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Home > Category Index for Science Quotations > Category Index E > Category: Equality

Equality Quotes (31 quotes)

A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.
In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.
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A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.
In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.
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A “critic” is a man who creates nothing and thereby feels qualified to judge the work of creative men. There is logic in this; he is unbiased—he hates all creative people equally.
In Time Enough for Love: The Lives of Lazarus Long (1973), 365.
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Among innumerable footsteps of divine providence to be found in the works of nature, there is a very remarkable one to be observed in the exact balance that is maintained, between the numbers of men and women; for by this means is provided, that the species never may fail, nor perish, since every male may have its female, and of proportionable age. This equality of males and females is not the effect of chance but divine providence, working for a good end.
'An Argument for Divine Providence, taken from the Constant Regularity observ’d in the Births of both Sexes', Philosophical Transactions of the Royal Society, 1710-12, 27,186.
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Any opinion as to the form in which the energy of gravitation exists in space is of great importance, and whoever can make his opinion probable will have, made an enormous stride in physical speculation. The apparent universality of gravitation, and the equality of its effects on matter of all kinds are most remarkable facts, hitherto without exception; but they are purely experimental facts, liable to be corrected by a single observed exception. We cannot conceive of matter with negative inertia or mass; but we see no way of accounting for the proportionality of gravitation to mass by any legitimate method of demonstration. If we can see the tails of comets fly off in the direction opposed to the sun with an accelerated velocity, and if we believe these tails to be matter and not optical illusions or mere tracks of vibrating disturbance, then we must admit a force in that direction, and we may establish that it is caused by the sun if it always depends upon his position and distance.
Letter to William Huggins (13 Oct 1868). In P. M. Hannan (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 1862-1873, 451-2.
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As the first monogamian family has improved greatly since the commencement of civilization, and very sensibly in our times, it is at least supposable that it is capable of still further improvement until the equality of the sexes is attained.
As quoted in Charles H. Seaholm, The Kelts and the Vikings (1974), 48.
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Free men are aware of the imperfection inherent in human affairs, and they are willing to fight and die for that which is not perfect. They know that basic human problems can have no final solutions, that our freedom, justice, equality, etc. are far from absolute, and that the good life is compounded of half measures, compromises, lesser evils, and gropings toward the perfect. The rejection of approximations and the insistence on absolutes are the manifestation of a nihilism that loathes freedom, tolerance, and equity.
In The Temper of Our Time (1967), 103.
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I am an adherent of the ideal of democracy, although I well know the weaknesses of the democratic form of government. Social equality and economic protection of the individual appeared to me always as the important communal aims of the state.
…...
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I will sette as I doe often in woorke use, a paire of paralleles, or gemowe times of one lengthe, thus: =, bicause noe 2 thynges, can be moare equalle.
Explaining the sign he initiated to mean equality.
The Whetstone of Witte (1557). The word gemowe (related to the name Gemini) means twins.)
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If one proves the equality of two numbers a and b by showing first that “a is less than or equal to b” and then “a is greater than or equal to b”, it is unfair, one should instead show that they are really equal by disclosing the inner ground for their equality.
As quoted, without citation, in biography by Hermann Wehl, Emmy Noether (1935), 18.
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In science, all facts no matter how trivial, enjoy democratic equality.
In 'The Fact in Fiction', On the Contrary: Articles of Belief (1961, 1966), 266.
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Inequality is the cause of all local movements. There is no rest without equality.
From Codex Atlanticus, folio 288 back a. In Edward McCurdy, The Notebooks of Leonardo Da Vinci (1939, 1958), Vol. 1, 89. [Compare with Newton’s Laws of Motion. Da Vinci died in 1519; Newton was born over 120 years later. Webmaster, despite much time looking, has not yet found the corresponding quote in the John Paul Richter translation. Can you help? —Webmaster]
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It is a happy world after all. The air, the earth, the water teem with delighted existence. In a spring noon, or a summer evening, on whichever side I turn my eyes, myriads of happy beings crowd upon my view. “The insect youth are on the wing.” Swarms of new-born flies are trying their pinions in the air. Their sportive motions, their wanton mazes, their gratuitous activity testify their joy and the exultation they feel in their lately discovered faculties … The whole winged insect tribe, it is probable, are equally intent upon their proper employments, and under every variety of constitution, gratified, and perhaps equally gratified, by the offices which the author of their nature has assigned to them.
Natural Theology: or, Evidences of the Existence and Attributes of The Deity, Collected from the Appearances of Nature (1802), 490-1.
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It is from this absolute indifference and tranquility of the mind, that mathematical speculations derive some of their most considerable advantages; because there is nothing to interest the imagination; because the judgment sits free and unbiased to examine the point. All proportions, every arrangement of quantity, is alike to the understanding, because the same truths result to it from all; from greater from lesser, from equality and inequality.
In On the Sublime and Beautiful, Part 3, sect. 2.
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Modern science has vindicated the natural equality of man.
Sybil: Or, the Two Nations (1907), 263
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My visceral perception of brotherhood harmonizes with our best modern biological knowledge ... Many people think (or fear) that equality of human races represents a hope of liberal sentimentality probably squashed by the hard realities of history. They are wrong. This essay can be summarized in a single phrase, a motto if you will: Human equality is a contingent fact of history. Equality is not true by definition; it is neither an ethical principle (though equal treatment may be) nor a statement about norms of social action. It just worked out that way. A hundred different and plausible scenarios for human history would have yielded other results (and moral dilemmas of enormous magnitude). They didn’t happen.
…...
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Not a single visible phenomenon of cell­division gives even a remote suggestion of qualitative division. All the facts, on the contrary, indicate that the division of the chromatin is carried out with the most exact equality.
The Cell in Development and Inheritance (1896), 306.
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Scientists are going to discover many subtle genetic factors in the makeup of human beings. Those discoveries will challenge the basic concepts of equality on which our society is based. Once we can say that there are differences between people that are easily demonstrable at the genetic level, then society will have to come to grips with understanding diversity—and we are not prepared for that.
(1983).
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So true is it that unnatural generally means only uncustomary, and that everything which is usual appears natural. The subjection of women to men being a universal custom, any departure from it quite naturally appears unnatural.
The Subjection of Women (1869), 270.
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Strictly speaking, it is really scandalous that science has not yet clarified the nature of number. It might be excusable that there is still no generally accepted definition of number, if at least there were general agreement on the matter itself. However, science has not even decided on whether number is an assemblage of things, or a figure drawn on the blackboard by the hand of man; whether it is something psychical, about whose generation psychology must give information, or whether it is a logical structure; whether it is created and can vanish, or whether it is eternal. It is not known whether the propositions of arithmetic deal with those structures composed of calcium carbonate [chalk] or with non-physical entities. There is as little agreement in this matter as there is regarding the meaning of the word “equal” and the equality sign. Therefore, science does not know the thought content which is attached to its propositions; it does not know what it deals with; it is completely in the dark regarding their proper nature. Isn’t this scandalous?
From opening paragraph of 'Vorwort', Über die Zahlen des Herrn H. Schubert (1899), iii. ('Foreword', On the Numbers of Mr. H. Schubert). Translated by Theodore J. Benac in Friedrich Waismann, Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics (1959, 2003), 107. Webmaster added “[chalk]”.
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The attitude of the intellectual community toward America is shaped not by the creative few but by the many who for one reason or another cannot transmute their dissatisfaction into a creative impulse, and cannot acquire a sense of uniqueness and of growth by developing and expressing their capacities and talents. There is nothing in contemporary America that can cure or alleviate their chronic frustration. They want power, lordship, and opportunities for imposing action. Even if we should banish poverty from the land, lift up the Negro to true equality, withdraw from Vietnam, and give half of the national income as foreign aid, they will still see America as an air-conditioned nightmare unfit for them to live in.
In 'Some Thoughts on the Present', The Temper of Our Time (1967), 107.
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The greatest spiritual revolutionary Western history, Saint Francis, proposed what he thought was an alternative Christian view of nature and man’s relation to it: he tried to substitute the idea of the equality of creatures, including man, for the idea of man’s limitless rule of creation. He failed. Both our present science and our present technology are so tinctured with orthodox Christian arrogance toward nature that no solution for our ecologic crisis can be expected from them alone. Since the roots of our trouble are so largely religious, the remedy must also be essentially religious, whether we call it that or not. We must rethink and refeel our nature and destiny. The profoundly religious, but heretical, sense of the primitive Franciscans for the spiritual autonomy of all parts of nature may point a direction. I propose Francis as a patron saint for ecologists.
In The Historical Roots of our Ecologic Crisis (1967), 1207.
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The whole art of making experiments in chemistry is founded on the principle: we must always suppose an exact equality or equation between the principles of the body examined and those of the products of its analysis.
From Traité Élémentaire de Chimie (1789), 140. Translation as given in James Riddick Partington, A Short History of Chemistry (1960), 124. This is an alternate translation of part of the same passage on this page that begins “We may lay it down as an incontestible axiom…”
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Therefore, the causes assigned to natural effects of the same kind must be, so far as possible, the same.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Book 3, Rule. of Reasoning in Philosophy, Rule 2, 795.
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Those who see their lives as spoiled and wasted crave equality and fraternity more than they do freedom. If they clamor for freedom, it is but freedom to establish equality and uniformity. The passion for equality is partly a passion for anonymity: to be one thread of the many which make up a tunic; one thread not distinguishable from the others. No one can then point us out, measure us against others and expose our inferiority.
In The True Believer: Thoughts on the Nature of Mass Movements (1951), 31-32.
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We cannot expect in the immediate future that all women who seek it will achieve full equality of opportunity. But if women are to start moving towards that goal, we must believe in ourselves or no one else will believe in us; we must match our aspirations with the competence, courage and determination to succeed.
From a speech given to students in Stockholm, Sweden, Oct 1977 as quoted in The Decade of Women (1980) by Suzanne Levine and Harriet Lyons
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We may lay it down as an incontestible axiom, that, in all the operations of art and nature, nothing is created; an equal quantity of matter exists both before and after the experiment; the quality and quantity of the elements remain precisely the same; and nothing takes place beyond changes and modifications in the combination of these elements. Upon this principle the whole art of performing chemical experiments depends: We must always suppose an exact equality between the elements of the body examined and those of the products of its analysis.
Elements of Chemistry trans. Robert. Kerr, (1790, 5th Ed. 1802), Vol. 1, 226.
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Whenever there is a great deal of energy in one region and very little in a neighboring region, energy tends to travel from the one region to the other, until equality is established. This whole process may be described as a tendency towards democracy.
In 'Science and Religion', collected in Al Seckel (ed.), >Bertrand Russell on God and Religion (1986), 175.
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[Professor W.L. Bragg asserts that] In sodium chloride there appear to be no molecules represented by NaCl. The equality in number of sodium and chlorine atoms is arrived at by a chess-board pattern of these atoms; it is a result of geometry and not of a pairing-off of the atoms.
In Henry E. Armstrong, 'Poor Common Salt!', Nature (1927), 120, 478.
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[The blame for the future 'plight of civilization] must rest on scientific men, equally with others, for being incapable of accepting the responsibility for the profound social upheavals which their own work primarily has brought about in human relationships.
Quoted in Thaddeus Trenn, 'The Central Role of Energy in Soddy's Holistic and Critical Approach to Nuclear Science, Economics, and Social Responsibility', British Journal for the History of Science (1979), 42, 261.
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[To the cultures of Asia and the continent of Africa] it is the Western impact which has stirred up the winds of change and set the processes of modernization in motion. Education brought not only the idea of equality but also another belief which we used to take for granted in the West—the idea of progress, the idea that science and technology can be used to better human conditions. In ancient society, men tended to believe themselves fortunate if tomorrow was not worse than today and anyway, there was little they could do about it.
Lecture at State University of Iowa (6 Apr 1961). In Barbara Ward, The Unity of the Free World (1961), 12.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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