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Home > Category Index for Science Quotations > Category Index T > Category: Type

Type Quotes (52 quotes)

...the study of butterflies—creatures selected as the types of airiness and frivolity—instead of being despised, will some day be valued as one of the most important branches of Biological science.
From The Naturalist on the River Amazons: A record of Adventures, Habits of Animals, Sketches of Brazilian and Indian life, and Aspects of Nature under the Equator, During Eleven Years of Travel (1864), 413.
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Mathematical truth has validity independent of place, personality, or human authority. Mathematical relations are not established, nor can they be abrogated, by edict. The multiplication table is international and permanent, not a matter of convention nor of relying upon authority of state or church. The value of π is not amenable to human caprice. The finding of a mathematical theorem may have been a highly romantic episode in the personal life of the discoverer, but it cannot be expected of itself to reveal the race, sex, or temperament of this discoverer. With modern means of widespread communication even mathematical notation tends to be international despite all nationalistic tendencies in the use of words or of type.
Anonymous
In 'Light Thrown on the Nature of Mathematics by Certain Aspects of Its Development', Mathematics in General Education (1940), 256. This is the Report of the Committee on the Function of Mathematics in General Education of the Commission on Secondary School Curriculum, which was established by the Executive Board of the Progressive Education Association in 1932.
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All important unit operations have much in common, and if the underlying principles upon which the rational design and operation of basic types of engineering equipment depend are understood, their successful adaptation to manufacturing processes becomes a matter of good management rather than of good fortune.
In William H. Walker, Warren K. Lewis and William H. MacAdams, The Principles of Chemical Engineering (1923), Preface to 1st. edition, v.
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Among both the Northern and Eastern Hamites are to be found some of the most beautiful types of humanity.
In An Introduction to Physical Anthropology (1960), 456.
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And as I had my father’s kind of mind—which was also his mother’s—I learned that the mind is not sex-typed.
Blackberry Winter: My Earlier Years (1973), 54.
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Are God and Nature then at strife,
That Nature lends such evil dreams?
So careful of the type she seems,
So careless of the single life; ...
'So careful of the type', but no.
From scarped cliff and quarried stone
She cries, 'A thousand types are gone:
I care for nothing, all shall go' ...
Man, her last work, who seemed so fair,
Such splendid purpose in his eyes,
Who rolled the psalm to wintry skies,
Who built him fanes of fruitless prayer,
Who trusted God was love indeed
And love Creation's final law—
Tho’ Nature red in tooth and claw
With ravine, shrieked against his creed...
In Memoriam A. H. H. (1850), Cantos 56-57. Collected in Alfred Tennyson and William James Rolfe (ed.) The Poetic and Dramatic works of Alfred, Lord Tennyson (1898), 176.
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Are God and Nature then at strife,
That Nature lends such evil dreams?
So careful of the type she seems,
So careless of the single life…
So careful of the type, but no.
From scarped cliff and quarried stone
She cries, “A thousand types are gone;
I care for nothing, all shall go.”
From poem, 'In Memoriam A.H.H.' written between 1833-50, and first published anonymously in 1850. Collected in Poetical Works of Alfred Tennyson (1860), Vol.2, 64.
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Before delivering your lectures, the manuscript should be in such a perfect form that, if need be, it could be set in type. Whether you follow the manuscript during the delivery of the lecture is purely incidental. The essential point is that you are thus master of the subject matter.
Advice to his son. As quoted in Ralph Oesper, The Human Side Of Scientists (1975), 185.
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Catastrophe Theory is—quite likely—the first coherent attempt (since Aristotelian logic) to give a theory on analogy. When narrow-minded scientists object to Catastrophe Theory that it gives no more than analogies, or metaphors, they do not realise that they are stating the proper aim of Catastrophe Theory, which is to classify all possible types of analogous situations.
From 'La Théorie des catastrophes État présent et perspective', as quoted in Erick Christopher Zeeman, (ed.), Catastrophe Theory: Selected Papers, 1972-1977 (1977), 637, as cited in Martin Krampe (ed.), Classics of Semiotics (1987), 214.
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Common to all these types is the anthropomorphic character of their conception of God. In general, only individuals of exceptional endowments, and exceptionally high-minded communities, rise to any considerable extent above this level. But there is a third stage of religious experience which belongs to all of them, even though it is rarely found in a pure form: I shall call it cosmic religious feeling. It is very difficult to elucidate this feeling to anyone who is entirely without it, especially as there is no anthropomorphic conception of God corresponding to it.
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Creative activity could be described as a type of learning process where teacher and pupil are located in the same individual.
In Drinkers of Infinity: Essays, 1955-1967 (1969), 235.
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Descartes is the completest type which history presents of the purely mathematical type of mind—that in which the tendencies produced by mathematical cultivation reign unbalanced and supreme.
In An Examination of Sir William Hamilton’s Philosophy (1878), 626.
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For the sake of persons of ... different types, scientific truth should be presented in different forms, and should be regarded as equally scientific, whether it appears in the robust form and the vivid coloring of a physical illustration, or in the tenuity and paleness of a symbolic expression.
…...
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I am quite aware that we have just now lightheartedly expelled in imagination many excellent men who are largely, perhaps chiefly, responsible for the buildings of the temple of science; and in many cases our angel would find it a pretty ticklish job to decide. But of one thing I feel sure: if the types we have just expelled were the only types there were, the temple would never have come to be, any more than a forest can grow which consists of nothing but creepers. For these people any sphere of human activity will do, if it comes to a point; whether they become engineers, officers, tradesmen, or scientists depends on circumstances.
…...
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I cannot conceive of a God who rewards and punishes his creatures, or has a will of the type of which we are conscious in ourselves. An individual who should survive his physical death is also beyond my comprehension, nor do I wish it otherwise; such notions are for the fears or absurd egoism of feeble souls.
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I feel that the recent ruling of the United States Army and Navy regarding the refusal of colored blood donors is an indefensible one from any point of view. As you know, there is no scientific basis for the separation of the bloods of different races except on the basis of the individual blood types or groups. (1942)
Spencie Love, One Blood: The Death and Resurrection of Charles R. Drew (1996), 155-56, quoting as it appeared in Current Biography (1944), 180.
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I want to note that, because there is the aforementioned difference between mountain and mountain, it will be appropriate, to avoid confusion, to distinguish one [type] from another by different terms; so I shall call the first Primary and the second Secondary.
De' Crostacei e degli altri Marini Corpi che si truovana su' monti (1740), 263, trans. Ezio Vaccari.
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In the end, science as we know it has two basic types of practitioners. One is the educated man who still has a controlled sense of wonder before the universal mystery, whether it hides in a snail’s eye or within the light that impinges on that delicate organ. The second kind of observer is the extreme reductionist who is so busy stripping things apart that the tremendous mystery has been reduced to a trifle, to intangibles not worth troubling one’s head about.
In 'Science and the Sense of the Holy,' The Star Thrower (1978), 190.
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In the printed page the only real things are the paper and the ink; the white spaces play the same part in aiding the eye to take in the meaning of the print as do the black letters.
From Under the Apple-Trees (1916), 302.
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It is tautological to say that an organism is adapted to its environment. It is even tautological to say that an organism is physiologically adapted to its environment. However, just as in the case of many morphological characters, it is unwarranted to conclude that all aspects of the physiology of an organism have evolved in reference to a specific milieu. It is equally gratuitous to assume that an organism will inevitably show physiological specializations in its adaptation to a particular set of conditions. All that can be concluded is that the functional capacities of an organism are sufficient to have allowed persistence within its environment. On one hand, the history of an evolutionary line may place serious constraints upon the types of further physiological changes that are readily feasible. Some changes might require excessive restructuring of the genome or might involve maladaptive changes in related functions. On the other hand, a taxon which is successful in occupying a variety of environments may be less impressive in individual physiological capacities than one with a far more limited distribution.
In W.R. Dawson, G.A. Bartholomew, and A.F. Bennett, 'A Reappraisal of the Aquatic Specializations of the Galapagos Marine Iguana (Amblyrhynchus cristatus)', Evolution (1977), 31, 891.
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It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule. This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.
In Leibnitz (1884), 44-45. [The first sentence is reworded to better introduce the quotation. —Webmaster]
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It [mathematics] is in the inner world of pure thought, where all entia dwell, where is every type of order and manner of correlation and variety of relationship, it is in this infinite ensemble of eternal verities whence, if there be one cosmos or many of them, each derives its character and mode of being,—it is there that the spirit of mathesis has its home and its life.
Is it a restricted home, a narrow life, static and cold and grey with logic, without artistic interest, devoid of emotion and mood and sentiment? That world, it is true, is not a world of solar light, not clad in the colours that liven and glorify the things of sense, but it is an illuminated world, and over it all and everywhere throughout are hues and tints transcending sense, painted there by radiant pencils of psychic light, the light in which it lies. It is a silent world, and, nevertheless, in respect to the highest principle of art—the interpenetration of content and form, the perfect fusion of mode and meaning—it even surpasses music. In a sense, it is a static world, but so, too, are the worlds of the sculptor and the architect. The figures, however, which reason constructs and the mathematic vision beholds, transcend the temple and the statue, alike in simplicity and in intricacy, in delicacy and in grace, in symmetry and in poise. Not only are this home and this life thus rich in aesthetic interests, really controlled and sustained by motives of a sublimed and supersensuous art, but the religious aspiration, too, finds there, especially in the beautiful doctrine of invariants, the most perfect symbols of what it seeks—the changeless in the midst of change, abiding things hi a world of flux, configurations that remain the same despite the swirl and stress of countless hosts of curious transformations.
In 'The Universe and Beyond', Hibbert Journal (1904-1906), 3, 314.
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Its [science’s] effectiveness is almost inevitable because it narrows the possibility of refutation and failure. Science begins by saying it can only answer this type of question and ends by saying these are the only questions that can be asked. Once the implications and shallowness of this trick are fully realised, science will be humbled and we shall be free to celebrate ourselves once again.
From Understanding the Present: An Alternative History of Science (2004), 249.
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I’m a little different from all those conservation types.
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Many persons have inquired concerning a recent message of mine that “a new type of thinking is essential if mankind is to survive and move to higher levels.”
From interview with Michael Amrine, 'The Real Problem is in the Hearts of Men', New York Times Magazine, (23 Jun 1946), 7. See more of the message from which Einstein quoted himself, see the longer quote that begins, “Our world faces a crisis as yet unperceived…,” on the Albert Einstein Quotes page of this website.
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Mathematics in its widest signification is the development of all types of formal, necessary, deductive reasoning.
In Universal Algebra (1898), Preface, vi.
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May not Music be described as the Mathematic of sense, Mathematic as Music of the reason? the soul of each the same! Thus the musician feels Mathematic, the mathematician thinks Music, Music the dream, Mathematic the working life each to receive its consummation from the other when the human intelligence, elevated to its perfect type, shall shine forth glorified in some future Mozart-Dirichlet or Beethoven-Gauss a union already not indistinctly foreshadowed in the genius and labours of a Helmholtz!
In paper read 7 Apr 1864, printed in 'Algebraical Researches Containing a Disquisition On Newton’s Rule for the Discovery of Imaginary Roots', Philosophical Transactions of the Royal Society of London (1865), 154, 613, footnote. Also in Collected Mathematical Papers, Vol. 2, 419.
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Men of science belong to two different types—the logical and the intuitive. Science owes its progress to both forms of minds. Mathematics, although a purely logical structure, nevertheless makes use of intuition. Among the mathematicians there are intuitives and logicians, analysts and geometricians. Hermite and Weierstrass were intuitives. Riemann and Bertrand, logicians. The discoveries of intuition have always to be developed by logic.
In Man the Unknown (1935), 123.
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Modern anthropology has taught us, through comparative investigation of so-called primitive cultures, that the social behavior of human beings may differ greatly, depending upon prevailing cultural patterns and the types of organisation which predominate in society. It is on this that those who are striving to improve the lot of man may ground their hopes: human beings are not condemned, because of their biological constitution, to annihilate each other or to be at the mercy of a cruel, self-inflicted fate.
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Now it is a well-known principle of zoological evolution that an isolated region, if large and sufficiently varied in its topography, soil, climate and vegetation, will give rise to a diversified fauna according to the law of adaptive radiation from primitive and central types. Branches will spring off in all directions to take advantage of every possible opportunity of securing food. The modifications which animals undergo in this adaptive radiation are largely of mechanical nature, they are limited in number and kind by hereditary, stirp or germinal influences, and thus result in the independent evolution of similar types in widely-separated regions under the law of parallelism or homoplasy. This law causes the independent origin not only of similar genera but of similar families and even of our similar orders. Nature thus repeats herself upon a vast scale, but the similarity is never complete and exact.
'The Geological and Faunal Relations of Europe and America during the Tertiary Period and the Theory of the Successive Invasions of an African Fauna', Science (1900), 11, 563-64.
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Our world faces a crisis as yet unperceived by those possessing power to make great decisions for good or evil. The unleashed power of the atom has changed everything save our modes of thinking and we thus drift toward unparalleled catastrophe. We scientists who released this immense power have an overwhelming responsibility in this world life-and-death struggle to harness the atom for the benefit of mankind and not for humanity’s destruction. … We need two hundred thousand dollars at once for a nation-wide campaign to let people know that a new type of thinking is essential if mankind is to survive and move toward higher levels. This appeal is sent to you only after long consideration of the immense crisis we face. … We ask your help at this fateful moment as a sign that we scientists do not stand alone.
In 'Atomic Education Urged by Einstein', New York Times (25 May 1946), 13. Extract from a telegram (24 May 1946) to “several hundred prominent Americans”, signed by Albert Einstein as Chairman, with other members, of the Emergency Committee of Atomic Scientists. It was also signed by the Federation of American Scientists.
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Since natural selection demands only adequacy, elegance of design is not relevant; any combination of behavioural adjustment, physiological regulation, or anatomical accommodation that allows survival and reproduction may be favoured by selection. Since all animals are caught in a phylogenetic trap by the nature of past evolutionary adjustments, it is to be expected that a given environmental challenge will be met in a variety of ways by different animals. The delineation of the patterns of the accommodations of diverse types of organisms to the environment contributes much of the fascination of ecologically relevant physiology.
In 'The roles of physiology and behaviour in the maintenance of homeostasis in the desert environment.', Symposia of the Society for Experimental Biology (1964), 11.
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The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognisable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past. One must not think then that the old-fashioned theories have been sterile and vain.
The Value of Science (1905), in The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method(1946), trans. by George Bruce Halsted, 208.
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The assumptions of population thinking are diametrically opposed to those of the typologist. The populationist stresses the uniqueness of everything in the organic world. What is true for the human species,–that no two individuals are alike, is equally true for all other species of animals and plants ... All organisms and organic phenomena are composed of unique features and can be described collectively only in statistical terms. Individuals, or any kind of organic entities, form populations of which we can determine the arithmetic mean and the statistics of variation. Averages are merely statistical abstractions, only the individuals of which the populations are composed have reality. The ultimate conclusions of the population thinker and of the typologist are precisely the opposite. For the typologist, the type (eidos) is real and the variation. an illusion, while for the populationist the type (average) is an abstraction and only the variation is real. No two ways of looking at nature could be more different.
Darwin and the Evolutionary Theory in Biology (1959), 2.
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The book of Nature is the book of Fate. She turns the gigantic pages,—leaf after leaf,—never re-turning one. One leaf she lays down, a floor of granite; then a thousand ages, and a bed of slate; a thousand ages, and a measure of coal; a thousand ages, and a layer of marl and mud: vegetable forms appear; her first misshapen animals, zoophyte, trilobium, fish; then, saurians,—rude forms, in which she has only blocked her future statue, concealing under these unwieldy monsters the fine type of her coming king. The face of the planet cools and dries, the races meliorate, and man is born. But when a race has lived its term, it comes no more again.
From 'Fate', collected in The Complete Works of Ralph Waldo Emerson, Volume 6: The Conduct of Life (1860), 15. This paragraph is the prose version of his poem, 'Song of Nature'.
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The Jewish scriptures admirably illustrate the development from the religion of fear to moral religion, a development continued in the New Testament. The religions of all civilized peoples, especially the peoples of the Orient, are primarily moral religions. The development from a religion of fear to moral religion is a great step in peoples’ lives. And yet, that primitive religions are based entirely on fear and the religions of civilized peoples purely on morality is a prejudice against which we must be on our guard. The truth is that all religions are a varying blend of both types, with this differentiation: that on the higher levels of social life the religion of morality predominates.
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The name is not the thing named but is of different logical type, higher than that of the thing named.
In Angels Fear: Towards an Epistemology of the Sacred (1979, 1987), 209.
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The original Upper Paleolithic people would, if they appeared among us today, be called Caucasoid, in the sense that they lacked the particular traits we associate with Negroid and Mongoloid types.
From The Structure of Personality in its Environment (1979), 341.
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The Patent-Office Commissioner knows that all machines in use have been invented and re-invented over and over; that the mariner’s compass, the boat, the pendulum, glass, movable types, the kaleidoscope, the railway, the power-loom, etc., have been many times found and lost, from Egypt, China and Pompeii down; and if we have arts which Rome wanted, so also Rome had arts which we have lost; that the invention of yesterday of making wood indestructible by means of vapor of coal-oil or paraffine was suggested by the Egyptian method which has preserved its mummy-cases four thousand years.
In Lecture, second in a series given at Freeman Place Chapel, Boston (Mar 1859), 'Quotation and Originality', Letters and Social Aims (1875, 1917), 178-179.
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The value of mathematical instruction as a preparation for those more difficult investigations, consists in the applicability not of its doctrines but of its methods. Mathematics will ever remain the past perfect type of the deductive method in general; and the applications of mathematics to the simpler branches of physics furnish the only school in which philosophers can effectually learn the most difficult and important of their art, the employment of the laws of simpler phenomena for explaining and predicting those of the more complex. These grounds are quite sufficient for deeming mathematical training an indispensable basis of real scientific education, and regarding with Plato, one who is … as wanting in one of the most essential qualifications for the successful cultivation of the higher branches of philosophy
In System of Logic, Bk. 3, chap. 24, sect. 9.
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There are now three types of scientists: experimental, theoretical, and computational.
Quoted by Victor F. Weisskopf, 'One Hundred Years of the Physical Review', in H. Henry Stroke, Physical Review: The First Hundred Years: a Selection of Seminal Papers and Commentaries, Vol. 1, 13.
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There are two types of mind … the mathematical, and what might be called the intuitive. The former arrives at its views slowly, but they are firm and rigid; the latter is endowed with greater flexibility and applies itself simultaneously to the diverse lovable parts of that which it loves.
In Discours sur les passions de l’amour (1653).
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There is only one type of science and the various fields are chapters of the same book.
As quoted in Lewis Wolpert and Alison Richards (eds.), Passionate Minds: The Inner World of Scientists (1997), 2.
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This fundamental discovery that all bodies owe their origin to arrangements of single initial corpuscular type is the beacon that lights the history of the universe to our eyes. In its own way, matter obeyed from the beginning that great law of biology to which we shall have to recur time and time again, the law of “complexification.”
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 48. Originally published in French as Le Phénomene Humain (1955).
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To write the true natural history of the world, we should need to be able to follow it from within. It would thus appear no longer as an interlocking succession of structural types replacing one another, but as an ascension of inner sap spreading out in a forest of consolidated instincts. Right at its base, the living world is constituted by conscious clothes in flesh and bone.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 151. Originally published in French as Le Phénomene Humain (1955).
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We dissect nature along lines laid down by our native languages. The categories and types that we isolate from the world of phenomena we do not find there because they stare every observer in the face; on the contrary, the world is presented in a kaleidoscopic flux of impressions which has to be organized by our minds—and this means largely by the linguistic systems in our minds.
In Four Articles on Metalinguistics (1950), 5.
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What a type of happy family is the family of the Sun! With what order, with what harmony, with what blessed peace, do his children the planets move around him, shining with light which they drink in from their parent’s in at once upon him and on one another!
…...
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While the method of the natural sciences is... analytic, the method of the social sciences is better described as compositive or synthetic. It is the so-called wholes, the groups of elements which are structurally connected, which we learn to single out from the totality of observed phenomena... Insofar as we analyze individual thought in the social sciences the purpose is not to explain that thought, but merely to distinguish the possible types of elements with which we shall have to reckon in the construction of different patterns of social relationships. It is a mistake... to believe that their aim is to explain conscious action ... The problems which they try to answer arise only insofar as the conscious action of many men produce undesigned results... If social phenomena showed no order except insofar as they were consciously designed, there would indeed be no room for theoretical sciences of society and there would be, as is often argued, only problems of psychology. It is only insofar as some sort of order arises as a result of individual action but without being designed by any individual that a problem is raised which demands a theoretical explanation... people dominated by the scientistic prejudice are often inclined to deny the existence of any such order... it can be shown briefly and without any technical apparatus how the independent actions of individuals will produce an order which is no part of their intentions... The way in which footpaths are formed in a wild broken country is such an instance. At first everyone will seek for himself what seems to him the best path. But the fact that such a path has been used once is likely to make it easier to traverse and therefore more likely to be used again; and thus gradually more and more clearly defined tracks arise and come to be used to the exclusion of other possible ways. Human movements through the region come to conform to a definite pattern which, although the result of deliberate decision of many people, has yet not be consciously designed by anyone.
…...
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[A plant] does not change itself gradually, but remains unaffected during all succeeding generations. It only throws off new forms, which are sharply contrasted with the parent, and which are from the very beginning as perfect and as constant, as narrowly defined, and as pure of type as might be expected of any species.
In Species and Varieties: Their Origin and Mutation (1905), 28-9.
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[From uranium] there are present at least two distinct types of radiation one that is very readily absorbed, which will be termed for convenience the α radiation, and the other of a more penetrative character, which will be termed the β radiation.
Originating the names for these two types of radiation. In 'Uranium Radiation and the Electrical Conduction Produced by It', Philosophical Magazine (1899), 47, 116.
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[On suburbia] We’re bringing up our children in one-class areas. When they grow up and move to a city or go abroad, they’re not accustomed to variety and they get uncertain and insecure. We should bring up our children where they’re exposed to all types of people.
As quoted in Frances Glennon, 'Student and Teacher of Human Ways', Life (14 Sep 1959), 147.
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[The] subjective [historical] element in geologic studies accounts for two characteristic types that can be distinguished among geologists: one considering geology as a creative art, the other regarding geology as an exact science.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 453.
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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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- 90 -
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Winston Churchill
- 80 -
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- 70 -
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- 60 -
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- 50 -
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- 40 -
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- 30 -
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- 20 -
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