Quotes about equation

A collection of quotes on the topic of equation, other, use, time.

Quotes about equation

“Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.”

Nikola Tesla (1856–1943) Serbian American inventor

"Radio Power Will Revolutionize the World" in Modern Mechanics and Inventions (July 1934)

Mathematics, Reality

“Only the insane equate pain with success."
"The uninformed must improve their deficit, or die."
_Cheshire Cat”

Lewis Carroll (1832–1898) English writer, logician, Anglican deacon and photographer

Source: Alice's Adventures in Wonderland & Other Stories

Pain, Cats, Success

“Life is and will ever remain an equation incapable of solution, but it contains certain known factors.”

Nikola Tesla (1856–1943) Serbian American inventor

Life

“I have given my life to try to alleviate the sufferings of Africa. There is something that all white men who have lived here like I must learn and know: that these individuals are a sub-race. They have neither the intellectual, mental, or emotional abilities to equate or to share equally with white men in any function of our civilization. I have given my life to try to bring them the advantages which our civilization must offer, but I have become well aware that we must retain this status: the superior and they the inferior. For whenever a white man seeks to live among them as their equals they will either destroy him or devour him. And they will destroy all of his work. Let white men from anywhere in the world, who would come to Africa, remember that you must continually retain this status; you the master and they the inferior like children that you would help or teach. Never fraternize with them as equals. Never accept them as your social equals or they will devour you. They will destroy you.”

Albert Schweitzer (1875–1965) French-German physician, theologian, musician and philosopher

This has usually been presented as something "said shortly before his death" without any definite source, but appears to be entirely spurious. The "FAQ about the life and thoughts of Albert Schweitzer" http://www.schweitzer.org/faq?lang=en#rasist asserts "This quote is utterly false and is an outrageously inaccurate picture of Dr. Schweitzer’s view of Africans. Dr. Schweitzer never said or wrote anything remotely like this. It does NOT appear in the book African Notebook." This refers to some citations of it being from Afrikanische Geschichten (1938), which was translated as From My African Notebook (1939) by Mrs. C. E. B Russell Misattributed

Life, Men, Children, World

“If we arrive at an equation containing on each side the same term but with different coefficients, we must take equals from equals until we get one term equal to another term. But, if there are on one or on both sides negative terms, the deficiencies must be added on both bides until all the terms on both sides are positive. Then we must take equals from equals until one term is left on each side.”

Diophantus Arithmetica

As quoted by Thomas Little Heath, Diophantos of Alexandria: https://books.google.com/books?id=ABkPAAAAIAAJ A Study in the History of Greek Algebra (1885) Arithmetica (c. 250 AD)

“They are shaman-artists who constantly strive to look into the blueprint of creation beyond the visual crowd and the noise of superficial details, the one on task to explore and communicate with a primary game of opposite values during composition and construction of a coherent imagery. They paint from both levels, the personal and the intimate and the universal one which emerges from life-giving tension. Every Ink image, every Sumi-e painting, is a unique crossroad of oppositions, of directions, of intentions. They are all constant reminders of the duality of creation and the accuracy of the equation where two equals one.”

Alfred Freddy Krupa (1971) Croatian contemporary painter, master draughtsman, book artist and art teacher, the pioneer of the New Ink Art m…

2010s

Painting, Personality, Game, Communication

“What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe.”

Stephen Hawking book A Brief History of Time

Source: A Brief History of Time (1988), Ch. 12
Context: Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?

Mathematics, Question, Universe, Science

“A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.”

Robert A. Heinlein Time Enough for Love

Time Enough for Love (1973)

Problem, Change, Fight, Cooking

“Maxwell's equations… originally consisted of eight equations. These equations are not "beautiful." They do not possess much symmetry. In their original form, they are ugly…. However, when rewritten using time as the fourth dimension, this rather awkward set of eight equations collapses into a single tensor equation. This is what a physicist calls "beauty," because both criteria are now satisfied.”

Michio Kaku book Hyperspace

Source: Hyperspace (1995), Ch.5 Quantum Heresy

Beauty, Time

“One of the fundamental points about religious humility is you say you don't know about the ultimate judgment. It's beyond your judgment. And if you equate God's judgment with your judgment, you have a wrong religion.”

Reinhold Niebuhr (1892–1971) American protestant theologian

Source: The Mike Wallace Interview (1958)

God, Religion

“War is an equation with many unknowns; and this already refutes the thesis of invincibility. History does not know invincible armies.”

Lev Mekhlis (1889–1953) Soviet politician

The wars of the past show us that even armies that had won brilliant victories for decades, in some cases were not only defeated but even disintegrated and ceased to exist. Such a fate, for example, befell the army of Napoleon, who for almost two decades kept the whole Europe under its boots. The army needs to instill a spirit of confidence in its power, but not in terms of boasting. Bragging about invincibility brings harm to the army.
Speech to Red Army personnel, 13 May 1940
Source: http://porto-fr.odessa.ua/index.php?art_num=art021&year=2008&nnumb=40

War, History

“~ I've made the most important discovery of my life. It's only in the mysterious equation of love that any logical reasons can be found. I'm only here tonight because of you. You're the only reason I am… you're all my reasons.~”

John Nash (1928–2015) American mathematician and Nobel Prize laureate

Love, Life

“You are old beyond your years Zoeybird. Believe in yourself and you will find a way. But remember darkness does not always equate to evil just like light does not always bring good.”

P. C. Cast book Marked

Source: Marked

Way, Light, Evil

“The specific character of [women's] oppression cannot be explained away by equating different situations through superficial and childish simplifications[:]

It is true that both the woman and the male worker are condemned to silence by their exploitation. But under the current system, the worker's wife is also condemned to silence by her worker-husband. In other words, in addition to the class exploitation common to both of them, women must confront a particular set of relations that exist between them and men, relations of conflict and violence that use physical differences as their pretext.”

Thomas Sankara (1949–1987) President of Upper Volta

Source: Women's Liberation and the African Freedom Struggle

Women, Men, Silence

“What truly is logic? Who decides reason? […] It is only in the mysterious equations of love that any logic or reason can be found.”

John Nash (1928–2015) American mathematician and Nobel Prize laureate

Love

“It is better to have been, then not to have been, then to have been nothing at all." What truly is logic? Who decides reason? "It is only in the mysterious equations of love that any logic or reason can be found."-JOHN NASH JR.”

John Nash (1928–2015) American mathematician and Nobel Prize laureate

Love

“But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

Earliest source located is the book Brighter than a Thousand Suns: A Personal History of the Atomic Scientists by Robert Jungk (1958), p. 249, which says that Einstein made the comment during "a walk with Ernst Straus, a young mathematician acting as his scientific assistant at Princeton." Variant: "Equations are more important to me, because politics is for the present, but an equation is something for eternity." From A Briefer History of Time by Stephen Hawking (2005), p. 144 http://books.google.com/books?id=4Y0ZBW19n_YC&lpg=PP1&pg=PA144#v=onepage&q&f=false. Earlier, Straus recalled the German version of the quote in Helle Zeit, Dunkle Zeit: In Memoriam Albert Einstein (1956) edited by Carl Seelig, p. 71. There the quote was given as Ja, so muß man seine Zeit zwischen der Politik und unseren Gleichungen teilen. Aber unsere Gleichungen sind mir doch viel wichtiger; denn die Politik ist für die Gegenwart da, aber solch eine Gleichung is etwas für die Ewigkeit. Attributed in posthumous publications Context: Yes, we now have to divide up our time like that, between politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever.

Mathematics

“Remember, darkness does not always equate to evil, just as light does not always bring good.”

P. C. Cast book Betrayed

Source: Betrayed

Light, Evil

“The greatest feminists have also been the greatest lovers. I'm thinking not only of Mary Wollstonecraft and her daughter Mary Shelley, but of Anais Nin, Edna St. Vincent Millay, and of course Sappho. You cannot divide creative juices from human juices. And as long as juicy women are equated with bad women, we will err on the side of being bad.”

Erica Jong (1942) Novelist, poet, memoirist, critic

Women, Lovers, Thinking, Daughters

“You've never heard of Chaos theory? Non-linear equations? Strange attractors? Ms. Sattler, I refuse to believe you're not familiar with the concept of attraction.”

Michael Crichton book Jurassic Park

Source: Jurassic Park

“We have to all realise that criticising some phenomena in our home country does not equate to hating it, wishing evil upon it nor is it an attempt to shake its balance, it's the total opposite. Any Saudi citizen might be upset by some incidents that occur in the Kingdom, but that is only a direct sign of one's interest in the betterment of one's own country and one's hope to see Saudi Arabia as a global leader.”

Loujain al-Hathloul (1989) Saudi Arabian activist

A Clarification (March 24, 2016)

Hate, Hope, Home, Evil

“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

“Someone told me that each equation I included in the book would halve the sales. I therefore resolved not to have any equations at all. In the end, however, I did put in one equation, Einstein's famous equation, E = mc^2. I hope that this will not scare off half of my potential readers.”

Stephen Hawking book A Brief History of Time

A Brief History of Time (1988)

Books, Hope

“Notwithstanding the eminent difficulties of the mathematical theory of sonorous vibrations, we owe to it such progress as has yet been made in acoustics. The formation of the differential equations proper to the phenomena is, independent of their integration, a very important acquisition, on account of the approximations which mathematical analysis allows between questions, otherwise heterogeneous, which lead to similar equations. This fundamental property, whose value we have so often to recognize, applies remarkably in the present case; and especially since the creation of mathematical thermology, whose principal equations are strongly analogous to those of vibratory motion. This means of investigation is all the more valuable on account of the difficulties in the way of direct inquiry into the phenomena of sound. We may decide the necessity of the atmospheric medium for the transmission of sonorous vibrations; and we may conceive of the possibility of determining by experiment the duration of the propagation, in the air, and then through other media; but the general laws of the vibrations of sonorous bodies escape immediate observation. We should know almost nothing of the whole case if the mathematical theory did not come in to connect the different phenomena of sound, enabling us to substitute for direct observation an equivalent examination of more favorable cases subjected to the same law. For instance, when the analysis of the problem of vibrating chords has shown us that, other things being equal, the number of oscillations is hi inverse proportion to the length of the chord, we see that the most rapid vibrations of a very short chord may be counted, since the law enables us to direct our attention to very slow vibrations. The same substitution is at our command in many cases in which it is less direct.”

Auguste Comte (1798–1857) French philosopher

Bk. 3, chap. 4; as cited in: Moritz (1914, 240)
System of positive polity (1852)

Law, Way, Mathematics, Question

“Money is a crystal formed of necessity in the course of the exchanges, whereby different products of labour are practically equated to one another and thus by practice converted into commodities.”

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

Vol. I, Ch. 2, pg. 99.
(Buch I) (1867)

Money

“Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world. …The most important thing accomplished by the three-degree radiation background in 1965 was to force us to take seriously the idea that there was an early universe.”

Steven Weinberg (1933) American theoretical physicist

1977
The First Three Minutes (1977; second edition 1993)

World, Idea, Universe

“Causality applies only to a system which is left undisturbed. If a system is small, we cannot observe it without producing a serious disturbance and hence we cannot expect to find any causal connexion between the results of our observations. Causality will still be assumed to apply to undisturbed systems and the equations which will be set up to describe an undisturbed system will be differential equations expressing a causal connexion between conditions at one time and conditions at a later time. These equations will be in close correspondence with the equations of classical mechanics, but they will be connected only indirectly with the results of observations.”

Paul Dirac book Principles of Quantum Mechanics

I. The Principle of Superposition - 1. The Need for a Quantum Theory
The Principles of Quantum Mechanics (4th ed. 1958)

Time

“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

“Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.”

Stephen Hawking (1942–2018) British theoretical physicist, cosmologist, and author

As quoted in Stephen Hawking: A Biography (2005) by Kristine Larsen, p. 43

Mathematics, Parting

“The rigid electron is in my view a monster in relation to Maxwell's equations, whose innermost harmony is the principle of relativity.”

Hermann Minkowski (1864–1909) German mathematician and physicist

as quoted by Dennis Overbye, Einstein in Love: A Scientific Romance (2001)

“Considering the pervasive importance of quantum mechanics in modern physics, it is odd how rarely one hears of efforts to test quantum mechanics experimentally with high precision.…The trouble is that it is very difficult to find any logically consistent generalization of quantum mechanics. One obvious target for generalization is the linearity of quantum mechanics, but if we arbitrarily add nonlinear terms to the Schrodinger equation, how do we know that the theory we obtain will have a sensible physical interpretation? At least in part, it is the dearth of generalized versions of quantum mechanics that has made it so hard to plan experimental tests of quantum mechanics.”

Steven Weinberg (1933) American theoretical physicist

"Testing Quantum Mechanics" http://www.sciencedirect.com/science/article/pii/0003491689902765, Annals of Physics (1989)

Effort, Parting

“The circumference of earth at equator is 40,000 km and by dividing it with 24 hours (earth completes its rotation in a day), it comes out to 1,667 km. This reverse phenomenon happened at 60 degrees latitude because their jet plane managed a speed of 833.5 km which is half of circumference of the earth.”

Jayant Narlikar (1938) Indian physicist

When Prof Jayant Narlikar saw the sun rise in the west

Speed

“A frequent source of misunderstanding has to do with the interpretation of fuzzy logic. The problem is that the term fuzzy logic has two different meanings. More specifically, in a narrow sense, fuzzy logic, FLn, is a logical system which may be viewed as an extension and generalization of classical multivalued logics. But in a wider sense, fuzzy logic, FLw is almost synonymous with the theory of fuzzy sets. In this context, what is important to recognize is that: (a) FLw is much broader than FLn and subsumes FLn as one of its branches; (b) the agenda of FLn is very different from the agendas of classical multivalued logics; and (c) at this juncture, the term fuzzy logic is usually used in its wide rather than narrow sense, effectively equating fuzzy logic with FLw</sub”

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

Zadeh (1995) in Foreword of George J. Klir Fuzzy sets and fuzzy logic: theory and applications.
1990s

Problem, Sense

“The origin of this research was an attempt to extend Cassel’s system of equations of price determination in one market to that of several trading countries. Although the point of departure is totally different, the results of that attempt (presented in chapter III) exhibit important similarities to Heckscher’s treatment in ‘‘The Effect of Foreign Trade on the Distribution of Income,’’ published one year earlier in Ekonomisk Tidskrift, 1920. There is no doubt that the author was unconsciously inﬂuenced by Heckscher’s paper both at this and at later stages of the work. The inﬂuence of this pathbreaking paper, both conscious and unconscious, has surely been particularly decisive in the development of the material in chapters I–III.”

Bertil Ohlin (1899–1979) Swedish economist and politician

Ohlin (1924), quoted (and translated) in: Eli Filip Heckscher, ‎Bertil Gotthard Ohlin, ‎Henry Flam Heckscher-Ohlin trade theory, (1991), p. 76.
1920s

Departure, Decision, Country

“But take a brief glance at real life. In present-day economic life you will find, not only competition and monopoly, but also their synthesis, which is not a formula but a movement. Monopoly produces competition, competition produces monopoly. That equation, however, far from alleviating the difficulties of the present situation, as bourgeois economists suppose, gives rise to a situation even more difficult and involved. Thus, by changing the basis upon which the present economic relations rest, by abolishing the present mode of production, you abolish not only competition, monopoly and their antagonism, but also their unity, their synthesis, the movement whereby a true balance is maintained between competition and monopoly.

Let me now give you an example of Mr Proudhon's dialectics. Freedom and slavery constitute an antagonism. There is no need for me to speak either of the good or of the bad aspects of freedom. As for slavery, there is no need for me to speak of its bad aspects. The only thing requiring explanation is the good side of slavery. I do not mean indirect slavery, the slavery of proletariat; I mean direct slavery, the slavery of the Blacks in Surinam, in Brazil, in the southern regions of North America. Direct slavery is as much the pivot upon which our present-day industrialism turns as are machinery, credit, etc. Without slavery there would be no cotton, without cotton there would be no modern industry. It is slavery which has given value to the colonies, it is the colonies which have created world trade, and world trade is the necessary condition for large-scale machine industry. Consequently, prior to the slave trade, the colonies sent very few products to the Old World, and did not noticeably change the face of the world. Slavery is therefore an economic category of paramount importance. Without slavery, North America, the most progressive nation, would he transformed into a patriarchal country. Only wipe North America off the map and you will get anarchy, the complete decay of trade and modern civilisation. But to do away with slavery would be to wipe America off the map. Being an economic category, slavery has existed in all nations since the beginning of the world. All that modern nations have achieved is to disguise slavery at home and import it openly into the New World. After these reflections on slavery, what will the good Mr Proudhon do? He will seek the synthesis of liberty and slavery, the true golden mean, in other words the balance between slavery and liberty. Mr Proudhon understands perfectly well that men manufacture worsted, linens and silks; and whatever credit is due for understanding such a trifle! What Mr Proudhon does not understand is that, according to their faculties, men also produce the social relations in which they produce worsted and linens. Still less does Mr Proudhon understand that those who produce social relations in conformity with their material productivity also produce the ideas, categories, i. e. the ideal abstract expressions of those same social relations. Indeed, the categories are no more eternal than the relations they express. They are historical and transitory products. To Mr Proudhon, on the contrary, the prime cause consists in abstractions and categories. According to him it is these and not men which make history. The abstraction, the category regarded as such, i. e. as distinct from man and his material activity, is, of course, immortal, immutable, impassive. It is nothing but an entity of pure reason, which is only another way of saying that an abstraction, regarded as such, is abstract. An admirable tautology! Hence, to Mr Proudhon, economic relations, seen in the form of categories, are eternal formulas without origin or progress. To put it another way: Mr Proudhon does not directly assert that to him bourgeois life is an eternal truth; he says so indirectly, by deifying the categories which express bourgeois relations in the form of thought. He regards the products of bourgeois society as spontaneous entities, endowed with a life of their own, eternal, the moment these present themselves to him in the shape of categories, of thought. Thus he fails to rise above the bourgeois horizon. Because he operates with bourgeois thoughts and assumes them to be eternally true, he looks for the synthesis of those thoughts, their balance, and fails to see that their present manner of maintaining a balance is the only possible one.”

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

Letter to Pavel Vasilyevich Annenkov, (28 December 1846), Rue d'Orleans, 42, Faubourg Namur, Marx Engels Collected Works Vol. 38, p. 95; International Publishers (1975). First Published: in full in the French original in M.M. Stasyulevich i yego sovremenniki v ikh perepiske, Vol. III, 1912

Life, Men, Truth, World

“In Indian astronomy, the prime meridian is the great circle of the Earth passing through the north and south poles, Ujjayinī and Laṅkā, where Laṅkā was assumed to be on the Earth's equator.”

Aryabhata (476–550) Indian mathematician-astronomer

In Aryabhatiya quoted in: J J O'Connor and E F Robertson Aryabhata the Elder http://www-history.mcs.st-andrews.ac.uk/Biographies/Aryabhata_I.html, School of Mathematics and Statistics University of St Andrews, Scotland.

“Any progress in the theory of partial differential equations must also bring about a progress in Mechanics.”

Carl Gustav Jacob Jacobi (1804–1851) German mathematician

Vorlesungen über Dynamik http://archive.org/details/cgjjacobisvorle00lottgoog [Lectures on Dynamics] (1842/3; publ. 1884).

“I don't suppose that applies so much to other physicists; I think it’s a peculiarity of myself that I like to play about with equations, just looking for beautiful mathematical relations which maybe don’t have any physical meaning at all. Sometimes they do.”

Paul Dirac (1902–1984) theoretical physicist

Interview with Dr. P. A. M. Dirac by Thomas S. Kuhn at Dirac's home, Cambridge, England, May 7, 1963 http://www.aip.org/history/ohilist/4575_3.html

Beauty, Mathematics, Thinking

“all the standard equations of mathematical physics can be separated and solved in Kerr geometry.”

Subrahmanyan Chandrasekhar (1910–1995) physicist

From Chandrasekhar's Nobel lecture, in his summary of his work on black holes; Republished in: D. G. Caldi, ‎George D. Mostow (1989) Proceedings of the Gibbs Symposium: Yale University, May 15-17, 1989 p. 230

Mathematics

“Where in the Schrödinger equation do you put the joy of being alive?”

Eugene Paul Wigner (1902–1995) mathematician and Nobel Prize-winning physicist

As quoted by Freeman Dyson from a private conversation, Infinite in All Directions (1988)

Joy

“We equate speciesism—the belief that one’s species is superior to all others—with racism and sexism.”

Wayne Pacelle (1965) American activist

"Sabotaging Animal Rights for Deer Hunt," 1986

“If you have bought one of those T-shirts with Maxwell's equations on the front, you may have to worry about its going out of style, but not about its becoming false. We will go on teaching Maxwellian electrodynamics as long as there are scientists.”

Steven Weinberg (1933) American theoretical physicist

"The Revolution That Didn't Happen" in The New York Review of Books (1998) http://www.nybooks.com/articles/735

Falseness

“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

“In mathematics there is a certain way of seeking the truth, a way which Plato is said first to have discovered and which was called "analysis" by Theon and was defined by him as "taking the thing sought as granted and proceeding by means of what follows to a truth which is uncontested"; so, on the other hand, "synthesis" is "taking the thing that is granted and proceeding by means of what follows to the conclusion and comprehension of the thing sought." And although the ancients set forth a twofold analysis, the zetetic and the poristic, to which Theon's definition particularly refers, it is nevertheless fitting that there be established also a third kind, which may be called rhetic or exegetic, so that there is a zetetic art by which is found the equation or proportion between the magnitude that is being sought and those that are given, a poristic art by which from the equation or proportion the truth of the theorem set up is investigated, and an exegetic art by which from the equation set up or the proportion, there is produced the magnitude itself which is being sought. And thus, the whole threefold analytic art, claiming for itself this office, may be defined as the science of right finding in mathematics…. the zetetic art does not employ its logic on numbers—which was the tediousness of the ancient analysts—but uses its logic through a logistic which in a new way has to do with species [of number]…”

François Viète (1540–1603) French mathematician

Source: In artem analyticem Isagoge (1591), Ch. 1 as quoted by Jacob Klein, Greek Mathematical Thought and the Origin of Algebra (1934-1936) Appendix.

Truth, Art, Way, Mathematics

“Through algebra you easily arrive at equations, but always to pass therefrom to the elegant constructions and demonstrations which usually result by means of the method of porisms is not so easy, nor is one's ingenuity and power of invention so greatly exercised and refined in this analysis.”

Isaac Newton (1643–1727) British physicist and mathematician and founder of modern classical physics

The Mathematical Papers of Isaac Newton (edited by Whiteside), Volume 7; Volumes 1691-1695 / pg. 261. http://books.google.com.br/books?id=YDEP1XgmknEC&printsec=frontcover Geometriae (Treatise on Geometry)

Exercises

“Part of our job, together, is to work to reject such extremism that infects too many of our young people. Part of that effort must be a continued rejection by Muslims of those who distort Islam to preach intolerance and promote violence, and it must also a rejection by non-Muslims of the ignorance that equates Islam with terror.”

Barack Obama (1961) 44th President of the United States of America

Remarks by President Obama to the United Nations General Assembly https://www.whitehouse.gov/the-press-office/2015/09/28/remarks-president-obama-united-nations-general-assembly (September 28, 2015) 2015

People, Effort, Parting

“It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress.”

Paul Dirac (1902–1984) theoretical physicist

The Evolution of the Physicist's Picture of Nature (1963)
Context: It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further development of the theory.

Beauty

“Every concept arises from the equation of unequal things.”

Friedrich Nietzsche (1844–1900) German philosopher, poet, composer, cultural critic, and classical philologist

On Truth and Lie in an Extra-Moral Sense (1873)
Context: Every word instantly becomes a concept precisely insofar as it is not supposed to serve as a reminder of the unique and entirely individual original experience to which it owes its origin; but rather, a word becomes a concept insofar as it simultaneously has to fit countless more or less similar cases — which means, purely and simply, cases which are never equal and thus altogether unequal. Every concept arises from the equation of unequal things. Just as it is certain that one leaf is never totally the same as another, so it is certain that the concept "leaf" is formed by arbitrarily discarding these individual differences and by forgetting the distinguishing aspects.

“Sir, an equation has no meaning for me unless it expresses a thought of GOD.”

Srinivasa Ramanujan (1887–1920) Indian mathematician

Statement to a friend, quoted in Ramanujan, the Man and the Mathematician (1967) by Shiyali Ramamrita Ranganathan, p. 88 Variant: An equation means nothing to me unless it expresses a thought of God. Quotations by 60 Greatest Indians http://resourcecentre.daiict.ac.in/eresources/iresources/quotations.html

God

“The slightest study of business conditions will satisfy anyone capable of forming a judgment that the personal equation is the most important factor in a business operation; that the business ability of the man at the head of any business concern, big or little, is usually the factor which fixes the gulf between striking success and hopeless failure.”

Theodore Roosevelt (1858–1919) American politician, 26th president of the United States

1900s, First Annual Message to Congress (1901)
Context: The captains of industry who have driven the railway systems across this continent, who have built up our commerce, who have developed our manufactures, have on the whole done great good to our people. Without them the material development of which we are so justly proud could never have taken place. Moreover, we should recognize the immense importance of this material development of leaving as unhampered as is compatible with the public good the strong and forceful men upon whom the success of business operations inevitably rests. The slightest study of business conditions will satisfy anyone capable of forming a judgment that the personal equation is the most important factor in a business operation; that the business ability of the man at the head of any business concern, big or little, is usually the factor which fixes the gulf between striking success and hopeless failure.

Failure, Business, Study, Success

“Equations are more important to me, because politics is for the present, but an equation is something for eternity. ”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

“We mistakenly equate flattery to friendship and criticism to opposition; one should evaluate truth first and then judge, for flattery and criticism are primarily opinion.”

Gandolfo – (RJ Intindola)

1975

Truth, Friendship

“Everyone knew that if you divided reality by expectation, you got a happiness quotient. But when you invert the equation - expectation divided by reality - you didn't get the opposite of happiness. What you got, Lewis realized, was hope.”

Jodi Picoult book Nineteen Minutes

Source: Nineteen Minutes

Hope, Reality, Happiness

“Jason looked like her was trying to figure out an equation. "Let me get this straight. Your table ran away… because you polished him with windex.”

Rick Riordan book The Demigod Diaries

Source: The Demigod Diaries

“Equations are the devil's sentences.”

Stephen Colbert (1964) American political satirist, writer, comedian, television host, and actor

“It is clear that the world is purely parodic, in other words, that each thing seen is the parody of another, or is the same thing in a deceptive form.
Ever since sentences started to circulate in brains devoted to reflection, an effort at total identification has been made, because with the aid of a copula each sentence ties one thing to another; all things would be visibly connected if one could discover at a single glance and in its totality the tracings of Ariadne’s thread leading thought into its own labyrinth.
But the copula of terms is no less irritating than the copulation of bodies. And when I scream I AM THE SUN an integral erection results, because the verb to be is the vehicle of amorous frenzy.
Everyone is aware that life is parodic and that it lacks an interpretation. Thus lead is the parody of gold. Air is the parody of water. The brain is the parody of the equator. Coitus is the parody of crime.”

Georges Bataille book The Solar Anus

The Solar Anus (1927)

Life, World, Effort, Water

“I've made the most important discovery of my life. It's only in the mysterious equation of love that any logic or reasons can be found.”

Sylvia Nasar book A Beautiful Mind

Source: A Beautiful Mind

Love, Life

“Love is not an equation… It is not a contract, and it's not a happy ending. It is the slate under the chalk and the ground buildings rise from and the oxygen in the air.”

Jodi Picoult (1966) Author

Source: Vanishing Acts

Love, Happiness

“If you have a sister and she dies, do you stop saying you have one? Or are you always a sister, even when the other half of the equation is gone?”

Jodi Picoult My Sister's Keeper

Source: My Sister's Keeper (2004)

Sister

“And an equation is the same whether it's written in red or green ink”

Vikram Seth A Suitable Boy

Source: A Suitable Boy

“In my perception, the world wasn't a graph or formula or an equation. It was a story.”

Cheryl Strayed book Wild: From Lost to Found on the Pacific Crest Trail

Source: Wild: From Lost to Found on the Pacific Crest Trail

World

“Incredible cosmic powers do not equate with high IQ.”

Brandon Sanderson (1975) American fantasy writer

Source: Steelheart

“Love is not an equation, it is not a contract, and it is not a happy ending. Love is the slate under the chalk, the ground that buildings rise, and the oxygen in the air. It is the place you come back to, no matter where your headed”

Jodi Picoult (1966) Author

Love, Happiness

“People are really trying their best. Just like being happy and sad, you will find yourself on both sides of the equation many times over your lifetime, either saying or hearing the wrong thing. Let's all give each other a pass, shall we?”

David Rakoff (1964–2012) writer

Source: Half Empty

People, Sadness, Time, Happiness

“(I’ve often noticed that people equate “having a sense of humour” with “being an insensitive moron.”)”

Sophie Kinsella book Finding Audrey

Source: Finding Audrey

People, Sense

“I know that I disagree with many other UML experts, but there is no magic about UML. If you can generate code from a model, then it is programming language. And UML is not a well-designed programming language.
The most important reason is that it lacks a well-defined point of view, partly by intent and partly because of the tyranny of the OMG standardization process that tries to provide everything to everybody. It doesn't have a well-defined underlying set of assumptions about memory, storage, concurrency, or almost anything else. How can you program in such a language?
The fact is that UML and other modelling language are not meant to be executable. The point of models is that they are imprecise and ambiguous. This drove many theoreticians crazy so they tried to make UML "precise", but models are imprecise for a reason: we leave out things that have a small effect so we can concentrate on the things that have big or global effects. That's how it works in physics models: you model the big effect (such as the gravitation from the sun) and then you treat the smaller effects as perturbation to the basic model (such as the effects of the planets on each other). If you tried to solve the entire set of equations directly in full detail, you couldn't do anything.”

James Rumbaugh (1947) Computer scientist, software engineer

James Rumbaugh in Federico Biancuzzi and Shane Warden eds. (2009) Masterminds of Programming. p. 339; cited in " Quote by James Rumbaugh http://www.ptidej.net/course/cse3009/winter13/resources/james" on ptidej.net. Last updated 2013-04-09 by guehene; Rumbaugh is responding to the question: "What do you think of using UML to generate implementation code?"

Memory, Sun

“We have already various treatises on Mechanics, but the plan of this one is entirely new. I intend to reduce the theory of this Science, and the art of solving problems relating to it, to general formulae, the simple development of which provides all the equations necessary for the solution of each problem. I hope that the manner in which I have tried to attain this object will leave nothing to be desired. No diagrams will be found in this work. The methods that I explain require neither geometrical, nor mechanical, constructions or reasoning, but only algebraical operations in accordance with regular and uniform procedure. Those who love Analysis will see with pleasure that Mechanics has become a branch of it, and will be grateful to me for having thus extended its domain.”

Joseph Louis Lagrange book Mécanique analytique

Mécanique analytique (1788) as quoted by E. W. Hobson, Mathematics, from the points of view of the Mathematician and of the Physicist (1912) an address delivered to the Mathematical and Physical Society of University College London, p.13. https://books.google.com/books?id=H7Y_AQAAIAAJ&pg=PA13

Love, Pleasure, Hope, Art

“Any thought which is printed, either here or in the paper, without subsequent attack is generally believed to be true. This is not so much a logical condition as it is a fault of human nature. A longstanding or constant idea is often equated with a true one.”

George Alec Effinger (1947–2002) Novelist, short story writer

Source: What Entropy Means to Me (1972), Chapter 9 “A Moral Dilemma” (p. 140).

Idea, Nature

“We have survived bitter divisions in our society. Reconciliation requires us to put aside our differences and forgive the injuries done to us just as justice is essential to that equation. Those who have done wrong and broken the law must be punished. There can be no setting to rights or settling of accounts without that element. Until that is done there will be no finality to our collective nightmare. Until we all accept that simple fact the sense of hurt and betrayal continue.”

Joni Madraiwiwi (1957–2016) Fijian politician

Our Country at the Crossroads - 2001 Parkinson Memorial Lecture Series, 15 August 2001 http://www.usp.ac.fj/journ/docs/news/wansolnews/wansol1508013.html.

Justice, Law, Forgiveness, Sense

“It was all about borders. And Arnold was on the wrong side of them. He’d end up spending the rest of his life in a 8’ x 10’ cell, another darling of the Left like Mumia Abu-Jamal or Lisl Auman, because he happened to be standing on one side of an arbitrary political boundary, a line as imaginary as the equator.”

Jacob M. Appel book The Man Who Wouldn't Stand Up

The Man Who Wouldn't Stand Up (2012)

Life

“Everything can be summed up into an equation.”

Alexei Maxim Russell (1976) Canadian writer

from Trueman Bradley - Aspie Detective.

“A great deal of the thinking here has been influenced by cybernetics and information theory, though this has been used as much to extend the scope of closed-system as to improve the sophistication of open system formulations. It was von Bertalanffy (1950) who, in terms of the general transport equation which he introduced, first fully disclosed the importance of openness or closedness to the environment as a means of distinguishing living organisms from inanimate objects.”

Fred Emery (1925–1997) Australian psychologist

Source: The Causal Texture of Organizational Environments (1963), p. 22.

Thinking

“The problem creationists have with evolution is not that it challenges belief in God, because it doesn’t. Their problem is that evolution, -like every other field of science- challenges the accuracy and authority of the storybooks which creationists equate to God. Consequently, they tend to reject science almost entirely, and will often take all the sciences they perceive as threatening, and lump them all together under one heading, which they then refer to as “evolution-ism”. It’s an attempt to minimize the sheer volume of sciences allied against them. This is also part of their intentionally-erected illusion of equality; a false dichotomy that if their legendary folklore isn’t the absolute authority -being both literally and completely true, then God couldn’t create or even exist any other way.”

Aron Ra (1962) Aron Ra is an atheist activist and the host of the Ra-Men Podcast

"6th Foundational Falsehood of Creationism" https://www.youtube.com/watch?v=t3k0dDFxkhM, Youtube (February 2, 2008) Youtube, Foundational Falsehoods of Creationism

God, Way, Problem, Science

“A mathematician is not a man who can readily manipulate figures; often he cannot. He is not even a man who can readily perform the transformation of equations by the use of calculus. He is primarily an individual who is skilled in the use of symbolic logic on a high plane, and especially he is a man of intuitive judgment in the choice of the manipulative processes he employs.”

Vannevar Bush book As We May Think

As We May Think (1945)

“This is why we are on record claiming that the missional conversation — refactoring mission back into the equation of church — contains the seeds of authenticity and renewal for Christianity in our time and place.”

Alan Hirsch (1959) South African missionary

Source: The Faith of Leap (2011), p. 159

Time

“First Shakespeare sonnets seem meaningless; first Bach fugues, a bore; first differential equations, sheer torture. But training changes the nature of our spiritual experiences. In due course, contact with an obscurely beautiful poem, an elaborate piece of counterpoint or of mathematical reasoning, causes us to feel direct intuitions of beauty and significance. It is the same in the moral world.”

Aldous Huxley book Ends and Means

Ends and Means (1937)

World, Beauty, Feeling, Mathematics

“Although Cardan reduced his particular equations to forms lacking a term in x^2, it was Vieta who began with the general formx^3 + px^2 + qx + r = 0and made the substitution x = y -\frac{1}{3}p, thus reducing the equation to the formy^3 + 3by = 2c.He then made the substitutionz^3 + yz = b, or y = \frac{b - z^2}{z},which led to the formz^6 + 2cz^2 = b^2,a sextic which he solved as a quadratic.”

David Eugene Smith (1860–1944) American mathematician

Source: History of Mathematics (1925) Vol.2, p.465

“Most, if not all, of the great ideas of modern mathematics have had their origin in observation. Take, for instance, the arithmetical theory of forms, of which the foundation was laid in the diophantine theorems of Fermat, left without proof by their author, which resisted all efforts of the myriad-minded Euler to reduce to demonstration, and only yielded up their cause of being when turned over in the blow-pipe flame of Gauss’s transcendent genius; or the doctrine of double periodicity, which resulted from the observation of Jacobi of a purely analytical fact of transformation; or Legendre’s law of reciprocity; or Sturm’s theorem about the roots of equations, which, as he informed me with his own lips, stared him in the face in the midst of some mechanical investigations connected (if my memory serves me right) with the motion of compound pendulums; or Huyghen’s method of continued fractions, characterized by Lagrange as one of the principal discoveries of that great mathematician, and to which he appears to have been led by the construction of his Planetary Automaton; or the new algebra, speaking of which one of my predecessors (Mr. Spottiswoode) has said, not without just reason and authority, from this chair, “that it reaches out and indissolubly connects itself each year with fresh branches of mathematics, that the theory of equations has become almost new through it, algebraic 31 geometry transfigured in its light, that the calculus of variations, molecular physics, and mechanics” (he might, if speaking at the present moment, go on to add the theory of elasticity and the development of the integral calculus) “have all felt its influence.”

James Joseph Sylvester (1814–1897) English mathematician

James Joseph Sylvester. "A Plea for the Mathematician, Nature," Vol. 1, p. 238; Collected Mathematical Papers, Vol. 2 (1908), pp. 655, 656.

Law, Mathematics, Idea, Effort

“These computing machines had already been designed, and some built, by {[w|Vannevar Bush}}, Norbert Wiener, and others, and were almost ready-made for the job. These scientists, as well as others such as von Neumann, Shannon and Bigelow, were in a position to see that machines of an electronic kind were ideally suited to carry out the whole of the operations of range-finding and location without any human intervention whatever.
These electronic computing machines were already developed to a very high degree of efficiency for the solution of mathematical equations, and some technical difficulties had led to the suggestion that a process of scanning, similar to that used in television, might be incorporated into the computer. Another innovation was the use of binary notation rather than decimal notation as in the early Harvard Mark I computer.”

Frank Honywill George (1921–1997) British psychologist

Source: The Brain As A Computer (1962), p.18

Mathematics

“There has never been just one best way to teach quantum mechanics. My goal is neither to sow nostalgia for the philosophically engaged style of Oppenheimer and Nordheim, nor to condemn the pragmatic approach of Fermi, Bethe and Feynman. It is rather to highlight the choices that physicists must always make when stepping into the classroom. Choices of topics to discuss and problems to assign reflect deeper decisions about the ideal type of physicist one seeks to train. Should the new generation be philosophically attuned, concerned with minute details of conceptual interpretation? Or should physicists hone their ability to calculate, pushing Heisenberg’s and Schrödinger’s equations into the service of ever more elaborate problems to solve and phenomena to analyse? Competing ideals have flourished under different pedagogical conditions.”

David Kaiser (1971) American physicist

Turning physicists into quantum mechanics (2007)

Way, Problem, Decision, Nostalgia

“Sarva-dharma-samabhAva was unknown to mainstream Hinduism before Mahatma Gandhi presented it as one of the sixteen mahAvratas (great vows). in his booklet, MaNgala-PrabhAta. It is true that mainstream Hinduism had always stood for tolerance towards all metaphysical points of view and ways of worship except that which led to AtatAyI-AchAra (gangsterism). But that tolerance had never become samabhAva, equal respect for all points of view. The acharyas of the different schools of Sanatana Dharma were all along engaged in debates over differences in various approaches to Sreyas (the Great Good). No Buddhist acharya is known to have equated the way of the Buddha to that of the Gita and vice versa, for instance. It is also true that overawed by the armed might of Islam, and deceived by the tall talk of the sufis, some Hindu saints in medieval India had equated Rama with Rahim, Krishna with Karim, Kashi with Kaba, the Brahmana with the Mullah, pUjA with namAz, and so on. But, the sects founded by these saints had continued to function on the fringes of Hindu society while the mainstream followed the saints and acharyas who never recognized Islam as a dharma. In modern times also, movements like the Brahmo Samaj which recognised Islam and Christianity as dharmas had failed to influence mainstream Hinduism, while Maharshi Dayananda and Swami Vivekananda who upheld the Veda and despised the Bible and the Quran, had had a great impact. This being the hoary Hindu tradition, Mahatma Gandhi’s recognition of Christianity and Islam not only as dharmas but also as equal to Sanatana Dharma was fraught with great mischief. For, unlike the earlier Hindu advocates of Islam and Christianity as dharmas, Mahatma Gandhi made himself known and became known as belonging to mainstream Hinduism.”

Sita Ram Goel (1921–2003) Indian activist

History of Hindu-Christian Encounters (1996)

School, Way, Time

“Lety5 - ay4 + by3 - cy2 + dy - e = 0be the general equation of the fifth degree and suppose that it can be solved algebraically,—i. e., that y can be expressed as a function of the quantities a, b, c, d, and e, composed of radicals. In this case, it is clear that y can be written in the formy = p + p1R1/m + p2R2/m +…+ pm-1R(m-1)/m,m being a prime number, and R, p, p1, p2, etc. being functions of the same form as y. We can continue in this way until we reach rational functions of a, b, c, d, and e. [Note: main body of proof is excluded]
…we can find y expressed as a rational function of Z, a, b, c, d, and e. Now such a function can always be reduced to the formy = P + R1/5 + P2R2/5 + P3R3/5 + P4R4/5, where P, R, P2, P3, and P4 are functions or the form p + p1S1/2, where p, p1 and S are rational functions of a, b, c, d, and e. From this value of y we obtainR1/5 = 1/5(y1 + α4y2 + α3y3 + α2y4 + α y5) = (p + p1S1/2)1/5,whereα4 + α3 + α2 + α + 1 = 0.Now the first member has 120 different values, while the second member has only 10; hence y can not have the form that we have found: but we have proved that y must necessarily have this form, if the proposed equation can be solved: hence we conclude that
It is impossible to solve the general equation of the fifth degree in terms of radicals.
It follows immediately from this theorem, that it is also impossible to solve the general equations of degrees higher than the fifth, in terms of radicals.”

Niels Henrik Abel (1802–1829) Norwegian mathematician

A Memoir on Algebraic Equations, Proving the Impossibility of a Solution of the General Equation of the Fifth Degree (1824) Tr. W. H. Langdon, as quote in A Source Book in Mathematics (1929) ed. David Eugene Smith

Way

“I reason, earth is short,
And anguish absolute.
And many hurt;
But what of that?

I reason, we could die:
The best vitality
Cannot excel decay;
But what of that?

I reason that in heaven
Somehow, it will be even,
Some new equation given;
But what of that?”

Emily Dickinson (1830–1886) American poet

Time and Eternity, p. 192
Collected Poems (1993)

Hurt

“The behavior of the economy as a whole, at the aggregate, macro-level, is built up from the individual equations at the micro-level.”

Paul Ormerod book The Death of Economics

Part I, Chapter 4, Professional Reservations, p. 79
The Death of Economics (1994)

Behavior

“The Society for General Systems Theory and its publication General Systems was a mixed bag. Few authors were actually doing research - they philosophized, and many prematurely resolved dilemmas by mathematical equations in a language poorly understood by the empirical investigator.”

Roy R. Grinker, Sr. (1900–1993) American psychiatrist and neurologist

Grinker (1976) in General systems. Vol.19, p. 57

Mathematics

“John Lofton: Do you think abortion is murder?
Ron Paul: Yes, but we have in our state laws, which enforce the law against murder, there are degrees. You have 1st, 2nd, and 3rd degree murder. I think somebody who takes a pill the day after probably isn't committing quite the horrible murder when you see somebody lying on the floor and somebody takes a gun and puts it to their head. I don't equate those…
John Lofton: What do you think ought to be the penalty for the abortionist and for the person who gets the abortion?
Ron Paul: I really don't have the wisdom to know exactly what it should be… The girl who goes and gets an abortion, she's a participant in it, I don't think she deserves the death penalty… But there are some abortionists that it wouldn't be very hard to give them a pretty harsh punishment, because, you know, nothing annoys me more than the fact that an abortionist can make money killing a live viable fetus, in the 3rd trimester, and they think nothing about it, and they make a living doing this. Any yet, one minute after birth, that same mother, who might throw the child away, rightfully is called to task, and actually charged with murder. So that inconsistency has to be resolved.”

Ron Paul (1935) American politician and physician

The American View, August 25, 2007 http://theamericanview.com/index.php?id=898 2000s, 2006-2009

Death, Wisdom, Money, Law

“The differential equation of the first order
\frac {dy}{dx} = f(x, y)
… prescribes the slope \frac {dy}{dx} at each point of the plane (or at each point of a certain region of the plane we call the field")…. a differential equation of the first order… can be conceived intuitively as a problem about the steady flow of a river: Being given the direction of the flow at each point, find the streamlines…. It leaves open the choice between the two possible directions in the line of a given slope. Thus… we should say specifically "direction of an unoriented straight line" and not merely "direction."”

George Pólya (1887–1985) Hungarian mathematician

Mathematical Methods in Science (1977)

Problem

“The physicist needs a facility in looking at problems from several points of view. The exact analysis of real physical problems is usually quite complicated, and any particular physical situation may be too complicated to analyze directly by solving the differential equation. But one can still get a very good idea of the behavior of a system if one has some feel for the character of the solution in different circumstances. Ideas such as the field lines, capacitance, resistance, and inductance are, for such purposes, very useful. … On the other hand, none of the heuristic models, such as field lines, is really adequate and accurate for all situations. There is only one precise way of presenting the laws, and that is by means of differential equations. They have the advantage of being fundamental and, so far as we know, precise. If you have learned the differential equations you can always go back to them. There is nothing to unlearn.”

Richard Feynman (1918–1988) American theoretical physicist

volume II; lecture 2, "Differential Calculus of Vector Fields"; section 2-1, "Understanding physics"; p. 2-1
The Feynman Lectures on Physics (1964)

Law, Way, Behavior, Feeling

“The nearer emotional life approaches to hysteria, to continual outward show, the less genuine it becomes. Feeling becomes equated with vehemence of expression, so that insincerity becomes permanent.”

Theodore Dalrymple (1949) English doctor and writer

A Neglected Genius http://www.city-journal.org/html/14_1_oh_to_be.html (Winter 2004). City Journal (1998 - 2008)

Life, Feeling

“Months later, Roger Cohen would write in The New York Time that preventing an attack on Banja Luka was "an acto of consummate Realpolitik" on our part, since letting the Federation [of Bosnia-Herzegovina] take the city would have "derailed" the peace process. Cohen, one of the most knowledgeable journalists to cover the was, misunderstood our motives in opposing an attack on Banja Luka. A true practitioner of Realpolitik would have encouraged the attack regardless of its human consequences. In fact, humanitarian concerns decided the case for me. Given the harsh behavior of Federation troops during the offensive, it seemed certain that the fall of Banja Luka would lead to forced evictions and random murders. I did not think the United States should contribute to the creation of new refugees and more human suffering in order to take a city that would have to be returned later. Revenge might be a central part of the ethos of the Balkans, but American policy could not be party of it. Our responsibility was to implement the American national interest, as best as we could determine it. But I am no longer certain we were right to oppose an attack on Banja Luka. Had we known then that the Bosnian Serbs would have been able to defy or ignore so many of the key political provisions of the peace agreement in 1996 and 1997, the negotiating team might not have opposed such an attack. However, even with American encouragement, it is by no means certain that an attack would have taken palce - or, if it had, that it would have been successful. Tuđman would have had to carry the burden of the attack, and the Serb lines were already stiffening. The Croatian Army had just taken heavy casualties on the Sarva. Furthermore, if it fell, Banja Luka would either have gone to the Muslims or been returned later to the Serbs, thus making it of dubious value to Tuđman. There was another intriguing factor in the equation - one of the few things that Milošević and Izetbegović had agreed on. Banja Luka, they both said, was the center of moderate, anti-Pale sentiment within the Bosnian Serb community, and should be built up in importance as a center of opposition to Pale. Izetbegovic himself was ambivalent about taking the city, and feared that if it fell, it would only add to Croat-Bosnian tensions.”

Richard Holbrooke (1941–2010) American diplomat

Source: 1990s, To End a War (1998), p. 166-167

Fear, Peace, Behavior, Communication

“On opportunities: People equate survival in Britain with success. If you are still around you must be doing OK. Nobody sees the lost opportunities. We are the world leaders in creating lost opportunities.”

Ivor Tiefenbrun (1946) Scottish businessman

2003

People, World, Success

“In reality, the likelihood of reaching the pinnacle of capitalist society today is only marginally better than were the chances of being accepted into the French nobility four centuries ago, though at least an aristocratic age was franker, and therefore kinder, about the odds. It did not relentlessly play up the possibilities open to all, … and so, in turn, did not cruelly equate an ordinary life with a failed one.”

Alain de Botton (1969) Swiss writer

Source: The Pleasures and Sorrows of Work (2009), p. 278.

Life, Age, Reality, Chance

“The intimate relation between interference and diffraction has its origin in the interference equation itself.”

F. J. Duarte (1954) Chilean-American physicist

in Dirac Optics, [F. J. Duarte, Tunable Laser Optics, Elsevier Academic, 2003, 0-12-222696-8, 37]

“Japan's racialized worldview equated virtue with strength, the North Koreans are taught that their virtue has rendered them as vulnerable as children in an evil world — unless they are protected by a great leader who keeps a watchful eye on military readiness. Unfortunately for the United States, there is no place in this for any improvement in relations between the two countries.”

Brian Reynolds Myers (1963) American professor of international studies

2010s, North Korea's Race Problem (February 2010)

Children, World, Evil, Country

“Finally, the claim that we equated punctuated equilibrium with saltation makes no sense within the logical structure of our theory — so, unless we are fools, how could we ever have asserted such a proposition? Our theory holds, as a defining statement, that ordinary allopatric speciation, unfolding gradually at microevolutionary scales, translates to punctuation in geological time.”

Stephen Jay Gould book The Structure of Evolutionary Theory

Source: The Structure of Evolutionary Theory (2002), p. 1009

Fools, Sense, Time

“Linear relationships can be captured with a straight line on a graph. Linear relationships are easy to think about…. Linear equations are solvable… Linear systems have an important modular virtue: you can take them apart, and put them together again — the pieces add up.”

James Gleick book Chaos: Making a New Science

Hanssen commented: "Following distinctions between linear and nonlinear systems from James Gleick's 1987 book on chaos theory may be helpful."
Source: Chaos: Making a New Science, 1987, p. 23 as cited in: James R. Hansen (2004), Trees of Texas: An Easy Guide to Leaf Identification, p. 246

Thinking

“The foolishness of that comment [equating meat-eating to the Holocaust] is so deep, I can only ascribe it to higher education. You have to have gone to college to say something that stupid.”

Dennis Prager (1948) American writer, speaker, radio and TV commentator, theologian

Dennis Prager as quoted in "P.E.T.A." http://listenonrepeat.com/watch/?v=hrmv6EPKfpg (1 April 2004), Penn & Teller's Bullshit!, Home Box Office: Regarding PETA's equating of the consumption of animals to the genocide of Jews in the Holocaust. 2000s

Stupidity, Education

“When an equation…clearly leads to two negative or imaginary roots, [Diophantus] retraces his steps and shows by how by altering the equation, he can get a new one that has rational roots. …Diophantus is a pure algebraist; and since algebra in his time did not recognize irrational, negative, and complex numbers, he rejected equations with such solutions.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 143.

Time