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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Home > Category Index for Science Quotations > Category Index S > Category: Systematic

Systematic Quotes (33 quotes)

Philosophie [ist] der systematische Mißbrauch einer eigens zu diesem Zwecke ersonnenen Terminologie.
Philosophy [is] the systematic abuse of a terminology specially designed for this purpose.
In Die Philosophie der Mathematik in der Gegenwart (1932), 1. English version from Google Translate.
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Alchemy. The link between the immemorial magic arts and modern science. Humankind’s first systematic effort to unlock the secrets of matter by reproducible experiment.
In Good Words to You (1987), 6.
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As systematic unity is what first raises ordinary knowledge to the rank of science, that is, makes a system out of a mere aggregate of knowledge, architectonic is the doctrine of the scientific in our knowledge, and therefore necessarily forms part of the doctrine of method.
In'The Transcendental Doctrine of Method', Critique of Pure Reason (2016), 653. Note: architectonic = the art of constructing systems.
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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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Chemists have made of phlogiston a vague principle which is not at all rigorously defined, and which, in consequence, adapts itself to all explanations in which it is wished it shall enter; sometimes it is free fire, sometimes it is fire combined with the earthy element; sometimes it passes through the pores of vessels, sometimes they are impenetrable to it; it explains both the causticity and non-causticity, transparency and opacity, colours and absence of colours. It is a veritable Proteus which changes its form every instant. It is time to conduct chemistry to a more rigorous mode of reasoning ... to distinguish fact and observation from what is systematic and hypothetical.
'Réflexions sur le phlogistique', Mémoires de l'Académie des Sciences, 1783, 505-38. Reprinted in Oeuvres de Lavoisier (1864), Vol. 2, 640, trans. M. P. Crosland.
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Consciously and systematically Klein sought to enthrall me with the problems of mathematical physics, and to win me over to his conception of these problems as developed it in lecture courses in previous years. I have always regarded Klein as my real teacher only in things mathematical, but also in mathematical physics and in my conception of mechanics.
As quoted in Paul Forman and Armin Hermann, 'Sommerfeld, Arnold (Johannes Wilhelm)', Biography in Dictionary of Scientific Biography (1975), Vol. 12, 526. Cited from 'Autobiographische Skizze', Gesammelte Schriften, Vol 4, 673–682.
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Does the evolutionary doctrine clash with religious faith? It does not. It is a blunder to mistake the Holy Scriptures for elementary textbooks of astronomy, geology, biology, and anthropology. Only if symbols are construed to mean what they are not intended to mean can there arise imaginary, insoluble conflicts. ... the blunder leads to blasphemy: the Creator is accused of systematic deceitfulness.
In 'Nothing in Biology Makes Sense Except in the Light of Evolution', The American Biology Teacher (Mar 1973), 125-129.
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Economists use the expression “opportunity costs” for losses incurred through certain choices made over others, including ignorance and inaction. For systematics, or more precisely the neglect of systematics and the biological research dependent upon it, the costs are very high.
In 'Edward O. Wilson: The Biological Diversity Crisis: A Challenge to Science', Issues in Science and Technology (Fall 1985), 2, No. 1, 25.
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Engineering is the professional and systematic application of science to the efficient utilization of natural resources to produce wealth.
T. J. Hoover and John Charles Lounsbury (J.C.L.) Fish, The Engineering Profession (1941), 10.
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In all disciplines in which there is systematic knowledge of things with principles, causes, or elements, it arises from a grasp of those: we think we have knowledge of a thing when we have found its primary causes and principles, and followed it back to its elements. Clearly, then, systematic knowledge of nature must start with an attempt to settle questions about principles.
Aristotle
In Physics Book 1, Chap 1, as translated in J.L. Ackrill, A New Aristotle Reader (1988), 81.
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In mathematics ... we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials ... being studied, and to correlate the material in a systematic and orderly
Geometry and the imagination (New York, 1952).
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In the field of thinking, the whole history of science from geocentrism to the Copernican revolution, from the false absolutes of Aristotle’s physics to the relativity of Galileo’s principle of inertia and to Einstein’s theory of relativity, shows that it has taken centuries to liberate us from the systematic errors, from the illusions caused by the immediate point of view as opposed to “decentered” systematic thinking.
As quoted in D. E. Berlyne, Structure and Direction in Thinking (1965), 232.
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It is the desire for explanations that are at once systematic and controllable by factual evidence that generates science; and it is the organization and classification of knowledge on the basis of explanatory principles that is the distinctive goal of the sciences.
The Structure of Science (1961), 4.
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It would not be difficult to come to an agreement as to what we understand by science. Science is the century-old endeavor to bring together by means of systematic thought the perceptible phenomena of this world into as thoroughgoing an association as possible. To put it boldly, it is the attempt at the posterior reconstruction of existence by the process of conceptualization. But when asking myself what religion is I cannot think of the answer so easily. And even after finding an answer which may satisfy me at this particular moment, I still remain convinced that I can never under any circumstances bring together, even to a slight extent, the thoughts of all those who have given this question serious consideration.
…...
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Let him [the author] be permitted also in all humility to add … that in consequence of the large arrears of algebraical and arithmetical speculations waiting in his mind their turn to be called into outward existence, he is driven to the alternative of leaving the fruits of his meditations to perish (as has been the fate of too many foregone theories, the still-born progeny of his brain, now forever resolved back again into the primordial matter of thought), or venturing to produce from time to time such imperfect sketches as the present, calculated to evoke the mental co-operation of his readers, in whom the algebraical instinct has been to some extent developed, rather than to satisfy the strict demands of rigorously systematic exposition.
In Philosophic Magazine (1863), 460.
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Man, biologically considered, and whatever else he may be into the bargain, is simply the most formidable of all the beasts of prey, and, indeed, the only one that preys systematically on its own species.
From 'Remarks at The Peace Banquet' (7 Oct 1904), Boston, on the closing day of the World’s Peace Congress. Printed in Atlantic Monthly (Dec 1904), 845-846. Collected in Essays in Religion and Morality (1982), Vol. 9, 121.
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Mathematical knowledge, therefore, appears to us of value not only in so far as it serves as means to other ends, but for its own sake as well, and we behold, both in its systematic external and internal development, the most complete and purest logical mind-activity, the embodiment of the highest intellect-esthetics.
In 'Ueber Wert und angeblichen Unwert der Mathematik', Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 13, 381.
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Mathematics, including not merely Arithmetic, Algebra, Geometry, and the higher Calculus, but also the applied Mathematics of Natural Philosophy, has a marked and peculiar method or character; it is by preeminence deductive or demonstrative, and exhibits in a nearly perfect form all the machinery belonging to this mode of obtaining truth. Laying down a very small number of first principles, either self-evident or requiring very little effort to prove them, it evolves a vast number of deductive truths and applications, by a procedure in the highest degree mathematical and systematic.
In Education as a Science (1879), 148.
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Organization is simply the means by which the acts of ordinary men can be made to add up to extraordinary results. To this idea of progress that does not wait on some lucky break, some chance discovery, or some rare stroke of genius, but instead is achieved through systematic, cumulative effort, the engineer has contributed brilliantly.
In A Professional Guide for Young Engineers (1949, 1967), 36.
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Our first endeavors are purely instinctive prompting of an imagination vivid and undisciplined. As we grow older reason asserts itself and we become more and more systematic and designing. But those early impulses, though not immediately productive, are o
http://web.archive.org/web/20070109161311/http://www.knowprose.com/node/12961
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Psychology … tells us that we rarely work through reasons and evidence in a systematic way; weighing information carefully and suspending the impulse to draw conclusions. Instead, much of the time we use mental shortcuts or rules of thumb that save us mental effort. These habits often work reasonably well, but they also can lead us to conclusions we might dismiss if we applied more thought.
As co-author with Kathleen Hall Jamieson, in unSpun: Finding Facts in a World of Disinformation (2007), 70.
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Suppose then I want to give myself a little training in the art of reasoning; suppose I want to get out of the region of conjecture and probability, free myself from the difficult task of weighing evidence, and putting instances together to arrive at general propositions, and simply desire to know how to deal with my general propositions when I get them, and how to deduce right inferences from them; it is clear that I shall obtain this sort of discipline best in those departments of thought in which the first principles are unquestionably true. For in all our thinking, if we come to erroneous conclusions, we come to them either by accepting false premises to start with—in which case our reasoning, however good, will not save us from error; or by reasoning badly, in which case the data we start from may be perfectly sound, and yet our conclusions may be false. But in the mathematical or pure sciences,—geometry, arithmetic, algebra, trigonometry, the calculus of variations or of curves,— we know at least that there is not, and cannot be, error in our first principles, and we may therefore fasten our whole attention upon the processes. As mere exercises in logic, therefore, these sciences, based as they all are on primary truths relating to space and number, have always been supposed to furnish the most exact discipline. When Plato wrote over the portal of his school. “Let no one ignorant of geometry enter here,” he did not mean that questions relating to lines and surfaces would be discussed by his disciples. On the contrary, the topics to which he directed their attention were some of the deepest problems,— social, political, moral,—on which the mind could exercise itself. Plato and his followers tried to think out together conclusions respecting the being, the duty, and the destiny of man, and the relation in which he stood to the gods and to the unseen world. What had geometry to do with these things? Simply this: That a man whose mind has not undergone a rigorous training in systematic thinking, and in the art of drawing legitimate inferences from premises, was unfitted to enter on the discussion of these high topics; and that the sort of logical discipline which he needed was most likely to be obtained from geometry—the only mathematical science which in Plato’s time had been formulated and reduced to a system. And we in this country [England] have long acted on the same principle. Our future lawyers, clergy, and statesmen are expected at the University to learn a good deal about curves, and angles, and numbers and proportions; not because these subjects have the smallest relation to the needs of their lives, but because in the very act of learning them they are likely to acquire that habit of steadfast and accurate thinking, which is indispensable to success in all the pursuits of life.
In Lectures on Teaching (1906), 891-92.
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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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Technology means the systematic application of scientific or other organized knowledge to practical tasks.
In 'The Imperatives of Technology', The New Industrial State (1967), Chap. 2, 12.
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The end of the eighteenth and the beginning of the nineteenth century were remarkable for the small amount of scientific movement going on in this country, especially in its more exact departments. ... Mathematics were at the last gasp, and Astronomy nearly so—I mean in those members of its frame which depend upon precise measurement and systematic calculation. The chilling torpor of routine had begun to spread itself over all those branches of Science which wanted the excitement of experimental research.
Quoted in Sophia Elizabeth De Morgan, Memoir of Augustus De Morgan (1882), 41
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The family unit is the institution for the systematic production of mental illness.
From interview on TV program, The Tonight Show With Johnny Carson. As quoted and cited in David Berg, Run, Brother, Run: A Memoir of a Murder in My Family (2013), 242.
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The life work of the engineer consists in the systematic application of natural forces and the systematic development of natural resources in the service of man.
Paper presented (15 Nov 1905) to the Association of American Agricultural Colleges and Experiment Stations, Washington, D.C., Proceedings of the 19th Annual Convention of the Association of American Agricultural Colleges and Experiment Stations (1906), Vol. 19-24, 90. Initials only given in this paper for H.W. Tyler (of Massachussetts); Webmaster tentatively matched with Harry Walter Tyler of M.I.T.
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The origin of a science is usually to be sought for not in any systematic treatise, but in the investigation and solution of some particular problem. This is especially the case in the ordinary history of the great improvements in any department of mathematical science. Some problem, mathematical or physical, is proposed, which is found to be insoluble by known methods. This condition of insolubility may arise from one of two causes: Either there exists no machinery powerful enough to effect the required reduction, or the workmen are not sufficiently expert to employ their tools in the performance of an entirely new piece of work. The problem proposed is, however, finally solved, and in its solution some new principle, or new application of old principles, is necessarily introduced. If a principle is brought to light it is soon found that in its application it is not necessarily limited to the particular question which occasioned its discovery, and it is then stated in an abstract form and applied to problems of gradually increasing generality.
Other principles, similar in their nature, are added, and the original principle itself receives such modifications and extensions as are from time to time deemed necessary. The same is true of new applications of old principles; the application is first thought to be merely confined to a particular problem, but it is soon recognized that this problem is but one, and generally a very simple one, out of a large class, to which the same process of investigation and solution are applicable. The result in both of these cases is the same. A time comes when these several problems, solutions, and principles are grouped together and found to produce an entirely new and consistent method; a nomenclature and uniform system of notation is adopted, and the principles of the new method become entitled to rank as a distinct science.
In A Treatise on Projections (1880), Introduction, xi. Published as United States Coast and Geodetic Survey, Treasury Department Document, No. 61.
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The results of systematic symbolical reasoning must always express general truths, by their nature; and do not, for their justification, require each of the steps of the process to represent some definite operation upon quantity. The absolute universality of the interpretation of symbols is the fundamental principle of their use.
In 'The Foundations of Higher Mathematics', The Philosophy of the Inductive Sciences (1847), Part I, Bk. 2, 149.
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This is what nonscientists don’t know, and this is what scientists are too bashful to talk about publicly, at least until they grow old enough to be shameless. Science at its highest level is ultimately the organization of, the systematic pursuit of, and
John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren't There More Happy People?: Smart Quotes for Dumb Times (2009), 274.
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This science, Geometry, is one of indispensable use and constant reference, for every student of the laws of nature; for the relations of space and number are the alphabet in which those laws are written. But besides the interest and importance of this kind which geometry possesses, it has a great and peculiar value for all who wish to understand the foundations of human knowledge, and the methods by which it is acquired. For the student of geometry acquires, with a degree of insight and clearness which the unmathematical reader can but feebly imagine, a conviction that there are necessary truths, many of them of a very complex and striking character; and that a few of the most simple and self-evident truths which it is possible for the mind of man to apprehend, may, by systematic deduction, lead to the most remote and unexpected results.
In The Philosophy of the Inductive Sciences Part 1, Bk. 2, chap. 4, sect. 8 (1868).
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When I was a little over eight years old,… I was sent to a day-school…. [By this time] my taste for natural history, and more especially for collecting, was well developed. I tried to make out the names of plants, and collected all sorts of things, shells, seals, franks, coins, and minerals. The passion for collecting which leads a man to be a systematic naturalist, a virtuoso, or a miser, was very strong in me.
In Charles Darwin and Francis Darwin (ed.), 'Autobiography', The Life and Letters of Charles Darwin (1887, 1896), Vol. 1, 26.
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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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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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- 80 -
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