Minimum Quotes (13 quotes)
Cosmology, for centuries consisting of speculation based on a minimum of observational evidence and a maximum of philosophical predilection, became in the twentieth century an observational science, its theories now subject to verification or refutation to a degree previously unimaginable.
Opening sentence in 'Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe', Historical Studies in the Physical Sciences (1982), 13, No. 1, 41.
Devised with a maximum of erudition and a minimum of common sense.
Aphorism 56 in Notebook D (1773-1775), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 52.
It is the constant aim of the mathematician to reduce all his expressions to their lowest terms, to retrench every superfluous word and phrase, and to condense the Maximum of meaning into the Minimum of language.
In Address (22 Feb 1877) for Commemoration Day at Johns Hopkins University. Published as a pamphlet, and reprinted in The Collected Mathematical Papers of James Joseph Sylvester: (1870-1883) (1909), Vol. 3, 72-73.
Mathematicians deal with possible worlds, with an infinite number of logically consistent systems. Observers explore the one particular world we inhabit. Between the two stands the theorist. He studies possible worlds but only those which are compatible with the information furnished by observers. In other words, theory attempts to segregate the minimum number of possible worlds which must include the actual world we inhabit. Then the observer, with new factual information, attempts to reduce the list further. And so it goes, observation and theory advancing together toward the common goal of science, knowledge of the structure and observation of the universe.
Lecture to Sigma Xi, 'The Problem of the Expanding Universe' (1941), printed in Sigma Xi Quarterly (1942), 30, 104-105. Reprinted in Smithsonian Institution Report of the Board of Regents (1943), 97, 123. As cited by Norriss S. Hetherington in 'Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe', Historical Studies in the Physical Sciences (1982), 13, No. 1, 63.
My belief (is) that one should take a minimum of care and preparation over first experiments. If they are unsuccessful one is not then discouraged since many possible reasons for failure can be thought of, and improvements can be made. Much can often be learned by the repetition under different conditions, even if the desired result is not obtained. If every conceivable precaution is taken at first, one is often too discouraged to proceed at all.
Nobel Lectures in Chemistry (1999), Vol. 3, 364.
Now this supreme wisdom, united to goodness that is no less infinite, cannot but have chosen the best. For as a lesser evil is a kind of good, even so a lesser good is a kind of evil if it stands in the way of a greater good; and the would be something to correct in the actions of God if it were possible to the better. As in mathematics, when there is no maximum nor minimum, in short nothing distinguished, everything is done equally, or when that is not nothing at all is done: so it may be said likewise in respect of perfect wisdom, which is no less orderly than mathematics, that if there were not the best (optimum) among all possible worlds, God would not have produced any.
Theodicy: Essays on the Goodness of God and Freedom of Man and the Origin of Evil (1710), 128.
Our children will enjoy in their homes electrical energy too cheap to meter. … Transmutation of the elements, unlimited power, ability to investigate the working of living cells by tracer atoms, the secret of photosynthesis about to be uncovered, these and a host of other results, all in about fifteen short years. It is not too much to expect that our children will know of great periodic regional famines in the world only as matters of history, will travel effortlessly over the seas and under the and through the air with a minimum of danger and at great speeds, and will experience a life span far longer than ours, as disease yields and man comes to understand what causes him to age.
Speech at the 20th anniversary of the National Association of Science Writers, New York City (16 Sep 1954), as quoted in 'Abundant Power From Atom Seen', New York Times (17 Sep 1954) 5.
Our progress in education has truly been a curious one. We have gone from the hard and arbitrary curriculum, with its primary insistence upon training the memory and the consequent devitalization of valuable and beneficial subjects, to the free elective system, with its wholesale invitations to follow the paths of least resistance, back to a half-hearted compromise somewhere between the two extremes, and we have arrived at what? Certainly at little more than an educational jumble. A maelstrom in which the maximum amount of theory and the minimum amount of practice whirl those who are thrown into it round and round for definitely fixed periods of time, to be cast out as flotsam for another period until corporate business and industrial organizations can accomplish that which could and should have been done by general education.
Co-author with Louis Jay Heath, in A New Basis for Social Progress (1917), 151-152.
The fact is that up to now the free society has not been good for the intellectual. It has neither accorded him a superior status to sustain his confidence nor made it easy for him to acquire an unquestioned sense of social usefulness. For he derives his sense of usefulness mainly from directing, instructing, and planning-from minding other people’s business-and is bound to feel superfluous and neglected where people believe themselves competent to manage individual and communal affairs, and are impatient of supervision and regulation. A free society is as much a threat to the intellectual’s sense of worth as an automated economy is to the workingman’s sense of worth. Any social order that can function with a minimum of leadership will be anathema to the intellectual.
In 'Concerning Individual Freedom', The Ordeal of Change (1963), 141.
The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression, more exact, compact, and ready than ordinary language. The great body of physical science, a great deal of the essential facts of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of the great complex world-wide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write.
Mankind in the Making (1903), 204. This is seen in a shorter form, somewhat misquoted in a paraphrase as: “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.” However, note that in fact, Wells refers only to “mathematical analysis” such as “averages and maxima and minima” — and did not specify (more complex) “statistics” at all! For citation of the paraphrase, see Samuel Wilks Quotations on this site.
The owner of the means of production is in a position to purchase the labor power of the worker. By using the means of production, the worker produces new goods which become the property of the capitalist. The essential point about this process is the relation between what the worker produces and what he is paid, both measured in terms of real value. In so far as the labor contract is free what the worker receives is determined not by the real value of the goods he produces, but by his minimum needs and by the capitalists’ requirements for labor power in relation to the number of workers competing for jobs. It is important to understand that even in theory the payment of the worker is not determined by the value of his product.
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The problem for a writer of a text-book has come now, in fact, to be this—to write a book so neatly trimmed and compacted that no coach, on looking through it, can mark a single passage which the candidate for a minimum pass can safely omit. Some of these text-books I have seen, where the scientific matter has been, like the lady’s waist in the nursery song, compressed “so gent and sma’,” that the thickness barely, if at all, surpasses what is devoted to the publisher’s advertisements. We shall return, I verily believe, to the Compendium of Martianus Capella. The result of all this is that science, in the hands of specialists, soars higher and higher into the light of day, while educators and the educated are left more and more to wander in primeval darkness.
In Presidential Address British Association for the Advancement of Science (1885), Nature, 32, 448. [Martianus Capella, who flourished c.410-320, wrote a compendium of the seven liberal arts. —Webmaster]
The reason Dick's [Richard Feynman] physics was so hard for ordinary people to grasp was that he did not use equations. The usual theoretical physics was done since the time of Newton was to begin by writing down some equations and then to work hard calculating solutions of the equations. This was the way Hans [Bethe] and Oppy [Oppenheimer] and Julian Schwinger did physics. Dick just wrote down the solutions out of his head without ever writing down the equations. He had a physical picture of the way things happen, and the picture gave him the solutions directly with a minimum of calculation. It was no wonder that people who had spent their lives solving equations were baffled by him. Their minds were analytical; his was pictorial.
Quoted in Michio Kaku and Jennifer Trainer Thompson, Beyond Einstein: the Cosmic Quest for the Theory of the Universe (1987, 1999), 56-57, citing Freeman Dyson, Disturbing the Universe (1979, 1981), 55-56.