepancy. I think that disagreement with former results should never be taken easily, but every effort should be made to find a true explanation. This can be done in many more cases than it actually is; and as a result, it can be done more easily by the man “on the spot” who is already familiar with the essential details. But it may require a great deal of imagination, and very often it will require supplementary experiments.
From 'August Krogh' in Festkrift Křbenhavns Universitet 1950 (1950), 18, as cited by E. Snorrason, 'Krogh, Schack August Steenberg', in Charles Coulton Gillispie (ed.), Dictionary of Scientific Biography (1973), Vol 7, 501. The DSB quote is introduced, “All his life Krogh was more interested in physical than in chemiical problems in biology, and he explained his critical attitude thus.”
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While it is never safe to affirm that the future of Physical Science has no marvels in store even more astonishing than those of the past, it seems probable that most of the grand underlying principles have been firmly established, and that further advances are to be sought chiefly in the rigorous applications of these principles to all the phenomena which come under our notice. It is here that the science of measurement shows its importance—where the quantitative results are more to be desired than qualitative work. An eminent physicist has remarked that the future truths of Physical Science are to be looked for in the sixth place of decimals.
University of Chicago, Annual Register 1894-1895 (1894), 150. Michelson also incorporated these lines in his address, 'Some of the Objects and Methods of Physical Science', at the opening of the Physics and Electrical Engineering Laboratory at the University of Kansas, reprinted in The Electrical Engineer (1 Jan 1896), 21, No. 400, 9.
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[Henry Cavendish] fixed the weight of the earth; he established the proportions of the constituents of the air; he occupied himself with the quantitative study of the laws of heat; and lastly, he demonstrated the nature of water and determined its volumetric composition. Earth, air, fire, and water—each and all came within the range of his observations.
Essays in Historical Chemistry (1894), 86.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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- 40 -
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