Quotes about inverse (132 quotes, page 2)

“Many facts have lately transpired which tend to overthrow the hypothesis that heat is itself a body, and to prove that it consists in a motion of the ultimate particles of bodies. If this be so, the general principles of mechanics may be applied to heat; this motion may be converted into work, the loss of vis viva in each particular case being proportional to the quantity of work produced.
These circumstances, of which Carnot was also well aware, and the importance of which he expressly admitted, pressingly demand a comparison between heat and work, to be undertaken with reference to the divergent assumption that the production of work is not only due to an alteration in the distribution of heat, but to an actual consumption thereof; and inversely, that by the expenditure of work, heat may be produced.”

Rudolf Clausius (1822–1888) German mathematical physicist

First Memoir.
The Mechanical Theory of Heat (1867)

Loss

“And so these parties divided upon that midnight plain, each passing back the way the other had come, pursuing as all travelers must inversions without end upon other men’ s journeys.”

Cormac McCarthy book Blood Meridian

Source: Blood Meridian (1985), Chapter IX

Men , Way , Travel

“The time spent on any item of the agenda will be in inverse proportion to the sum involved.”

C. Northcote Parkinson (1909–1993) British naval historian

Source: Parkinson's Law: and Other Studies in Administration. (1957), p. 24. : Popularly known as Parkinson's Law of Triviality).

Time

“A theorist can explain any correlation, and its inverse.”

Thomas Gold

Quoted by Virginia Trimble, New Scientist, 3 Nov 2007 p. 97.

“The approach that dominates organizational theory, teaching, and practice for most of the twentieth century looked at organizations from the top-down, starting with a view of the CEO as the "leader" who shapes the organization's strategy, structure, culture, and performance potential. The nature of work and the role of the workforce enter the analysis much later, after considerations of technology and organization design have been considered. However, if the key source of value in the twenty-first-century organization is to be derived from the workforce itself, an inversion of the dominant approach will be needed. The new perspective will start not at the top of the organization, but at but at the front lines, with people and the work itself — which is where value is created. Such an inversion will lead to a transformation in the management and organization of work workers, and knowledge. This transformation was signalled by McGregor, but we must go further.”

Douglas McGregor (1906–1964) American professor

(2006; 366) Section "Beyond McGregor's Theory Y," by Thomas A. Kochan. Prepared for the Sloan School 50th Anniversary Session on October 11 (2002).
The Human Side of Enterprise (1960)

People , Nature , Knowledge

“The inversion of external compulsion into the compulsion of conscience … produces the machine-like assiduity and pliable allegiance required by the new rationality.”

Max Horkheimer (1895–1973) German philosopher and sociologist

Source: "The End of Reason" (1941), p. 34.

“The moon is not kept in her orbit round the earth, nor the earth in her orbit round the sun, by a force that varies merely in the inverse ratio of the squares of the distances.”

Thomas Robert Malthus (1766–1834) British political economist

Source: An Essay on The Principle of Population (First Edition 1798, unrevised), Chapter XIII, paragraph 2, lines 19-22

Sun

“We witness a strange inversion: on the one hand, the endeavor to turn the social contract into a less calculating and more feeling connection among its members; on the other hand, the endeavor to turn the erotic relationship into a contractual one.”

Allan Bloom (1930–1992) American philosopher, classicist, and academician

Source: Love and Friendship (1993), p. 15.

Feeling

“Later evolutionary theorists of linear progress had to advance the overtly physical and historical claim that an ancestral lineage of arthropods actually turned over to become the first vertebrates (for the classical statement of the inversion theory, see William Patten, The Grand Strategy of Evolution, 1920).”

Stephen Jay Gould book Leonardo's Mountain of Clams and the Diet of Worms

Source: Leonardo's Mountain of Clams and the Diet of Worms (1998) "Brotherhood by Inversion", p. 327

“The secret and sacred word that binds him to the farm is 'belong'. Out in the veld by himself he can breathe the word aloud: I belong on the farm. What he really believes but does not utter, what he keeps to himself for fear that the spell will end, is a different form of the word: I belong to the farm. He tells no one because the word is misunderstood so easily, turned so easily to its inverse: The farm belongs to me. The farm will never belong to him, he will never be more than a visitor: he accepts that.”

J.M. Coetzee (1940) South African writer

Boyhood (1998)

Secret , Fear

“She always dressed well, but he recognized the signs of insecurity; certitude was inversely proportional to the amount of makeup.”

Gregory Benford Artifact

Part 5, Chapter 3 (p. 243)
Artifact (1985)

“Kevin Kruse in his book One Nation Under God: How Corporate America Invented Christian America details how industrialists in the 1930s and 1940s poured money and resources into an effort to silence the social witness of the mainstream church, which was home to many radicals, socialists and proponents of the New Deal. These corporatists promoted and funded a brand of Christianity—which is today dominant—that conflates faith with free enterprise and American exceptionalism. The rich are rich, this creed goes, not because they are greedy or privileged, not because they use their power to their own advantage, not because they oppress the poor and the vulnerable, but because they are blessed. And if we have enough faith, this heretical form of Christianity claims, God will bless the rest of us too. It is an inversion of the central message of the Gospel. You don’t need to spend three years at Harvard Divinity School as I did to figure that out.”

Chris Hedges (1956) American journalist

"The Suicide of the Liberal Church", January 24, 2016 http://www.truthdig.com/report/item/the_suicide_of_the_liberal_church_20160124

Money , God , Books , School

“Your letter firmed me up a lot. It certainly is a comfort to know that my work is respected by someone whom I respect and am as fond as you. It confirms my beliefe that life is notall nonsense and cruelty—the inversion of Victorian complacency—but has hard spots of sense and love bobbing about in it here and there.”

E.M. Forster (1879–1970) English novelist

Letter 330, to Christopher Isherwood, 28 August 1938
Selected Letters (1983-1985)

Love , Life , Sense

“[Kelley argued that OS's judgment of an inverse relation between inducement magnitude and attitude inference] is probably associated with assumptions (unchecked in Bern’s work, as far as I know) that there is a distribution of opinion toward the task, and only the more favorable subjects complied in the $1 case and almost all, favorable or not, complied in the $20 case.”

Harold Kelley (1921–2003) American psychologist & academic

Source: "Attribution theory in social psychology." 1967, p. 226; as cited in: Yaacov Trope, "Inferential processes in the forced compliance situation: A Bayesian analysis." Journal of Experimental Social Psychology 10.1 (1974): 1-16.

“I shall endeavor to show that induction is really the inverse process of deduction.”

William Stanley Jevons (1835–1882) English economist and logician

Source: The Principles of Science: A Treatise on Logic and Scientific Method (1874) Vol. 1, p. 14

“How ironic. In order to avoid the "nutty" theory of inversion, Gaskell invented the even odder notion of stomachs turning into brains with new guts forming below. No wonder then, that later biologists cast a plague on both speculative houses and opted instead for the obvious alternative: arthropods and vertebrates do not share the same anatomical plan at all, but rather represent two separate evolutionary developments of similar complexity from a much simpler common ancestor that grew neither a discrete gut nor a central nerve cord.”

Stephen Jay Gould book Leonardo's Mountain of Clams and the Diet of Worms

"Brotherhood by Inversion", p. 327
Leonardo's Mountain of Clams and the Diet of Worms (1998)

Housing

“On symbolic use of equalities and proportions. Chapter II.
The analytical method accepts as proven the most famous [ as known from Euclid ] symbolic use of equalities and proportions that are found in items such as:
1. The whole is equal to the sum of its parts.
2. Quantities being equal to the same quantity have equality between themselves. [a = c & b = c => a = b]
3. If equal quantities are added to equal quantities the resulting sums are equal.
4. If equals are subtracted from equal quantities the remains are equal.
5. If equal equal amounts are multiplied by equal amounts the products are equal.
6. If equal amounts are divided by equal amounts, the quotients are equal.
7. If the quantities are in direct proportion so also are they are in inverse and alternate proportion. [a:b::c:d=>b:a::d:c & a:c::b:d]
8. If the quantities in the same proportion are added likewise to amounts in the same proportion, the sums are in proportion. [a:b::c:d => (a+c):(b+d)::c:d]
9. If the quantities in the same proportion are subtracted likewise from amounts in the same proportion, the differences are in proportion. [a:b::c:d => (a-c):(b-d)::c:d]
10. If proportional quantities are multiplied by proportional quantities the products are in proportion. [a:b::c:d & e:f::g:h => ae:bf::cg:dh]
11. If proportional quantities are divided by proportional quantities the quotients are in proportion. [a:b::c:d & e:f::g:h => a/e:b/f::c/g:d/h]
12. A common multiplier or divisor does not change an equality nor a proportion. [a:b::ka:kb & a:b::(a/k):(b/k)]
13. The product of different parts of the same number is equal to the product of the sum of these parts by the same number. [ka + kb = k(a+b)]
14. The result of successive multiplications or divisions of a magnitude by several others is the same regardless of the sequential order of quantities multiplied times or divided into that magnitude.
But the masterful symbolic use of equalities and proportions which the analyst may apply any time is the following:
15. If we have three or four magnitudes and the product of the extremes is equal to the product means, they are in proportion. [ad=bc => a:b::c:d OR ac=b2 => a:b::b:c]
And conversely
10. If we have three or four magnitudes and the first is to the second as the second or the third is to the last, the product of the extremes is equal to that of means. [a:b::c:d => ad=bc OR a:b::b:c => ac=b2]
We can call a proportion the establishment of an equality [equation] and an equality [equation] the resolution of a proportion.”

François Viète (1540–1603) French mathematician

From Frédéric Louis Ritter's French Tr. Introduction à l'art Analytique (1868) utilizing Google translate with reference to English translation in Jacob Klein, Greek Mathematical Thought and the Origin of Algebra (1968) Appendix
In artem analyticem Isagoge (1591)

Change , Time , Success , Parting

“The long-form endings have pushed away the short-form endings completely in the oblique cases. In the last few years, there are attempts in Croatia to bring back again the short forms in the usage. This attempts are the part of the new sociolinguistic politics to bring back the archaic words and forms in the usage and to construct new words, neologisms, in place of customary words - all that with the aim to make the language in the west of the Serbo-Croatian language community as different as possible from the language in the east of the Serbo-Croatian language community. Leaders of the new language politics proclaim as incorrect what was customary, and as correct what was rare, archaic or even did not exist in the usage, and then they carry it out in practice through the control of the media, text-books etc. Such inversion of the criteria for what is correct and what is not correct in the language usage makes the native speakers unsure and frustrated.”

Snježana Kordić (1964) Croatian linguist

[Kordić, Snježana, w:Snježana Kordić, Snježana Kordić, Serbo-Croatian, Languages of the World/Materials 148, Munich & Newcastle, Lincom Europa, 1997, 18, 3-89586-161-8, 37959860]

Books , Communication , Parting

“And so we see that the term conservative has little value as a label; in fact, one might say that its label-value varies inversely with one's right to wear it.”

Albert Jay Nock (1870–1945) American journalist

A Little Conserva-tive (1936)
Context: Lucius Cary, Viscount Falkland, managed to make himself a most conspicuous example of every virtue and every grace of mind and manner; and this was the more remarkable because in the whole period through which he lived — the period leading up to the Civil War — the public affairs of England were an open playground for envy, hatred, malice, and all uncharitableness. … He could not see that there was any inconsistency in his attitude. He then went on to lay down a great general principle in the ever — memorable formula, "Mr. Speaker, when it is not necessary to change, it is necessary not to change."
Here we get on track of what conservatism is. We must carefully observe the strength of Falkland's language. He does not say that when it is not necessary to change, it is expedient or advisable not to change; he says it is necessary not to change. Very well, then, the differentiation of conservatism rests on the estimate of necessity in any given case. Thus conservatism is purely an ad hoc affair; its findings vary with conditions, and are good for this day and train only. Conservatism is not a body of opinion, it has no set platform or creed, and hence, strictly speaking, there is no such thing as a hundred-per-cent conservative group or party … Nor is conservatism an attitude of sentiment. Dickens's fine old unintelligent characters who "kept up the barrier, sir, against modern innovations" were not conservatives. They were sentimental obstructionists, probably also obscurantists, but not conservatives.
Nor yet is conservatism the antithesis of radicalism; the antithesis of radical is superficial. Falkland was a great radical; he was never for a moment caught by the superficial aspect of things. A person may be as radical as you please, and still may make an extremely conservative estimate of the force of necessity exhibited by a given set of conditions. A radical, for example, may think we should get on a great deal better if we had an entirely different system of government, and yet, at this time and under conditions now existing, he may take a strongly conservative view of the necessity for pitching out our system, neck and crop, and replacing it with another. He may think our fiscal system is iniquitous in theory and monstrous in practice, and be ever so sure he could propose a better one, but if on consideration of all the circumstances he finds that it is not necessary to change that system, he is capable of maintaining stoutly that it is necessary not to change it. The conservative is a person who considers very closely every chance, even the longest, of "throwing out the baby with the bath-water," as the German proverb puts it, and who determines his conduct accordingly. And so we see that the term conservative has little value as a label; in fact, one might say that its label-value varies inversely with one's right to wear it.... It covers so much that looks like mere capriciousness and inconsistency that one gets little positive good out of wearing it; and because of its elasticity it is so easily weaseled into an impostor-term or a term of reproach, or again into one of derision, as implying complete stagnation of mind, that it is likely to do one more harm than it is worth.

“Passion was inversely proportional to the amount of real information available.”

Gregory Benford book Timescape

Source: Timescape (1980), Chapter 14 (p. 182, known as Benford's law of controversy)
Context: It was an example of what he thought of as the Law of Controversy: Passion was inversely proportional to the amount of real information available.

Passion

“The current search for new educational funnels must be reversed into the search for their institutional inverse: educational webs which heighten the opportunity for each one to transform each moment of his living into one of learning, sharing, and caring.”

Ivan Illich book Deschooling Society

Introduction (November 1970).
Deschooling Society (1971)
Context: Universal education through schooling is not feasible. It would be no more feasible if it were attempted by means of alternative institutions built on the style of present schools. Neither new attitudes of teachers toward their pupils nor the proliferation of educational hardware or software (in classroom or bedroom), nor finally the attempt to expand the pedagogue's responsibility until it engulfs his pupils' lifetimes will deliver universal education. The current search for new educational funnels must be reversed into the search for their institutional inverse: educational webs which heighten the opportunity for each one to transform each moment of his living into one of learning, sharing, and caring. We hope to contribute concepts needed by those who conduct such counterfoil research on education — and also to those who seek alternatives to other established service industries.

Education , Search , Learning

“He looks with impartial eye upon the endless variety of systems, maintained with equal confidence and self-sufficiency, by men of equal ability and honesty. He is weary of wandering over the world, and of finding every petty race wedded to its own opinions; claiming the monopoly of Truth; holding all others to be in error, and raising disputes whose violence, acerbity and virulence are in inverse ratio to the importance of the disputed matter.”

Richard Francis Burton (1821–1890) British explorer, geographer, translator, writer, soldier, orientalist, cartographer, ethnologist, spy, lin…

The Kasîdah of Hâjî Abdû El-Yezdî (1870), Note I : Hâjî Abdû, The Man
Context: He looks with impartial eye upon the endless variety of systems, maintained with equal confidence and self-sufficiency, by men of equal ability and honesty. He is weary of wandering over the world, and of finding every petty race wedded to its own opinions; claiming the monopoly of Truth; holding all others to be in error, and raising disputes whose violence, acerbity and virulence are in inverse ratio to the importance of the disputed matter. A peculiarly active and acute observation taught him that many of these jarring families, especially those of the same blood, are par in the intellectual processes of perception and reflection; that in the business of the visible working world they are confessedly by no means superior to one another; whereas in abstruse matters of mere Faith, not admitting direct and sensual evidence, one in a hundred will claim to be right, and immodestly charge the other ninety-nine with being wrong.
Thus he seeks to discover a system which will prove them all right, and all wrong; which will reconcile their differences; will unite past creeds; will account for the present, and will anticipate the future with a continuous and uninterrupted development; this, too, by a process, not negative and distinctive, but, on the contrary, intensely positive and constructive. I am not called upon to sit in the seat of judgment; but I may say that it would be singular if the attempt succeeded. Such a system would be all-comprehensive, because not limited by space, time, or race; its principle would be extensive as Matter itself, and, consequently, eternal. Meanwhile he satisfies himself, — the main point.

Men , Truth , World , Error

“Indeed, the most urgent, the most essential task is the education of children and youth... It is usually customary to confuse education with upbringing, but it is time to understand that school education, as it is established in most cases, not only does not contribute to the moral upbringing of youth, but acts inversely. In the Anglo-Saxon countries the schools are occupied mainly with the physical development of youth to the detriment of their mental development. But the excessive enthusiasm for sports leads to the coarsening of character, to mental degeneration, and to new diseases. True, not much better is the situation in home education under the conditions of the modern family. Therefore, it is time to pay most serious attention to the grave and derelict situation of children and youth from the moral point of view. Many lofty concepts are completely out of habitual use, having been replaced by everyday formulas for the easy achievement of the most vulgar comforts and status...The program of education is as broad as life itself. The possibilities for improvement are inexhaustible...We are on the eve of a new approach to and reconstruction of the entire school education... The quantity and speed of new discoveries in all domains of science grow so rapidly that soon contemporary school education will not be able to walk in step with and respond to the new attainments and demands of the time; new methods in the entire system of education will have to be devised...”

Helena Roerich (1879–1955) Russian philosopher

19 April 1938

Sport , Home , Family , School

“When, through radiation or other causes, chromosomes are broken within a single nucleus, 2-by-2 fusions may occur between the broken ends. These fusions may lead to rearrangements of parts of the chromatin complement, giving rise to various chromosomal aberrations which are detected as reciprocal translocations, inversions, deficiencies, etc. Since, in the well-investigated cases, the breakages occurred within a single nucleus, the conditions that lead to fusions of broken ends could not easily be ascertained.”

Barbara McClintock The Fusion of Broken Ends of Chromosomes Following Nuclear Fusion

[Proc Natl Acad Sci U S A, November 1942, 28, 11, 458–463, 10.1073/pnas.28.11.458, The Fusion of Broken Ends of Chromosomes Following Nuclear Fusion, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1078518/?page=1]

Parting

“There is, he’d said, an inverse correlation between the amount of power a person has and the level at which his or her mind functions. A person of ordinary intelligence who acquires power, of whatever kind, tends to develop an exaggerated view of his own capabilities. Sycophants gather. There is little or no criticism of decisions. As his ability to disrupt the lives of others advances, these tendencies become stronger. Eventually you end with Louis the Fourteenth, who thinks he’s done a good job for France, although the country he left behind was ruined.”

Jack McDevitt book Infinity Beach

Source: Infinity Beach (2000), Chapter 15 (p. 219)

Country , Personality , Intelligence , Thinking

“Favorable conditions for establishing a permanent camp in guerrilla warfare are inverse to the degree of productive development of a place… because everything that is favorable to human life, communications, urban and semi-urban concentrations of large numbers of people, land easily worked by machine, all these place the guerrilla fighter in a disadvantageous situation.”

Ernesto Che Guevara book Guerrilla Warfare

Source: Guerrilla Warfare (1961), Ch. I: 5. Warfare on Unfavorable Ground

Life , People , Communication

“No mathematical idea has ever been published in the way it was discovered. Techniques have been developed and are used, if a problem has been solved, to turn the solution procedure upside down, or if it is a larger complex of statements and theories, to turn definitions into propositions, and propositions into definitions, the hot invention into icy beauty. This then if it has affected teaching matter, is the didactical inversion, which as it happens may be anti-didactical.”

Hans Freudenthal (1905–1990) Dutch mathematician

Rather than behaving anti-didactically, one should recognise that the learner is entitled to recapitulate in a fashion of mankind. Not in the trivial matter of an abridged version, but equally we cannot require the new generation to start at the point where their predecessors left off.
Source: The Concept and the Role of the Model in Mathematics and Natural and Social Sciences (1961), p. ix

Beauty , Problem , Mathematics , Way

“I have throughout introduced the Integral Calculus in connexion with the Differential Calculus. …Is it always proper to learn every branch of a direct subject before anything connected with the inverse relation is considered? If so why are not multiplication and involution in arithmetic made to follow addition and precede subtraction?”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

The portion of the Integral Calculus, which properly belongs to any given portion of the Differential Calculus increases its power a hundred-fold...
The Differential and Integral Calculus (1836)

Relation ships , Learning