Insoluble Quotes (15 quotes)
A modern branch of mathematics, having achieved the art of dealing with the infinitely small, can now yield solutions in other more complex problems of motion, which used to appear insoluble. This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion, admits the conception of the infinitely small, and so conforms to the chief condition of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when dealing with separate elements of motion instead of examining continuous motion. In seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable human wills, is continuous. To understand the laws of this continuous movement is the aim of history. … Only by taking an infinitesimally small unit for observation (the differential of history, that is, the individual tendencies of man) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.
War and Peace (1869), Book 11, Chap. 1.
After Gibbs, one the most distinguished [American scientists] was Langley, of the Smithsonian. … He had the physicist’s heinous fault of professing to know nothing between flashes of intense perception. … Rigidly denying himself the amusement of philosophy, which consists chiefly in suggesting unintelligible answers to insoluble problems, and liked to wander past them in a courteous temper, even bowing to them distantly as though recognizing their existence, while doubting their respectability.
The Education of Henry Adams: An Autobiography? (1918), 377.
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.
Dust consisting of fine fibers of asbestos, which are insoluble and virtually indestructible, may become a public health problem in the near future. At a recent international conference on the biological effects of asbestos sponsored by the New York Academy of Sciences, participants pointed out on the one hand that workers exposed to asbestos dust are prone in later life to develop lung cancer, and on the other hand that the use of this family of fibrous silicate compounds has expanded enormously during the past few decades. A laboratory curiosity 100 years ago, asbestos today is a major component of building materials.
— Magazine
In Scientific American (Sep 1964). As cited in '50, 100 & 150 Years Ago', Scientific American (Dec 2014), 311, No. 6, 98.
If two masters of the same art differ in their statement of it, in all likelihood the insoluble problem lies midway between them.
In The Maxims and Reflections of Goethe (1906), 186.
In the sphere of natural science let us remember that we have always to deal with an insoluble problem. Let us prove keen and honest in attending to anything which is in any way brought to our notice, most of all when it does not fit in with our previous ideas. For it is only thereby that we perceive the problem, which does indeed lie in nature, but still more in man.
In The Maxims and Reflections of Goethe (1906), 183.
Philosophy … consists chiefly in suggesting unintelligible answers to insoluble problems..
In The Education of Henry Adams: An Autobiography (1918), 377.
Search the scriptures of human achievement and you cannot find any to equal in beneficence the introduction of Anæsthesia, Sanitation, with ail that it includes, and Asepsis—a short half century’s contribution towards the practical solution of the problems of human suffering, regarded as eternal and insoluble.
Address to the Canadian Medical association, Montreal (1902). Collected in 'Chavinism in Medicine', Aequanimitas (1904), 283.
The empirical domain of objective contemplation, and the delineation of our planet in its present condition, do not include a consideration of the mysterious and insoluble problems of origin and
existence.
In lecture, 'Organic Life', collected in Cosmos, the Elements of the Physical World (1849), 348, as translated by E.C. Otté. Also seen translated as “The mysterious and unsolved problem of how things came to be does not enter the empirical province of objective research, which is confined to a description of things as they are.”
The message from the Moon which we have flashed to the far corners of this planet is that no problem need any longer be considered insoluble.
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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.
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.
The pursuit of science leads only to the insoluble.
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The real achievement in discoveries … is seeing an analogy where no one saw one before. … The essence of discovery is that unlikely marriage of … previously unrelated forms of reference or universes of discourse, whose union will solve the previously insoluble problem.
In Act of Creation (1964), 201.
Through the discovery of Buchner, Biology was relieved of another fragment of mysticism. The splitting up of sugar into CO2 and alcohol is no more the effect of a 'vital principle' than the splitting up of cane sugar by invertase. The history of this problem is instructive, as it warns us against considering problems as beyond our reach because they have not yet found their solution.
The Dynamics of Living Matter (1906), 22.
Winwood Reade … remarks that while a man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never foretell what any one man will do, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician.
Character Sherlock Holmes recommends Winwood Reade’s book The Martyrdom of Man to Dr. Watson in The Sign of the Four (1890), 196. Earlier in the novel, Holmes calls Reade’s book “one of the most remarkable ever penned.” Reade is a real person and his book was published in 1872. The actual statement in it reads: “As a single atom man is an enigma: as a whole he is a mathematical problem.”