Quotes about ratio

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

Quotes about ratio

“Anxiety increases in direct ratio and proportion as man departs from God.”

Fulton J. Sheen (1895–1979) Catholic bishop and television presenter

Source: Peace of Soul (1949), Ch. 2, p. 19

“I realized that the world did not exist for my benefit. It followed that the ratio of pleasant and unpleasant things around me would not change. It wasn't up to me. It was clear that the best thing to do was to adopt a sort of muddled cheerfulness.”

Banana Yoshimoto book Kitchen

Source: Kitchen

World, Change

“He learned to communicate with birds and discovered their conversation was fantastically boring. It was all to do with windspeed, wingspans, power-to-weight ratios and a fair bit about berries.”

Douglas Adams book So Long, and Thanks for All the Fish

Source: So Long, and Thanks for All the Fish

Communication, Bird, Learning

“Bullialdus wrote that all force respecting the Sun as its center & depending on matter must be reciprocally in a duplicate ratio of the distance from the center.”

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

Letter to Edmund Halley (June 20, 1686) quoted in I. Bernard Cohen and George E. Smith, ed.s, The Cambridge Companion to Newton (2002) p. 204

Sun, Dependency

“Common sense in matters medical is rare, and is usually in inverse ratio to the degree of education.”

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

"Teaching and Thinking" in The Montreal Medical Journal (1895).

Education, Sense

“Art is not to be looked at. Art is looking at us. What is art to others is not necessarily art to me. Nor for the same reason and vice versa. What was art to me or was not some time ago might have lost that value or gained it in the meantime and maybe again though art is not an object but experience. To be able to perceive it we need to be receptive. Therefore art is there where art meets us now. The content of art is visual formulation of our relation to life. The measure of art, the ratio of effort to effect, the aim of art revelation and evocation of vision.”

Josef Albers (1888–1976) German-American artist and educator

Homage to the square' (1964), Oral history interview with Josef Albers' (1968)

Life, Art, Effort, Time

“In organisms of all kinds the young are launched upon their careers endowed with a certain amount of biological capital derived from their parents. This varies enormously in amount in different species, but, in all, there has been, before the offspring is able to lead an independent existence, a certain expenditure of nutriment in addition, almost universally, to some expenditure of time or activity, which the parents are induced by their instincts to make for the advantage of their young. Let us consider the reproductive value of these offspring at the moment when this parental expenditure on their behalf has just ceased. If we consider the aggregate of an entire generation of such offspring it is clear that the total reproductive value of the males in this group is exactly equal to the total value of all the females, because each sex must supply half the ancestry of all future generations of the species. From this it follows that the sex ratio will so adjust itself, under the influence of Natural Selection, that the total parental expenditure incurred in respect of children of each sex, shall be equal; for if this were not so and the total expenditure incurred in producing males, for instance, were less than the total expenditure incurred in producing females, then since the total reproductive value of the males is equal to that of the females, it would follow that those parents, the innate tendencies of which caused them to produce males in excess, would, for the same expenditure, produce a greater amount of reproductive value; and in consequence would be the progenitors of a larger fraction of future generations than would parents having a congenital bias towards the production of females. Selection would thus raise the sex-ratio until the expenditure upon males became equal to that upon females.”

Ronald Fisher book The Genetical Theory of Natural Selection

On natural selection acting on sex ratio: Fisher's principle, Ch. 6, p. 141.
The Genetical Theory of Natural Selection (1930)

Children, Sex, Nature, Parent

“I need scarcely observe that a poem deserves its title only inasmuch as it excites, by elevating the soul. The value of the poem is in the ratio of this elevating excitement. But all excitements are, through a psychal necessity, transient.”

Edgar Allan Poe (1809–1849) American author, poet, editor and literary critic

The Poetic Principle (1850)
Context: I hold that a long poem does not exist. I maintain that the phrase, "a long poem," is simply a flat contradiction in terms.
I need scarcely observe that a poem deserves its title only inasmuch as it excites, by elevating the soul. The value of the poem is in the ratio of this elevating excitement. But all excitements are, through a psychal necessity, transient. That degree of excitement which would entitle a poem to be so called at all, cannot be sustained throughout a composition of any great length.

Soul

“My recollection is that Bob Lucas and Ed Prescott were initially very enthusiastic about rational expectations econometrics. After all, it simply involved imposing on ourselves the same high standards we had criticized the Keynesians for failing to live up to. But after about five years of doing likelihood ratio tests on rational expectations models, I recall Bob Lucas and Ed Prescott both telling me that those tests were rejecting too many good models.”

Thomas J. Sargent (1943) American economist

Thomas J. Sargent interviewed by George W. Evans & Seppo Honkapohja, Macroeconomic Dynamics, 9, 2005, 561–583.

“A promise is binding in the inverse ratio of the numbers to whom it is made.”

Thomas De Quincey book Confessions of an English Opium-Eater

Appendix.
Confessions of an English Opium-Eater (1822-1856)

“The centre of gravity of any hemisphere [is on the straight line which] is its axis, and divides the said straight line in such a way that the portion of it adjacent to the surface of the hemisphere has to the remaining portion the ratio which 5 has to 3.”

Archimedes book The Method of Mechanical Theorems

Proposition 6.
The Method of Mechanical Theorems

Way

“The concept-systems of antithesis are concepts that are indeed thoroughly determined by negative predicates but are not positively representable.
Just because a precise and complete representation of these concept-systems is impossible, they are inaccessible to direct investigation and elaboration by our reflection. They may, however, be regarded as lying at the limit of the representable, i. e., we can form a concept-system lying within the representable, which passes over into the given system by simple change of magnitude ratio. By abstracting from the ratios of the quantities, the concept-system remains unchanged in case of transition to the limit. At the limit itself, however, some of the correlative concepts of the system lose their susceptibility of being represented, and those, indeed, that mediate the relation between other concepts.”

Bernhard Riemann (1826–1866) German mathematician

General Relation of the Concept System of Thesis and Antithesis
Gesammelte Mathematische Werke (1876)

Lying, Change

“Why have stockholders?… What contribution do they make, entitling them to heirship of half the profits of the industrial system, receivable partly in the form of dividends, and partly in the form of increased market values resulting from undistributed corporate gains? Stockholders toil not, neither do they spin, to earn that reward. They are beneficiaries by position only. Justification for their inheritance must be sought outside classic economic reasoning…. [and] can be founded only upon social grounds… that justification turns on the distribution as well as the existence of wealth. Its force exists only in direct ratio to the number of individuals who hold such wealth. Justification for the stockholder's existence thus depends on increasing distribution within the American population. Ideally the stockholder's position will be impregnable only when every American family has its fragment of that position and of the wealth by which the opportunity to develop individuality becomes fully actualized.”

Adolf A. Berle (1895–1971) American diplomat

1967, p. xxiii
The Modern Corporation and Private Property. 1932/1967

Family, Dependency, Wealth

“The two preponderant forces at work are technological development, which made for a relative increase in demand and hence in the income ratio… and increased access to schooling, which made for a relative decrease.”

Jan Tinbergen (1903–1994) Dutch economist

Source: Income Distribution (1975), p. 35; Cited in: Acemoglu (2000, p. 16)

School

“I'd like to stand up for the rights of people who put everything on their burger -- chutney, mustard, pickle, mustard pickle, tomato sauce… It is common knowledge in my family that I can't tell the difference between a veggie burger and a meat one, because the ratio of burger to pickles is so high. [either misquoted or mis-thought, since not to be able to tell would mean the burger:pickles ratio is so low]”

Terry Pratchett (1948–2015) English author

Usenet

People, Family, Knowledge

“For each human being there is an optimum ratio between change and stasis. Too little change, he grows bored. Too little stability, he panics and loses his ability to adapt.”

Larry Niven book Flash Crowd

Flash Crowd, section 9, in Three Trips in Time and Space (1973), edited by Robert Silverberg, p. 74

Change

“As regards the security of a country against foreign invasion, it is interesting to note that it depends only on the relative, and not the absolute, number of the individuals or magnitude of the forces, and that, if every country should reduce the war-force in the same ratio, the security would remain unaltered. An international agreement with the object of reducing to a minimum the war-force which, in view of the present still imperfect education of the masses, is absolutely indispensable, would, therefore, seem to be the first rational step to take toward diminishing the force retarding human movement.”

Nikola Tesla (1856–1943) Serbian American inventor

The Problem of Increasing Human Energy (1900)

Education, War, Dependency, Country

“In a spiral galaxy, the ratio of dark-to-light matter is about a factor of ten. That's probably a good number for the ratio of our ignorance-to-knowledge. We're out of kindergarten, but only in about third grade.”

Vera Rubin (1928–2016) American astronomer

Light, Knowledge

“Behind every man now alive stand 30 ghosts, for that is the ratio by which the dead outnumber the living.”

Arthur C. Clarke book 2001: A Space Odyssey

1960s
Source: 2001: A Space Odyssey (1968) "Foreword"

Dead

“Geometry has two great treasures: one is the Theorem of Phythagoras, the other the division of a line in extreme and mean ratio. The first we can compare to a mass of gold; the other we may call a precious jewel.”

Johannes Kepler book Mysterium Cosmographicum

As quoted by Karl Fink, Geschichte der Elementar-Mathematik (1890) translated as A Brief History of Mathematics https://books.google.com/books?id=3hkPAAAAIAAJ (1900, 1903) by Wooster Woodruff Beman, David Eugene Smith. Also see Carl Benjamin Boyer, A History of Mathematics (1968). <br class="br">Mysterium Cosmographicum (1596)

“Proposition 18. The earth is to the moon in a ratio greater than that which 1259712 has to 79507, but less than that which 216000 has to 6859.”

Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)
Variant: Proposition 17. The diameter of the earth is to the diameter of the moon in a ratio greater than that which 108 has to 43, but less than that which 60 has to 19.

“We are now in a position to prove the following propositions : —
1. The distance of the sun from the earth is greater than eighteen times, but less than twenty times, the distance of the moon (from the earth); this follows from the hypothesis about the halved moon.
2. The diameter of the sun has the same ratio (as aforesaid) to the diameter of the moon.
3. The diameter of the sun has to the diameter of the earth a ratio greater than that which 19 has to 3, but less than that which 43 has to 6; this follows from the ratio thus discovered between the distances, the hypothesis about the shadow, and the hypothesis that the moon subtends one fifteenth part of a sign of the zodiac.”

Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

Time, Sun, Parting

“John Philoponus (c. 490-570) of Alexandria… refuted Aristotle's theory that the velocities of falling bodies in a given medium are proportional to their weight, making the observation that "if one lets fall simultaneously from the same height two bodies differing greatly in weight, one will find that the ratio of the times of their motion does not correspond to the ratios of their weights, but the difference in time is a very small one." …He also criticized Aristotle's antiperistasis theory of projectile motion, which states that the air displaced by the object flows back to push it from behind. Instead Philoponus concluded that "some incorporeal kinetic power is imparted by the thrower to the object thrown" and that "if an arrow or a stone is projected by force in a void, the same will happen much more easily, nothing being necessary except the thrower."”

John Freely (1926–2017) American physicist

This is the famous "impetus theory," which was revived in medieval Islam and again in fourteenth century Europe, giving rise to the beginning of modern dynamics.
Source: Before Galileo, The Birth of Modern Science in Medieval Europe (2012), p. 8

Time

“The first period embraces the time between the first records of empirical determinations of the ratio of the circumference to the diameter of a circle until the invention of the Differential and Integral Calculus, in the middle of the seventeenth century. This period, in which the ideal of an exact construction was never entirely lost sight of, and was occasionally supposed to have been attained, was the geometrical period, in which the main activity consisted in the approximate determination of π by the calculation of the sides or the areas of regular polygons in- and circum-scribed to the circle. The theoretical groundwork of the method was the Greek method of Exhaustions. In the earlier part of the period the work of approximation was much hampered by the backward condition of arithmetic due to the fact that our present system of numerical notation had not yet been invented; but the closeness of the approximations obtained in spite of this great obstacle are truly surprising. In the later part of this first period methods were devised by which the approximations to the value of π were obtained which required only a fraction of the labour involved in the earlier calculations. At the end of the period the method was developed to so high a degree of perfection that no further advance could be hoped for on the lines laid down by the Greek Mathematicians; for further progress more powerful methods were required.”

E. W. Hobson (1856–1933) British mathematician

Source: Squaring the Circle (1913), pp. 10-11

Hope, Time, Parting, Perfection

“[S]tresses in one direction produce not only a deformation along this direction but also transversally, the relation of both being expressed by the so-called Poisson ratio. However, the consideration… is of no great importance for the first, approximate judgement.”

Eduardo Torroja (1899–1961) Spanish architect

p, 125
Philosophy of Structures (1958)

“The premises being thus settled, I proceed to observe that the concatenation of self-existence, proceeding in a reciprocal duplicate ratio, naturally produces a problematical dialogism, which in some measure proves that the essence of spirituality may be referred to the second predicable.”

Oliver Goldsmith book The Vicar of Wakefield

Source: The Vicar of Wakefield (1766), Ch. 7.

Nature

“In fact, the thickness of the Earth's atmosphere, compared with the size of the Earth, is in about the same ratio as the thickness of a coat of shellac on a schoolroom globe is to the diameter of the globe. That's the air that nurtures us and almost all other life on Earth, that protects us from deadly ultraviolet light from the sun, that through the greenhouse effect brings the surface temperature above the freezing point. (Without the greenhouse effect, the entire Earth would plunge below the freezing point of water and we'd all be dead.) Now that atmosphere, so thin and fragile, is under assault by our technology. We are pumping all kinds of stuff into it. You know about the concern that chlorofluorocarbons are depleting the ozone layer; and that carbon dioxide and methane and other greenhouse gases are producing global warming, a steady trend amidst fluctuations produced by volcanic eruptions and other sources. Who knows what other challenges we are posing to this vulnerable layer of air that we haven't been wise enough to foresee?”

Carl Sagan (1934–1996) American astrophysicist, cosmologist, author and science educator

In Wonder and Skepticism, Skeptical Enquirer (Jan-Feb 1995), 19, No. 1.

Life, Light, Water, Sun

“Ancient DNA available from this time in Anatolia shows no evidence of steppe ancestry similar to that in the Yamnaya (although the evidence here is circumstantial as no ancient DNA from the Hittites themselves has yet been published). This suggests to me that the most likely location of the population that first spoke an Indo-European language was south of the Caucasus Mountains, perhaps in present-day Iran or Armenia, because ancient DNA from people who lived there matches what we would expect for a source population both for the Yamnaya and for ancient Anatolians. If this scenario is right the population sent one branch up into the steppe-mixing with steppe hunter-gatherers in a one-to-one ratio to become the Yamnaya as described earlier- and another to Anatolia to found the ancestors of people there who spoke languages such as Hittite.”

David Reich (geneticist) book Who We Are and How We Got Here

David Reich, Who We Are and How We Got Here: Ancient DNA and the New Science of the Human Past, Knopf Doubleday Publishing Group, 2018, p.120

People, Mountain, Time

“Consider an event, for example the outburst if a nova… Suppose this event is observed from two stars in line with the nova, and suppose further that the two stars are moving uniformly with respect to each other in this line. Let the epoch at which these stars passed by each other be taken as the zero of time measurement, and let an observer A on one of the stars estimate the distance and epoch of the nova outburst to be x units of length and t units of time, respectively. Suppose the other star is moving toward the nova with velocity v relative to A. Let an observer B on the star estimate the distance and epoch of the nova outburst to be x' units of length and t' units of time, respectively. Then the Lorentz formulae, relating x' to t', arex' = \frac {x-vt}{\sqrt{1-\frac{v^2}{c^2}}}; \qquad t' = \frac {t-\frac{vx}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}}
These formulae are… quite general, applying to any event in line with two uniformly moving observers. If we let c become infinite then the ratio of v to c tends to zero and the formulae becomex' = x - vt; \qquad t' = t.”

Gerald James Whitrow (1912–2000) British mathematician

p, 125
The Structure of the Universe: An Introduction to Cosmology (1949)

Star, Time

“Cubism demonstrated in its constructions its modernity in relation to scale, but in painting and contre-relief we have in front of us an absolute scale which is this - forms in their natural size in the ratio 1 : 1. If however we wish to transform the contre-relief into an architectural structure and therefore enlarge it by one hundred times, then the scale ceases to be absolute and becomes relative in the ratio of 1 : 100. Then we get the American statue of liberty in whose head there is room for four men and from whose hand the light streams out.”

El Lissitsky (1890–1941) Soviet artist, designer, photographer, teacher, typographer and architect

1915 - 1925, Suprematism' in World Reconstruction (1920)

Men, Nature, Light, Time

“The Freikorps movement was surprisingly heterogeneous… The 158 Jews members of Bavarian Freikorps amounted to about 0.5 percent of the members of the Bavarian Freikorps movement. This was a figure not out of proportion with the overall ratio of Jews among the Bavarian population,…”

Thomas Weber (historian) (1974) German historian

Source: Becoming Hitler: The Making of a Nazi (2017), pp. 61-62

“Writing improves in direct ratio to the number of things we can keep out of it that shouldn't be there.”

William Zinsser (1922–2015) writer, editor, journalist, literary critic, professor

Source: On Writing Well (Fifth Edition, orig. pub. 1976), Chapter 3, Clutter, p. 13

“Proposition 15. The diameter of the sun has, to the diameter of the earth a ratio greater than that which 19 has to 3, but less than that which 43 has to 6.”

Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)
Variant: Proposition 10. The sun has to the moon a ratio greater than that which 5832 has to 1, but less than that which 8000 has to 1.

Sun

“I wasn't aware of Chargaff's rules when he said them, but the effect on me was quite electric because I realized immediately that if you had this sort of scheme that John Griffith was proposing, of adenine being paired with thymine, and guanine being paired with cytosine, then you should get Chargaff's rules. I was very excited, but I didn't actually tell Chargaff because it was something I was doing with John Griffith…. This was very exciting, and we thought "ah ha!" and we realized - I mean what anyone who is familiar with the history of science ought to realize - that when you have one-to-one ratios, it means things go to together. And how on Earth no one pointed out this simple fact in those years, I don't know.”

Francis Crick (1916–2004) British molecular biologist, biophysicist, neuroscientist; co-discoverer of the structure of DNA

The DNA Story (1973, film, VSM Productions)

History, Science

“Perhaps the most precious possession of man is his abiding awareness of the Analogy of Proper Proportionality, the key to all metaphysical insight, and perhaps the very condition of consciousness itself. This analogical awareness is constituted of a perpetual play of ratios among ratios. A is to B, what C is to D, which is to say the ratio between A and B, is proportionable to the ratio between C and D, there being a ratio between these ratios, as well, this lively awareness of the most exquisite delicacy depends upon there being no connection whatsoever between the components. If A were linked to B, or C to D, mere logic would take the place of analogical perception, thus one of the penalties paid for literacy and a high visual culture is a strong tendency to encounter all things through a rigorous storyline, as it were. Paradoxically, connected spaces and situations exclude participation, whereas discontinuity affords room for involvement. Visual space is connected and creates detachment or non-involvement. It also tends to exclude the participation of the other senses.”

Marshall McLuhan (1911–1980) Canadian educator, philosopher, and scholar-- a professor of English literature, a literary critic, and a …

Source: 1960s, Through the Vanishing Point (1968), p.240

Penalty, Sense, Strong, Dependency

“In Quintilian’s expositions there appears a note of melancholy when he discovers that toward the decline of life, the ratio sneaks in gradually, choking up insight into the original.”

Ernesto Grassi (1902–1991) Italian philosopher

Source: Rhetoric as Philosophy (1980), p. 51

Life, Appearance

“The concept of 'number' in its most elementary sense as the signless integer appears to be an immediate abstraction from quantitative reality subjected to processes of counting and measurement. Vulgar fractions arise from division of a quantity into equal parts. But in what sense is zero a number? Are there negative numbers? Are there numbers corresponding to incommensurable ratios? Each question requires for its solution a fresh exercise of that kind of creative imagination which we call mathematical abstraction.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

Exercises, Imagination, Mathematics, Question

“Archimedes is said to have requested his friends and relatives to place upon his tomb a representation of a cylinder circumscribing a sphere within it, together with the inscription giving the ratio (3/2) which the cylinder bears to the sphere; from which we may infer that he himself regarded the discovery of this ration as his greatest achievement.”

Thomas Little Heath (1861–1940) British civil servant and academic

p, 125
Achimedes (1920)

“How do wealth-income and capital-output ratios evolve in the long run, and why? Until recently it was difficult to properly address this question, for one simple reason: national accounts were mostly about ﬂows, not stocks. Economists had at their disposal a large body of historical series on ﬂows of output, income and consumption – but limited data on stocks of assets and liabilities. When needed, for example for growth accounting exercises, estimates of capital stocks were typically obtained by cumulating past ﬂows of saving and investment. This is ﬁne for some purposes, but severely limits the set of questions one can ask.”

Thomas Piketty (1971) French economist

Piketty, Thomas, and Gabriel Zucman. Capital is back: Wealth-income ratios in rich countries, 1700-2010 http://piketty.pse.ens.fr/files/PikettyZucman2013WP.pdf. Centre for Economic Policy Research, 2013.

Exercises, Question, Past, Wealth

“One reason nature pleases us is its endless use of a few simple principles: the cube-square law; fractals; spirals; the way that waves, wheels, trig functions, and harmonic oscillators are alike; the importance of ratios between small primes; bilateral symmetry; Fibonacci series, golden sections, quantization, strange attractors, path-dependency, all the things that show up in places where you don’t expect them…these rules work with and against each other ceaselessly at all levels, so that out of their intrinsic simplicity comes the rich complexity of the world around us. That tension—between the simple rules that describe the world and the complex world we see—is itself both simple in execution and immensely complex in effect. Thus exactly the levels, mixtures, and relations of complexity that seem to be hardwired into the pleasure centers of the human brain—or are they, perhaps, intrinsic to intelligence and perception, pleasant to anything that can see, think, create?—are the ones found in the world around us.”

John Barnes book Mother of Storms

Source: Mother of Storms (1994), pp. 470-471

Pleasure, World, Law, Way

“Christianity, for Blake, bled from Jesus his real substance as prophet/poet. Reason, or Ratio, on the other side, born with the scientific revolution, divided the world from the self, the human from the natural, the inside from the outside, and the outside itself into ever finer degrees of manipulable parts.”

Curtis White (1951) American academic

"The spirit of disobedience: an invitation to resistance"

World, Nature, Parting

“We hold that efficiency cannot itself be a "value." Rather, it operates in the interstices of a value system; it prescribes relationships (ratios or proportions) among parts of the value system; it receives its "moral content" by syntax, by absorption. Things are not simply "efficient" or "inefficient." They are efficient or inefficient for given purposes, and efficiency for one purpose may mean inefficiency for another.”

Dwight Waldo (1913–2000) American political scientist

Source: The Administrative State, 1948, p. 202

Parting

“Had population and food increased in the same ratio, it is probable that man might never have emerged from the savage state.”

Thomas Robert Malthus (1766–1834) British political economist

Source: An Essay on The Principle of Population (First Edition 1798, unrevised), Chapter XVIII, paragraph 11, lines 16-17

Food

“People are lucky and unlucky not according to what they get absolutely, but according to the ratio between what they get and what they have been led to expect.”

Samuel Butler (1835–1902) novelist

Lucky and Unlucky
The Note-Books of Samuel Butler (1912), Part XIV - Higgledy-Piggledy

People

“It is above all the impersonal and economically rationalized (but for this very reason ethically irrational) character of purely commercial relationships that evokes the suspicion, never clearly expressed but all the more strongly felt, of ethical religions. For every purely personal relationship of man to man, of whatever sort and even including complete enslavement, may be subjected to ethical requirements and ethically regulated. This is true because the structures of these relationships depend upon the individual wills of the participants, leaving room in such relations for manifestations of the virtue of charity. But this is not the situation in the realm of economically rationalised relationships, where personal control is exercised in inverse ratio to the degree of rational differentiation of the economic structure.”

Max Weber (1864–1920) German sociologist, philosopher, and political economist

Source: Sociology of Religion (1922), pp. 216-217

Religion, Exercises, Dependency, Personality

“Media, by altering the environment, evoke in us unique ratios of sense perception…When these ratios change, men change.”

Marshall McLuhan (1911–1980) Canadian educator, philosopher, and scholar-- a professor of English literature, a literary critic, and a …

1960s, The Medium is the Message (1967)

Men, Sense, Change

“Belief in the stable state serves primarily to protect us from apprehension of the threats inherent in change. Belief in stability is a means of maintaining stability, or at any rate the illusion of stability. But the most threatening situations are those that confront us with uncertainty, and by ‘uncertainty’, I don’t mean risk, which is a probability ratio which we all know how to handle, particularly those who are managers of industry. We can deal with risk.”

Donald A. Schön (1930–1997) American academic

Donald Schon " REITH LECTURES 1970: Change and Industrial Society: Lecture 1: The Loss of the Stable State http://downloads.bbc.co.uk/rmhttp/radio4/transcripts/1970_reith1.pdf" at the BBC, 15 November 1970 – Radio 4; cited in: Richard Duane Carter (1981) Future challenges of management education. p. 102

Change

“Music is nothing but ratios and harmonic math, anyways.”

Andrew Sega (1975) musician from America

Static Line interview, 1998

Music

“Solidarity can grow only in inverse ratio to personality.”

Émile Durkheim (1858–1917) French sociologist (1858-1917)

Source: The Division of Labor in Society (1893), p. 129 (in 1933 edition)

Personality

“In a country where feeling for art is not one of the national characteristics, it is particularly difficult to arrive at a common understanding of the term "art". There are many obstacles in the way, and some of them are imposed by the mere existence of such a body as the Royal Academy, for lacking any intuition in this matter of art, the majority of people turn to that institution for guidance, and naturally assume that any work receiving its blessing must be a work of art in the strict meaning of the word, and consequently the artistic quality of a painting is, in the popular estimation, measured in ratio to its degree of photographic realism.”

James Bolivar Manson (1879–1945) British artist

Manson, J.B. The Tate Gallery, p. 8, Thomas Nelson and Sons.

People, Art, Way, Feeling

“Our visual discrimination is far better than our linguistic system at dealing with complex ratios and continuous variations in space, line, shape, and color.”

Jay Lemke (1946) American academic

Source: Textual politics: Discourse and social dynamics, 1995, p. 110

Color

“We started out in the middle ages creating music which had certain desirable physical properties (for example, a major chord sounds "nice" because the frequencies are in integer ratios to each other). And then as society evolved, we created these emotional contexts for certain instruments and progressions. Major-chord arpeggios sound "happy", minor chords sound "sad", chromatic scales can sound "scary", et cetera. In the 20th century, film soundtracks reinforced this point as people associated certain kinds of music with certain visual and emotional experiences. It's a giant feedback loop, really; once you grow up in a given culture, it leaves this musical fingerprint on you which colors your experiences.”

Andrew Sega (1975) musician from America

Andrew Sega Shrine interview, 2011

People, Age, Sadness, Music

“The following Treatise… has been endeavoured to make the theory of limits, or ultimate ratios… the sole foundation of the science, without any aid whatsoever from the theory of series, or algebraical expansions. I am not aware that any work exists in which this has been avowedly attempted, and I have been the more encouraged to make the trial from observing that the objections to the theory of limits have usually been founded either upon the difficulty of the notion itself, or its unalgebraical character, and seldom or never upon anything not to be defined or not to be received in the conception of a limit…”

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

Advertisement, p.3
The Differential and Integral Calculus (1836)

Science

“The last decade has seen a steady increase in the application of concepts from the theory of games to the study of evolution. Fields as diverse as sex ratio theory, animal distribution, contest behaviour and reciprocal altruism have contributed to what is now emerging as a universal way of thinking about phenotypic evolution.”

John Maynard Smith book Evolution and the Theory of Games

Source: Evolution and the Theory of Games (1973), p. vii.

Sex, Way, Game, Thinking

“It is some improvement that for married couples – or male-female couples in general – the fertility indicator expressing the nation’s demographic situation has risen from 1.2 to 1.44, and this is promising, but 1.44 is still very far from 2. In order to feel safe demographically, the average statistical ratio of children to Hungarian couples should be 2.1. In practice this is hard to implement, but this is the average figure we should have. Until we reach that point, Hungarians must be seen as an endangered species demographically; and the people – but the Government above all – should understand the imperative which is implicit in this.”

Viktor Orbán (1963) Hungarian politician, chairman of Fidesz

Children, People, Feeling, Understanding

“I have lately spent some Thoughts relative to the Nature of Light, whether it be subject to the common Laws of Motion. In this particular Newton seems to contradict himself. For in his Principia Sect. 14th he applies the common Laws of Motion to account for Reflection and Refraction, as he does also in one Part of his Optics where he proves the Sine of Incid. to Sine Refr, in a given in a given Ratio. But in another Part he says, “nothing more is requisite for producing all the Variety of Colours and Degrees of Refrangibility than that the Rays of Light be Bodies of different Sizes, the least of which may make Violet, and the Greatest the Red"; this manifestly is not consistent with the Theory of Motion applied to Bodies, where the Magnitude of the Bodies is of no Consequence. Now it is evident that if the common Theory of Motion can be applied to Light, the Red Light must have had the greatest Velocity before Incidence, as it suffers the least Deviation, for if the Vels of all the Difft colour'd Light were equal before Incidence, they must by Newton's Principia Sect. Sect. 8. Prop. 1. have continued equal after, and therefore must have suffered the same Deviation. The Determination of this Point seems to be of considerable Importance, as we so often apply the Theory of Motion to Light.”

Samuel Vince (1749–1821) British mathematician, astronomer and physicist

As quoted in: Russell McCormmach (2011) Weighing the World: The Reverend John Michell of Thornhill. p. 193

Law, Nature, Light, Suffering

“Over a period of 500 years the City has supported deregulation at every turn. The consequences of this are massive. You had fraudulent products – the cause of the crash – debt being repackaged as an asset and then being used as leverage. The assets they held and credit they generated were on a ratio of 50-1. There was no effective regulation of this, no effective oversight. They have been exposed by the bailout. They have refused more than ten years of requests from us [London Citizens UK organisation] and suddenly they agree to meet. I think they are concerned that the political parties will move to a more manufacturing, less financially-based economy.”

Maurice Glasman, Baron Glasman (1961) British philosopher

Red Pepper magazine, 22 November 2009 http://www.redpepper.org.uk/confronting-the-city/

Support, Thinking

“Population, when unchecked, increases in a geometrical ratio, Subsistence, increases only in an arithmetical ratio.”

Thomas Robert Malthus (1766–1834) British political economist

Source: An Essay on The Principle of Population (First Edition 1798, unrevised), Chapter I, paragraph 18, lines 1-2

“Leisure stands in a perpendicular position with respect to the working process — in just the same way as the "simple gaze" of intellectus does not consist in the "duration" (so to speak) of ratios working-out process, but instead cuts through it at the perpendicular (the ancients compared the ratio with time, the intellectus with the "always now" of eternity).”

Josef Pieper (1904–1997) German philosopher

Source: Leisure, the Basis of Culture (1948), Leisure, the Basis of Culture, p. 34

Way, Time

“In the last few years there has been a harvest of books and lectures about the "Mysterious Universe." The inconceivable magnitudes with which astronomy deals produce a sense of awe which lends itself to a poetic and philosophical treatment. "When I consider thy heavens, the work of thy hands, the moon and the starts, whuch thou hast ordained: what is man that thou art mindful of him? The literary skill with which this branch of science has been exploited compels one's admiration, but alos, a little, one's sense of the ridiculous. For other facts than those of astronomy, oother disciplines than of mathematics, can produce the same lively feelings of awe and reverence: the extraordinary finenness of their adjustments to the world outside: the amazing faculties of the human mind, of which we know neither whence it comes not whither it goes. In some fortunate people this reverence is produced by the natural bauty of a landscape, by the majesty of an ancient building, by the heroism of a rescue party, by poetry, or by music. God is doubtless a Mathematician, but he is also a Physiologist, an Engineer, a Mother, an Architect, a Coal Miner, a Poet, and a Gardener. Each of us views things in his own peculiar war, each clothes the Creator in a manner which fits into his own scheme. My God, for instance, among his other professions, is an Inventor: I picture him inventing water, carbon dioxide, and haemoglobin, crabs, frogs, and cuttle fish, whales and filterpassing organisms ( in the ratio of 100,000,000,000,000,000,000,000 to 1 in size), and rejoicing greatly over these weird and ingenious things, just as I rejoice greatly over some simple bit of apparatus. But I would nor urge that God is only an Inventor: for inventors are apt, as those who know them realize, to be very dull dogs. Indeed, I should be inclined rather to imagine God to be like a University, with all its teachers and professors together: not omittin the students, for he obviously possesses, judging from his inventions, that noblest human characteristic, a sense of humour.”

Archibald Hill (1886–1977) English physiologist and biophysicist

The Ethical Dilemma of Science and Other Writings https://books.google.com.mx/books?id=zaE1AAAAIAAJ&printsec=frontcover#v=onepage&q&f=false (1960, Cap 1. Scepticism and Faith, p. 41)

God, War, People, Books

“Proposition 14. The straight line joined from the centre of the earth to the centre of the moon has to the straight line cut off from the axis towards the centre of the moon by the straight line subtending the (circumference) within the earth's shadow a ratio greater than that which 675 has to 1.”

Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

“Arithmetic and geometry, according to Plato, are the two wings of the mathematician. The object indeed of all mathematical questions, is to determine the ratios of numbers, or of magnitudes; and it may even be said, to continue the comparison of the ancient philosopher, that arithmetic is the mathematician's right wing; for it is an incontestable truth, that geometrical determinations would, for the most part, present nothing satisfactory to the mind, if the ratios thus determined could not be reduced to numerical ratios. This justifies the common practice, which we shall here follow, of beginning with arithmetic.”

Jacques Ozanam (1640–1718) French mathematician

Source: Recreations in Mathematics and Natural Philosophy, (1803), p. 2

Truth, Mathematics, Question, Parting

“Proposition 13. The straight line subtending the portion intercepted within the earth's shadow of the circumference of the circle in which the extremities of the diameter of the circle dividing the dark and the bright portions in the moon move is less than double of the diameter of the moon, but has to it a ratio greater than that which 88 has to 45; and it is less than 1/9th part of the diameter of the sun, but has to it a ratio greater than that which 22 has to 225. But it has to the straight line drawn from the centre of the sun at right angles to the axis and meeting the sides of the cone a ratio greater than that which 979 has to 10125.”

Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

Sun, Parting

“He knows that every piece of selfknowledge which one cannot keep to oneself makes one smaller and smaller, he knows that he who cannot keep silent his wishes to be recognized in the greatness of his selfknowledge which is no selfknowledge if it cannot be kept silent, and one becomes hypersensitive one feels betrayed because one wants to be recognized by people, one becomes ridiculous ambitious in inverse ratio to ones selfknowledge”

Max Frisch book Gantenbein

Gantenbein (1964)

People, Feeling

“Getting to near zero marginal cost and nearly free goods and services is a function of advances in productivity. Productivity is “a measure of productive efficiency calculated as the ratio of what is produced to what is required to produce it.” If the cost of producing an additional good or service is nearly zero, that would be the optimum level of productivity.”

Jeremy Rifkin (1945) American economist

The Zero Marginal Cost Society: The Internet of Things, the Collaborative Commons, and the Eclipse of Capitalism (2014)

“Knowing that training is little more than breaking down muscle, I figured that what rebuilds that same muscle must be a major factor for recovery and therefore quicker improvement. If I was able to recover from each workout faster, I would be able to schedule them closer together and therefore train more than my competition. I would improve faster. As I suspected, food was the answer—high-quality, nutrient-dense, alkaline-forming, easily digestible food in proper proportions … Nutrition has a dramatic effect on recovery—that was unmistakable. … The result was astounding. Not only did my recovery time plummet but my energy level, strength-to-weight ratio, and endurance shot up. … On the cellular level, this diet was able to speed the renewal of muscle tissue. That meant that following this diet would actually help the body regenerate more frequently, suggesting that it could help reduce biological age.”

Brendan Brazier (1975) Canadian triathlete, publisher, writer, editor

Introduction
The Thrive Diet

Age, Food, Time, Help

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

Bernhard Riemann (1826–1866) German mathematician

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

Imagination, Parting, Dependency

“What is essential to the idea of a slave? We primarily think of him as one who is owned by another. To be more than nominal, however, the ownership must be shown by control of the slave's actions — a control which is habitually for the benefit of the controller. That which fundamentally distinguishes the slave is that he labours under coercion to satisfy another's desires. The relation admits of sundry gradations. Remembering that originally the slave is a prisoner whose life is at the mercy of his captor, it suffices here to note that there is a harsh form of slavery in which, treated as an animal, he has to expend his entire effort for his owner's advantage. Under a system less harsh, though occupied chiefly in working for his owner, he is allowed a short time in which to work for himself, and some ground on which to grow extra food. A further amelioration gives him power to sell the produce of his plot and keep the proceeds. Then we come to the still more moderated form which commonly arises where, having been a free man working on his own land, conquest turns him into what we distinguish as a serf; and he has to give to his owner each year a fixed amount of labour or produce, or both: retaining the rest himself. Finally, in some cases, as in Russia before serfdom was abolished, he is allowed to leave his owner's estate and work or trade for himself elsewhere, under the condition that he shall pay an annual sum. What is it which, in these cases, leads us to qualify our conception of the slavery as more or less severe? Evidently the greater or smaller extent to which effort is compulsorily expended for the benefit of another instead of for self-benefit. If all the slave's labour is for his owner the slavery is heavy, and if but little it is light. Take now a further step. Suppose an owner dies, and his estate with its slaves comes into the hands of trustees; or suppose the estate and everything on it to be bought by a company; is the condition of the slave any the better if the amount of his compulsory labour remains the same? Suppose that for a company we substitute the community; does it make any difference to the slave if the time he has to work for others is as great, and the time left for himself is as small, as before? The essential question is—How much is he compelled to labour for other benefit than his own, and how much can he labour for his own benefit? The degree of his slavery varies according to the ratio between that which he is forced to yield up and that which he is allowed to retain; and it matters not whether his master is a single person or a society. If, without option, he has to labour for the society, and receives from the general stock such portion as the society awards him, he becomes a slave to the society.”

Herbert Spencer (1820–1903) English philosopher, biologist, sociologist, and prominent classical liberal political theorist

The Man versus the State (1884), The Coming Slavery

Life, Food, Communication, Idea

“When the ratio of nutrients to calories is high, fat melts away, and health is restored. The more nutrient-dense food you consume, the more you'll be satisfied with fewer calories, and the less you'll crave fat and high-calorie foods.”

Joel Fuhrman (1953) Family Physician and author

Introduction
The End of Dieting (2014)

Health, Food

“No one forced me to focus on technology. I just did it because I had a passion for it. When I started, there weren’t a lot of women role models. It was Carol Bartz, Judy Estrin. I think there’s been a lot of progress since then, and I think that if women have a passion and really want to succeed, they can. On a relative basis, the male-female ratio is certainly skewed to men, but on an absolute basis, there are a lot of very successful women in technology.”

Mary Meeker (1959) American venture capitalist and securities analyst

Interview with Wired: "The Indomitable Mary Meeker" https://www.wired.com/2012/09/mf-mary-meeker/ (21 September 2012)

Women, Men, Thinking, Passion

“Every measurable thing except numbers is imagined in the manner of a continuous quantity. Therefore, for the mensuration of such a thing, it is necessary that points, lines, and surfaces, or their properties, be imagined. For in them… measure or ratio is initially found… Therefore, every intensity which can be acquired successively ought to be imagined by a straight line perpendicularly erected on some point of the space or subject of the intensible thing, e. g., a quality… And since the quantity or ratio of lines is better known and is more readily conceived by us—nay the line is in the first species of continua, therefore such intensity ought to be imagined by lines… Therefore, equal intensities are designated by equal lines, a double intensity by a double line, and always in the same way if one proceeds proportionally.”

Nicole Oresme (1323–1382) French philosopher

Tractatus de Configurationibus et Qualitatibus et Motuum (c. 1350)

Way, Imagination, Success

“The line of march of all spirits is always progressive, never retrograde. They raise themselves gradually In the hierarchy of existence they never descend from the rank at which they have once arrived. In the course of their different corporeal existences they may descend in rank as men, but not as spirits. Thus the soul of one who has been at the pinnacle of earthly power may, in a subsequent incarnation, animate the humblest day-labourer, and vice versa; for the elevation of ranks among men is often In the inverse ratio of that of the moral sentiments. Herod was a king, and Jesus, a carpenter.”

Allan Kardec (1804–1869) systematizer of Spiritism

Source: The Spirits' Book, p. 128.

Men, Soul, Animals

“The Pythagoreans discovered the existence of incommensurable lines, or of irrationals. This was, doubtless, first discovered with reference to the diagonal of a square which is incommensurable with the side, being in the ratio to it of √2 to 1. The Pythagorean proof of this particular case survives in Aristotle and in a proposition interpolated in Euclid's Book X.; it is by a reductio ad absurdum proving that, if the diagonal is commensurable with the side, the same number must be both odd and even. This discovery of the incommensurable… showed that the theory of proportion invented by Pythagoras was not of universal application and therefore that propositions proved by means of it were not really established…. The fatal flaw thus revealed in the body of geometry was not removed till Eudoxus discovered the great theory of proportion (expounded in Euclid's Book V.), which is applicable to incommensurable as well as to commensurable magnitudes.”

Thomas Little Heath (1861–1940) British civil servant and academic

p, 125
Achimedes (1920)

Books, Universe

“Dark Energy. It can be found in the observable Universe. Found in ratios of 75% more than any other substance. Dark Energy. It can be found in religious extremists, in cheerleaders. To come to the conclusion that Dark signifies mean and malevolent would define 75% of the Universe as an evil force. Alternatively, to think that some cheerleaders don't have razors in their snatch is to be foolishly unarmed.”

Tori Amos (1963) American singer

American Doll Posse, biography by Pip

Thinking, Universe, Evil

“Plato argued that in a good society the ratio of the richest to the poorest person's income should be at the most four to one.”

Harvey S. Rosen (1949) American economist

Source: Public Finance - International Edition - Sixth Edition, Chapter 7, Income Redistribution Conceptual Issues, p. 147

Personality

“The definite mass ratios involved in reactions suggested a convenient method for counting the number of atoms of each element participating in the reaction. These results, summarized as the laws of chemical combination, provided overwhelming, if indirect, evidence for the existence of atoms and molecules.”

David W. Oxtoby (1951) President of Pomona college

Principles of Modern Chemistry (7th ed., 2012), Ch. 1 : The Atom in Modern Chemistry

Law

“Reason, or the ratio of all we have already known, is not the same that it shall be when we know more.”

William Blake (1757–1827) English Romantic poet and artist

There Is No Natural Religion (1788)
1780s

“As the natural sciences have developed to encompass increasingly complex systems, scientific rationality has become ever more statistical, or probabilistic. The deterministic classical mechanics of the enlightenment was revolutionized by the near-equilibrium statistical mechanics of late 19th century atomists, by quantum mechanics in the early 20th century, and by the far-from-equilibrium complexity theorists of the later 20th century. Mathematical neo-Darwinism, information theory, and quantitative social sciences compounded the trend. Forces, objects, and natural types were progressively dissolved into statistical distributions: heterogeneous clouds, entropy deviations, wave functions, gene frequencies, noise-signal ratios and redundancies, dissipative structures, and complex systems at the edge of chaos.”

Nick Land (1962) British philosopher

"Statistical Mentality" https://web.archive.org/web/20110718052233/http://www.thatsmags.com/shanghai/index.php/article/detail/522/statistical-mentality (2011)

Mathematics, Nature, Science

“The Definition in the Elements, according to Clavius, is this: Magnitudes are said to be in the same Reason [ratio], a first to a second, and a third to a fourth, when the Equimultiples of the first and third according to any Multiplication whatsoever are both together either short of, equal to, or exceed the Equimultiples of the second and fourth, if those be taken, which answer one another…. Such is Euclid’s Definition of Proportions; that scare-Crow at which the over modest or slothful Dispositions of Men are generally affrighted: they are modest, who distrust their own Ability, as soon as a Difficulty appears, but they are slothful that will not give some Attention for the learning of Sciences; as if while we are involved in Obscurity we could clear ourselves without Labour. Both of 300 which Sorts of Persons are to be admonished, that the former be not discouraged, nor the latter refuse a little Care and Diligence when a Thing requires some Study.”

Isaac Barrow (1630–1677) English Christian theologian, and mathematician

Source: Mathematical Lectures (1734), p. 388

Men, Study, Learning, Appearance

“I think there are things of which I and the people who have worked with me can feel deservedly proud. They include restoring Russia's territorial integrity, strengthening the state, progress towards establishing a multiparty system, strengthening the parliamentary system, restoring the Armed Forces' potential and, of course, developing the economy. As you know, our economy has been growing by 6.9 percent a year on average over this time, and our GDP has increased by 7.7 percent over the first four months of this year alone.
When I began my work in the year 2000, 30 percent of our population was living below the poverty line. There has been a two-fold drop in the number of people living below the poverty line since then and the figure today is around 15 percent. By 2009-2010, we will bring this figure down to 10 percent, and this will bring us in line with the European average.
We had enormous debts, simply catastrophic for our economy, but we have paid them off in full now. Not only have we paid our debts, but we now have the best foreign debt to GDP ratio in Europe. Our gold and currency reserve figures are well known: in 2000, they stood at just $12 billion and we had a debt of more than 100 percent of GDP, but now we have the third-biggest gold and currency reserves in the world and they have increased by $90 billion over the first four months of this year alone.
During the 1990s and even in 2000-2001, we had massive capital flight from Russia with $15 billion, $20 billion or $25 billion leaving the country every year. Last year we reversed this situation for the first time and had capital inflow of $41 billion. We have already had capital inflow of $40 billion over the first four months of this year. Russia's stock market capitalisation showed immense growth last year and increased by more than 50 percent. This is one of the best results in the world, perhaps even the best. Our economy was near the bottom of the list of world economies in terms of size but today it has climbed to ninth place and in some areas has even overtaken some of the other G8 countries' economies. This means that today we are able to tackle social problems. Real incomes are growing by around 12 percent a year. Real income growth over the first four months of this year came to just over 18 percent, while wages rose by 11-12 percent.
Looking at the problems we have yet to resolve, one of the biggest is the huge income gap between the people at the top and the bottom of the scale. Combating poverty is obviously one of our top priorities in the immediate term and we still have to do a lot to improve our pension system too because the correlation between pensions and the average wage is still lower here than in Europe. The gap between incomes at the top and bottom end of the scale is still high here – a 15.6-15.7-fold difference. This is less than in the United States today (they have a figure of 15.9) but more than in the UK or Italy (where they have 13.6-13.7). But this remains a big gap for us and fighting poverty is one of our biggest priorities.”

Vladimir Putin (1952) President of Russia, former Prime Minister

When asked in June 2007 at the interview with G8 journalists about main achievements of his presidency http://web.archive.org/web/20070607221025/http://www.kremlin.ru/eng/speeches/2007/06/04/2149_type82916_132772.shtml.

People, World, Feeling, Problem

“There's hardly a more effective way to solve the problems we face in our educational system than to reduce class size. A ratio of no more than 17 students per teacher ensures more 1-on-1 contact, better classroom discipline, you name it.”

Jesse Ventura (1951) American politician and former professional wrestler

I Ain't Got Time To Bleed (1999)

Education, Way, Problem, Teachers

“The arrangement I worked out with Fordham was that I would do my alternate service there as a conscientious objector, working with McLuhan directly during the 1967–1968 academic year and then experimenting with video for 1968–1969. It was terrific. I had an office two doors away from his. McLuhan would stop me in the hall and with great excitement tell me about a book he read the night before on the sense ratio of Russian peasants. Once he invited me into his office to talk about a paper I had written about war. He sat on this couch, spun around, lay on his back, held the paper up, read a bit from it, put it down, and continued to lie on the couch for a good hour, free-associating.”

Paul Ryan (video artist) (1943–2013) American video artist

Scott, Felicity D. Mark Wasiuta, and Paul Ryan. " Guerrilla Warfare Revisited: From Klein Worms to Relational Circuits http://www.earthscore.org/pdf/grey44.pdfCybernetic," Grey Room 44, Summer 2011

War, Lie, Books, Sense

“I can now present the first fundamental law of capitalism, which links the capital stock to the flow of income from capital. The capital/income ratio β is related in a simple way to the share of income from capital in national income, denoted α. The formula is
α = r × β
Where r is the rate of return on capital.
For example, if β=600% and r = 5%, then α = r × β = 30%.
In other words, if national wealth represents the equivalent of six years of national income, and the rate of return on capital is 5 percent per year, then capital’s share in national income is 30 percent.”

Thomas Piketty book Capital in the Twenty-First Century

Source: Capital in the Twenty-First Century (2013), p. 52.

Law, Way, Wealth

“Infanticide and infant neglect exist in inverse ratio to the accessibility of abortion services.”

Sheri S. Tepper (1929–2016) American fiction writer

Source: Gibbon's Decline & Fall (1996), Chapter 10 (p. 173)

“Proposition 12. The diameter of the circle which divides the dark and the bright portions in the moon is less than the diameter of the moon, but has to it a ratio greater than that which 89 has to 90.”

Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

“They are unfettered by precedent in the administration of justice. Customs have been handed down by ages of repetition, but the punishment for ignoring a custom is a matter for individual treatment by a jury of the culprit’s peers, and I may say that justice seldom misses fire, but seems rather to rule in inverse ratio to the ascendency of law. In one respect at least the Martians are a happy people; they have no lawyers.”

Edgar Rice Burroughs book A Princess of Mars

Source: A Princess of Mars (1917), Chapter 9

People, Age, Justice, Law

“Organized religion, he saw, back in the day, had been purely a signal-to-noise proposition, at once the medium and the message, a one-channel universe. For Europe, that channel was Christian, and broadcasting from Rome, but nothing could be broadcast faster than a man could travel on horseback. There was a hierarchy in place, and a highly organized methodology of top-down signal dissemination, but the time lag enforced by tech-lack imposed a near-disastrous ratio, the noise of heresy constantly threatening to overwhelm the signal.”

William Gibson book Spook Country

Source: Spook Country‎ (2007), Ch. 23, Two Moors, p. 117

Religion, Travel, Universe, Time

“Gravitation is not only similar to inertia in its generality, it is also measured by the same number… the mass. The inertial mass is what Newton calls the "quantity of matter": it is a measure for the resistance offered by a body to a force trying to alter its state of motion. It might be called the "passive mass." The gravitational mass, on the other hand, is a measure of the force exerted by the body in attracting other bodies. We might call it the "active" mass. The equality of active and passive, or gravitational and inertial, mass was in Newton's system a most remarkable accidental co-incidence, something like a miracle. Newton himself decidedly felt it as such, and made experiments to verify it, by swinging a pendulum with a hollow bob which could be filled with different materials. The force acting on the pendulum is proportional to its gravitational mass, the inertia to its inertial mass: the period of its swing thus depends on the ratio between these two masses. The fact that the period is always the same therefore proves that the gravitational and inertial masses are equal.”

Willem de Sitter (1872–1934) Dutch cosmologist

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

Dependency

“By one estimate, 90% of international transactions were accounted for by trade before 1970, and only 10% by capital flows. Today, despite a vast increase in global trade, that ratio has been reversed, with 90% of transactions accounted for by financial flows not directly related to trade in goods and services.”

Didier Sornette (1957) French scientist

Source: Why Stock Markets Crash - Critical Events in Complex Systems (2003), Chapter 8, Bubbles And Crashes In Emergent Markets, p. 304.

“If there's four Vietcong in a village with knives and punji sticks, we'll bring in a B-52. And I think, sometimes we need to learn to fight smarter instead of to fight richer. And this is what I mean, you know, education, "oh, education's expensive;" no it's not, books are cheap, (the) internet's cheap, we can fight smarter, we can learn. So, that's where resource-to-kill-ratio comes from.”

Max Brooks (1972) American author

Lecture of Opportunity | Max Brooks: World War Z https://www.youtube.com/watch?v=-nGG5E04cog

Books, Education, Thinking, Learning

“Does the interiorization of media such as letters alter the ratio among our senses and change mental processes?”

Marshall McLuhan (1911–1980) Canadian educator, philosopher, and scholar-- a professor of English literature, a literary critic, and a …

Source: 1960s, The Gutenberg Galaxy (1962), p. 28

Sense, Change

“There is a predicament of ‘the girl child’. From Life expectancy to literary rates, from school enrollment ratios, from employment to inheritance, there is hardly any society in the world where women are treated at par with men. This wrong and unfortunate discrimination is extended to the girl child.”

Shankar Dayal Sharma (1918–1999) Indian politician

Source: Commissions and Omissions by Indian Presidents and Their Conflicts with the Prime Ministers Under the Constitution: 1977-2001, P.255.

Life, Women, Men, World

“In shows selected by artists where there is no consciousness of sex, as in the American Abstract Artist Shows which began in the late 1930's or the Artists Annuals of the early 1950's, the ratio [between male and female artists presented there] seemed to be between one third and one quarter women. The only way to arrive at a true ratio, I suppose, would again be to have artist-juried shows.”

Elaine de Kooning (1918–1989) American painter

n.p.
1950 - 1971, Why Have There Been No Great Women Artists' - Rosalyn Drexler with Elaine de Kooning (1971)

Women, Sex, Way

“The refraction of light agrees with the grand principle that Nature always uses the simplest means to accomplish its effects. From this principle, can be derived whenever light passes from one medium to another, the ratio of the sine of the angle of refraction to the sine of the angle of refraction equals the inverse ratio of the speeds at which light moves in each medium.
But this "budget", this expense of action that Nature minimizes in the refraction of light, is it also minimized in the direct propagation and reflection of light? Yes, it always has the smallest possible value.”

Pierre Louis Maupertuis (1698–1759) French mathematician, philosopher and man of letters

Accord de différentes loix de la nature qui avoient jusqu’ici paru incompatibles (1744)

Nature, Light, Speed

“One has been led to the conception of electrons, i. e. of extremely small particles, charged with electricity, which are present in immense numbers in all ponderable bodies, and by whose distribution and motions we endeavor to explain all electric and optical phenomena that are not confined to the free ether…. according to our modern views, the electrons in a conducting body, or at least a certain part of them, are supposed to be in a free state, so that they can obey an electric force by which the positive particles are driven in one, and the negative electrons in the opposite direction. In the case of a non-conducting substance, on the contrary, we shall assume that the electrons are bound to certain positions of equilibrium. If, in a metallic wire, the electrons of one kind, say the negative ones, are travelling in one direction, and perhaps those of the opposite kind in the opposite direction, we have to do with a current of conduction, such as may lead to a state in which a body connected to one end of the wire has an excess of either positive or negative electrons. This excess, the charge of the body as a whole, will, in the state of equilibrium and if the body consists of a conducting substance, be found in a very thin layer at its surface.
In a ponderable dielectric there can likewise be a motion of the electrons. Indeed, though we shall think of each of them as haying a definite position of equilibrium, we shall not suppose them to be wholly immovable. They can be displaced by an electric force exerted by the ether, which we conceive to penetrate all ponderable matter… the displacement will immediately give rise to a new force by which the particle is pulled back towards its original position, and which we may therefore appropriately distinguish by the name of elastic force. The motion of the electrons in non-conducting bodies, such as glass and sulphur, kept by the elastic force within certain bounds, together with the change of the dielectric displacement in the ether itself, now constitutes what Maxwell called the displacement current. A substance in which the electrons are shifted to new positions is said to be electrically polarized.
Again, under the influence of the elastic forces, the electrons can vibrate about their positions of equilibrium. In doing so, and perhaps also on account of other more irregular motions, they become the centres of waves that travel outwards in the surrounding ether and can be observed as light if the frequency is high enough. In this manner we can account for the emission of light and heat. As to the opposite phenomenon, that of absorption, this is explained by considering the vibrations that are communicated to the electrons by the periodic forces existing in an incident beam of light. If the motion of the electrons thus set vibrating does not go on undisturbed, but is converted in one way or another into the irregular agitation which we call heat, it is clear that part of the incident energy will be stored up in the body, in other terms [words] that there is a certain absorption. Nor is it the absorption alone that can be accounted for by a communication of motion to the electrons. This optical resonance, as it may in many cases be termed, can likewise make itself felt even if there is no resistance at all, so that the body is perfectly transparent. In this case also, the electrons contained within the molecules will be set in motion, and though no vibratory energy is lost, the oscillating particles will exert an influence on the velocity with which the vibrations are propagated through the body. By taking account of this reaction of the electrons we are enabled to establish an electromagnetic theory of the refrangibility of light, in its relation to the wave-length and the state of the matter, and to form a mental picture of the beautiful and varied phenomena of double refraction and circular polarization.
On the other hand, the theory of the motion of electrons in metallic bodies has been developed to a considerable extent…. important results that have been reached by Riecke, Drude and J. J. Thomson… the free electrons in these bodies partake of the heat-motion of the molecules of ordinary matter, travelling in all directions with such velocities that the mean kinetic energy of each of them is equal to that of a gaseous molecule at the same temperature. If we further suppose the electrons to strike over and over again against metallic atoms, so that they describe irregular zigzag-lines, we can make clear to ourselves the reason that metals are at the same time good conductors of heat and of electricity, and that, as a general rule, in the series of the metals, the two conductivities change in nearly the same ratio. The larger the number of free electrons, and the longer the time that elapses between two successive encounters, the greater will be the conductivity for heat as well as that for electricity.”

Hendrik Lorentz (1853–1928) Dutch physicist

Source: The Theory of Electrons and Its Applications to the Phenomena of Light and Radiant Heat (1916), Ch. I General principles. Theory of free electrons, pp. 8-10

Beauty, Way, Travel, Communication

“A distinguished writer (Siméon Denis Poisson) has thus stated the fundamental definitions of the science:
:"The probability of an event is the reason we have to believe that it has taken place, or that it will take place."
:"The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible" (equally like to happen).
From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary.”

George Boole (1815–1864) English mathematician, philosopher and logician

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 243-4; As cited in: "George Boole (1815–64)" in: Oxford Dictionary of Scientific Quotations, Edited by W. F. Bynum and Roy Porter, January 2006

Mathematics, Knowledge, Thinking, Science

“In developing his theory of gravitation, Newton assigned to every material body another property which is called its gravitational mass. Gravitational mass determines the force exerted by the body on other bodies, and so its function appears to be quite distinct from that of inertial mass. Nevertheless, the two are found to be identical in magnitude. Newton made experiments to verify this remarkable equality by swinging a pendulum with a bob which could be made with different materials. The period of the swing depended on the ratio of the inertial and gravitational masses of the pendulum, but in all cases it was found to be the same… In 1890 Eötvös made a much more refined test with the aid of a… torsion balance. Repeated experiments showed that inertial mass and gravitational mass were equal to within one part in 100 million. Einstein suggested that this was because inertia and gravitation are identical.”

Gerald James Whitrow (1912–2000) British mathematician

p, 125
The Structure of the Universe: An Introduction to Cosmology (1949)

Appearance, Parting, Dependency

“THE ORIGIN OF ART: The discrepancy between physical fact and psychic effect. THE CONTENT OF ART: Visual information of our reaction to life. THE MEASURE OF ART: The ratio of effort to effect. THE AIM OF ART: Revelation and evocation of vision.”

Josef Albers (1888–1976) German-American artist and educator

'The Origin of Art'
Homage to the square' (1964)

Life, Art, Effort

“His days were full of meaningless ceremonies whose sacredness appeared to be in inverse ratio to their comprehensibility or usefulness.”

Mervyn Peake (1911–1968) English writer, artist, poet and illustrator

Source: Gormenghast (1950), Chapter 80 (p. 802)