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Home > Category Index for Science Quotations > Category Index V > Category: Vague

Vague Quotes (26 quotes)

A little science is something that they must have. I should like my nephews to know what air is, and water; why we breathe, and why wood burns; the nutritive elements essential to plant life, and the constituents of the soil. And it is no vague and imperfect knowledge from hearsay I would have them gain of these fundamental truths, on which depend agriculture and the industrial arts and our health itself; I would have them know these things thoroughly from their own observation and experience. Books here are insufficient, and can serve merely as aids to scientific experiment.
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Another advantage of a mathematical statement is that it is so definite that it might be definitely wrong; and if it is found to be wrong, there is a plenteous choice of amendments ready in the mathematicians’ stock of formulae. Some verbal statements have not this merit; they are so vague that they could hardly be wrong, and are correspondingly useless.
From 'Mathematics of War and Foreign Politics', in James R. Newman, The World of Mathematics (1956), Vol. 2, 1248.
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Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.
In 'The Future of Data Analysis', Annals of Mathematical Statistics (1962), 33, No. 1, 13-14.
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Gel’fand amazed me by talking of mathematics as though it were poetry. He once said about a long paper bristling with formulas that it contained the vague beginnings of an idea which could only hint at and which he had never managed to bring out more clearly. I had always thought of mathematics as being much more straightforward: a formula is a formula, and an algebra is an algebra, but Gel’fand found hedgehogs lurking in the rows of his spectral sequences!
In '1991 Ruth Lyttle Satter Prize', Notices of the American Mathematical Society (Mar 1991), 38, No. 3, 186. This is from her acceptance of the 1991 Ruth Lyttle Satter Prize.
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Germs of a theory, though in their present condition they are vague and formless … may be said to resemble stones in the quarry, rough and unhewn, but which may some time become corner-stones, columns, and entablatures in the future edifice.
In Report on the Geology of the High Plateaus of Utah (1880), 114.
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Governments and parliaments must find that astronomy is one of the sciences which cost most dear: the least instrument costs hundreds of thousands of dollars, the least observatory costs millions; each eclipse carries with it supplementary appropriations. And all that for stars which are so far away, which are complete strangers to our electoral contests, and in all probability will never take any part in them. It must be that our politicians have retained a remnant of idealism, a vague instinct for what is grand; truly, I think they have been calumniated; they should be encouraged and shown that this instinct does not deceive them, that they are not dupes of that idealism.
In Henri Poincaré and George Bruce Halsted (trans.), The Value of Science: Essential Writings of Henri Poincare (1907), 84.
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Humanism is only another name for spiritual laziness, or a vague half-creed adopted by men of science and logicians whose heads are too occupied with the world of mathematics and physics to worry about religious categories.
In The Outsider (1956), 279.
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I never said a word against eminent men of science. What I complain of is a vague popular philosophy which supposes itself to be scientific when it is really nothing but a sort of new religion and an uncommonly nasty one. When people talked about the fall of man, they knew they were talking about a mystery, a thing they didn’t understand. Now they talk about the survival of the fittest: they think they do understand it, whereas they have not merely no notion, they have an elaborately false notion of what the words mean.
In The Club of Queer Trades (1903, 1905), 241.
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I would like to be rather more special, and I would like to be understood in an honest way rather than in a vague way.
In The Character of Physical Law (1965, 2001), 13.
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In every case the awakening touch has been the mathematical spirit, the attempt to count, to measure, or to calculate. What to the poet or the seer may appear to be the very death of all his poetry and all his visions—the cold touch of the calculating mind,—this has proved to be the spell by which knowledge has been born, by which new sciences have been created, and hundreds of definite problems put before the minds and into the hands of diligent students. It is the geometrical figure, the dry algebraical formula, which transforms the vague reasoning of the philosopher into a tangible and manageable conception; which represents, though it does not fully describe, which corresponds to, though it does not explain, the things and processes of nature: this clothes the fruitful, but otherwise indefinite, ideas in such a form that the strict logical methods of thought can be applied, that the human mind can in its inner chamber evolve a train of reasoning the result of which corresponds to the phenomena of the outer world.
In A History of European Thought in the Nineteenth Century (1896), Vol. 1, 314.
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In reality the origin of the notion of derivatives is in the vague feeling of the mobility of things, and of the greater or less speed with which phenomena take place; this is well expressed by the terms fluent and fluxion, which were used by Newton and which we may believe were borrowed from the ancient mathematician Heraclitus.
From address to the section of Algebra and Analysis, International Congress of Arts and Sciences, St. Louis (22 Sep 1904), 'On the Development of Mathematical Analysis and its Relation to Certain Other Sciences,' as translated by M.W. Haskell in Bulletin of the American Mathematical Society (May 1905), 11, 407.
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Mathematical proofs are essentially of three different types: pre-formal; formal; post-formal. Roughly the first and third prove something about that sometimes clear and empirical, sometimes vague and ‘quasi-empirical’ stuff, which is the real though rather evasive subject of mathematics.
In Mathematics, Science and Epistemology (1980), Vol. 2, 69.
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No problem can be solved until it is reduced to some simple form. The changing of a vague difficulty into a specific, concrete form is a very essential element in thinking.
Seen, for example, in The Grain and Feed Review (1931), 21, 34.
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Our popular lecturers on physics present us with chains of deductions so highly polished that it is a luxury to let them slip from end to end through our fingers. But they leave nothing behind but a vague memory of the sensation they afforded.
Said by the fictional character Lydia in Cashel Byron’s Profession (1886, 1906), 88.
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Quantity is that which is operated with according to fixed mutually consistent laws. Both operator and operand must derive their meaning from the laws of operation. In the case of ordinary algebra these are the three laws already indicated [the commutative, associative, and distributive laws], in the algebra of quaternions the same save the law of commutation for multiplication and division, and so on. It may be questioned whether this definition is sufficient, and it may be objected that it is vague; but the reader will do well to reflect that any definition must include the linear algebras of Peirce, the algebra of logic, and others that may be easily imagined, although they have not yet been developed. This general definition of quantity enables us to see how operators may be treated as quantities, and thus to understand the rationale of the so called symbolical methods.
In 'Mathematics', Encyclopedia Britannica (9th ed.).
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Tactics used by many practitioners of pseudoscience: make a large number of vaguely scientific arguments in the hope of making the desired conclusion seem inevitable. It is essential to recognize that a disconnected assemblage of weak arguments does not create a single, strong scientific argument.
Co-author with Matt Ford, Chris Lee and Jonathan Gitlin, in 'Diluting the Scientific Method: Ars Looks at Homeopathy' (11 Sep 2007) on arstechnica.com web site.
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That sometimes clear … and sometimes vague stuff … which is … mathematics.
In Mathematics, Science and Epistemology (1980), Vol. 2, 69. This quote condensed from a longer quote which begins, “Mathematical proofs are…”, on the Imre Lakatos Quotes page of this website.
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The arithmetization of mathematics … which began with Weierstrass … had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics. These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought. But how can we avoid the use of human language? The … symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic.
In Tobias Dantzig and Joseph Mazur (ed.), Number: The Language of Science (1930, ed. by Joseph Mazur 2007), 99.
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The anxious precision of modern mathematics is necessary for accuracy, … it is necessary for research. It makes for clearness of thought and for fertility in trying new combinations of ideas. When the initial statements are vague and slipshod, at every subsequent stage of thought, common sense has to step in to limit applications and to explain meanings. Now in creative thought common sense is a bad master. Its sole criterion for judgment is that the new ideas shall look like the old ones, in other words it can only act by suppressing originality.
In Introduction to Mathematics (1911), 157.
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The employment of mathematical symbols is perfectly natural when the relations between magnitudes are under discussion; and even if they are not rigorously necessary, it would hardly be reasonable to reject them, because they are not equally familiar to all readers and because they have sometimes been wrongly used, if they are able to facilitate the exposition of problems, to render it more concise, to open the way to more extended developments, and to avoid the digressions of vague argumentation.
From Recherches sur les Principes Mathématiques de la Théorie des Richesses (1838), as translated by Nathaniel T. Bacon in 'Preface', Researches Into Mathematical Principles of the Theory of Wealth (1897), 3-4. From the original French, “L’emploi des signes mathématiques est chose naturelle toutes les fois qu'il s'agit de discuter des relations entre des grandeurs ; et lors même qu’ils ne seraient pas rigoureusement nécessaires, s’ils peuvent faciliter l’exposition, la rendre plus concise, mettre sur la voie de développements plus étendus, prévenir les écarts d’une vague argumentation, il serait peu philosophique de les rebuter, parce qu'ils ne sont pas également familiers à tous les lecteurs et qu'on s'en est quelquefois servi à faux.”
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The observer is not he who merely sees the thing which is before his eyes, but he who sees what parts the thing is composed of. To do this well is a rare talent. One person, from inattention, or attending only in the wrong place, overlooks half of what he sees; another sets down much more than he sees, confounding it with what he imagines, or with what he infers; another takes note of the kind of all the circumstances, but being inexpert in estimating their degree, leaves the quantity of each vague and uncertain; another sees indeed the whole, but makes such an awkward division of it into parts, throwing into one mass things which require to be separated, and separating others which might more conveniently be considered as one, that the result is much the same, sometimes even worse than if no analysis had been attempted at all.
In A System of Logic Ratiocinative and Inductive (1858), 216.
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The sciences are like a beautiful river, of which the course is easy to follow, when it has acquired a certain regularity; but if one wants to go back to the source, one will find it nowhere, because it is everywhere; it is spread so much [as to be] over all the surface of the earth; it is the same if one wants to go back to the origin of the sciences, one will find only obscurity, vague ideas, vicious circles; and one loses oneself in the primitive ideas.
In Essai sur les machines en général (1783), conclusion, as translated in Ivor Grattan-Guinness, Convolutions in French Mathematics, 1800-1840 (1990), Vol. 1, 32.
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Think of how many religions attempt to validate themselves with prophecy. Think of how many people rely on these prophecies, however vague, however unfulfilled, to support or prop up their beliefs. Yet has there ever been a religion with the prophetic accuracy and reliability of science? ... No other human institution comes close.
The Demon-Haunted World: Science as a Candle in the Dark (1997), 30.
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To see the clear, logical ideas gradually being disentangled from vagueness and confusion is vastly more instructive than simply starting with the logical ideas.
In 'Projective Geometery', Prelude to Mathematics (1955), 145.
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Vagueness is very much more important in the theory of knowledge than you would judge it to be from the writings of most people. Everything is vague to a degree you do not realize till you have tried to make it precise, and everything precise is so remote from everything that we normally think, that you cannot for a moment suppose that is what we really mean when we say what we think.
In The Philosophy of Logical Atomism (1918, 1919), 2.
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We can see our forests vanishing, our water-powers going to waste, our soil being carried by floods into the sea; and the end of our coal and our iron is in sight. But our larger wastes of human effort, which go on every day through such of our acts as are blundering, ill-directed, or inefficient, … are less visible, less tangible, and are but vaguely appreciated.
In The Principles of Scientific Management (1911), 5.
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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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Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
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Francis Bacon
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- 10 -
Aristotle
John Watson
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Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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