Quotes about equation (379 quotes, page 2)

“The aim of research is the discovery of the equations which subsist between the elements of phenomena.”

Ernst Mach (1838–1916) Austrian physicist and university educator

Source: 20th century, Popular Scientific Lectures, (Chicago, 1910), p. 205; On aim of research.

“Science does not speak of the world in the language of words alone, and in many cases it simply cannot do so. The natural language of science is a synergistic integration of words, diagrams, pictures, graphs, maps, equations, tables, charts, and other forms of visual and mathematical expression… [Science thus consists of] the languages of visual representation, the languages of mathematical symbolism, and the languages of experimental operations.”

Jay Lemke (1946) American academic

Jay Lemke (2003), "Teaching all the languages of science: Words , symbols, images and actions," p. 3; as cited in: Scott, Phil, Hilary Asoko, and John Leach. "Student conceptions and conceptual learning in science." Handbook of research on science education (2007): 31-56.

World , Mathematics , Nature , Science

“I know my equations are true,” she mused aloud. “I need to know if they are fact.”

Michael Flynn book Eifelheim

Source: Eifelheim (2006), Chapter 7 (p. 384)

“My specific… object has been to contain, within the prescribed limits, the whole of the student's course, from the confines of elementary algebra and trigonometry, to the entrance of the highest works on mathematical physics. A learner who has a good knowledge of the subjects just named, and who can master the present treatise, taking up elementary works on conic sections, application of algebra to geometry, and the theory of equations, as he wants them, will, I am perfectly sure, find himself able to conquer the difficulties of anything he may meet with; and need not close any book of Laplace, Lagrange, Legendre, Poisson, Fourier, Cauchy, Gauss, Abel, Hindenburgh and his followers. or of any one of our English mathematicians, under the idea that it is too hard for him.”

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

Preface, p. iii
The Differential and Integral Calculus (1836)

Books , Mathematics , Idea , Knowledge

“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

“The eulogy of the non-lover in the speech of Lysias … stresses the fact that the non-lover … does not commit extreme acts under the influence of passions. Since he acts from calculation, he never has occasion for remorse. … The non-lover demonstrates his superiority through prudence and objectivity. … We must now observe how these points of superiority correspond to those of “semantically purified” speech, … the kind of speech approaching pure notation in the respect that it communicates abstract intelligence without impulsion. It is a simple instrumentality, showing no affection for the object of its symbolizing and incapable of inducing bias in the hearer. In its ideal conception, it would have less power to move than 2 + 2 = 4, since it is generally admitted that mathematical equations may have the beauty of elegance, and hence are not above suspicion where beauty is suspect. But this neuter language will be an unqualified medium of transmission of meanings from mind to mind, and by virtue of it minds can remain in an unprejudiced relationship to the world and also to other minds. … Instead of passion, it offers the serviceability of objectivity … It distrusts any departure from the literal and prosaic.”

Richard M. Weaver (1910–1963) American scholar

“The Phaedrus and the Nature of Rhetoric,” pp. 6-7.
The Ethics of Rhetoric (1953)

World , Beauty , Intelligence , Communication

“If we believe that the task of physics is the discovery of a timeless mathematical equation that captures every aspect of the universe, then we believe that the truth about the universe lies outside the universe.”

Lee Smolin (1955) American cosmologist

Time Reborn: From the Crisis in Physics to the Future of the Universe (2013)

Truth , Mathematics , Universe

“Instead, we try to apply Aesop's 2,600-year-old equation to opportunities in which we have reasonable confidence as to how many birds are in the bush and when they will emerge (a formulation that my grandsons would probably update to "A girl in a convertible is worth five in the phonebook.").”

Warren Buffett (1930) American business magnate, investor, and philanthropist

2000 Chairman's Letter
Letters to Shareholders (1957 - 2012)

Confidence , Girl , Bird

“If you wish to alter or annihilate a pyramid of numbers in a serial relation, you alter or remove the bottom number. If we wish to annihilate the junk pyramid, we must start with the bottom of the pyramid: the Addict in the Street, and stop tilting quixotically for the "higher ups" so called, all of whom are immediately replaceable. The addict in the street who must have junk to live is the one irreplaceable factor in the junk equation. When there are no more addicts to buy junk there will be no junk traffic. As long as junk need exists, someone will service it.”

William S. Burroughs book Naked Lunch

Introduction
Naked Lunch (1959)

“We know by actual observation only a comparatively small part of the whole universe. I will call this "our neighborhood." Even within the confines of this province our knowledge decreases very rapidly as we get away from our own particular position in space and time. It is only within the solar system that our empirical knowledge extends to the second order of small quantities (and that only for g44 and not for the other gαβ), the first order corresponding to about 10-8. How the gαβ outside our neighborhood are, we do not know, and how they are at infinity of space or time we shall never know. Infinity is not a physical but a mathematical concept, introduced to make our equations more symmetrical and elegant. From the physical point of view everything that is outside our neighborhood is pure extrapolation, and we are entirely free to make this extrapolation as we please to suit our philosophical or aesthetical predilections—or prejudices. It is true that some of these prejudices are so deeply rooted that we can hardly avoid believing them to be above any possible suspicion of doubt, but this belief is not founded on any physical basis. One of these convictions, on which extrapolation is naturally based, is that the particular part of the universe where we happen to be, is in no way exceptional or privileged; in other words, that the universe, when considered on a large enough scale, is isotropic and homogeneous.”

Willem de Sitter (1872–1934) Dutch cosmologist

"The Astronomical Aspect of the Theory of Relativity" (1933)

Way , Mathematics , Nature , Knowledge

“We need a new form of capitalism, a contemporary form of capitalism. I would like to add “humanistic” to that equation.”

Brunello Cucinelli (1953) Italian entrepreneur and philanthropist

“My algebra was relatively poor. I found it very difficult to use equations that substituted numbers — to which I had a synesthetic and emotional response — for letters, to which I had none. It was because of this that I decided not to continue math at Advanced level, but chose to study history, French and German instead.”

Daniel Tammet book Born on a Blue Day

Source: Born on a Blue Day (2006), Chapter 6: Adolescence.

History , Study

“Which comes first — price being set by the intersection of supply and demand, or individual firms equating marginal cost to price?”

Steve Keen (1953) Australian economist

Source: Debunking Economics - The Naked Emperor Of The Social Sciences (2001), Chapter 4, Size Does Matter, p. 101

“E = mc2 really applies only to isolated bodies at rest. In general, when you have moving bodies, or interacting bodies, energy and mass aren't proportional. E = mc2 simply doesn't apply. …For moving bodies, the correct mass-energy equation is
E=\frac {mc^2} {\sqrt{1-\frac{v^2} {c^2}}}
where v is the velocity. For a body at rest (v=0), this becomes E = mc2. …we must consider the special case of particles with zero mass… examples include photons, color gluons, and gravitons. If we attempt to put m = 0 and v = c in our general mass-energy equation, both the numerator and denominator on the right-hand-side vanish, and we get the nonsensical relation E = 0/0. The correct result is that the energy of a photon can take any value. …The energy E of a photon is proportional to the frequency f of the light it represents. …they are related by the Planck-Einstein-Schrödinger equation E = hf, where h is Plank's constant.”

Frank Wilczek (1951) physicist

when the velocity <math>v</math> approaches the speed of light c, the denominator approaches 0 thus E approaches infinity, unless m = 0.
Source: The Lightness of Being – Mass, Ether and the Unification of Forces (2008), Ch. 3, p. 19 & Appendix A

Color , Light

“I was appalled to find that the mathematical notation on which I had been raised failed to fill the needs of the courses I was assigned, and I began work on extensions to notation that might serve. In particular, I adopted the matrix algebra used in my thesis work, the systematic use of matrices and higher-dimensional arrays (almost) learned in a course in Tensor Analysis rashly taken in my third year at Queen’s, and (eventually) the notion of Operators in the sense introduced by Heaviside in his treatment of Maxwell’s equations.”

Kenneth E. Iverson (1920–2004) Canadian computer scientist

"Kenneth E. Iverson" http://keiapl.info/rhui/autobio.htm, autobiographical sketch from an unfinished work (ca. 2004), on his experience at Harvard with "a Masters program in Automatic Data Processing in 1955; in effect, the first computer science program."

Mathematics , Sense , Learning

“The urge to break with a tradition is only appropriate when you're dealing with an outdated, troublesome tradition: I never really thought about that because I take the old-fashioned approach of equating tradition with value (which may be a failing). But whatever the case, positive tradition can also provoke opposition if it's too powerful, too overwhelming, too demanding. That would basically be about the human side of wanting to hold your own.”

Gerhard Richter (1932) German visual artist, born 1932

Quote of Richter from an interview with Jeanne Anne Nugent, 2006; as cited on collected quotes on the website of Gerhard Richter: 'on Other subjects' https://www.gerhard-richter.com/en/quotes/other-aspects-6
after 2000

Fashion

“An "empty world," i. e., a homogeneous manifold at all points at which equations (1) are satisfied, has, according to the theory, a constant Riemann curvature, and any deviation from this fundamental solution is to be directly attributed to the influence of matter or energy.”

Howard P. Robertson (1903–1961) American mathematician and physicist

"On Relativistic Cosmology" (1928)

World

“If Dirac’s idea restores the stability of the spectrum by introducing a stable vacuum where all negative energy states are occupied, the so-called Dirac sea, it also leads directly to the conclusion that a single-particle interpretation of the Dirac equation is not possible.”

Luis Álvarez-Gaumé Spanish physicist

Source: An Invitation to Quantum Field Theory (2012), Ch. 1 : Why Do We Need Quantum Field Theory After All?

Idea , Sea

“I discovered that a whole range of problems of the most diverse character relating to the scientiﬁc organization of production (questions of the optimum distribution of the work of machines and mechanisms, the minimization of scrap, the best utilization of raw materials and local materials, fuel, transportation, and so on) lead to the formulation of a single group of mathematical problems (extremal problems). These problems are not directly comparable to problems considered in mathematical analysis. It is more correct to say that they are formally similar, and even turn out to be formally very simple, but the process of solving them with which one is faced [i. e., by mathematical analysis] is practically completely unusable, since it requires the solution of tens of thousands or even millions of systems of equations for completion.
I have succeeded in ﬁnding a comparatively simple general method of solving this group of problems which is applicable to all the problems I have mentioned, and is sufﬁciently simple and effective for their solution to be made completely achievable under practical conditions.”

Leonid Kantorovich (1912–1986) Russian mathematician

Kantorovich (1960) "Mathematical Methods of Organizing and Planning Production." Management Science, 6(4):366–422, 1960, p. 368); As cited in: Cockshott, W. Paul. " Mises, Kantorovich and economic computation http://www.dcs.gla.ac.uk/publications/PAPERS/8707/standalonearticle.pdf." (2007).

Mathematics , Question , Problem

“The nature of the personal computer is simply not fully understood by companies like Apple (or anyone else for that matter). Apple makes the arrogant assumption of thinking that it knows what you want and need. It, unfortunately, leaves the “why” out of the equation — as in “why would I want this?” The Macintosh uses an experimental pointing device called a “mouse”. There is no evidence that people want to use these things.”

John C. Dvorak (1952) US journalist and radio broadcaster

In a review of the Macintosh in The San Francisco Examiner (19 February 1984)
1980s & 1990s

People , Nature , Thinking , Personality

“Baseball players or cricketers do not need to be able to solve explicitly the non-linear differential equations which govern the flight of the ball. They just catch it.”

Paul Ormerod book The Death of Economics

Part I, Chapter 5, Mechanistic Modelling, p. 108
The Death of Economics (1994)

“Kings, like children, tend to be opportunistic. Generosity only spoils them. They equate affability with weakness and hasten to exploit it.”

Jack Vance Lyonesse Trilogy

Source: Lyonesse Trilogy (1983-1989), Suldrun's Garden (1983), Chapter 12, section 2 (p. 122)

Children

“Stop any person on the street and they will tell you their own version of what it means to be an American, perhaps accurately, but mostly not. Some might say that being an American means wearing the US flag as a lapel pin. Others might say that in order to be defined as an American, one must attend the right church and be the right type of Christian. Still others will tell you that supporting the troops and, above that even, supporting the President is what makes one American.

Some might even venture that being born in this country or of parents who are citizens of this country is surely enough. On this last point there is some truth, but only in terms of rights, not responsibilities. As such, it presents only half of the equation.”

Larisa Alexandrovna (1971) Ukrainian-American journalist, essayist, poet

What is an American? in You Are An American http://www.huffingtonpost.com/larisa-alexandrovna/you-are-an-american_b_5928.html.

Truth , Support , Parent , Personality

“One of the first applications of the simplex algorithm was to the determination of an adequate diet that was of least cost. In the fall of 1947, Jack Laderman of the Mathematical Tables Project of the National Bureau of Standards undertook, as a test of the newly proposed simplex method, the first large-scale computation in this field. It was a system with nine equations in seventy-seven unknowns. Using hand-operated desk calculators, approximately 120 man-days were required to obtain a solution. … The particular problem solved was one which had been studied earlier by George Stigler (who later became a Nobel Laureate) who proposed a solution based on the substitution of certain foods by others which gave more nutrition per dollar. He then examined a "handful" of the possible 510 ways to combine the selected foods. He did not claim the solution to be the cheapest but gave his reasons for believing that the cost per annum could not be reduced by more than a few dollars. Indeed, it turned out that Stigler's solution (expressed in 1945 dollars) was only 24 cents higher than the true minimum per year $39.69.”

George Dantzig (1914–2005) American mathematician

cited in: John J. O'Connor & Edmund F.; Robertson (2003) " George Dantzig http://www-history.mcs.st-and.ac.uk/Biographies/Dantzig_George.html". in: MacTutor History of Mathematics archive, University of St Andrews.
Linear programming and extensions (1963)

Food , Way , Mathematics , Problem

“Think of Adam and Eve like an imaginary number, like the square root of minus one: you can never see any concrete proof that it exists, but if you include it in your equations, you can calculate all manner of things that couldn’t be imagined without it.”

Philip Pullman His Dark Materials trilogy

Source: His Dark Materials, The Golden Compass (1995), Ch. 21 : Lord Asriel's Welcome

Imagination , Thinking

“Motion with respect to the universal ocean of aether eludes us. We say, "Let V be the velocity of a body through the aether", and form the various electromagnetic equations in which V is scattered liberally. Then we insert the observed values, and try to eliminate everything which is unknown except V. The solution goes on famously; but just as we have got rid of all the other unknowns, behold! V disappears as well, and we are left with the indisputable but irritating conclusion —
::: 0 = 0
This is a favourite device that mathematical equations resort to, when we propound stupid questions.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

Source: The Nature of the Physical World (1928), Ch. 2 Relativity

Stupidity , Mathematics , Question , Universe

“Despite the roar of voices wanting to equate strategy with ambition, leadership, “vision,” planning, or the economic logic of competition, strategy is none of these. The core of strategy work is always the same: discovering the critical factors in a situation and designing a way of coordinating and focusing actions to deal with those factors.”

Richard Rumelt (1942) American economist

Source: Good Strategy Bad Strategy, 2011, p. 3

Way

“If God has made the world a perfect mechanism, He has at least conceded so much to our imperfect intellect that in order to predict little parts of it, we need not solve innumerable differential equations, but can use dice with fair success.”

Max Born (1882–1970) physicist

"Einstein's Statistical Theories" in Albert Einstein : Philosopher-Scientist (1951) edited by Paul Arthur Schilpp, p. 176

God , World , Success , Parting

“Cellular automata are now being used to model varied physical phenomena normally modelled by wave equations, fluid dynamics, Ising models, etc. We hypothesize that there will be found a single cellular automaton rule that models all of microscopic physics; and models it exactly. We call this field DM, for digital mechanics.”

Edward Fredkin (1934) American physicist and computer scientist, a pioneer of digital physics

[An informational process based on reversible universal cellular automata, Physica D: Nonlinear Phenomena, 45, 1–3, September 1990, 254–270, https://www.sciencedirect.com/science/article/pii/016727899090186S, 10.1016/0167-2789(90)90186-S]

“What should a society be, so that in his last years a man might still be a man?
The answer is simple: he would always have to have been treated as a man. By the fate that it allots to its members who can no longer work, society gives itself away — it has always looked upon them as so much material. Society confesses that as far as it is concerned, profit is the only thing that counts, and that its "humanism" is mere window-dressing. In the nineteenth century the ruling classes explicitly equated the proletariat with barbarism. The struggles of the workers succeeded in making the proletariat part of mankind once more. But only in so far as it is productive. Society turns away from the aged worker as though he belonged to another species. That is why the whole question is buried in a conspiracy of silence.”

Simone de Beauvoir (1908–1986) French writer, intellectual, existentialist philosopher, political activist, feminist, and social theorist

Conclusion, p. 542
The Coming of Age (1970)

Fate , Age , Question , Silence

“The technology needed for an early Internet-connection implant is no more than 25 years off. Imagine that you could understand any language, remember every joke, solve any equation, get the latest news, balance your checkbook, communicate with others, and have near-instant access to any book ever published, without ever having to leave the privacy of yourself.”

Bran Ferren (1953) American technologist

Technology Predictions: Wired for Life: The Internet Implant (June 1998 Columns), Columns Magazine, University of Washington, August 31, 1998, September 8, 2013 http://www.washington.edu/alumni/columns/june98/technology.html,

Books , Imagination , Communication , Understanding

“I finally understood that the half page of code on the bottom of page 13 of the Lisp 1.5 manual was Lisp in itself. These were “Maxwell’s Equations of Software!””

Alan Kay (1940) computer scientist

ACM Queue A Conversation with Alan Kay Vol. 2, No. 9 - Dec/Jan 2004-2005 http://www.acmqueue.com/modules.php?name=Content&pa=showpage&pid=273&page=4
2000s

“Cardan's originality in the matter seems to have been shown chiefly in four respects. First, he reduced the general equation to the type x^3 + bx = c; second, in a letter written August 4, 1539, he discussed the question of the irreducible case; third, he had the idea of the number of roots to be expected in the cubic; and, fourth, he made a beginning in the theory of symmetric functions. …With respect to the irreducible case… we have the cube root of a complex number, thus reaching an expression that is irreducible even though all three values of x turn out to be real. With respect to the number of roots to be expected in the cubic… before this time only two roots were ever found, negative roots being rejected. As to the question of symmetric functions, he stated that the sum of the roots is minus the coefficient of x2</sup”

David Eugene Smith (1860–1944) American mathematician

Source: History of Mathematics (1925) Vol.2, pp.461-464

Idea , Question , Time

“About a year ago, I started seeing these ads in the paper for 'Laser Vaginal Rejuvenation'. First it was a little ad. The next week, it was twice as big. And after a month, it was a full page-it just took over. Something in that triggered a bunch of associations and projections. Like, what kind of activities do you have to engage in to get to the point where you need to bring a laser into the equation?”

Beck (1970) American Musician (b.1970)

Spin magazine, December 1999

“The conformal invariance of the Yang-Mills equations in four dimensions greatly facilitates the study of the temporal asymptotic behavior of their solutions.”

John C. Baez (1961) American mathematician and mathematical physicist

[Scattering for the Yang-Mills equations, Trans. Amer. Math. Soc., 315, 1989, 823–832, 10.1090/S0002-9947-1989-0949897-7] (p. 823)

Behavior , Study

“We live in a world where bulk is equated with quality.”

Robertson Davies book A Voice from the Attic

A Voice from the Attic (1960)

World

“Ironically, conventional quantum mechanics itself involves a vast expansion of physical reality, which may be enough to avoid Einstein Insanity. The equations of quantum dynamics allow physicists to predict the future values of the wave function, given its present value. According to the Schrödinger equation, the wave function evolves in a completely predictable way. But in practice we never have access to the full wave function, either at present or in the future, so this “predictability” is unattainable. If the wave function provides the ultimate description of reality — a controversial issue!”

Frank Wilczek (1951) physicist

we must conclude that “God plays a deep yet strictly rule-based game, which looks like dice to us.”
Einstein’s Parable of Quantum Insanity (2015)

God , Way , Game , Reality

“[W]e've got to break this equation of "I'm right, you're evil. So everything you do is suspect, everything you say is a lie, your facts are fake news." Because that is an acid on politics. We've got to get rid of that.”

Mike Murphy (political consultant) (1962) American political consultant

Interview with Elex Michaelson https://www.facebook.com/ElexMichaelson/videos/318261475405835/ (2018)
2010s, 2018

Lie , Evil

“The core of the Syrian tragedy consists of the fact that Assad and ISIS represent the two faces of the same coin. Both want the Syrian people, or what is left of them inside the country, scripted out of the equation. Both have enough of a popular base to hang on for some more time even if they did not receive succor from the outside which they regularly do. At the same time neither is strong enough or is ever likely to have the popular base to impose its agenda on Syria.”

Amir Taheri (1942) Iranian journalist

Opinion: The Syrian Orphan and a Club of Cynics http://english.aawsat.com/2015/09/article55345155/opinion-the-syrian-orphan-and-a-club-of-cynics, Ashraq Al-Awsat (18 Sep, 2015).

People , Strong , Time , Country

“India is a geographical term. It is no more a united nation than the equator.”

Winston S. Churchill (1874–1965) Prime Minister of the United Kingdom

Speech at Royal Albert Hall, London (18 March 1931).
The 1930s

“It is difficult to say when algebra as a science began in China. Problems which we should solve by equations appear in works as early as the Nine Sections (K'iu-ch'ang Suan-shu) and so may have been known by the year 1000 B. C. In Liu Hui's commentary on this work (c. 250) there are problems of pursuit, the Rule of False Position… and an arrangement of terms in a kind of determinant notation. The rules given by Liu Hui form a kind of rhetorical algebra.
The work of Sun-tzï contains various problems which would today be considered algebraic. These include questions involving indeterminate equations. …Sun-tzï solved such problems by analysis and was content with a single result…
The Chinese certainly knew how to solve quadratics as early as the 1st century B. C., and rules given even as early as the K'iu-ch'ang Suan-shu… involve the solution of such equations.
Liu Hui (c. 250) gave various rules which would now be stated as algebraic formulas and seems to have deduced these from other rules in much the same way as we should…
By the 7th century the cubic equation had begun to attract attention, as is evident from the Ch'i-ku Suan-king of Wang Hs'iao-t'ung (c. 625).
The culmination of Chinese is found in the 13th century. …numerical higher equations attracted the special attention of scholars like Ch'in Kiu-shao (c.1250), Li Yeh (c. 1250), and Chu-Shï-kié (c. 1300), the result being the perfecting of an ancient method which resembles the one later developed by W. G. Horner”

David Eugene Smith (1860–1944) American mathematician

1819
Source: History of Mathematics (1925) Vol.2, Ch. 6: Algebra

Way , Question , Problem , Appearance

“Today we preach that science is not science unless it is quantitative. We substitute correlations for causal studies, and physical equations for organic reasoning. Measurements and equations are supposed to sharpen thinking, but, in my observation, they more often tend to make the thinking noncausal and fuzzy. They tend to become the object of scientific manipulation instead of auxiliary tests of crucial inferences.
Many - perhaps most - of the great issues of science are qualitative, not quantitative, even in physics and chemistry. Equations and measurements are useful when and only when they are related to proof; but proof or disproof comes first and is in fact strongest when it is absolutely convincing without any quantitative measurement.
Or to say it another way, you can catch phenomena in a logical box or in a mathematical box. The logical box is coarse but strong. The mathematical box is fine-grained but flimsy. The mathematical box is a beautiful way of wrapping up a problem, but it will not hold the phenomena unless they have been caught in a logical box to begin with.”

John R. Platt (1918–1992) American physicist

John R. Platt (1964) " Science, Strong Inference -- Proper Scientific Method (The New Baconians) http://256.com/gray/docs/strong_inference.html. In: Science Magazine 16 October 1964, Volume 146, Number 3642. Cited in: Gerald Weinberg (1975) Introduction to General Systems Thinking. p. 1, and in multiple other sources.

Beauty , Way , Mathematics , Problem

“I do not know why we equate—and with such examples before us—a white skin with civilisation.”

Helen Suzman (1917–2009) South African politician

As quoted in "The Hon. Member For Houghton" https://web.archive.org/web/19960913173321/https://www.newyorker.com/magazine/1987/04/20/the-hon-member-for-houghton (20 April 1987), by E. J. Kahn, The New Yorker

“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

“You know what the magic word, the only thing that matters in American sexual mores today is? One thing. You can do anything, the Left will promote and understand and tolerate anything, so long as there is one element. Do you know what it is? Consent. If there is consent on both or all three or all four, however many are involved in the sex act, it's perfectly fine. Whatever it is. But if the left ever senses and smells that there's no consent in part of the equation then here come the rape police. But consent is the magic key to the left.”

Rush Limbaugh (1951) U.S. radio talk show host, Commentator, author, and television personality

" Limbaugh: The Left Sends Out "The Rape Police" Whenever There's Sex With "No Consent" (Also Known As Rape) http://mediamatters.org/video/2016/10/12/limbaugh-left-sends-out-rape-police-whenever-theres-sex-no-consent-also-known-rape/213787", Media Matters (October 12, 2016).

Sex , Understanding , Sense , Parting

“Socialism is offered as a remedy. It is pretty to look at, but it does not mean liberty. It means just the other thing, because it brings us face to face with the same old equation. We know what the socialist leaders would do, for human nature does not change.”

George Howard Earle, Jr. (1856–1928) American lawyer

From "George H. Earle, Jr., Doctor to Ailing Corporations". Munsey's Magazine (February 1910:683-691)

Nature , Change

“Painting has nothing to do with thinking, because in painting thinking is painting. Thinking is language – record-keeping – and has to take place before and after. Einstein did not think when he was calculating: he calculated – producing the next equation in reaction to the one that went before – just as in painting one form is a response to another and so on.”

Gerhard Richter (1932) German visual artist, born 1932

undated quotes, The Daily Practice of Painting, Writings (1962-1993)

Thinking , Painting

“The law that entropy always increases, holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations — then so much the worse for Maxwell's equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

Source: The Nature of the Physical World (1928), Ch. 4 The Running-Down of the Universe

Law , Hope , Nature , Thinking

“When we seek a textbook case for the proper operation of science, the correction of certain error offers far more promise than the establishment of probable truth. Confirmed hunches, of course, are more upbeat than discredited hypotheses. Since the worst traditions of “popular” writing falsely equate instruction with sweetness and light, our promotional literature abounds with insipid tales in the heroic mode, although tough stories of disappointment and loss give deeper insight into a methodology that the celebrated philosopher Karl Popper once labeled as “conjecture and refutation.””

Stephen Jay Gould (1941–2002) American evolutionary biologist

"An Essay on a Pig Roast", p. 437
Bully for Brontosaurus (1991)

Truth , Disappointment , Error , Literature

“…[A]ll duels followed a pattern. They began with heat and fury, then settled into a contest of wills. With two equally matched opponents there would come a time when the worm of doubt entered the equation. The truly skilled recognized such moments, and fed them. It was at this time that the endgame would begin.”

David Gemmell book Stormrider

Source: Rigante series, Stormrider, Ch. 7

Time

“This paper reviews prior applications of ) between 1977 and 1994. After documenting and characterizing the number of applications over time, we discuss important methodological issues related to structural equation modeling and assess the quality of previous applications in terms of three aspects: issues related to the initial specification of theoretical models of interest; issues related to data screening prior to model estimation and testing; and issues related to the estimation and testing of theoretical models on empirical data. On the basis of our findings, we identify problem areas and suggest avenues for improvement.”

Christian Homburg (1962) German academic

Article abstract
"Applications of structural equation modeling in marketing and consumer research", 1996

Problem , Time

“This view of a law and of its validity (we call it the positivistic theory) has rendered jurists and the people alike defenceless against arbitrary, cruel, or criminal laws, however extreme they might be. In the end, the positivistic theory equates law with power; there is law only where there is power.”

Gustav Radbruch (1878–1949) German politician

"Five Minutes of Legal Philosophy" (1945)

People , Law

“It is difficult to say who it is who first recognized the advantage of always equating to zero in the study of the general equation. It may very likely have been Napier, for he wrote his De Arte Logistica before 1594, and in this there is evidence that he understood the advantage of this procedure. Bürgi also recognized the value of making the second member zero, Harriot may have done the same, and the influence of Descartes was such that the usage became fairly general.”

David Eugene Smith (1860–1944) American mathematician

History of Mathematics (1925) Vol.2

Art , Study

“The vision for Europe needs to renew its commitment to true subsidiarity. Having structures of economic, political and social relationships that liberate subsidiarity will make accepting complexity more realistic. It seems to me that current debates about what Europe is have fallen into the trap of equating strength and unity with simplicity. As I have just said, the opposite seems to be true. Attempts to explain European structures and identity with a single overarching story have ended in failure because they have not allowed sufficient flexibility for these structures to be lived out below the continental level.”

Justin Welby (1956) British Anglican bishop; the 105th Archbishop of Canterbury

Address to the Catholic Institute of Paris (November 19, 2016)

Failure

“As a transportation hub, agriculture leader, and home to more than half a million small businesses, Missouri is positioned to be at the cutting edge of growth and innovation in this country. But, we need the right policies to get us there and pro-growth tax cuts and regulatory reform are a critical part of that equation. I couldn’t agree more with the president’s call to get this done, and I look forward to working with him and my colleagues in Congress to provide much-needed tax relief for Missouri families and small businesses.”

Roy Blunt (1950) American politician

Families and small business need tax relief http://www.kansascity.com/opinion/readers-opinion/guest-commentary/article170867657.html (September 3, 2017)

Family , Home , Business , Parting

“If government, or those in positions of power and authority, can silence criticism by the argument that such criticism might be misunderstood somewhere, there is an end to all criticism, and perhaps an end to our kind of political system. For men in authority will always think that criticism of their policies is dangerous. They will always equate their policies with patriotism, and find criticism subversive.”

Henry Steele Commager (1902–1998) American historian

"The Problem of Dissent" in Saturday Review, Volume 48 (December 1965), p. 81; also read into the US Congressional Record (26 June 1969)

Men , Thinking , Silence

“Our planet, the Earth, is, as far as we know, unique in the universe. It contains life. Even in its most barren stretches, there are animals. Around the equator, where those two essentials for life, sunshine and moisture, are most abundant, great forests grow. And here plants and animals proliferate in such numbers that we still have not even named all the different species. Here, animals and plants, insects and birds, mammals and man live together in intimate and complex communities, each dependent on one another. Two thirds of the surface of this unique planet are covered by water, and it was here indeed that life began. From the oceans, it has spread even to the summits of the highest mountains as animals and plants have responded to the changing face of the Earth.”

David Attenborough (1926) British broadcaster and naturalist

Opening narration
The Living Planet (1984)

Life , Mountain , Communication , Bird

“What I'm continuing to do is cutting out the equation that wastes the most amount of time — and that is working within the system.”

Rod Coronado (1966) Native American eco-anarchist and animal rights activist

Activists Uncaged http://www.statenews.com/article.phtml?pk=23918

Time

“Almost all of fluid dynamics follows from a differential equation called the Navier-Stokes equation. But this general equation has not, in practice, led to solutions of real problems of any complexity. In this sense, the curve of a baseball is not understood; the Navier-Stokes equation applied to a base ball has not been solved.”

Robert Adair (physicist) (1924) Physicist and author

Source: The Physics Of Baseball (Second Edition - Revised), Chapter 2, The Flight Of The baseball, p. 22

Problem , Sense

“The "Schrödinger equation", equation (3') in "Quantisierung als Eigenwertproblem, Vierte Mitteilung", Annalen der Physik (1926)”

Erwin Schrödinger (1887–1961) Austrian physicist

“In the algebra of fantasy, A times B doesn't have to equal B times A. But, once established, the equation must hold throughout the story.”

Lloyd Alexander (1924–2007) American children's writer

"The Flat-Heeled Muse", Horn Book Magazine (1 April 1965)

Time

“I do feel strongly that this is nonsense! … So perhaps I could entertain future historians by saying I think all this superstring stuff is crazy and is in the wrong direction. I think all this superstring stuff is crazy and is in the wrong direction. … I don’t like it that they’re not calculating anything. … why are the masses of the various particles such as quarks what they are? All these numbers … have no explanations in these string theories – absolutely none! … I don’t like that they don’t check their ideas. I don’t like that for anything that disagrees with an experiment, they cook up an explanation—a fix-up to say, “Well, it might be true.” For example, the theory requires ten dimensions. Well, maybe there’s a way of wrapping up six of the dimensions. Yes, that’s all possible mathematically, but why not seven? When they write their equation, the equation should decide how many of these things get wrapped up, not the desire to agree with experiment. In other words, there’s no reason whatsoever in superstring theory that it isn’t eight out of the ten dimensions that get wrapped up and that the result is only two dimensions, which would be completely in disagreement with experience. So the fact that it might disagree with experience is very tenuous, it doesn’t produce anything.”

Richard Feynman (1918–1988) American theoretical physicist

interview published in Superstrings: A Theory of Everything? (1988) edited by Paul C. W. Davies and Julian R. Brown, p. 193-194

Way , Feeling , Mathematics , Idea

“In the beginning of 1917, two solutions of the field equations for a homogeneous isotropic universe had been found, which I… call the solutions "A" and "B."… at that time only static solutions were looked for. It was thought that the universe must be a stable structure… In one of these solutions (B) the average density was zero, it was empty; the other one (A) had a finite density…. In B, to get the real universe, we should have to put in a few galactic systems, in A we should have to condense the evenly distributed matter into galactic systems. The universe A… has an average density, but no expansion. It is therefore called the static universe. B, on the other hand… expands, and it could only parade in the garb of a static universe because there is nothing in it to show the expansion. B is therefore called the empty universe. Thus we had two approximations : the static universe with matter and without expansion, and the empty one without matter and with expansion. The actual universe… has both matter and expansion… In 1917… the actual value of the density was still entirely unknown, and the expansion had not yet been discovered.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

Universe , Time

“The law which asserts that the equation X = 0, complete or incomplete, can have no more real positive roots than it has changes of sign, and no more real negative roots than it has permanences of sign, was apparently known to Cardan; but a satisfactory statement is possibly due to Harriot (died 1621) and certainly to Descartes.”

David Eugene Smith (1860–1944) American mathematician

Source: History of Mathematics (1925) Vol.2, p.469

Law , Change

“Insulting people does not work if your objective is to persuade them. When a person is insulted, they become even more dogmatic in holding their incorrect belief. If you are going to say that the Lord called you to go into politics, then you need to act like it. If you are not going to act like it, then you need to take His name out of the equation.”

Trey Gowdy (1964) American politician

Trey Gowdy - Liberty University Convocation https://www.youtube.com/watch?v=gQNf97GZjuA&app=desktop (March 23, 2015)

People , Personality

“The methods of the Bernoullis and of Taylor, were held, at the time of their invention, to be most complete and exact. Several imperfections, however, belong to them. They do not apply to problems involving three or more properties; nor do they extend to cases involving differentials of a higher order than the first: for instance, they will not solve the problem, in which a curve is required, that with its radius of curvature and evolute shall contain the least area. Secondly, they do not extend to cases, in which the analytical expression contains, besides x, y, and their differentials, integral expressions; for instance, they will not solve the second case proposed in James Bernoulli's Programma if the Isoperimetrical condition be excluded; for then the arc s, an integral, since it =\int \! dx \sqrt(1+\frac{dy^2}{dx^2}), is not given. Thirdly, they do not extend to cases, in which the differential function, expressing the maximum should depend on a quantity, not given except under the form of a differential equation, and that not integrable; for instance, they will not solve the case of the curve of the quickest descent, in a resisting medium, the descending body being solicited by any forces whatever.”

Robert Woodhouse (1773–1827) English mathematician

A Treatise on Isoperimetrical Problems, and the Calculus of Variations (1810)

Problem , Time , Dependency

“Anyone who understands algebraic notation, reads at a glance in an equation results reached arithmetically only with great labour and pains.”

Antoine Augustin Cournot Researches into the Mathematical Principles of the Theory of Wealth

Source: Researches into the Mathematical Principles of the Theory of Wealth, 1897, p. 4; Cited in: Moritz (1914, 197): About mathematics as language

Pain , Understanding , Reading

“So far as we know, all the fundamental laws of physics, like Newton’s equations, are reversible.”

Richard Feynman (1918–1988) American theoretical physicist

volume I; lecture 46, "Ratchet and Pawl"; section 46-5, "Order and entropy"; p. 46-8
The Feynman Lectures on Physics (1964)

Law

“Starting from Einstein's theory of general relativity, Oppenheimer and Snyder found solutions… that described what happens to a massive star when it has exhausted its supplies of nuclear energy. The star collapses gravitationally and disappears from the visible universe, leaving behind only an intense gravitational field to mark its presence. The star remains in a state of permanent free fall, collapsing endlessly inward into the gravitational pit without ever reaching the bottom. … In my opinion, the black hole is incomparably the most exciting and the most important consequence of general relativity. But Einstein … was actively hostile to the idea of black holes. … Oddly enough, Oppenheimer too in later life was uninterested in black holes, although… they were his most important contribution to science. … Oppenheimer in his later years believed that the only problem worthy of attention of a serious theoretical physicist was the discovery of fundamental equations of physics. Einstein certainly felt the same way.”

Freeman Dyson (1923) theoretical physicist and mathematician

The Scientist As Rebel (2006)

Life , Hostility , Way , Star

“The sequence of different positions of the same particle at different times forms a one-dimensional continuum in the four-dimensional space-time, which is called the world-line of the particle. All that physical experiments or observations can teach us refers to intersections of world-lines of different material particles, light-pulsations, etc., and how the course of the world-line is between these points of intersection is entirely irrelevant and outside the domain of physics. The system of intersecting world-lines can thus be twisted about at will, so long as no points of intersection are destroyed or created, and their order is not changed. It follows that the equations expressing the physical laws must be invariant for arbitrary transformations.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

World , Law , Light , Change

“These burdens and frustrations are accepted by most Americans with maturity and understanding. They may long for the days when war meant charging up San Juan Hill-or when our isolation was guarded by two oceans — or when the atomic bomb was ours alone — or when much of the industrialized world depended upon our resources and our aid. But they now know that those days are gone — and that gone with them are the old policies and the old complacency's. And they know, too, that we must make the best of our new problems and our new opportunities, whatever the risk and the cost.
But there are others who cannot bear the burden of a long twilight struggle. They lack confidence in our long-run capacity to survive and succeed. Hating communism, yet they see communism in the long run, perhaps, as the wave of the future. And they want some quick and easy and final and cheap solution — now.
There are two groups of these frustrated citizens, far apart in their views yet very much alike in their approach. On the one hand are those who urge upon us what I regard to be the pathway of surrender-appeasing our enemies, compromising our commitments, purchasing peace at any price, disavowing our arms, our friends, our obligations. If their view had prevailed, the world of free choice would be smaller today.
On the other hand are those who urge upon us what I regard to be the pathway of war: equating negotiations with appeasement and substituting rigidity for firmness. If their view had prevailed, we would be at war today, and in more than one place.
It is a curious fact that each of these extreme opposites resembles the other. Each believes that we have only two choices: appeasement or war, suicide or surrender, humiliation or holocaust, to be either Red or dead. Each side sees only "hard" and "soft" nations, hard and soft policies, hard and soft men. Each believes that any departure from its own course inevitably leads to the other: one group believes that any peaceful solution means appeasement; the other believes that any arms build-up means war. One group regards everyone else as warmongers, the other regards everyone else as appeasers. Neither side admits that its path will lead to disaster — but neither can tell us how or where to draw the line once we descend the slippery slopes of appeasement or constant intervention.
In short, while both extremes profess to be the true realists of our time, neither could be more unrealistic. While both claim to be doing the nation a service, they could do it no greater disservice. This kind of talk and easy solutions to difficult problems, if believed, could inspire a lack of confidence among our people when they must all — above all else — be united in recognizing the long and difficult days that lie ahead. It could inspire uncertainty among our allies when above all else they must be confident in us. And even more dangerously, it could, if believed, inspire doubt among our adversaries when they must above all be convinced that we will defend our vital interests.
The essential fact that both of these groups fail to grasp is that diplomacy and defense are not substitutes for one another. Either alone would fail. A willingness to resist force, unaccompanied by a willingness to talk, could provoke belligerence — while a willingness to talk, unaccompanied by a willingness to resist force, could invite disaster.”

John F. Kennedy (1917–1963) 35th president of the United States of America

1961, Address at the University of Washington

Men , Hate , War , People

“The miracle of physics that I'm talking about here is something that was actually known since the time of Einstein's general relativity; that gravity is not always attractive. Gravity can act repulsively. Einstein introduced this in 1916… in the form of the cosmological constant, and the original motivation of modifying the equations of general relativity to allow this was because Einstein thought that the universe was static, and he realized that ordinary gravity would cause the universe to collapse if it was static. …The fact that general relativity can support this gravitational repulsion, still being consistent with all the principles that general relativity incorporates, is the important thing which Einstein himself did discover..”

Alan Guth (1947) American theoretical physicist and cosmologist

Lecture 1: Inflationary Cosmology: Is Our Universe Part of a Multiverse? Part I.
The Early Universe (2012)

Motivation , Support , Universe , Time

“Not everyone has to be a high-powered neurosurgeon to add significantly to the equation that brings about success here.”

Ben Carson (1951) 17th and current United States Secretary of Housing and Urban Development; American neurosurgeon

Source: Think Big (1996), p. 100

Success

“It is growing harder and harder to equate elite university branding with proof of knowledge. Barack Obama, another Harvard Law graduate, proved this depressing fact a number of times when he asserted that the Maldives were the Falklands, "corpsmen" was pronounced with a hard p, Austrians spoke a language called Austrian, there were 57 states, and Hawaii was in Asia.”

Victor Davis Hanson (1953) American military historian, essayist, university professor

2010s, The Deflation of the Academic Brand (2018)

Law , Knowledge , Universe , Time

“Ours, according to Leibnitz, is the best of all possible worlds, and the laws of nature can therefore be described in terms of extremal principles. Thus, arising from corresponding variational problems, the differential equations of mechanics have invariance properties relative to certain groups of coordinate transformations.”

Carl Ludwig Siegel (1896–1981) German mathematician

[Lectures on Celestial Mechanics, https://books.google.com/books?id=mZtrCQAAQBAJ&pg=PA1] (p. 1)

World , Law , Nature , Problem

“But what has happened is that the Indian State actively patronizes the exercise aimed at making all religions mean the same things, and persecutes those who defy the exercise. A whole army of 'secularist' scribes in the media and the academia has been employed and paid handsomely for whitewashing Islam and Christianity so that whatever is bigoted in the scriptures and blood-soaked histories of these creeds, is carefully exorcised. On the other hand, whatever is liberal and large-hearted, humane and civilized in the pluralistic spirituality of India is remorseless pruned to the prescribed and proper size. In the process, Christianity has been made to mean only the Sermon on the Mount, and Islam equated with two Quranic sentences torn out of context - "Unto you your religion, and unto me my religion" and "There is no compulsion in religion."”

Sita Ram Goel (1921–2003) Indian activist

Freedom of expression - Secular Theocracy Versus Liberal Democracy (1998)

Religion , Exercises , History , Heart

“Having begun my life in science searching for the equation beyond time, I now believe that the deepest secret of the universe is that its essence rests in how it unfolds moment by moment in time.”

Lee Smolin (1955) American cosmologist

Time Reborn: From the Crisis in Physics to the Future of the Universe (2013)

Life , Secret , Search , Universe

“The analytical equations, unknown to the ancient geometers, which Descartes was the first to introduce into the study of curves and surfaces, are not restricted to the properties of figures, and to those properties which are the object of rational mechanics; they extend to all general phenomena. There cannot be a language more universal and more simple, more free from errors and from obscurities, that is to say more worthy to express the invariable relations of natural things.
Considered from this point of view, mathematical analysis is as extensive as nature itself; it defines all perceptible relations, measures times, spaces, forces, temperatures; this difficult science is formed slowly, but it preserves every principle which it has once acquired; it grows and strengthens itself incessantly in the midst of the many variations and errors of the human mind.
Its chief attribute is clearness; it has no marks to express confused notions. It brings together phenomena the most diverse, and discovers the hidden analogies which unite them.”

Joseph Fourier book The Analytical Theory of Heat

Preliminary Discourse, p.7 Note: often quoted as Mathematics [or mathematical analysis] compares the most diverse phenomena and discovers the secret analogies that unite them.
The Analytical Theory of Heat (1878)

Error , Mathematics , Nature , Study

“Television has already been wholly colonized by corporate interests, which are now laying claim to our schools. The goal is not simply to sell products and strengthen the consumer culture. It is also to create a political culture that equates the corporate interest with the human interest in the public mind.”

David Korten book When Corporations Rule the World

Source: When Corporations Rule the World (1995,2015), p. 149

School

“One of the many importants ideas introduced by Minkowski into the study of convex bodies was that of gauge function. Roughly, the gauge function is the equation of a convex body. Minkowski showed that the gauge function could be defined in a purely geometric way and that it must have certain properties analogous to those possessed by the distance of a point from the origin. He also showed that conversely given any function possessing these properties, there exists a convex body with the given function as its gauge function.”

Carl Ludwig Siegel (1896–1981) German mathematician

[Lectures on the Geometry of Numbers, https://books.google.com/books?id=dyH4CAAAQBAJ&pg=PA6] (p. 6)

Way , Idea , Gauge , Study

“If time is treated in modern physics as a dimension on a par with the dimensions of space, why should we a priori exclude the possibility that we are pulled as well as pushed along its axis? The future has, after all, as much or as little reality as the past, and there is nothing logically inconceivable in introducing, as a working hypothesis, an element of finality, supplementary to the element of causality, into our equations. It betrays a great lack of imagination to believe that the concept of "purpose" must necessarily be associated with some anthropomorphic deity.”

Arthur Koestler (1905–1983) Hungarian-British author and journalist

Epilogue
The Sleepwalkers: A History of Man's Changing Vision of the Universe (1959)

Imagination , Reality , Time , Past

“The Reform Party does not, however, equate "high profile" with electability.”

Preston Manning book The New Canada

Source: The New Canada (1992), Chapter Eighteen, The Road to a More Democratic Canada, p. 331

“There is no direct observational evidence for the curvature [of space], the only directly observed data being the mean density and the expansion, which latter proves that the actual universe corresponds to the non-statical case. It is therefore clear that from the direct data of observation we can derive neither the sign nor that value of the curvature, and the question arises whether it is possible to represent the observed facts without introducing the curvature at all. Historically the term containing the 'cosmological constant λ' was introduced into the field equations in order to enable us to account theoretically for the existence of a finite mean density in a static universe. It now appears that in the dynamical case this end can be reached without the introduction of λ.”

Willem de Sitter (1872–1934) Dutch cosmologist

Joint memoir with Einstein (1932) as quoted by Gerald James Whitrow, The Structure of the Universe: An Introduction to Cosmology (1949)

Question , Universe , Appearance

“But before I proceed farther it may be proper to take notice, that since the time when I gave their lordships an account of the near agreement of Mr. Professor Mayer's lunar tables with the observations that had been then made at the Royal Observatory, I have compared several others, which concurred to prove that the difference between the observed and computed places nowhere amounted to more than about one minute and a half; and I find that the difference (small as it is) may yet be diminished by making alterations in some of the equations, whose true quantity could not be determined without proper observations; after making the needful corrections it appeared, by the comparison of above eleven hundred observations taken here since the new instruments were fixed up, that the difference did nowhere amount to more than a minute: it may therefore be reasonably concluded, that so far as it will depend upon the lunar tables the true longitude of a ship at sea may in all cases be found within about half a degree, and generally much nearer.”

James Bradley (1693–1762) English astronomer; Astronomer Royal

Miscellaneous Works and Correspondence (1832), To Mr. Cleveland Secretary of the Admiralty (April 14, 1760)

Appearance , Time , Dependency , Sea

“Summing up, Nanoscale Communication Networks is a demanding but also very interesting book, an ambitious primer. It is definitely a good starting point for further reading. The author guides the reader through all the aspects of nanonetworks, giving in most cases a clear description of his thinking process within transitions between equations. There are also many cross references between chapters and sections which give a broader view of the topic and help to memorize it. One can also find many pictures, diagrams and tables throughout this book in order to systematize the presented knowledge.”

Stephen F Bush

Book Reviews, REVIEWER: JAKUB PALIDER, NANOSCALE COMMUNICATION NETWORKS STEPHEN F. BUSH, ARTECH HOUSE, 2010, ISBN-13: 978-1-60807-003-9, HARDCOVER, 308 PAGES, IEEE Communications Magazine, August 2011.

Books , Communication , Knowledge , Thinking

“When you’d lived long enough, she’d sometimes reflected, when certain habits had become ingrained no matter what refreshment of the neural pathways the immortality genes could bestow, ethics and etiquette became ever less distinct. Hitherto the involuntary equation had read one way, in disproportionate pangs of conscience over a small breach of manners. Now the terms had been inverted, and she felt over the Council majority’s horrible, criminal, potentially murderous mistake the sort of acute embarrassment that might have been appropriate for some ghastly faux pas. Dreadfully sorry, I’m such a ditz about these nuclear attack protocols…”

Ken MacLeod book Learning the World

Source: Learning the World (2005), Chapter 19 “A Full and Frank Exchange of Views” (p. 326)

Way , Reading

“Ram and Kirshan whom Hindus worship are insignificant creatures, and have been begotten by their parents… Ram could not protect his wife whom Ravan took away by force. How can he (Ram) help others?… It is thousands of times shameful that some people should think of Ram and Kirshan as rulers of all the worlds… To think that Ram and Rahman are the same, is extremely foolish. The creator and the creature can never be one… The controller of the Cosmos was never called Ram and Kirshan before the latter were born. What has happened after their birth that they have come to be equated with Allah, and the worship of Ram and Kirshan is described as the worship of Allah? May Allah save us!
Our prophets who number one lakh and twenty-four thousand have encouraged the created ones to worship the Creator… The gods of the Hindus (on the other hand) have encouraged the people to worship them (the gods) instead… They are themselves misguided, and are leading others astray… See, how the (two) ways are different!”

Ahmad Sirhindi (1564–1624) Indian philosopher

Maktubat-i-Imam Rabbani translated into Urdu by Maulana Muhammad Sa’id Ahmad Naqshbandi, Deoband, 1988, Volume I, 396 Letter was written to Hirday Ram Hindu who had “expressed affinity” with Sirhindi’s school of thought.
From his letters

God , People , World , Way

“Brook Taylor… in his Methodus Incrementorum Directa et Inversa (1715), sought to clarify the ideas of the calculus but limited himself to algebraic functions and algebraic differential equations. …Taylor's exposition, based on what we would call finite differences, failed to obtain many backers because it was arithmetical in nature when the British were trying to tie the calculus to geometry or to the physical notion of velocity.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 427

Idea , Nature

“The solution of the higher indeterminates depends almost entirely on very favourable numerical conditions and his methods are defective. But the extraordinary ability of Diophantus appears rather in the other department of his art, namely the ingenuity with which he reduces every problem to an equation which he is competent to solve.”

James Gow (scholar) (1854–1923) scholar

p, 125
A Short History of Greek Mathematics (1884)

Art , Problem , Appearance , Dependency

“The first writer on algebra whose works have come down to us is Ahmes. He has certain problems in linear equations and in series, and these form the essentially new feature in his work. His treatment of the subject is largely rhetorical.”

David Eugene Smith (1860–1944) American mathematician

Source: History of Mathematics (1925) Vol.2, Ch. 6: Algebra

Problem

“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

“We are witnessing the end of the late 20th- century progressive welfare democracy. Its fiscal bankruptcy is merely a symptom of a more fundamental bankruptcy: its insufficiency as an animating principle for society. The children and grandchildren of those fascists and republicans who waged a bitter civil war for the future of Spain now shrug when a bunch of foreigners blow up their capital. Too sedated even to sue for terms, they capitulate instantly. Over on the other side of the equation, the modern multicultural state is too watery a concept to bind huge numbers of immigrants to the land of their nominal citizenship. So they look elsewhere and find the jihad. The Western Muslim’s pan-Islamic identity is merely the first great cause in a world where globalized pathologies are taking the place of old-school nationalism.”

Mark Steyn book America Alone: The End of the World as We Know It

America Alone: The End of the World as We Know It (2006)

War , Children , World , School

“Thought-economy is most highly developed in mathematics, that science which has reached the highest formal development, and on which natural science so frequently calls for assistance. Strange as it may seem, the strength of mathematics lies in the avoidance of all unnecessary thoughts, in the utmost economy of thought-operations. The symbols of order, which we call numbers, form already a system of wonderful simplicity and economy. When in the multiplication of a number with several digits we employ the multiplication table and thus make use of previously accomplished results rather than to repeat them each time, when by the use of tables of logarithms we avoid new numerical calculations by replacing them by others long since performed, when we employ determinants instead of carrying through from the beginning the solution of a system of equations, when we decompose new integral expressions into others that are familiar,—we see in all this but a faint reflection of the intellectual activity of a Lagrange or Cauchy, who with the keen discernment of a military commander marshalls a whole troop of completed operations in the execution of a new one.”

Ernst Mach (1838–1916) Austrian physicist and university educator

Source: 20th century, "Populär-wissenschafliche Vorlesungen" (1908), pp. 224-225: On thought-economy in m., 203.

Mathematics , Nature , Science , Time

“There are one or two things, which you can directly do in very critical times. But otherwise, this indirect influence that you can exercise on the affairs of the State is the most important role he can play. And, he can play it successfully only if he is, his ideas and his nature of functioning are seen by the public in tune with their standards. The President has to be a citizen and there must be some equation between the people and the President, and if some advice or something is to be given to the executive, it would be received with grace, it would be sometimes accepted, if it is known that the public opinion is on the side of the kind of advice the President is giving. Otherwise, he cannot exercise much influence.”

K. R. Narayanan (1920–2005) 9th Vice President and the 10th President of India

Shri K. R. Narayanan President of India in Conversation with N. Ram on Doordarshan and All India Radio

People , Exercises , Idea , Nature

“L. Walras first formulated the state of the economic system at any point of time as the solution of a system of simultaneous equations representing the demand for goods by consumers, the supply of goods by producers and the equilibrium condition that supply equal demand on every market.”

Kenneth Arrow (1921–2017) American economist

Source: 1950s-1960s, "Existence of an equilibrium for a competitive economy." 1954, p. 265

Time

“I think we in the mainstream media — especially cable television — sometimes bungled coverage of Trump. There was too much uncritical television coverage of Trump because he was good for ratings; then there was not enough investigation of his business dealings, racism and history of sexual assaults, and too much false equivalency that equated the two candidates as equally flawed. More broadly, we in the mainstream media are out of touch with working-class America; we spend too much time chatting up senators, and not enough visiting unemployed steel workers. Yet for all of our sins in the mainstream media, these alt-right websites are both far more pernicious and increasingly influential.”

Nicholas D. Kristof (1959) journalist, author, columnist

Lies in the Guise of News in the Trump Era (November 12, 2016)

History , Business , Thinking , Time

“"What, now?" "Soon equates to good, later to worse, Uagen Zlepe, scholar. Therefore, immediacy."”

Iain Banks Culture series

Look to Windward page 213.
Culture series, Look to Windward (2000)

“In my essay I refuted the Hayek-Robbins argument by showing how a market mechanism could be established in a socialist economy which would lead to the solution of the simultaneous equations by means of an empirical procedure of trial and error. […] Were I to rewrite my essay today my task would be much simpler. My answer to Hayek and Robbins would be: so what’s the trouble?
Let us put the simultaneous equations on an electronic computer and we shall obtain the solution in less than a second. The market process with its cumbersome tatonnements appears old-fashioned. Indeed, it may be considered as a computing device of the preelectronic age.”

Oskar R. Lange (1904–1965) Polish economist

"The computer and the market" (1967)

Age , Error , Fashion , Appearance

“While in Kyoto I tried to learn Japanese with a vengeance. I worked much harder at it, and got to a point where I could go around in taxis and do things. I took lessons from a Japanese man every day for an hour.
One day he was teaching me the word for "see." "All right," he said. "You want to say, 'May I see your garden?' What do you say?"
I made up a sentence with the word that I had just learned.
"No, no!" he said. "When you say to someone, 'Would you like to see my garden?' you use the first 'see.' But when you want to see someone else's garden, you must use another 'see,' which is more polite."
"Would you like to glance at my lousy garden?" is essentially what you're saying in the first case, but when you want to look at the other fella's garden, you have to say something like, "May I observe your gorgeous garden?" So there's two different words you have to use.
Then he gave me another one: "You go to a temple, and you want to look at the gardens…"
I made up a sentence, this time with the polite "see."
"No, no!" he said. "In the temple, the gardens are much more elegant. So you have to say something that would be equivalent to 'May I hang my eyes on your most exquisite gardens?"
Three or four different words for one idea, because when I'm doing it, it's miserable; when you're doing it, it's elegant.
I was learning Japanese mainly for technical things, so I decided to check if this same problem existed among the scientists.
At the institute the next day, I said to the guys in the office, "How would I say in Japanese, 'I solve the Dirac Equation'?"
They said such-and-so.
"OK. Now I want to say, 'Would you solve the Dirac Equation?'”

Richard Feynman (1918–1988) American theoretical physicist

how do I say that?"
"Well, you have to use a different word for 'solve,' " they say.
"Why?" I protested. "When I solve it, I do the same damn thing as when you solve it!"
"Well, yes, but it's a different word — it's more polite."
I gave up. I decided that wasn't the language for me, and stopped learning Japanese.
Part 5: "The World of One Physicist", "Would <U>You</U> Solve the Dirac Equation?", p. 245-246
Surely You're Joking, Mr. Feynman! (1985)

Guy , Idea , Problem , Learning

“For too long, African societies have been identified as superstitious, consisting of people who cannot question, reason or think critically. Dogma and blind faith in superstition, divinity and tradition are said to be the mainstay of popular thought and culture. African science is often equated with witchcraft and the occult; African philosophy with magical thinking, myth-making and mysticism, African religion with stone-age spiritual abracadabra, African medicine with folk therapies often involving pseudoscientific concoctions inspired by magical thinking. Science, critical thinking and technological intelligence are portrayed as Western — as opposed to universal — values, and as alien to Africa and to the African mindset. An African who thinks critically or seeks evidence and demands proofs for extraordinary claims is accused of taking a “white” or Western approach. An African questioning local superstitions and traditions is portrayed as having abandoned or betrayed the essence of African identity. Skepticism and rationalism are regarded as Western, un-African, philosophies. Although there is a risk of overgeneralizing, there are clear indicators that the continent is still socially, politically and culturally trapped by undue credulity. Many irrational beliefs exist and hold sway across the region. These are beliefs informed by fear and ignorance, misrepresentations of nature and how nature works. These misconceptions are often instrumental in causing many absurd incidents, harmful traditional practices and atrocious acts.”

Leo Igwe (1970) Nigerian human rights activist

A Manifesto for a Skeptical Africa (2012)

People , Age , Fear , Faith

Quotes about equation page 2

Quotes about equation
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