Quotes about variability (211 quotes) | Quotes of famous people

“A ring of polynomials in any number of variables over a ring of coeffcients that has an identity element and a finite basis, itself has a finite basis.”

Emmy Noether (1882–1935) German mathematician

As quoted in Morris Kline, Mathematical Thought From Ancient to Modern Times (1972) p. 1153.

“There are many variables intertwined in every problem and components of all the variable involved have to be carefully studied. Forming solutions by studying and synthesizing the relationship among key variables seems to be very much in need. The ability to identify a meaning from observable and obtained data is the core of human characteristics in such changing society. Hence, inductive thinking has to be instilled in every learner for a productive citizenship in the changing world of tomorrow.”

Sukavich Rangsitpol (1935) Thai politician

citizenship in the changing world of tomorrow.

Study , Problem , Thinking , World

“Dr. Watson's summary list of Sherlock Holmes's strengths and weaknesses:

"1. Knowledge of Literature: Nil.
2. Knowledge of Philosophy: Nil.
3. Knowledge of Astronomy: Nil.
4. Knowledge of Politics: Feeble.
5. Knowledge of Botany: Variable. Well up in belladonna, opium, and poisons generally. Knows nothing of practical gardening.
6. Knowledge of Geology: Practical but limited. Tells at a glance different soils from each other. After walks has shown me splashes upon his trousers, and told me by their colour and consistence in what part of London he had received them.
7. Knowledge of Chemistry: Profound.
8. Knowledge of Anatomy: Accurate but unsystematic.
9. Knowledge of Sensational Literature: Immense. He appears to know every detail of every horror perpetrated in the century.
10. Plays the violin well.
11. Is an expert singlestick player, boxer, and swordsman.
12. Has a good practical knowledge of British law.”

Arthur Conan Doyle book A Study in Scarlet

Source: A Study in Scarlet

Law , Literature , Knowledge , Appearance

“O, swear not by the moon, th’ inconstant moon,
That monthly changes in her circle orb,
Lest that thy love prove likewise variable.”

William Shakespeare book Romeo and Juliet

Source: Romeo and Juliet

Love , Change

“There is no reason to think that the impact [of monetary policy] will be captured in any single [variable]…, whether it is a monetary stock or a market interest rate.”

James Tobin (1918–2002) American economist

Source: "A general equilibrium approach to monetary theory" (1969), p. 29 as cited in: Andrés, Javier, J. David López-Salido, and Edward Nelson. " Tobin's imperfect asset substitution in optimizing general equilibrium http://research.stlouisfed.org/wp/2004/2004-003.pdf." Journal of Money, Credit and Banking (2004): 665-690.

Thinking

“First of all I want to remind you of the essential features of models. In my opinion they are: (i) drawing up a list of the variables to be considered; (ii) drawing up a list of the equations or relations the variables have to obey and (iii) testing the validity of the equations, which implies the estimation of their coefficients, if any. As a consequence of especially (iii) we may have to revise (i) and (ii) so as to arrive at a satisfactory degree of realism of the theory embodied in the model. Then, the model may be used for various purposes, that is, for the solution of various problems. The advantages of models are, on one hand, that they force us to present a "complete" theory by which I mean a theory taking into account all relevant phenomena and relations and, on the other hand, the confrontation with observation, that is, reality. Of course these remarks are far from new.”

Jan Tinbergen (1903–1994) Dutch economist

"The Use of Models: Experience," 1969

Problem , Reality , Drawing

“As the variable capital always stays in the hands of the capitalist in some form or other, it cannot be claimed in any way that it converts itself into revenue for anyone.”

Karl Marx (1818–1883) German philosopher, economist, sociologist, journalist and revolutionary socialist

Vol. II, Ch. XX, p. 452.
(Buch II) (1893)

Way

“In economic surveys of households, many variables have the following characteristics: The variable has a lower, or upper, limit and takes on the limiting value for a substantial number of respondents. For the remaining respondents, the variable takes on a For the remaining respondents, the variable takes on a wide range of values above, or below, the limit.”

James Tobin (1918–2002) American economist

Tobin, James. " Estimation of relationships for limited dependent variables http://cowles.econ.yale.edu/P/cp/p01a/p0117.pdf." Econometrica: journal of the Econometric Society (1958): 24-36.
1950s-60s

“With the publication of J. M. Keynes’s General Theory in 1936 and the mathematical formalizations of his theory by J. R. Hicks (1937) and others, the language of macro-economic theory became systems of simultaneous equations. These are general equilibrium systems of interdependence in the sense that the relationships describe an entire national economy, not just a particular industry or sector. The systems are usually not completely closed; they depend on exogenous parameters including instruments controlled by policy-makers. Seeking definite relationships of economic outcomes to policies and other exogenous variables, qualitative and quantitative, these models sacrifice detail and generality, limiting the number of variables and equations by aggregations over agents, commodities, assets, and time.”

James Tobin (1918–2002) American economist

Source: "Money and Finance in the Macro-Economic Process" (1982), p. 12

Mathematics , Sense , Time , Dependency

“Richard Feynman used to go up to people all the time and he'd say "You won't believe what happened to me today… you won't believe what happened to me" and people would say "What?" and he'd say "Absolutely nothing". Because we humans believe that everything that happens to us is special and significant. And that — and Carl Sagan wrote beautifully about that in The Demon-Haunted World — that is much of the source of religion. Everything that happens is unusual and I expect that the likelihood that Richard and I ever would've met. If you think about all the variables: the probability that we were in the same place at the same time, ate breakfast the same. Whatever. It's zero. Every event that happens has small probability… but it happens and then when it happens; if it's weird, if you dream one million nights and it's nonsense but one night you dream that your friend is gonna break his leg and the next day he breaks his arm… *sound of revelation* So the real thing that physics tell us about the universe is that it's big, rare events happen all the time — including life — and that doesn't mean it's special.”

Lawrence M. Krauss (1954) American physicist

"A Universe From Nothing" by Lawrence Krauss, AAI 2009 http://www.youtube.com/watch?v=7ImvlS8PLIo#t=1h03m20s Closing words (01:03:20 - 01:04:30)

Life , People , World , Religion

“For example, a man who had seen a great many white swans might argue, by our principle, that on the data it was probable that all swans were white, and this might be a perfectly sound argument. The argument is not disproved by the fact that some swans are black, because a thing may very well happen in spite of the fact that some data render it improbable. In the case of the swans, a man might know that colour is a very variable characteristic in many species of animals, and that, therefore, an induction as to colour is peculiarly liable to error. But this knowledge would be a fresh datum, by no means proving that the probability relatively to our previous data had been wrongly estimated. The fact, therefore, that things often fail to fulfill our expectations is no evidence that our expectations will not probably be fulfilled in a given case or a given class of cases. Thus our inductive principle is at any rate not capable of being disproved by an appeal to experience. The inductive principle, however, is equally incapable of being proved by an appeal to experience.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

"On Induction"
1910s, The Problems of Philosophy (1912)

Error , Knowledge , Animals

“Since the [Cepheid] variables are probably at nearly the same distance from the Earth, their periods are apparently associated with their actual emission of light, as determined by their mass, density, and surface brightness.”

Henrietta Swan Leavitt (1868–1921) astronomer

Periods of 25 Variable Stars in the Small Magellanic Cloud http://adsabs.harvard.edu/abs/1912HarCi.173....1L (1912)

Light

“The relational model provides different categories, different underlying structures into which experience can be organized. Here the establishment of strong connections to others, in reality or in fantasy, is presumed to be primary. Forms of relationship are seen as fundamental, and life is understood largely as an array of metaphors for expressing and playing out relational patterns: discovery, penetration, domination, surrender, control, longing, evasion, revelation, envelopment, merger, differentiation, and so on. The body is still centrally important. Sexuality and bodily experiences are viewed as particularly apt arenas for this activity, since sexuality is enormously multiform and plastic. The number of different body parts, the variability of interactions, the poignancy of the sensations, the immense number of combinations — the almost infinite variety of human sexual possibilities make this an enormously fertile reservoir of metaphors for expressing different types of relationships, different configurations of connections, between self and others.”

Stephen Mitchell (1946–2000) American psychologist

Relational Concepts in Psychoanalysis (Cambridge, Massachusetts: Harvard University Press, 1988), p. 91

Life , Reality , Strong , Parting

“Pure Mathematics is the class of all propositions of the form “p implies q,” where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Principles of Mathematics (1903), Ch. I: Definition of Pure Mathematics, p. 3
1900s

Truth , Mathematics

“For reasons mentioned at the beginning of this section, we cannot offer here a precise structural definition of semantical category and will content ourselves with the following approximate formulation: two expressions belong to the same semantical category if (I) there is a sentential function which contains one of these expressions, and if (2) no sentential function which contains one of these expressions ceases to be a sentential function if this expression is replaced in it by the other. It follows from this that the relation of belonging to the same category is reflective, symmetrical and transitive. By applying the principle of abstraction, all the expressions of the language which are parts of sentential functions can be divided into mutually exclusive classes, for two expressions are put into one and the same class if and only if they belong to the same semantical category, and each of these classes is called a semantical category. Among the simplest examples of semantical categories it suffices to mention the category of the sentential functions, together with the categories which include respectively the names of individuals, of classes of individuals, of two-termed relations between individuals, and so on. Variables (or expressions with variables) which represent names of the given categories likewise belong to the same category.”

Alfred Tarski (1901–1983) Polish-American logician

Source: The Semantic Conception of Truth (1952), p. 45; as cited in: Schaff (1962) pp. 36-37.

Parting

“To know the quantum mechanical state of a system implies, in general, only statistical restrictions on the results of measurements. It seems interesting to ask if this statistical element be thought of as arising, as in classical statistical mechanics, because the states in question are averages over better defined states for which individually the results would be quite determined. These hypothetical 'dispersion free' states would be specified not only by the quantum mechanical state vector but also by additional 'hidden variables' - 'hidden' because if states with prescribed values of these variables could actually be prepared, quantum mechanics would be observably inadequate.”

John S. Bell (1928–1990) Northern Irish physicist

On the problem of hidden variables in quantum mechanics (1966)

Question

“It is not human nature which can assign the variable limits necessary to our needs. They are thus unlimited so far as they depend on the individual alone. Irrespective of any external regulatory force, our capacity for feeling is in itself an insatiable and bottomless abyss.”

Émile Durkheim book Suicide

Suicide (1897)

Feeling , Nature , Dependency

“A linguistic variable is a variable whose values are words or sentences in a natural or synthetic language.”

Lotfi A. Zadeh (1921–2017) Electrical engineer and computer scientist

Variant: A linguistic variable is defined as a variable whose values are sentences in a natural or artificial language.
Source: 1970s, Outline of a new approach to the analysis of complex systems and decision processes (1973), p. 28

Nature

“When a constant electric current flows along a cylindrical wire, its strength is the same at every part of the section of the wire. But if the current is variable, self-induction produces a deviation from this… induction opposes variations of the current in the centre of the wire more strongly than at the circumference, and consequently the current by preference flows along the outer portion of the wire. When the current changes its direction… this deviation increases rapidly with the rate of alternation; and when the current alternates many million times per second, almost the whole of the interior of the wire must, according to theory, appear free from current, and the flow must confine itself to the very skin of the wire. Now in such extreme cases… preference must be given to another conception of the matter which was first presented by Messrs. 0. Heaviside and J. H. Poynting, as the correct interpretation of Maxwell's equations as applied to this case. According to this view, the electric force which determines the current is not propagated in the wire itself, but under all circumstances penetrates from without into the wire, and spreads into the metal with comparative slowness and laws similar to those which govern changes of temperature in a conducting body.
…Inasmuch as I made use of electric waves in wires of exceedingly short period in my experiments on the propagation of electric force, it was natural to test by means of these the correctness of the conclusions deduced. As a matter of fact the theory was found to be confirmed by the experiments…”

Heinrich Hertz (1857–1894) German physicist

"On the Propagation of Electric Waves by Means of Wires" (1889) Wiedemann's Annalen. 37 p. 395, & pp.160-161 of Electric Waves
Electric Waves: Being Researches on the Propagation of Electric Action with Finite Velocity Through Space (1893)

Law , Nature , Appearance , Change

“It is well known that in three-dimensional elliptic or spherical geometry the so-called Clifford's parallelism or parataxy has many interesting properties. A group-theoretical reason for the most important of these properties is the fact that the universal covering group of the proper orthogonal group in four variables is the direct product of the universal covering groups of two proper orthogonal groups in three variables. This last-mentioned property has no analogue for orthogonal groups in n (>4) variables. On the other hand, a knowledge of three-dimensional elliptic or spherical geometry is useful for the study of orientable Riemannian manifols of four dimensions, because their tangent spaces possess a geometry of this kind.”

Shiing-Shen Chern (1911–2004) mathematician (1911–2004), born in China and later acquiring U.S. citizenship; made fundamental contributio…

[On Riemannian manifolds of four dimensions, Bulletin of the American Mathematical Society, 51, 12, 1945, 964–971, http://www.ams.org/journals/bull/1945-51-12/S0002-9904-1945-08483-3/S0002-9904-1945-08483-3.pdf]

Knowledge , Study , Universe

“These ideas have implications not only for theoretical and econometric practices but also for the ways in which policymakers and their advisers think about the choices confronting them. In particular, the rational expectations approach directs attention away from particular isolated actions and toward choices among feasible rules of the game, or repeated strategies for choosing policy variables. While Keynesian and monetarists macroeconomic models have been used to try to analyze what the effects of isolated actions would be, it is now clear that the answers they have given have necessarily been bad, if only because such questions are ill-posed.”

Thomas J. Sargent (1943) American economist

"Rational expectations and the dynamics of hyperinflation." 1973

Way , Game , Idea , Question

“That’s the thing about a human life-there’s no control group, no way to ever know how any of us would have turned out if any variables had been changed.”

Elizabeth Gilbert (1969) American writer

Source: Eat, pray, love: one woman's search for everything

Life , Way , Change

“That's the thing about human life--there is no control group, no way to ever know how any of us would have turned out if any variables had been changed.”

Daniel Keyes book Flowers for Algernon

Source: Flowers for Algernon

Life , Way , Change

“It had been different during his first year of graduate school, when he temporarily forsook physics to explore instead the realm of the senses. Applying logic to the late-blooming quandries of maturity, he had parsed the elements of encounter, banter, negotiation, and consummation, separating and solving the variables one by one until the problem—if not generally solved—did appear to have tractable special solutions.”

David Brin book Earth

Part V (p. 236)
Earth (1990)

School , Problem , Sense , Appearance

“Rather, for all objects and experiences there is a quantity that has an optimum value. Above that quantity, the variable becomes toxic. To fall below that value is to be deprived.”

Gregory Bateson (1904–1980) English anthropologist, social scientist, linguist, visual anthropologist, semiotician and cyberneticist

Source: Mind and Nature: A Necessary Unity, 1979, p. 56

“The investigation of the form and brightness of the rings or rays surrounding the image of a star as seen in a good telescope, when a diaphragm bounded by a rectilinear contour is placed upon the object-glass, though sometimes tedious is never difficult. The expressions which it is necessary to integrate are always sines and cosines of multiples of the independent variable, and the only trouble consists in taking properly the limits of integration. Several cases of this problem have been completely worked out, and the result, in every instance, has been entirely in accordance with observation. These experiments… have seldom been made except by those whose immediate object was to illustrate the undulatory theory of light. There is however a case of a somewhat different kind; which in practice recurs perpetually, and which in theory requires for its complete investigation the value of a more difficult integral; I mean the usual case of an object-glass with a circular aperture. The desire of submitting to mathematical investigation every optical phænomenon of frequent occurrence has induced me to procure the computation of the numerical values of the integral that presents itself in this inquiry: and I now beg leave to lay before the Society the calculated table, with a few remarks upon its application.”

George Biddell Airy (1801–1892) English mathematician and astronomer

Star , Mathematics , Problem , Light

“.. the point of a randomizing device like a coin flip, [is] to make the result uncontrollable by making it sensitive to so many variables that no feasible, finite list of conditions can be singled out as the cause.”

Daniel Dennett book Freedom Evolves

Freedom Evolves (2003)

“A study of attorneys found that the attorneys whose pictures were judged independently to be the better-looking ones were able to earn about 12% more per year than the less good-looking ones. The better-looking attorneys worked longer hours, but even when that and dozens of other variables were controlled for, the better-looking attorneys were able to bill significantly more per hour. Needless to say, the male attorneys were ranked as much less attractive than the women, increasing the gap in women’s pay over men’s. The bigger the gap in looks, the bigger was the gap in pay. The more time passed, the more the gap widened. Sometimes life isn’t fair.”

Warren Farrell (1943) author, spokesperson, expert witness, political candidate

Source: Why Men Earn More (2005), p. 199-200.

Life , Women , Men , Study

“The formal structure of a decision problem in any area can be put into four parts: ( 1 ) the choice of an objective function denning the relative desirability of different outcomes; (2) specification of the policy alternatives which are available to the agent, or decisionmaker, (3) specification of the model, that is, empirical relations that link the objective function, or the variables that enter into it, with the policy alternatives and possibly other variables; and (4) computational methods for choosing among the policy alternatives that one which performs best as measured by the objective function.”

Kenneth Arrow (1921–2017) American economist

Source: 1970s-1980s, The Economics of Information (1984), p. 55

Problem , Decision , Parting

“As yet the efficiency of selling goods has not been worked out. Most salesmen believe it cannot be done. They claim that there are too many variables in the problem. Perhaps there are, but nobody knows until the experiment has been thoroughly tried. In every case the victories of Efficiency have been won in spite of the most stubborn opposition from the men who were being helped. And one fact is sure - that the first Advertisers and Sales Managers who try out Efficiency and succeed will find themselves in a gold mine. They will have found a better way to enter a market that handles, in an average year, thirty thousand million dollars worth of goods.”

Herbert N. Casson (1869–1951) Canadian journalist and writer

Source: 1910s, Ads and Sales (1911), p. 7

Men , Way , Problem , Victory

“When plugged in, the least elaborate computer can be relied on to work to the fullest extent of its capacity. The greatest mind cannot be relied on for the simplest thing; its variability is its superiority.”

Jacques Barzun (1907–2012) Historian

"The Masterpiece," in A Stroll with William James (1983)

“[T]he last 15 years have witnessed the ascent of an alternative view, that of embodied or enactive cognition. This new wave arose because the computationalist doctrine failed to account even for the most elementary coping with the world: walking, perceiving object in a natural setting, imagination. Slowly the cards turned into considering that the basis of mind is the body in coupled action, that is, the sensory-motor circuits establish the organism as viable in situated contexts. From this perspective the brain appears as a dynamical process (and not a syntactic one) of real time variables with a rich self-organizing capacity (and not a representational machinery). So in this sense the mind is not in the head since it is roots in the body as a whole and also in the extended environment where the organism finds itself.”

Francisco Varela (1946–2001) Chilean biologist

Varela (1998) " The Cosmos Letter http://www.expo-cosmos.or.jp/letter/letter12e.html", Expo'90 Foundation, Japan

World , Imagination , Nature , Sense

“The vision we have of conversational programming takes in much more than rapid turn around time and convenient debugging aids: our most interesting programs are never wrong and never final. […] What is new is the requirement to make variable in our languages what we had previously taken as fixed. I do not refer to new data classes now, but to variables whose values are programs or parts of programs, syntax or parts of syntax, and regimes of control.”

Alan Perlis (1922–1990) American computer scientist

The Synthesis of Algorithmic Systems, 1966

Time , Parting

“As professor in the Polytechnic School [autumn of 1858] in Zurich I found myself for the first time obliged to lecture upon the elements of the differential calculus and felt, more keenly than ever before, the lack of a really scientific foundation for arithmetic. In discussing the notion of the approach of a variable magnitude to a fixed limiting value, and especially in proving the theorem that every magnitude which grows continually, but not beyond all limits, must certainly approach a limiting value, I had recourse to geometric evidences. Even now such resort to geometric intuition in a first presentation of the differential calculus, I regard as exceedingly useful, from the didactic standpoint, and indeed indispensable, if one does not wish to lose too much time. But that this form of introduction into the differential calculus can make no claim to being scientific, no one will deny. For myself this feeling of dissatisfaction was so overpowering that I made the fixed resolve to keep meditating on the question till I should find a purely arithmetic and perfectly rigorous foundation for the principles of infinitesimal analysis.”

Richard Dedekind (1831–1916) German mathematician

p, 125
Stetigkeit und irrationale Zahlen (1872)

School , Feeling , Question , Autumn

“Public policy does not admit of definition and is not easily explained. It is a variable quantity; it must vary and does vary with the habits, capacities, and opportunities of the public.”

Arthur Kekewich (1832–1907) British judge

Davies v. Davies (1887), L. R. 36 C. D. 364; see also Egerton v. Earl Brownlow, 4 H. L. C. 1.

“But I was very unwilling to give up my belief; I feel sure of this, for I can well remember often and often inventing day-dreams of old letters between distinguished Romans, and manuscripts being discovered at Pompeii or elsewhere, which confirmed in the most striking manner all that was written in the Gospels. But I found it more and more difficult, with free scope given to my imagination, to invent evidence which would suffice to convince me. Thus disbelief crept over me at a very slow rate, but was at last complete. The rate was so slow that I felt no distress.Although I did not think much about the existence of a personal God until a considerably later period of my life, I will here give the vague conclusions to which I have been driven. The old argument from design in Nature, as given by Paley, which formerly seemed to me so conclusive, fails, now that the law of natural selection has been discovered. We can no longer argue that, for instance, the beautiful hinge of a bivalve shell must have been made by an intelligent being, like the hinge of a door by man. There seems to be no more design in the variability of organic beings, and in the action of natural selection, than in the course which the wind blows. But I have discussed this subject at the end of my book on the Variation of Domesticated Animals and Plants, and the argument there given has never, as far as I can see, been answered.”

Charles Darwin (1809–1882) British naturalist, author of "On the origin of species, by means of natural selection"

volume I, chapter VIII: "Religion", pages 308-309 http://darwin-online.org.uk/content/frameset?pageseq=326&itemID=F1452.1&viewtype=image

Francis Darwin calls these "extracts, somewhat abbreviated, from a part of the Autobiography, written in 1876". The original version is presented below.
The Life and Letters of Charles Darwin (1887)
Variant: p>But I was very unwilling to give up my belief;—I feel sure of this for I can well remember often and often inventing day-dreams of old letters between distinguished Romans and manuscripts being discovered at Pompeii or elsewhere which confirmed in the most striking manner all that was written in the Gospels. But I found it more and more difficult, with free scope given to my imagination, to invent evidence which would suffice to convince me. Thus disbelief crept over me at a very slow rate, but was at last complete. The rate was so slow that I felt no distress, and have never since doubted even for a single second that my conclusion was correct. I can indeed hardly see how anyone ought to wish Christianity to be true; for if so the plain language of the text seems to show that the men who do not believe, and this would include my Father, Brother and almost all my best friends, will be everlastingly punished.And this is a damnable doctrine.Although I did not think much about the existence of a personal God until a considerably later period of my life, I will here give the vague conclusions to which I have been driven. The old argument of design in nature, as given by Paley, which formerly seemed to me so conclusive, fails, now that the law of natural selection has been discovered. We can no longer argue that, for instance, the beautiful hinge of a bivalve shell must have been made by an intelligent being, like the hinge of a door by man. There seems to be no more design in the variability of organic beings and in the action of natural selection, than in the course which the wind blows. Everything in nature is the result of fixed laws. But I have discussed this subject at the end of my book on the Variation of Domesticated Animals and Plants, and the argument there given has never, as far as I can see, been answered.</p

Imagination , Animals , Personality , Thinking

“The concepts of purposive behavior and teleology have long been associated with a mysterious, self-perfecting or goal-seeking capacity or final cause, usually of superhuman or super-natural origin. To move forward to the study of events, scientific thinking had to reject these beliefs in purpose and these concepts of teleological operations for a strictly mechanistic and deterministic view of nature. This mechanistic conception became firmly established with the demonstration that the universe was based on the operation of anonymous particles moving at random, in a disorderly fashion, giving rise, by their multiplicity, to order and regularity of a statistical nature, as in classical physics and gas laws. The unchallenged success of these concepts and methods in physics and astronomy, and later in chemistry, gave biology and physiology their major orientation. This approach to problems of organisms was reinforced by the analytical preoccupation of the Western European culture and languages. The basic assumptions of our traditions and the persistent implications of the language we use almost compel us to approach everything we study as composed of separate, discrete parts or factors which we must try to isolate and identify as potential causes. Hence, we derive our preoccupation with the study of the relation of two variables. We are witnessing today a search for new approaches, for new and more comprehensive concepts and for methods capable of dealing with the large wholes of organisms and personalities.”

Lawrence K. Frank (1890–1968) American cyberneticist

L.K. Frank (1948) "Foreword". In L. K. Frank, G. E. Hutchinson, W. K. Livingston, W. S. McCulloch, & N. Wiener, Teleological mechanisms. Ann. N. Y. Acad. Sc., 1948, 50, 189-96; As cited in: Ludwig von Bertalanffy (1968) "General System Theory: Foundations, Development, Applications". p. 16-17

Law , Behavior , Search , Fashion

“In recent years, the studies of the effects of drugs on the behavior of animals have been playing an increasingly important role. Animal studies have been an advantage over studies with human subjects because better control of experimental variables and a possibility of using a wider range of the doses. It is also permissible to administer toxix compounds to animals. One can interfere surgically with various parts of the central nervous system while investigating the effects of the drugs. The whole field of comparative psychopharmacology has been recently reviewed”

Thaddus E. Weckowicz (1919–2000) Canadian psychologist

Weckowicz (1967) "Chapter VI - Animal Studies of Hallucinogenic Drugs" in: Abram Hoffer, Humphry Osmond (1967) The hallucinogens. p. 555

Behavior , Study , Animals , Parting

“Lack of flexibility manifests itself as stress. …stress will occur when one or more variables of the system are pushed to their extreme values, which induces increased rigidity throughout the system.”

Fritjof Capra (1939) American physicist

Epilogue: Ecological Literacy
The Web of Life (1996)

“Adaptive system — whether on the biological, psychological, or sociocultural level — must manifest (1) some degree of "plasticity" and "irritability" vis-a-vis its environment such that it carries on a constant interchange with acting on and reacting to it; (2) some source or mechanism for variety, to act as a potential pool of adaptive variability to meet the problem of mapping new or more detailed variety and constraints in a changeable environment; (3) a set of selective criteria or mechanisms against which the "variety pool" may be sifted into those variations in the organization or system that more closely map the environment and those that do not; and (4) an arrangement for preserving and/or propagating these "successful" mappings.”

Walter F. Buckley (1922–2006) American sociologist

Source: Sociology and modern systems theory (1967), p. 491.

Problem , Success

“The need for a fundamentally different approach to the study of physical processes at the molecular level motivated the development of relevant statistical methods, which turned out to be applicable not only to the study of molecular processes (statistical mechanics), but to a host of other areas such as the actuarial profession, design of large telephone exchanges, and the like. In statistical methods, specific manifestations of microscopic entities (molecules, individual telephone sites, etc.) are replaced with their statistical averages, which are connected with appropriate macroscopic variables. The role played in Newtonian mechanics by the calculus, which involves no uncertainty, is replaced in statistical mechanics by probability theory, a theory whose very purpose is to capture uncertainty of a certain type.”

George Klir (1932–2016) American computer scientist

Source: Fuzzy sets and fuzzy logic (1995), p. 1-2.

Motivation , Study

“Most effects in psychology are relatively unimportant. That is, most variables, considered in isolation, have relatively little impact on behavior. This doesn't mean… that we should all abandon psychology and become plumbers instead. The small magnitude of most effects in psychology is itself a discovery of psychology. One might argue, in fact, that it is one of the great metadiscoveries of the field. Most variables have little impact, and thus most of the phenomena studied by psychologists are products of a multiplicity of variables.”

Steve Stewart-Williams (1971)

Source: The Ape that Kicked the Hornet's Nest (2013), p. 251

Behavior , Study

“The field of study [of information science ] is so wide and varied; research is necessarily restricted to accessible areas; it often (and rightly) has the practical aim of providing guidance in a specific situation, rather than searching for generalisations; the isolation of variables for investigation is often so difficult; rarely can confirmatory experiments be undertaken.”

Brian Campbell Vickery (1918–2009) British information theorist

Source: Information Systems (1973), p. 332.

Search , Study , Science

“To every ω-consistent recursive class κ of formulae there correspond recursive class signs r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg (κ) (where v is the free variable of r).”

Kurt Gödel (1906–1978) logician, mathematician, and philosopher of mathematics

Proposition VI, On Formally Undecidable Propositions in Principia Mathematica and Related Systems I (1931); Informally, recursive systems of axioms cannot be complete.

“It is known that the mathematics prescribed for the high school [Gymnasien] is essentially Euclidean, while it is modern mathematics, the theory of functions and the infinitesimal calculus, which has secured for us an insight into the mechanism and laws of nature. Euclidean mathematics is indeed, a prerequisite for the theory of functions, but just as one, though he has learned the inflections of Latin nouns and verbs, will not thereby be enabled to read a Latin author much less to appreciate the beauties of a Horace, so Euclidean mathematics, that is the mathematics of the high school, is unable to unlock nature and her laws. Euclidean mathematics assumes the completeness and invariability of mathematical forms; these forms it describes with appropriate accuracy and enumerates their inherent and related properties with perfect clearness, order, and completeness, that is, Euclidean mathematics operates on forms after the manner that anatomy operates on the dead body and its members.
On the other hand, the mathematics of variable magnitudes—function theory or analysis—considers mathematical forms in their genesis. By writing the equation of the parabola, we express its law of generation, the law according to which the variable point moves. The path, produced before the eyes of the 113 student by a point moving in accordance to this law, is the parabola.
If, then, Euclidean mathematics treats space and number forms after the manner in which anatomy treats the dead body, modern mathematics deals, as it were, with the living body, with growing and changing forms, and thus furnishes an insight, not only into nature as she is and appears, but also into nature as she generates and creates,—reveals her transition steps and in so doing creates a mind for and understanding of the laws of becoming. Thus modern mathematics bears the same relation to Euclidean mathematics that physiology or biology … bears to anatomy. But it is exactly in this respect that our view of nature is so far above that of the ancients; that we no longer look on nature as a quiescent complete whole, which compels admiration by its sublimity and wealth of forms, but that we conceive of her as a vigorous growing organism, unfolding according to definite, as delicate as far-reaching, laws; that we are able to lay hold of the permanent amidst the transitory, of law amidst fleeting phenomena, and to be able to give these their simplest and truest expression through the mathematical formulas”

Christian Heinrich von Dillmann (1829–1899) German educationist

Source: Die Mathematik die Fackelträgerin einer neuen Zeit (Stuttgart, 1889), p. 37.

School , Law , Beauty , Mathematics

“You mention the circle and I agree with your definition.... why does the circle fascinates me? It is (1) the most modern form, but asserts itself unconditionally, (2) a precise but inexhaustible variable, (3) simultaneously stable and unstable, (4) simultaneously loud and soft, (5) a single tension that caries countless tensions within it. The circle is the synthesis of the greatest oppositions. It combines the concentric and the eccentric in a single form, and in balance. Of the three primary forms (triangle, square, circle), it points most clearly to the fourth dimension.”

Wassily Kandinsky (1866–1944) Russian painter

Quote from Kandinsky's letter to Will Grohmann, c. 1926; as cited in Kandinsky, Frank Whitford, Paul Hamlyn Ltd, London 1967, p. 36
1920 - 1930

“But his genetic and physical inference from cases of ethnic durability cannot account for the considerable variability, wide range and frequent absorptions and dissolutions of instances of ethnic affiliation, and the fact that many ethnies have undergone large-scale changes of culture and, in some cases, of demography. This is the case even in such a culturally long-lived example as the Greeks, where undoubted evidence of massive rupture of demographic continuity by the influx of Albanians and Slavs on the Greek mainland from the sixth to eighth centuries AD and of considerable, though not complete, culture change after the conversion to Orthodoxy, call into question the continuity and influence of a common ancient Greek biological and genetic inheritance on modern Greeks.”

Anthony D. Smith (1939–2016) British academic

Source: Nationalism and Modernism (1998), p. 150.

Question , Change

“[About Fortran] On October 11, 1963, my suggestion was to pass on a request of our customers to relax the ALGOL 60 rule of compulsory declaration of variable names and adopt some reasonable default convention such as that of FORTRAN. […] The story of the Mariner space rocket to Venus, lost because of the lack of compulsory declarations in FORTRAN, was not to be published until later.”

C. A. R. Hoare (1934) British computer scientist

The Emperor's Old Clothes

“Variability is the law of life, and as no two faces are the same, so no two bodies are alike, and no two individuals react alike and behave alike under the abnormal conditions which we know as disease.”

William Osler (1849–1919) Canadian pathologist, physician, educator, bibliophile, historian, author, cofounder of Johns Hopkins Hospi…

On the Educational Value of the Medical Society (1903)

Life , Disease , Law

“If in the case of a notion whose specialisations form a continuous manifoldness, one passes from a certain specialisation in a definite way to another, the specialisations passed over form a simply extended manifoldness, whose true character is that in it a continuous progress from a point is possible only on two sides, forwards or backwards. If one now supposes that this manifoldness in its turn passes over into another entirely different, and again in a definite way, namely so that each point passes over into a definite point of the other, then all the specialisations so obtained form a doubly extended manifoldness. In a similar manner one obtains a triply extended manifoldness, if one imagines a doubly extended one passing over in a definite way to another entirely different; and it is easy to see how this construction may be continued. If one regards the variable object instead of the determinable notion of it, this construction may be described as a composition of a variability of n + 1 dimensions out of a variability of n dimensions and a variability of one dimension.”

Bernhard Riemann (1826–1866) German mathematician

On the Hypotheses which lie at the Bases of Geometry (1873)

Way , Imagination

“In the second place, a system would involve more variables than those which may be supposed to enter into demand relationships, and so the preliminary work of estimating the necessary time series would also be increased. In the third place, in the simultaneous method of estimation the estimates of the original parameters come to depend on most of the remaining estimates, and so it is quite likely that they will have large sampling variances.”

Richard Stone (1913–1991) British economist, Nobel Memorial Prize winner

Studies in the National Income and Expenditure of the United Kingdom, 1954

Time , Dependency

“System costs can be considered in many different ways. For example, the cost for making the system and the cost for operating it may be used as a basic for judging the total cost. The total cost may also be arrived at in another fashion, as, for example, the sum of the fixed cost, variable cost, past investment and other charges. Furthermore, in many cases where systems engineering is required several time phases are involved for which the cost factors may be significant, such as the study phase, the breadboard phase, the prototype phase, and the production phase.”

Harold Chestnut (1917–2001) American engineer

Source: Systems Engineering Tools, (1965), Systems Engineering Methods (1967), p. 13

Way , Fashion , Study , Time

“… a rather different class of applications of the idea of best allocation of scarce resources… usually referred to as the theory of optimal economic growth. In most studies of this kind made in the countries with market economies there is not an identifiable client to whom the findings are submitted as policy recommendations. Nor is there an obvious choice of objective function, such as cost minimization or profit maximization in the studies addressed to individual enterprises. The field has more of a speculative character. The models studied usually contain only a few highly aggregated variables. One considers alternative objective functions that incorporate or emphasize various strands of ethical, political, or social thought. These objectives are then tried out to see what future paths of the economy they imply under equally simplified assumptions of technology or resource availability.”

Tjalling Koopmans (1910–1985) Dutch American economist

Source: Concepts of Optimality and Their Uses, 1975, p. 244

Idea , Optimism , Study , Future

“Construction methods are… variable for each specific material.”

Eduardo Torroja (1899–1961) Spanish architect

p, 125
Philosophy of Structures (1958)

“Racism should be viewed as an intervening variable. You give me a set of conditions and I can produce racism in any society. You give me a different set of conditions and I can reduce racism. You give me a situation where there are a sufficient number of social resources so people don't have to compete for those resources, and I will show you a society where racism is held in check. If we could create the conditions that make racism difficult, or discourage it, then there would be less stress and less need for affirmative action programs. One of those conditions would be an economic policy that would create tight labor markets over long periods of time. Now does that mean that affirmative action is here only temporarily? I think the ultimate goal should be to remove it.”

William Julius Wilson (1935) American sociologist

Interview with Mother Jones.

People , Thinking , Time

“We shall approach practical objectives through a series of approximations. Keeping the maximization of the rate of return as the central theoretical objective, we shall develop a number of subsidiary objectives (which the economists call proxy variables) which contribute in different ways to improvement in the return and which are also measurable in business practice. A firm which meets high performance in most of its subsidiary objectives will substantially enhance its long-term rate of return. (The defect in our approach is that we cannot prove that the result will be a ‘‘maximum’’ possible overall return.) As will be seen, this road has its own obstacles: the difficulties of long term maximization are replaced by the problem of reconciling claims of conflicting objectives.”

Igor Ansoff (1918–2001) American mathematician

Source: Corporate Strategy, 1965, p. 47; cited in: Graham Kenny, (2012),"From the stakeholder viewpoint: designing measurable objectives", Journal of Business Strategy, Vol. 33 Iss: 6 pp. 40-46

Way , Business , Problem

“The development of modern science is marked by a pronounced tendency toward indeterminism. A somewhat brutal description of this tendency may be states as follows. In relation to some phenomena, instead of trying to establish a (deterministic) functional relationship between a variable y, and some other variables x1, x2, …, xn, we try to build a (stochastic or probabilistic) model of these phenomena, predicting frequencies with which, in specified conditions, the same variable y will assume all of its possible values.”

Jerzy Neyman (1894–1981) Polish statistician

p. 401 of "Statistics—servant of all sciences." http://www.jstor.org/stable/1751553 Science 122, no. 3166 (1955): 401–406.

Science

“Synthesis of systems is much more difficult. Here science and engineering begin to take on aspects of art. A systems designer or planner not only must construct systems that work harmoniously individually and in tandem, he must also know a lot about the environment that the system is intended to match. Consideration of environmental factors requires foresight and experience; no one can ever foresee all the variables of importance and a choice of which to include is often a difficult one to make.”

Arthur D. Hall (1925–2006) American electrical engineer

Source: Definition of System, 1956, p. 28

Art , Science

“Unlike Hegel’s progress model of history, which moves by stages, each containing its own logic of growth and decline, the economic model develops as the simple function of one money-variable over time, with a long-term trend which increases monotonically.”

John Carroll (1944) Australian professor and author

Source: Break-Out from the Crystal Palace (1974), p. 168

Money , History , Time

“There is no effective difference between guessing a variable that is not random, but for which information is partial or deficient (…), and a random one (…). In this sense, guessing (what I don't know, but what someone else may know) and predicting (what has not taken place yet) are the same thing.”

Nassim Nicholas Taleb (1960) Lebanese-American essayist, scholar, statistician, former trader and risk analyst

Source: The Black Swan: The Impact of the Highly Improbable (2007), p. 142

Sense

“In Darwin's time no serious attempt had been made to examine the manifestations of variability. A vast assemblage of miscellaneous facts could formerly be adduced as seemingly comparable illustrations of the phenomenon "Variation." Time has shown this mass of evidence to be capable of analysis. When first promulgated it produced the impression that variability was a phenomenon generally distributed amongst living things in such a way that the specific divisions must be arbitrary. When this variability is sorted out, and is seen to be in part a result of hybridisation, in part a consequence of the persistence of hybrids by parthenogenetic reproduction, a polymorphism due to the continued presence of individuals representing various combinations of Mendelian allelomorphs, partly also the transient effect of alteration in external circumstances, we see how cautious we must be in drawing inferences as to the indefiniteness of specific limits from a bare knowledge that intermediates exist.”

William Bateson (1861–1926) British geneticist and biologist

Source: Problems In Genetics (1913), p. 15

Way , Knowledge , Time , Parting

“In mathematics, logic, linguistics, and other abstract disciplines, the systems are not assigned to objects. They are defined by an enumeration of the variables, their admissible values, and their algebraic, topological, grammatical, and other properties which, in the given case, determine the relations between the variables under consideration.”

George Klir (1932–2016) American computer scientist

Source: An approach to general systems theory (1969), p. 40.

Mathematics

“Physiologic facts concerning the origin of species in nature were unknown in the time of Darwin... The experience of the breeders was quite inadequate to the use which Darwin made of it. It was neither scientific, nor critically accurate. Laws of variation were barely conjectured; the different types of variability were only imperfectly distinguished. The breeders' conception was fairly sufficient for practical purposes, but science needed a clear understanding of the factors in the general process of variation. Repeatedly Darwin tried to formulate these causes, but the evidence available did not meet his requirements.
Quetelet's law of variation had not yet been published. Mendel's claim of hereditary units for the explanation of certain laws of hybrids discovered by him, was not yet made. The clear distinction between spontaneous and sudden changes, as compared with the ever-present fluctuating variations, is only of late coming into recognition by agriculturists. Innumerable minor points which go to elucidate the breeders' experience, and with which we are now quite familiar, were unknown in Darwin's time. No wonder that he made mistakes, and laid stress on modes of descent, which have since been proved to be of minor importance or even of doubtful validity.”

Hugo De Vries (1848–1935) Dutch botanist

Species and Varieties: Their Origin by Mutation (1904), The Open Court Publishing Company, Chicago, p. 5-6

Law , Understanding , Nature , Science

“If we decide – and this is our decision; it’s not imposed on us from above – if we decide that reducing the amount of suffering in the world is a good ethical principle to live by, then it becomes entirely unjustified and arbitrary to extend this principle to human beings but not also to extend it to other animals capable of suffering. Why should the suffering of nonhumans be less important than that of humans? Surely a universe with less suffering is better than one with more, regardless of whether the locus of suffering is a human being or not, a rational being or not, a member of the moral community or not. Suffering is suffering, and these other variables are morally irrelevant.”

Steve Stewart-Williams (1971)

Source: Darwin, God and the Meaning of Life: How Evolutionary Theory Undermines Everything You Think You Know (2010), p. 274

World , Communication , Decision , Suffering

“Simplicity in a system tends to increase that system’s efficiency. Because less can go wrong with fewer parts, less will. Complexity in a system tends to increase that system’s inefficiency; the greater the number of variables, the greater the probability of those variables clashing, and in turn, the greater the potential for conflict and disarray. Because more can go wrong, more will. That is why centralized systems are inclined to break down quickly and become enmeshed in greater unintended consequences.”

L. K. Samuels (1951) American writer

Source: In Defense of Chaos: The Chaology of Politics, Economics and Human Action, (2013), p. 191

Parting

“Economics is a young science, and there is still much to be learned. Economists sometimes disagree because they have different hunches about the validity of alternative theories or about the size of important parameters that measure how economic variables are related.”

N. Gregory Mankiw (1958) American economist

Source: Principles of Economics (1998-), Ch. 2. Thinking Like an Economist; p. 30

Learning , Science

“Organizational design often focuses on structural alternatives such as matrix, decentralization, and divisionalization. However, control variables (e. g., reward structures, task characteristics, and information systems) offer a more flexible approach. The purpose of this paper is to explore these control variables for organizational design. This is accomplished by integration and testing of two perspectives, organization theory and economics, notably agency theory. The resulting hypotheses link task characteristics, information systems, and business uncertainty to behavior vs. outcome based control strategy. These hypothesized linkages are examined empirically in a field study of the compensation practices for retail salespeople in 54 stores. The findings are that task programmability is strongly related to the choice of compensation package. The amount of behavioral measurement, the cost of measuring outcomes, and the uncertainty of the business also affect compensation. The findings have management implications for the design of compensation and reward packages, performance evaluation systems, and control systems, in general. Such systems should explicitly consider the task, the information system in place to measure performance, and the riskiness of the business. More programmed tasks require behavior based controls while less programmed tasks require more elaborate information systems or outcome based controls.”

Kathleen M. Eisenhardt American economist

Source: "Control: Organizational and economic approaches," 1985, p. 134; Article abstract

Behavior , Business , Study

“Geography is that discipline that seeks to describe and interpret the variable character from place to place of the earth as the world of man.”

Richard Hartshorne (1899–1992) American Geographer

Source: Perspective on the nature of geography (1958), p. 47

World

“The hundreds of scientific studies of this phenomenon come to one general conclusion: Leadership is highly variable or "contingent" upon a large variety of important variables such as nature of task, size of the group, length of time the group has existed, type of personnel within the group and their relationships with each other, and amount of pressure the group is under. It docs not seem likely that we'll be able to devise a way to select the best leader for a particular situation. Even if we could, that situation would probably change in a short time and thus would require a somewhat different type of leader.”

Charles Perrow (1925–2019) American sociologist

Source: 1970s, "The short and glorious history of organizational theory", 1973, p. 13

Way , Nature , Study , Change

“Learning can be defined as occurring under two conditions. First, learning occurs when an organisation achieves what it intended; that is, there is a match between its design for action and the actual outcome. Second, learning occurs when a mismatch between intention and outcome is identified and corrected; that is, a mismatch is turned into a match…. Single-loop learning occurs when matches are created, or when mismatches are corrected by changing actions. Double-loop learning occurs when mismatches are corrected by first examining and altering the governing variables and then the actions.”

Chris Argyris (1923–2013) American business theorist/Professor Emeritus/Harvard Business School/Thought Leader at Monitor Group

Chris Argyris (1982) as cited in: "Chris Argyris: The Manager's Academic" in Business (2003). p. 965

Learning , Change

“Our "pathway" is straight to the ballot box, with no variableness nor shadow of turning…We demand in the Reconstruction suffrage for all the citizens of the Republic. I would not talk of Negroes or women, but of citizens.”

Elizabeth Cady Stanton (1815–1902) Suffragist and Women's Rights activist

Letter to Thomas Wentworth Higginson (1868-01-13).

Women , Box

“He is not affected by our mutability; our changes do not alter Him. When we are restless, He remains serene and calm; when we are low, selfish, mean or dispirited, He is still the unalterable I AM, the same yesterday, to-day, and forever, in whom is no variableness, neither shadow of turning. What God is in Himself, not what we may chance to feel Him in this or that moment to be, that is our hope. My soul, "hope thou in God."”

Frederick William Robertson (1816–1853) British writer and theologian

Source: Dictionary of Burning Words of Brilliant Writers (1895), P. 93.

God , Hope , Feeling , Soul

“Apparently no sharp dividing line can be drawn between true Algol stars and those whose variations are continuous. Periods of nine variables in this region, which are of the Algol type or closely resemble it, have been determined and are here discussed.”

Henrietta Swan Leavitt (1868–1921) astronomer

"Ten Variable Stars of the Algol Type" (1908) Annals of the Astronomical Observatory of Harvard College Vol.60. No.5

Star

“Variable but forecastable renewables (wind and solar cells) are very reliable when integrated with each other, existing supplies and demand. For example, three German states were more than 30 percent wind-powered in 2007—and more than 100 percent in some months. Mostly renewable power generally needs less backup than utilities already bought to combat big coal and nuclear plants' intermittence.”

Amory B. Lovins (1947) American physicist

Missing the Market Meltdown http://www.newsweek.com/id/137501 (May 2008)

“The general method involved may be very simply stated. In cases where the equilibrium values of our variables can be regarded as the solutions of an extremum (maximum or minimum) problem, it is often possible regardless of the number of variables involved to determine unambiguously the qualitative behavior of our solution values in respect to changes of parameters.”

Paul A. Samuelson book Foundations of Economic Analysis

Source: 1940s, Foundations of Economic Analysis, 1947, Ch. 2 : The Theory of Maximizing Behavior

Behavior , Problem , Change

“If the variables are continuous, this definition [Ashby’s fundamental concept of machine] corresponds to the description of a dynamic system by a set of ordinary differential equations with time as the independent variable. However, such representation by differential equations is too restricted for a theory to include biological systems and calculating machines where discontinuities are ubiquitous.”

Ludwig von Bertalanffy (1901–1972) austrian biologist and philosopher

Source: General System Theory (1968), 4. Advances in General Systems Theory, p. 96, as cited in: Vincent Vesterby (2013) From Bertalanffy to Discipline-Independent-Transdisciplinarity http://journals.isss.org/index.php/proceedings56th/article/viewFile/1886/672

Time

“It is not necessary to think of gambling places; the statistician who applies statistical tests is engaged in a dignified sort of gambling, and in his case the distribution of the random variables changes from occasion to occasion.”

William Feller (1906–1970) Croatian-American mathematician

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter X, Law Of large Numbers, p. 253.

Thinking , Change

“By the basis of power we mean the relationship between O and P which is the source of that power. It is rare that we can say with certainty that a given empirical case of power is limited to one source. Normally, the relation between O and P will be characterized by several qualitatively different variables which are bases of power (30). Although there are undoubtedly many possible bases of power which may be distinguished, we shall here define five which seem especially common and important. These five bases of O's power are:
(a) reward power, based on P's perception that O has the ability to mediate rewards for him;
(b) coercive power, based on P's perception that O has the ability to mediate punishments for him;
(c) legitimate power, based on the perception by P that O has a legitimate right to prescribe behavior for him;
(d) referent power, based on P's identification with O;
(e) expert power, based on the perception that O has some special knowledge or expertness.”

John R. P. French (1913–1995) American psychologist

Source: "The bases of social power." 1959, p. 155-6

Behavior , Knowledge

“Maybe "just one little global variable" isn't too unmanageable, but that style leads to code that is useless except to its original programmer”

Bjarne Stroustrup book The C++ Programming Language

[Stroustrup, Bjarne, The C++ Programming Language, 467]

“"Personal density," Kurt Mondaugen in his Peenemünde office not too many steps away from here, enunciating the Law which will one day bear his name, "is directly proportional to temporal bandwidth."
"Temporal bandwidth," is the width of your present, your now. It is the familiar "∆ t" considered as a dependent variable. The more you dwell in the past and in the future, the thicker your bandwidth, the more solid your persona. But the narrower your sense of Now, the more tenuous you are.”

Thomas Pynchon book Gravity's Rainbow

Gravity's Rainbow (1973)

Law , Sense , Past , Future

“Because of the variables and the complexity of their interaction, the data assembled by descriptive musicology yield relatively few observable regularities.”

Leonard B. Meyer (1918–2007) American composer and philosopher

"Universalism and Relativism in the Study of Ethnic music", Ethnomusicology 4, no. 2:49-54 (1960); reprinted in Reading in Ethnomusicology, p. 270-71.

“Based upon evidence such as already presented, it appears feasible to set up criteria by which to determine when assignable causes of variation in quality have been eliminated so that the product may then be considered to be controlled within limits. This state of control appears to be, in general, a kind of limit to which we may expect to go economically in finding and removing causes of variability without changing a major portion of the manufacturing process as, for example, would be involved in the substitution of new materials or designs.”

Walter A. Shewhart (1891–1967) American statistician

Source: Economic Control of Quality of Manufactured Product,1931, p. 24

Appearance , Change

“Dynamical variables are what count in physics, not coordinate or gauge transformations.”

John Clive Ward (1924–2000) British-Australian nuclear physicist

J. C. Ward, Memoirs of a Theoretical Physicist (Optics Journal, Rochester, 2004).

Gauge

“I contend that the continued racial classification of Homo sapiens represents an outmoded approach to the general problem of differentiation within a species. In other words, I reject a racial classification of humans for the same reasons that I prefer not to divide into subspecies the prodigiously variable West Indian land snails that form the subject of my own research.”

Stephen Jay Gould book Ever Since Darwin

"Why We Should Not Name Human Races—A Biological View", p. 231
Ever Since Darwin (1977)

Problem

“There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

"Über die verschiedenen Ansichten in Bezug auf die actualunendlichen Zahlen" ["Over the different views with regard to the actual infinite numbers"] - Bihand Till Koniglen Svenska Vetenskaps Akademiens Handigar (1886)

Sense

“For many purposes of organizational analysis technology might not be an independent variable but a dependent one.”

Charles Perrow (1925–2019) American sociologist

Charles Perrow (1967), in: Industrial Relations Research Association, Proceedings of the ... Annual Winter Meeting, Vol. 19 (1967), p. 163
1960s

Dependency

“Daddy says that, in a dilemma, it is helpful to change any variable, then reexamine the problem.”

Robert A. Heinlein book Have Space Suit—Will Travel

Source: Have Space Suit—Will Travel (1958), Chapter 5

Problem , Change , Help

“the distribution of flexibility among the many variables of a system is a matter of very great importance. The healthy system … may be compared to an acrobat on a high wire. To maintain the ongoing truth of his basic premise (“I am on the wire”), he must be free to move from one position of instability to another, i. e., certain variables such as the position of his arms and the rate of movement of his arms must have great flexibility, which he uses to maintain the stability of other more fundamental and general characteristics. If his arms are fixed or paralyzed (isolated from communication), he must fall.”

Gregory Bateson book Steps to an Ecology of Mind

7.4 Ecology and Flexibility in Urban Civilization
Steps to an Ecology of Mind (1972)

Truth , Communication

“The problem with managing either a business or a prison by periodic rather than continuous inspection is that the "variables" are likely to be seriously out of control before the discrepancy is noted.”

Anthony Stafford Beer (1926–2002) British theorist, consultant, and professor

Source: Management Science (1968), Chapter 6, The Viable Governor, p. 146.

Business , Problem

“For those who want to develop or use semantical methods, the decisive question is not the alleged ontological question of the existence of abstract entities but rather the question whether the rise of abstract linguistic forms or, in technical terms, the use of variables beyond those for things (or phenomenal data), is expedient and fruitful for the purposes for which semantical analyses are made, viz. the analysis, interpretation, clarification, or construction of languages of communication, especially languages of science.”

Rudolf Carnap (1891–1970) German philosopher

Source: Empiricism, Semantics, and Ontology (1950), Ch. 5. Conclusion

Communication , Question , Decision , Science

“Managers construct, rearrange, single out, and demolish many “objective” features of their surroundings. When people act they unrandomize variables, insert vestiges of orderliness, and literally create their own constraints.”

Karl E. Weick (1936) Organisational psychologist

Source: 1970s, Social Psychology of Organizing, (1979), p. 243 ; As cited in: Dr. Adrian McLean (2013), Leaderhip and Cultural Webs in Organisations: Weavers' Tales. p. 213

People

“Technology has always been a central variable in organizational theory, informing research and practice. Despite years of investigative effort there is little agreement on the definition and measurement of technology, and no compelling evidence on the precise role of technology in organizational affairs. I will argue that the divergent definitions and opposing perspectives associated with technological research have limited our understanding of how technology interacts with organizations, and that these incompatibilities cannot be resolved by mutual concession. What is needed is a reconstruction of the concept of technology, which fundamentally re-examines our current notions of technology and its role in organizations.”

Wanda Orlikowski American computer scientist

Source: "The duality of technology" 1992, p. 389

Understanding , Effort

“A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.”

Leonhard Euler (1707–1783) Swiss mathematician

§4
Introduction to the Analysis of the Infinite (1748)

Way

“For Space, when the position of points is expressed by rectilinear co-ordinates, ds = \sqrt{ \sum (dx)^2 }; Space is therefore included in this simplest case. The next case in simplicity includes those manifoldnesses in which the line-element may be expressed as the fourth root of a quartic differential expression…. I restrict myself… to those manifoldnesses in which the line element is expressed as the square root of a quadric differential expression…. Manifoldnesses in which, as in the Plane and in Space, the line-element may be reduced to the form \sqrt{ \sum (dx)^2 }, are… only a particular case of the manifoldnesses to be here investigated; they require a special name, and therefore these manifoldnesses… I will call flat. In order now to review the true varieties of all the continua which may be represented in the assumed form, it is necessary to get rid of difficulties arising from the mode of representation, which is accomplished by choosing the variables in accordance with a certain principle.”

Bernhard Riemann (1826–1866) German mathematician

On the Hypotheses which lie at the Bases of Geometry (1873)

“Let us imagine that from any given point the system of shortest lines going out from it is constructed; the position of an arbitrary point may then be determined by the initial direction of the geodesic in which it lies, and by its distance measured along that line from the origin. It can therefore be expressed in terms of the ratios dx0 of the quantities dx in this geodesic, and of the length s of this line. …the square of the line-element is \sum (dx)^2 for infinitesimal values of the x, but the term of next order in it is equal to a homogeneous function of the second order… an infinitesimal, therefore, of the fourth order; so that we obtain a finite quantity on dividing this by the square of the infinitesimal triangle, whose vertices are (0,0,0,…), (x1, x2, x3,…), (dx1, dx2, dx3,…). This quantity retains the same value so long as… the two geodesics from 0 to x and from 0 to dx remain in the same surface-element; it depends therefore only on place and direction. It is obviously zero when the manifold represented is flat, i. e., when the squared line-element is reducible to \sum (dx)^2, and may therefore be regarded as the measure of the deviation of the manifoldness from flatness at the given point in the given surface-direction. Multiplied by -¾ it becomes equal to the quantity which Privy Councillor Gauss has called the total curvature of a surface. …The measure-relations of a manifoldness in which the line-element is the square root of a quadric differential may be expressed in a manner wholly independent of the choice of independent variables. A method entirely similar may for this purpose be applied also to the manifoldness in which the line-element has a less simple expression, e. g., the fourth root of a quartic differential. In this case the line-element, generally speaking, is no longer reducible to the form of the square root of a sum of squares, and therefore the deviation from flatness in the squared line-element is an infinitesimal of the second order, while in those manifoldnesses it was of the fourth order. This property of the last-named continua may thus be called flatness of the smallest parts. The most important property of these continua for our present purpose, for whose sake alone they are here investigated, is that the relations of the twofold ones may be geometrically represented by surfaces, and of the morefold ones may be reduced to those of the surfaces included in them…”

Bernhard Riemann (1826–1866) German mathematician

On the Hypotheses which lie at the Bases of Geometry (1873)

Imagination , Parting , Dependency

“Jazz music is a lifestyle. It’s not notes, chords and arpeggios. Today’s improvisation is too based on the knowledge of chords and the way they practice the chords. It’s not a melodic thing anymore like the older days. It was much more important to play shorter and to play more variable, valid stuff. Today, a lot of solos are long and uninteresting and the influence usually comes from John Coltrane’s group. He himself was a master musician, but he put so much emphasis on chord knowledge and technique, and now the kids want to show how fast they can play. This is the same with piano players and most instrumentalists—it’s speed. That’s gonna change again and hopefully the kids who are now 16 and 17 years old have a little more sense and maybe some more stories to tell.”

Joe Zawinul (1932–2007) austrian composer and pianist

Reflecting on the new generation's take on jazz music
Prasad interview (1997)

Music , Way , Knowledge , Sense

“What makes a piece of mathematical economics not only mathematics but also economics is, I believe, this: When we set up a system of theoretical relationships and use economic names for the otherwise purely theoretical variables involved, we have in mind some actual experiment, or some design of an experiment, which we could at least imagine arranging, in order to measure those quantities in real economic life that we think might obey the laws imposed on their theoretical namesakes.”

Trygve Haavelmo (1911–1999) Norwegian economist and econometrician

Trygve Haavelmo, "The probability approach in econometrics" in: Supplement to Econometrica. 12 91944), p. 5; Cited in Pearl (2012, 1-2)

Life , Law , Imagination , Mathematics

“Most managers have some conception of at least some of the types of decisions they must make. Their conceptions, however, are likely to be deficient in a very critical way, a way that follows from an important principle of scientific economy: The less we understand a phenomenon, the more variables we require to explain it.”

Russell L. Ackoff (1919–2009) Scientist

Source: 1960s, Management misinformation systems, 1967, p. 149.

Way , Understanding , Decision

“The classical theory of probability was devoted mainly to a study of the gamble's gain, which is again a random variable; in fact, every random variable can be interpreted as the gain of a real or imaginary gambler in a suitable game.”

William Feller (1906–1970) Croatian-American mathematician

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter IX, Random Variables; Expectation, p. 212.

Game , Study

“Once some engineers from the veneer trust laboratory came to me for consultation with a quite skilful presentation of their problems. Diﬀerent productivity is obtained for veneer-cutting machines for diﬀerent types of materials; linked to this the output of production of this group of machines depended, it would seem, on the chance factor of which group of raw materials to which machine was assigned. How could this fact be used rationally?
This question interested me, but nevertheless appeared to be quite particular and elementary, so I did not begin to study it by giving up everything else. I put this question for discussion at a meeting of the mathematics department, where there were such great specialists as Gyunter, Smirnov himself, Kuz’min, and Tartakovskii. Everyone listened but no one proposed a solution; they had already turned to someone earlier in individual order, apparently to Kuz’min. However, this question nevertheless kept me in suspense. This was the year of my marriage, so I was also distracted by this. In the summer or after the vacation concrete, to some extent similar, economic, engineering, and managerial situations started to come into my head, that also required the solving of a maximization problem in the presence of a series of linear constraints.
In the simplest case of one or two variables such problems are easily solved—by going through all the possible extreme points and choosing the best. But, let us say in the veneer trust problem for ﬁve machines and eight types of materials such a search would already have required solving about a billion systems of linear equations and it was evident that this was not a realistic method. I constructed particular devices and was probably the ﬁrst to report on this problem in 1938 at the October scientiﬁc session of the Herzen Institute, where in the main a number of problems were posed with some ideas for their solution.
The universality of this class of problems, in conjunction with their difficulty, made me study them seriously and bring in my mathematical knowledge, in particular, some ideas from functional analysis.
What became clear was both the solubility of these problems and the fact that they were widespread, so representatives of industry were invited to a discussion of my report at the university.”

Leonid Kantorovich (1912–1986) Russian mathematician

L.V. Kantorovich (1996) Descriptive Theory of Sets and Functions. p. 39; As cited in: K. Aardal, ‎George L. Nemhauser, ‎R. Weismantel (2005) Handbooks in Operations Research and Management Science, p. 15-26

Marriage , Search , Mathematics , Idea