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Who said: “A people without children would face a hopeless future; a country without trees is almost as helpless.”
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Base Quotes (120 quotes)

... we must first base such words as “between” upon clear concepts, a thing which is quite feasible but which I have not seen done.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 83.
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“In order to ascertain the height of the tree I must be in such a position that the top of the tree is exactly in a line with the top of a measuring-stick—or any straight object would do, such as an umbrella—which I shall secure in an upright position between my feet. Knowing then that the ratio that the height of the tree bears to the length of the measuring stick must equal the ratio that the distance from my eye to the base of the tree bears to my height, and knowing (or being able to find out) my height, the length of the measuring stick and the distance from my eye to the base of the tree, I can, therefore, calculate the height of the tree.”
“What is an umbrella?”
In Mr. Fortune’s Maggot (1927), 175.
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[Davy's] March of Glory, which he has run for the last six weeks—within which time by the aid and application of his own great discovery, of the identity of electricity and chemical attractions, he has placed all the elements and all their inanimate combinations in the power of man; having decomposed both the Alkalies, and three of the Earths, discovered as the base of the Alkalies a new metal... Davy supposes there is only one power in the world of the senses; which in particles acts as chemical attractions, in specific masses as electricity, & on matter in general, as planetary Gravitation... when this has been proved, it will then only remain to resolve this into some Law of vital Intellect—and all human knowledge will be Science and Metaphysics the only Science.
In November 1807 Davy gave his famous Second Bakerian Lecture at the Royal Society, in which he used Voltaic batteries to “decompose, isolate and name” several new chemical elements, notably sodium and potassium.
Letter to Dorothy Wordsworth, 24 November 1807. In Earl Leslie Griggs (ed.), The Collected Letters of Samuel Taylor Coleridge (1956), Vol. 3, 38.
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A habit of basing convictions upon evidence, and of giving to them only that degree or certainty which the evidence warrants, would, if it became general, cure most of the ills from which the world suffers.
In Bertrand Russell and Paul Edwards (ed.), 'Preface', Why I Am Not a Christian: And Other Essays on Religion and Related Subjects (1957), vi.
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A man who is all theory is like “a rudderless ship on a shoreless sea.” … Theories and speculations may be indulged in with safety only as long as they are based on facts that we can go back to at all times and know that we are on solid ground.
In Nature's Miracles: Familiar Talks on Science (1899), Vol. 1, Introduction, vii.
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A precisian professor had the habit of saying: “… quartic polynomial ax4+bx3+cx2+dx+e, where e need not be the base of the natural logarithms.”
Given, without citation, in A Mathematician’s Miscellany (1953), reissued as Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 60. [Note: a precisian is a rigidly precise or punctilious person. —Webmaster]
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A scientist works largely by intuition. Given enough experience, a scientist examining a problem can leap to an intuition as to what the solution ‘should look like.’ ... Science is ultimately based on insight, not logic.
…...
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All progress is based upon a universal innate desire of every organism to live beyond its means.
…...
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Aluminum is at once as white as silver, as incorrodible as gold, as tenacious as iron, as fusible as copper, and as light as glass. It is easily worked; it is widely spread in nature, alumina forming the bases of most rocks; it is three times lighter than iron; in short, it seems to have been created expressly to furnish material for our projectile!
Planning a spacecraft to be fired from a cannon to the moon. In From the Earth to the Moon (1865, 1890), 38.
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An extra-terrestrial philosopher, who had watched a single youth up to the age of twenty-one and had never come across any other human being, might conclude that it is the nature of human beings to grow continually taller and wiser in an indefinite progress towards perfection; and this generalization would be just as well founded as the generalization which evolutionists base upon the previous history of this planet.
Scientific Method in Philosophy (1914), 12.
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Arithmetic, as we shall see by and by, is overdone, in a certain sense, in our schools; just so far as the teaching is based upon the concrete, so far is it profitable; but when the book-makers begin to make it too abstract, as they very often do, it becomes a torture to both teacher and learners, or, at best, a branch of imaginary knowledge unconnected with real life.
From 'Introduction', Mathematical Teaching and its Modern Methods (1886), 10.
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As scientific men we have all, no doubt, felt that our fellow men have become more and more satisfying as fish have taken up their work which has been put often to base uses, which must lead to disaster. But what sin is to the moralist and crime to the jurist so to the scientific man is ignorance. On our plane, knowledge and ignorance are the immemorial adversaries. Scientific men can hardly escape the charge of ignorance with regard to the precise effect of the impact of modern science upon the mode of living of the people and upon their civilisation. For them, such a charge is worse than that of crime.
From Banquet Speech (10 Dec 1922), Nobel Prize in Chemistry, collected in Carl Gustaf Santesson (ed.), Les Prix Nobel en 1921-1922 (1923).
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Attempts have been made from a study of the changes produced by mutation to obtain the relative order of the bases within various triplets, but my own view is that these are premature until there is more extensive and more reliable data on the composition of the triplets.
In Nobel Lecture (11 Dec 1962). Collected in Nobel Lectures, Physiology or Medicine 1942-1962 (1964).
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Behold the mighty dinosaur,
Famous in prehistoric lore,
Not only for his power and strength
But for his intellectual length.
You will observe by these remains
The creature had two sets of brains—
One in his head (the usual place),
The other at his spinal base.
Thus he could reason 'A priori'
As well as 'A posteriori'.
No problem bothered him a bit
So wise was he, so wise and solemn,
Each thought filled just a spinal column.
If one brain found the pressure strong
It passed a few ideas along.
If something slipped his forward mind
'Twas rescued by the one behind.
And if in error he was caught
As he thought twice before he spoke
He had no judgment to revoke.
Thus he could think without congestion
Upon both sides of every question.
Oh, gaze upon this model beast
Defunct ten million years at least.
'The Dinosaur: A Poem' (1912). In E. H. Colbert (ed.), The Dinosaur Book (1951), 78.
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But the strong base and building of my love
Is as the very centre of the earth,
Drawing all things to 't.
Character Cressidus to Pandarus in play Troilus and Cressida (c.1601), Act 4, lines 200-202. In Troilus and Cressida (1811), 92.
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By virtue of the way it has organized its technological base, contemporary industrial society tends to be totalitarian. For 'totalitarian' is not only a terroristic political coordination of society, but also a non-terroristic economic-technical coordination which operates through the manipulation of needs by vested interests. It thus precludes the emergence of an effective opposition against the whole. Not only a specific form of government or party rule makes for totalitarianism, but also a specific system of production and distribution which may well be compatible with a 'pluralism' of parties, newspapers, 'countervailing powers,' etc.
One Dimensional Man (1964), 3.
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Chemistry is one of those branches of human knowledge which has built itself upon methods and instruments by which truth can presumably be determined. It has survived and grown because all its precepts and principles can be re-tested at any time and anywhere. So long as it remained the mysterious alchemy by which a few devotees, by devious and dubious means, presumed to change baser metals into gold, it did not flourish, but when it dealt with the fact that 56 g. of fine iron, when heated with 32 g. of flowers of sulfur, generated extra heat and gave exactly 88 g. of an entirely new substance, then additional steps could be taken by anyone. Scientific research in chemistry, since the birth of the balance and the thermometer, has been a steady growth of test and observation. It has disclosed a finite number of elementary reagents composing an infinite universe, and it is devoted to their inter-reaction for the benefit of mankind.
Address upon receiving the Perkin Medal Award, 'The Big Things in Chemistry', The Journal of Industrial and Engineering Chemistry (Feb 1921), 13, No. 2, 163.
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Commenting on Archimedes, for whom he also had a boundless admiration, Gauss remarked that he could not understand how Archimedes failed to invent the decimal system of numeration or its equivalent (with some base other than 10). … This oversight Gauss regarded as the greatest calamity in the history of science.
In Men of Mathematics (1937), 256.
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Einstein’s space is no closer to reality than Van Gogh’s sky. The glory of science is not in a truth more absolute than the truth of Bach or Tolstoy, but in the act of creation itself. The scientist’s discoveries impose his own order on chaos, as the composer or painter imposes his; an order that always refers to limited aspects of reality, and is based on the observer's frame of reference, which differs from period to period as a Rembrandt nude differs from a nude by Manet.
In The Act of Creation (1964), 252.
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Evolution is the law of policies: Darwin said it, Socrates endorsed it, Cuvier proved it and established it for all time in his paper on 'The Survival of the Fittest.' These are illustrious names, this is a mighty doctrine: nothing can ever remove it from its firm base, nothing dissolve it, but evolution.
'Three Thousand Years Among the Microbes', Which Was the Dream? (1967), Chap. 8. In Mark Twain and Brian Collins (ed.), When in Doubt, Tell the Truth: and Other Quotations from Mark Twain (1996), 47.
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Felling a tree was possibly the original deed of appropriation of the natural earth by early mankind in Europe. Thousands of years ago,… man lifted a heavy flint tool and struck at the base of a tree. He may have wanted the tree for shelter and fuel, or possibly to make a bridge over a river or a path through a bog…. [E]ventually the tree crashed to the floor, and the first act in the slow possession of the land by its people was complete.
In The Man Who Made Things Out of Trees: The Ash in Human Culture and History (2015), Chap. 1.
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Few will deny that even in the first scientific instruction in mathematics the most rigorous method is to be given preference over all others. Especially will every teacher prefer a consistent proof to one which is based on fallacies or proceeds in a vicious circle, indeed it will be morally impossible for the teacher to present a proof of the latter kind consciously and thus in a sense deceive his pupils. Notwithstanding these objectionable so-called proofs, so far as the foundation and the development of the system is concerned, predominate in our textbooks to the present time. Perhaps it will be answered, that rigorous proof is found too difficult for the pupil’s power of comprehension. Should this be anywhere the case,—which would only indicate some defect in the plan or treatment of the whole,—the only remedy would be to merely state the theorem in a historic way, and forego a proof with the frank confession that no proof has been found which could be comprehended by the pupil; a remedy which is ever doubtful and should only be applied in the case of extreme necessity. But this remedy is to be preferred to a proof which is no proof, and is therefore either wholly unintelligible to the pupil, or deceives him with an appearance of knowledge which opens the door to all superficiality and lack of scientific method.
In 'Stücke aus dem Lehrbuche der Arithmetik', Werke, Bd. 2 (1904), 296.
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First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
In Ueber den Mathematischen Unterricht an den hoheren Schulen; Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 11, 131.
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For several years this great man [Isaac Newton] was intensely occupied in endeavoring to discover a way of changing the base metals into gold. … There were periods when his furnace fires were not allowed to go out for six weeks; he and his secretary sitting up alternate nights to replenish them.
In 'Sir Isaac Newton', People’s Book of Biography: Or, Short Lives of the Most Interesting Persons of All Ages and Countries (1868), 256.
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He who joyfully marches to music in rank and file has already earned my contempt. He has been given a large brain by mistake, since for him the spinal cord would fully suffice. This disgrace to civilisation should be done away with at once. Heroism at command, senseless brutality, deplorable love-of-country stance, how violently I hate all this, how despicable and ignoble war is; I would rather be torn to shreds than be part of so base an action! It is my conviction that killing under the cloak of war is nothing but an act of murder.
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Historical science is not worse, more restricted, or less capable of achieving firm conclusions because experiment, prediction, and subsumption under invariant laws of nature do not represent its usual working methods. The sciences of history use a different mode of explanation, rooted in the comparative and observational richness in our data. We cannot see a past event directly, but science is usually based on inference, not unvarnished observation (you don’t see electrons, gravity, or black holes either).
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Historically [chemistry] arose from a constellation of interests: the empirically based technologies of early metallurgists, brewers, dyers, tanners, calciners and pharmacists; the speculative Greek philosphers' concern whether brute matter was invariant or transformable; the alchemists' real or symbolic attempts to achieve the transmutation of base metals into gold; and the iatrochemists' interst in the chemistry and pathology of animal and human functions. Partly because of the sheer complexity of chemical phenomena, the absence of criteria and standards of purity, and uncertainty over the definition of elements ... but above all because of the lack of a concept of the gaseous state of matter, chemistry remained a rambling, puzzling and chaotic area of natural philosophy until the middle of the eighteenth century.
The Chemical Tree: A History of Chemistry (2000), xxii.
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Houston, Tranquility Base here, the Eagle has landed.
First words transmitted from the moon (20 Jul 1969).
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How strange is the lot of us mortals! Each of us is here for a brief sojourn; for what purpose he knows not, though he sometimes thinks he senses it. But without deeper reflection one knows from daily life that one exists for other people–first of all for those upon whose smiles and well-being our own happiness is wholly dependent, and then for the many, unknown to us, to whose destinies we are bound by the ties of sympathy. A hundred times every day I remind myself that my inner and outer life are based on the labors of other men, living and dead, and that I must exert myself in order to give in the same measure as I have received and am still receiving.
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I am not ... asserting that humans are either genial or aggressive by inborn biological necessity. Obviously, both kindness and violence lie with in the bounds of our nature because we perpetrate both, in spades. I only advance a structural claim that social stability rules nearly all the time and must be based on an overwhelmingly predominant (but tragically ignored) frequency of genial acts, and that geniality is therefore our usual and preferred response nearly all the time ... The center of human nature is rooted in ten thousand ordinary acts of kindness that define our days.
In Eight Little Piggies: Reflections in Natural History (1993), 282.
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I don’t think we’ll go there [Mars] until we go back to the Moon and develop a technology base for living and working and transporting ourselves through space.
As quoted on the nmspacemuseum.org website of the New Mexico Museum of Space History.
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I feel like a white granular mass of amorphous crystals—my formula appears to be isomeric with Spasmotoxin. My aurochloride precipitates into beautiful prismatic needles. My Platinochloride develops octohedron crystals,—with fine blue florescence. My physiological action is not indifferent. One millionth of a grain injected under the skin of a frog produced instantaneous death accompanied by an orange blossom odor. The heart stopped in systole. A base—L3H9NG4—offers analogous reaction to phosmotinigstic acid.
In letter to George M. Gould (1889), collected in Elizabeth Bisland The Writings of Lafcadio Hearn (1922), Vol. 14, 89.
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I hear one day the word “mountain,” and I ask someone “what is a mountain? I have never seen one.”
I join others in discussions of mountains.
One day I see in a book a picture of a mountain.
And I decide I must climb one.
I travel to a place where there is a mountain.
At the base of the mountain I see there are lots of paths to climb.
I start on a path that leads to the top of the mountain.
I see that the higher I climb, the more the paths join together.
After much climbing the many paths join into one.
I climb till I am almost exhausted but I force myself and continue to climb.
Finally I reach the top and far above me there are stars.
I look far down and the village twinkles far below.
It would be easy to go back down there but it is so beautiful up here.
I am just below the stars.
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I suppose that the first chemists seemed to be very hard-hearted and unpoetical persons when they scouted the glorious dream of the alchemists that there must be some process for turning base metals into gold. I suppose that the men who first said, in plain, cold assertion, there is no fountain of eternal youth, seemed to be the most cruel and cold-hearted adversaries of human happiness. I know that the economists who say that if we could transmute lead into gold, it would certainly do us no good and might do great harm, are still regarded as unworthy of belief. Do not the money articles of the newspapers yet ring with the doctrine that we are getting rich when we give cotton and wheat for gold rather than when we give cotton and wheat for iron?
'The Forgotten Man' (1883). In The Forgotten Man and Other Essays (1918), 468.
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I want to argue that the ‘sudden’ appearance of species in the fossil record and our failure to note subsequent evolutionary change within them is the proper prediction of evolutionary theory as we understand it ... Evolutionary ‘sequences’ are not rungs on a ladder, but our retrospective reconstruction of a circuitous path running like a labyrinth, branch to branch, from the base of the bush to a lineage now surviving at its top.
…...
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I was unable to devote myself to the learning of this al-jabr [algebra] and the continued concentration upon it, because of obstacles in the vagaries of Time which hindered me; for we have been deprived of all the people of knowledge save for a group, small in number, with many troubles, whose concern in life is to snatch the opportunity, when Time is asleep, to devote themselves meanwhile to the investigation and perfection of a science; for the majority of people who imitate philosophers confuse the true with the false, and they do nothing but deceive and pretend knowledge, and they do not use what they know of the sciences except for base and material purposes; and if they see a certain person seeking for the right and preferring the truth, doing his best to refute the false and untrue and leaving aside hypocrisy and deceit, they make a fool of him and mock him.
A. P. Youschkevitch and B. A. Rosenfeld, 'Al-Khayyami', in C. C. Gillispie (ed.), Dictionary of Scientific Biography (1973), Vol. 7, 324.
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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. There was a sort of musical comedy effect where I forgot what the bases were and I had to go to the library to check, and I went back to John Griffith to find out which places he said. Low and behold, it turned out that John Griffith’s ideas fitted in with Chargaff’s rules!
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.
From Transcript of documentary by VSM Productions, The DNA Story (1973). As excerpted on web page 'Chargaff’s Rules', Linus Pauling and the Race for DNA on website scarc.library.oregonstate.edu
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If the [Vestiges] be true, the labours of sober induction are in vain; religion is a lie; human law is a mass of folly, and a base injustice; morality is moonshine; our labours for the black people of Africa were works of madmen; and man and woman are only better beasts!
Letter to Charles Lyell (9 Apr 1845). In John Willis Clark and Thomas McKenny Hughes (eds.), The Life and Letters of the Reverend Adam Sedgwick (1890), Vol. 2, 84.
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If the actual order of the bases on one of the pair of chains were given, one could write down the exact order of the bases on the other one, because of the specific pairing. Thus one chain is, as it were, the complement of the other, and it is this feature which suggests how the deoxyribonucleic acid molecule might duplicate itself.
[Co-author with Francis Crick]
In 'Genetic Implications of the Structure of Deoxyribonucleic Acid', Nature (1958), 171, 965-966.
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If the question were, “What ought to be the next objective in science?” my answer would be the teaching of science to the young, so that when the whole population grew up there would be a far more general background of common sense, based on a knowledge of the real meaning of the scientific method of discovering truth.
Marion Savin Selections from the Scientific Correspondence of Elihu Thomson (1971), v.
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If we turn to the problems to which the calculus owes its origin, we find that not merely, not even primarily, geometry, but every other branch of mathematical physics—astronomy, mechanics, hydrodynamics, elasticity, gravitation, and later electricity and magnetism—in its fundamental concepts and basal laws contributed to its development and that the new science became the direct product of these influences.
Opening of Presidential Address (27 Apr 1907) to the American Mathematical Society, 'The Calculus in Colleges and Technical Schools', published in Bulletin of the American Mathematical Society (Jun 1907), 13, 449.
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Improvements in industry can be left to chance in the hope that someone, sometime, will think of something useful. that some good invention will show up. The other way is to organize so that new knowledge shall always be coming from the researches in the fundamental sciences and engineering arts on which business is based. From that steady stream will arise inventions and new methods. This is the way of Bell Laboratories.
From a Bell Telephone System advertisement, 'The Search That Never Ends', placed, for example, in Life Magazine (17 Jan 1944), 33.
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In every combustion there is disengagement of the matter of fire or of light. A body can burn only in pure air [oxygen]. There is no destruction or decomposition of pure air and the increase in weight of the body burnt is exactly equal to the weight of air destroyed or decomposed. The body burnt changes into an acid by addition of the substance that increases its weight. Pure air is a compound of the matter of fire or of light with a base. In combustion the burning body removes the base, which it attracts more strongly than does the matter of heat, which appears as flame, heat and light.
'Memoire sur la combustion en général', Mémoires de l'Académie des Sciences, 1777, 592. Reprinted in Oeuvres de Lavoisier (1864), Vol. 2, 225-33, trans. M. P. Crosland.
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In mathematics it is notorious that we start from absurdities to reach a realm of law, and our whole (mathematical) conception of the world is based on a foundation which we believe to have no existence.
In The Dance of Life (1923), 86.
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In using the present in order to reveal the past, we assume that the forces in the world are essentially the same through all time; for these forces are based on the very nature of matter, and could not have changed. The ocean has always had its waves, and those waves have always acted in the same manner. Running water on the land has ever had the same power of wear and transportation and mathematical value to its force. The laws of chemistry, heat, electricity, and mechanics have been the same through time. The plan of living structures has been fundamentally one, for the whole series belongs to one system, as much almost as the parts of an animal to the one body; and the relations of life to light and heat, and to the atmosphere, have ever been the same as now.
In 'Introduction', Manual of Geology: Treating of the Principles of the Science (1863), 7.
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In Winter, [the Antarctic] is perhaps the dreariest of places. Our base, Little America, lay in a bowl of ice, near the edge of the Ross Ice Barrier. The temperature fell as low as 72 degrees below zero. One could actually hear one's breath freeze.
In 'Hoover Presents Special Medal to Byrd...', New York Times (21 Jun 1930), 1.
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Intelligence is the capacity to learn. Learning is based on the acquisition of new knowledge about the environment. Memory is its retention.
…...
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It feels unacceptable to many people even to think of having a cosmology based on science. … They see fanciful origin stories as spicing up the culture. … Aspects of many origin stories can enrich our understanding of the scientific picture, but they cannot take its place.
As co-author with Nancy Ellen Abrams, in The View from the Center of the Universe: Discovering Our Extraordinary Place in the Cosmos (2006), 85.
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It is not I who seek to base Man's dignity upon his great toe, or insinuate that we are lost if an Ape has a hippocampus minor. On the contrary, I have done my best to sweep away this vanity. I have endeavoured to show that no absolute structural line of demarcation, wider than that between the animals which immediately succeed us in the scale, can be drawn between the animal world and ourselves; and I may add the expression of my belief that the attempt to draw a physical distinction is equally futile, and that even the highest facuities of feeling and of intellect begin to germinate in lower forms of life. At the same time, no one is more strongly convinced than I am of the vastness of the gulf between civilized man and the brutes; or is more certain that whether from them or not, he is assuredly not of them.
'On the Relations of Man to the Lower Animals' (1863). In Collected Essays (1894), Vol. 7. 152-3.
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It is one of the striking generalizations of biochemistry—which surprisingly is hardly ever mentioned in the biochemical text-books—that the twenty amino acids and the four bases, are, with minor reservations, the same throughout Nature. As far as I am aware the presently accepted set of twenty amino acids was first drawn up by Watson and myself in the summer of 1953 in response to a letter of Gamow's.
'On the Genetic Code', Nobel Lecture, 11 December 1962. In Nobel Lectures: Physiology or Medicine 1942-1962 (1964), 811.
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It is well to remember that most arguments in favor of not trying an experiment are too flimsily based.
Quoted in a lecture published in Experientia, Supplementum II (1955), 226.
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Just as the arts of tanning and dyeing were practiced long before the scientific principles upon which they depend were known, so also the practice of Chemical Engineering preceded any analysis or exposition of the principles upon which such practice is based.
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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Let us make an arbitrary decision (by a show of hands if necessary) to define the base of every stratigraphical unit in a selected section. This may be called the Principle of the Golden Spike. Then stratigraphical nomenclature can be forgotten and we can get on with the real work of stratigraphy, which is correlation and interpretation.
In The Nature of the Stratigraphical Record (1973), 73.
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Man, the cutting edge of terrestrial life, has no rational alternative but to expand the environmental and resource base beyond earth.
On the 'extraterrestrial imperative,' recalled on his death 11 Dec 84
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Mathematical reasoning is deductive in the sense that it is based upon definitions which, as far as the validity of the reasoning is concerned (apart from any existential import), needs only the test of self-consistency. Thus no external verification of definitions is required in mathematics, as long as it is considered merely as mathematics.
In Universal Algebra (1898), Preface, vi.
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Mathematicians create by acts of insight and intuition. Logic then sanctions the conquests of intuition. It is the hygiene that mathematics practices to keep its ideas healthy and strong. Moreover, the whole structure rests fundamentally on uncertain ground, the intuition of humans. Here and there an intuition is scooped out and replaced by a firmly built pillar of thought; however, this pillar is based on some deeper, perhaps less clearly defined, intuition. Though the process of replacing intuitions with precise thoughts does not change the nature of the ground on which mathematics ultimately rests, it does add strength and height to the structure.
In Mathematics in Western Culture (1964), 408.
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Mathematics is a structure providing observers with a framework upon which to base healthy, informed, and intelligent judgment. Data and information are slung about us from all directions, and we are to use them as a basis for informed decisions. … Ability to critically analyze an argument purported to be logical, free of the impact of the loaded meanings of the terms involved, is basic to an informed populace.
In 'Mathematics Is an Edifice, Not a Toolbox', Notices of the AMS (Oct 1996), 43, No. 10, 1108.
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Mathematics, indeed, is the very example of brevity, whether it be in the shorthand rule of the circle, c = πd, or in that fruitful formula of analysis, e = -1, —a formula which fuses together four of the most important concepts of the science,—the logarithmic base, the transcendental ratio π, and the imaginary and negative units.
In 'The Poetry of Mathematics', The Mathematics Teacher (May 1926), 19, No. 5, 293.
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Methods of fishing are becoming more and more efficient, but the whole fishing industry is based on the exploitation of a wild population. This is almost a prehistoric concept on land, but it has never been questioned at sea.
In Men, Machines, and Sacred Cows (1984), 162.
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Mistakes are at the very base of human thought feeding the structure like root nodules. If we were not provided with the knack of being wrong, we could never get anything useful done.
In The Medusa and the Snail (1979), 37.
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Most variables can show either an upward or downward trend, depending on the base year chosen.
'Penetrating the Rhetoric', The Vision of the Anointed (1996), 102.
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My own thinking (and that of many of my colleagues) is based on two general principles, which I shall call the Sequence Hypothesis and the Central Dogma. The direct evidence for both of them is negligible, but I have found them to be of great help in getting to grips with these very complex problems. I present them here in the hope that others can make similar use of them. Their speculative nature is emphasized by their names. It is an instructive exercise to attempt to build a useful theory without using them. One generally ends in the wilderness.
The Sequence Hypothesis
This has already been referred to a number of times. In its simplest form it assumes that the specificity of a piece of nucleic acid is expressed solely by the sequence of its bases, and that this sequence is a (simple) code for the amino acid sequence of a particular protein...
The Central Dogma
This states that once 'information' has passed into protein it cannot get out again. In more detail, the transfer of information from nucleic acid to nucleic acid, or from nucleic acid to protein may be possible, but transfer from protein to protein, or from protein to nucleic acid is impossible. Information means here the precise determination of sequence, either of bases in the nucleic acid or of amino acid residues in the protein. This is by no means universally held—Sir Macfarlane Burnet, for example, does not subscribe to it—but many workers now think along these lines. As far as I know it has not been explicitly stated before.
'On Protein Synthesis', Symposia of the Society for Experimental Biology: The Biological Replication of Macromolecules, 1958, 12, 152-3.
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Nature's economy shall be the base for our own, for it is immutable, but ours is secondary. An economist without knowledge of nature is therefore like a physicist without knowledge of mathematics.
'Tankar om grunden til oeconomien', 1740, 406. Trans. Lisbet Koerner, Linnaeus: Nature and Nation (1999), 103.
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Nothing is known in our profession by guess; and I do not believe, that from the first dawn of medical science to the present moment, a single correct idea has ever emanated from conjecture: it is right therefore, that those who are studying their profession should be aware that there is no short road to knowledge; and that observation on the diseased living, examination of the dead, and experiments upon living animals, are the only sources of true knowledge; and that inductions from these are the sole bases of legitimate theory.
Astley Paston Cooper, Astley Cooper, Bransby Blake Cooper, A Treatise on Dislocations and Fractures of the Joints (1851), 155.
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Of the nucleosides from deoxyribonucleic acids, all that was known with any certainty [in the 1940s] was that they were 2-deoxy-­D-ribosides of the bases adenine, guanine, thymine and cytosine and it was assumed that they were structurally analogous to the ribonucleosides. The chemistry of the nucleotides—the phosphates of the nucleosides—was in a correspondingly primitive state. It may well be asked why the chemistry of these groups of compounds was not further advanced, particularly since we recognize today that they occupy a central place in the history of the living cell. True, their full significance was for a long time unrecognized and emerged only slowly as biochemical research got into its stride but I think a more important reason is to be found in the physical properties of compounds of the nucleotide group. As water-soluble polar compounds with no proper melting points they were extremely difficult to handle by the classic techniques of organic chemistry, and were accordingly very discouraging substances to early workers. It is surely no accident that the major advances in the field have coincided with the appearance of new experimental techniques such as paper and ion-exchange chromatography, paper electrophoresis, and countercurrent distribution, peculiarly appropriate to the compounds of this group.
In 'Synthesis in the Study of Nucleotides', Nobel Lecture, 11 December 1957. In Nobel Lectures: Chemistry 1942-1962 (1964), 524.
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Our ideals. laws and customs should he based on the proposition that each, in turn, becomes the custodian rather than the absolute owner of our resources and each generation has the obligation to pass this inheritance on to the future.
…...
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Our mind is so fortunately equipped, that it brings us the most important bases for our thoughts without our having the least knowledge of this work of elaboration. Only the results of it become unconscious.
cit. L.L. Whyte The Unconscious Before Freud (1960)
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Our situation on this earth seems strange. Every one of us appears here involuntarily and uninvited for a short stay, without knowing the whys and the wherefore. In our daily lives we only feel that man is here for the sake of others, for those whom we love and for many other beings whose fate is connected with our own. I am often worried at the thought that my life is based to such a large extent on the work of my fellow human beings and I am aware of my great indebtedness to them.
…...
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Our ultimate task is to find interpretative procedures that will uncover each bias and discredit its claims to universality. When this is done the eighteenth century can be formally closed and a new era that has been here a long time can be officially recognised. The individual human being, stripped of his humanity, is of no use as a conceptual base from which to make a picture of human society. No human exists except steeped in the culture of his time and place. The falsely abstracted individual has been sadly misleading to Western political thought. But now we can start again at a point where major streams of thought converge, at the other end, at the making of culture. Cultural analysis sees the whole tapestry as a whole, the picture and the weaving process, before attending to the individual threads.
As co-author with Baron Isherwood, The World of Goods: Towards an Anthropology of Consumption (1979, 2002), 41-42.
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Recently, we’ve reported that we have made all five bases, the compounds that spell out the instructions for all life and are a part of the nucleic acids, RNA and DNA. Not only did we make all five bases but we found them in a meteorite! So that these two things coming together really assure us that the molecules necessary for life can be found in the absence of life. This was the biggest stumbling block.
In Space World (1985), 5, 25.
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Rocks have, no doubt, their grandeur, and there is a beauty in running waters, and even in placid lakes; but, let the rock be naked of vegetation down to and around its base, and its grandeur is painful,—it seems a ruin.
Using pseudonym Peter Parley, in Peter Parley’s Cyclopedia of Botany (1838), Chap. 1, ix.
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Science was born as a result and consequence of philosophy; it cannot survive without a philosophical base. If philosophy perishes, science will be next to go.
For the New Intellectual: The Philosophy of Ayn Rand (1963), 44.
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Scientists alone can establish the objectives of their research, but society, in extending support to science, must take account of its own needs. As a layman, I can suggest only with diffidence what some of the major tasks might be on your scientific agenda, but … First, I would suggest the question of the conservation and development of our natural resources. In a recent speech to the General Assembly of the United Nations, I proposed a world-wide program to protect land and water, forests and wildlife, to combat exhaustion and erosion, to stop the contamination of water and air by industrial as well as nuclear pollution, and to provide for the steady renewal and expansion of the natural bases of life.
From Address to the Centennial Convocation of the National Academy of Sciences (22 Oct 1963), 'A Century of Scientific Conquest'. Online at The American Presidency Project.
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Scientists should always state the opinions upon which their facts are based.
…...
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Study is like the heaven’s glorious sun,
That will not be deep-search’d with saucy looks:
Small have continual plodders ever won,
Save base authority from others’ books.
Dialog for Biron, written in Love’s Labour Lost (1598), Act 1, Scene 1, line 74-77.
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Suppose then I want to give myself a little training in the art of reasoning; suppose I want to get out of the region of conjecture and probability, free myself from the difficult task of weighing evidence, and putting instances together to arrive at general propositions, and simply desire to know how to deal with my general propositions when I get them, and how to deduce right inferences from them; it is clear that I shall obtain this sort of discipline best in those departments of thought in which the first principles are unquestionably true. For in all our thinking, if we come to erroneous conclusions, we come to them either by accepting false premises to start with—in which case our reasoning, however good, will not save us from error; or by reasoning badly, in which case the data we start from may be perfectly sound, and yet our conclusions may be false. But in the mathematical or pure sciences,—geometry, arithmetic, algebra, trigonometry, the calculus of variations or of curves,— we know at least that there is not, and cannot be, error in our first principles, and we may therefore fasten our whole attention upon the processes. As mere exercises in logic, therefore, these sciences, based as they all are on primary truths relating to space and number, have always been supposed to furnish the most exact discipline. When Plato wrote over the portal of his school. “Let no one ignorant of geometry enter here,” he did not mean that questions relating to lines and surfaces would be discussed by his disciples. On the contrary, the topics to which he directed their attention were some of the deepest problems,— social, political, moral,—on which the mind could exercise itself. Plato and his followers tried to think out together conclusions respecting the being, the duty, and the destiny of man, and the relation in which he stood to the gods and to the unseen world. What had geometry to do with these things? Simply this: That a man whose mind has not undergone a rigorous training in systematic thinking, and in the art of drawing legitimate inferences from premises, was unfitted to enter on the discussion of these high topics; and that the sort of logical discipline which he needed was most likely to be obtained from geometry—the only mathematical science which in Plato’s time had been formulated and reduced to a system. And we in this country [England] have long acted on the same principle. Our future lawyers, clergy, and statesmen are expected at the University to learn a good deal about curves, and angles, and numbers and proportions; not because these subjects have the smallest relation to the needs of their lives, but because in the very act of learning them they are likely to acquire that habit of steadfast and accurate thinking, which is indispensable to success in all the pursuits of life.
In Lectures on Teaching (1906), 891-92.
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The bird which is drawn to the water by its need of finding there the prey on which it lives, separates the digits of its feet in trying to strike the water and move about on the surface. The skin which unites these digits at their base acquires the habit of being stretched by these continually repeated separations of the digits; thus in course of time there are formed large webs which unite the digits of ducks, geese, etc., as we actually find them. In the same way efforts to swim, that is to push against the water so as to move about in it, have stretched the membranes between the digits of frogs, sea-tortoises, the otter, beaver, etc.
On the other hand, a bird which is accustomed to perch on trees and which springs from individuals all of whom had acquired this habit, necessarily has longer digits on its feet and differently shaped from those of the aquatic animals that I have just named. Its claws in time become lengthened, sharpened and curved into hooks, to clasp the branches on which the animal so often rests.
We find in the same way that the bird of the water-side which does not like swimming and yet is in need of going to the water's edge to secure its prey, is continually liable to sink into the mud. Now this bird tries to act in such a way that its body should not be immersed in the liquid, and hence makes its best efforts to stretch and lengthen its legs. The long-established habit acquired by this bird and all its race of continually stretching and lengthening its legs, results in the individuals of this race becoming raised as though on stilts, and gradually obtaining long, bare legs, denuded of feathers up to the thighs and often higher still.
Philosophie Zoologique (1809), Vol. 1, 249-50, trans. Hugh Elliot (1914), 119-20.
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The century of biology upon which we are now well embarked is no matter of trivialities. It is a movement of really heroic dimensions, one of the great episodes in man’s intellectual history. The scientists who are carrying the movement forward talk in terms of nucleo-proteins, of ultracentrifuges, of biochemical genetics, of electrophoresis, of the electron microscope, of molecular morphology, of radioactive isotopes. But do not be misled by these horrendous terms, and above all do not be fooled into thinking this is mere gadgetry. This is the dependable way to seek a solution of the cancer and polio problems, the problems of rheumatism and of the heart. This is the knowledge on which we must base our solution of the population and food problems. This is the understanding of life.
Letter to H. M. H. Carsan (17 Jun 1949). Quoted in Raymond B. Fosdick, The Story of the Rockefeller Foundation (1952), 166.
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The consideration of mathematics is at the base of knowledge of the mind as it is at the base of the natural sciences, and for the same reason: the free and fertile work of thought dates from that epoch when mathematics brought to man the true norm of truth.
As translated in James Byrnie Shaw, Lectures on the Philosophy of Mathematics (1918), 193. From Léon Brunschvicg, Les Étapes de La Philosophie Mathématique (1912), 577, “La considération de la mathématique est à la base de la connaissance de l’esprit comme elle est à la base des sciences de la nature, et pour une même raison: l’œuvre libre et féconde de la pensée date de l’époque où la mathématique vint apporter à l’homme la norme véritable de la vérité.”
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The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever. By using them, one may draw any conclusion he pleases and that is why these series have produced so many fallacies and so many paradoxes.
From letter (Jan 1828) to his former teacher Berndt Holmböe. In Morris Kline, Mathematics: The Loss of Certainty (1982), 170.
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The empirical basis of objective science has nothing “absolute” about it. Science does not rest upon solid bedrock. The bold structure of its theories rises, as it were, above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or “given” base; and when we cease our attempts to drive our piles into a deeper layer, it is not because we have reached firm ground. We simply stop when we are satisfied that they are firm enough to carry the structure, at least for the time being.
The Logic of Scientific Discovery: Logik Der Forschung (1959, 2002), 94.
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The essential molecule of reproduction, DNA, … is composed of only four nitrogen bases (adenine, thymine, guanine, and cytosine), the sugar deoxyribose, and a phosphate. DNA’s intermediary, RNA, differs only by the substitution of the sugar ribose for deoxyribose and the nitrogen base uracil for thymine. The proteins of living organisms are made with a mere 20 amino acids, all arranged in a “left-handed” configuration. Taking into account all 28 building blocks, or “letters” (20 amino acids, five bases, two sugars, and one phosphate), the message is clear: With such a limited alphabet, all life must have had a common chemical origin.
In 'Cosmochemistry The Earliest Evolution', The Science Teacher (Oct 1983), 50, No. 7, 35.
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The evening was calm, the calmest we had known above the North Col. The smooth, outward dipping slabs glowed in the fast setting sun and, at an immense distance beneath, clouds concealed the valleys and lesser peaks. There was nothing to obstruct the tremendous prospect. Seen from Everest, great peaks that dominate the climber as he toils along the East Rongbuk Glacier, and up the slopes of the North Col, show like insignificant ripples at the base of a great ocean roller. Even the North Peak was but a stepping-stone to quick-footed vision.
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The experiments made on the mutual electrical relations of bodies have taught us that they can be divided into two classes: electropositive and electronegative. The simple bodies which belong to the first class, as well as their oxides, always take up positive electricity when they meet simple bodies or oxides belonging to the second class; and the oxides of the first class always behave with the oxides of the other like salifiable bases with acids.
Essai sur le théorie des proportions chimiques (1819). Translated in Henry M. Leicester and Herbert S. Klickstein, A Source Book in Chemistry 1400-1900 (1952), 260.
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The facts once classified, once understood, the judgment based upon them ought to be independent of the individual mind which examines them.
From The Grammar of Science (1892), 7.
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The field cannot be well seen from within the field. The astronomer must have his diameter of the earth's orbit as a base to fix the parallax of any other star
In James Wood, Dictionary of Quotations from Ancient and Modern, English and Foreign Sources (1893), 427:37.
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The field cannot well be seen from within the field. The astronomer must have his diameter of the earth’s orbit as a base to find the parallax of any star.
In Essay 10, 'Circles', Essays by R.W. Emerson (1841), 314.
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The harmony of the universe knows only one musical form - the legato; while the symphony of number knows only its opposite - the staccato. All attempts to reconcile this discrepancy are based on the hope that an accelerated staccato may appear to our senses as a legato.
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The individual feels the futility of human desires and aims and the sublimity and marvelous order which reveal themselves both in nature and in the world of thought. Individual existence impresses him as a sort of prison and he wants to experience the universe as a single significant whole. The beginnings of cosmic religious feeling already appear at an early stage of development, e.g., in many of the Psalms of David and in some of the Prophets. Buddhism, as we have learned especially from the wonderful writings of Schopenhauer, contains a much stronger element of this. The religious geniuses of all ages have been distinguished by this kind of religious feeling, which knows no dogma and no God conceived in man’s image; so that there can be no church whose central teachings are based on it. Hence it is precisely among the heretics of every age that we find men who were filled with this highest kind of religious feeling and were in many cases regarded by their contemporaries as atheists, sometimes also as saints. Looked at in this light, men like Democritus, Francis of Assisi, and Spinoza are closely akin to one another.
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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 language of the genes has a simple alphabet, not with twenty-six letters, but just four. These are the four different DNA bases—adenine, guanine, cytosine and thymine (A, G, C and T for short). The bases are arranged in words of three letters such as CGA or TGG. Most of the words code for different amino acids, which themselves are joined together to make proteins, the building blocks of the body.
The Language of the Genes: Biology, History and the Evolutionary Future (1993), 3.
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The magnitude of the railway works undertaken in this country will be still more clearly exhibited, if you consider the extent of the Earth-Works. Taking them at an average of 70,000 cubic yards to a mile, they will measure 550,000,000 cubic yards. What does this represent? We are accustomed to regard St. Paul’s as a test for height and space; but by the side of the pyramid of earth these works would rear, St. Paul’s would be but as a pigmy by a giant. Imagine a mountain half a mile in diameter at its base, and soaring into the clouds one mile and a half in height;—that would be the size of the mountain of earth which these earth-works would form.
From 'Railway System and its Results' (Jan 1856) read to the Institution of Civil Engineers, reprinted in Samuel Smiles, Life of George Stephenson (1857), 512.
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The man who is thoroughly convinced of the universal operation of the law of causation cannot for a moment entertain the idea of a being who interferes in the course of events–provided, of course, that he takes the hypothesis of causality really seriously. He has no use for the religion of fear and equally little for social or moral religion. A God who rewards and punishes is inconceivable to him for the simple reason that a man’s actions are determined by necessity, external and internal, so that in God’s eyes he cannot be responsible, any more than an inanimate object is responsible for the motions it undergoes. Science has therefore been charged with undermining morality, but the charge is unjust. A man’s ethical behavior should be based effectually on sympathy, education, and social ties and needs; no religious basis is necessary. Man would indeed be in a poor way if he had to be restrained by fear of punishment and hopes of reward after death.
From 'Religion And Science', as collected in Ideas And Opinions (1954), 39, given its source as: “Written expressly for the New York Times Magazine. Appeared there November 9, 1930 (pp. 1-4). The German text was published in the Berliner Tageblatt, November 11, 1930.” The NYT Magazine article in full, is reprinted in Edward H. Cotton (ed.), Has Science Discovered God? A Symposium of Modern Scientific Opinion (1931), 101. This original version directly from the magazine has significantly different wording, beginning, “For anyone who is pervaded with the sense of causal law….” See this alternate form on the Albert Einstein Quotes page on this website. As for why the difference, Webmaster speculates the book form editor perhaps used a revised translation from Einstein’s German article.
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The moral faculties are generally and justly esteemed as of higher value than the intellectual powers. But we should bear in mind that the activity of the mind in vividly recalling past impressions is one of the fundamental though secondary bases of conscience. This affords the strongest argument for educating and stimulating in all possible ways the intellectual faculties of every human being.
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The novel feature of the structure is the manner in which the two chains are held together by the purine and pyrimidine bases. The planes of the bases are perpendicular to the fibre axis. They are joined together in pairs, a single base from one chain being hydrogen-bonded to a single base from the other chain, so that the two lie side by side with identical z-co-ordinates. One of the pair must be 11 purine and the other a pyrimidine for bonding to occur. The hydrogen bonds are made as follows: purine position I to pyrimidine position I; purine position 6 to pyrimidine position 6.
[Co-author with Francis Crick]
In 'Molecular Structure of Nucleic Acids', Nature (1953), 171, 737.
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The opinion of Bacon on this subject [geometry] was diametrically opposed to that of the ancient philosophers. He valued geometry chiefly, if not solely, on account of those uses, which to Plato appeared so base. And it is remarkable that the longer Bacon lived the stronger this feeling became. When in 1605 he wrote the two books on the Advancement of Learning, he dwelt on the advantages which mankind derived from mixed mathematics; but he at the same time admitted that the beneficial effect produced by mathematical study on the intellect, though a collateral advantage, was “no less worthy than that which was principal and intended.” But it is evident that his views underwent a change. When near twenty years later, he published the De Augmentis, which is the Treatise on the Advancement of Learning, greatly expanded and carefully corrected, he made important alterations in the part which related to mathematics. He condemned with severity the pretensions of the mathematicians, “delidas et faslum mathematicorum.” Assuming the well-being of the human race to be the end of knowledge, he pronounced that mathematical science could claim no higher rank than that of an appendage or an auxiliary to other sciences. Mathematical science, he says, is the handmaid of natural philosophy; she ought to demean herself as such; and he declares that he cannot conceive by what ill chance it has happened that she presumes to claim precedence over her mistress.
In 'Lord Bacon', Edinburgh Review (Jul 1837). Collected in Critical and Miscellaneous Essays: Contributed to the Edinburgh Review (1857), Vol. 1, 395.
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The plexus called rectiform [rete mirabile] by anatomists, is the most wonderful of the bodies located in this region. It encircles the gland [the hypophysis] itself and extends far to the rear; for nearly the whole base of the encephalon has this plexus lying beneath it. It is not a simple network but [looks] as if you had taken several fisherman’s nets and superimposed them. It is characteristic of this net of Nature’s, however, that the meshes of one layer are always attached to those of another, and it is impossible to remove anyone of them alone; for, one after another, the rest follow the one you are removing, because they are all attached to one another successively.
On the Usefulness of the Parts of the Body, Book IX, 4. Trans. Margaret Tallmadge May (1968), Vol. 1, 430-1.
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The question of a possible physiological significance, in the resemblance between the action of choline esters and the effects of certain divisions of the involuntary nervous system, is one of great interest, but one for the discussion of which little evidence is available. Acetyl-choline is, of all the substances examined, the one whose action is most suggestive in this direction. The fact that its action surpasses even that of adrenaline, both in intensity and evanescence, when considered in conjunction with the fact that each of these two bases reproduces those effects of involuntary nerves which are absent from the action of the other, so that the two actions are in many directions at once complementary and antagonistic, gives plenty of scope for speculation.
In 'The Action of Certain Esters and Ethers of Choline, and Their Relation to Muscarine', The Journal of Pharmacology and Experimental Therapeutics, 1914-15, 6, 188.
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The sediments of the past are many miles in collective thickness: yet the feeble silt of the rivers built them all from base to summit.
Lecture at the Royal Dublin Society, 6 Feb 1914. Published in Science Progress, Vol. 9, 37. Republished in The Birth-Time of the World and Other Scientific Essays, (1915), 4.
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The steady progress of physics requires for its theoretical formulation a mathematics which get continually more advanced. ... it was expected that mathematics would get more and more complicated, but would rest on a permanent basis of axioms and definitions, while actually the modern physical developments have required a mathematics that continually shifts its foundation and gets more abstract. Non-euclidean geometry and noncommutative algebra, which were at one time were considered to be purely fictions of the mind and pastimes of logical thinkers, have now been found to be very necessary for the description of general facts of the physical world. It seems likely that this process of increasing abstraction will continue in the future and the advance in physics is to be associated with continual modification and generalisation of the axioms at the base of mathematics rather than with a logical development of any one mathematical scheme on a fixed foundation.
Introduction to a paper on magnetic monopoles, 'Quantised singularities in the electromagnetic field', Proceedings of the Royal Society of Lonndon (1931), A, 133 60. In Helge Kragh, Dirac: a Scientific Biography (1990), 208.
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The theory of medicine, therefore, presents what is useful in thought, but does not indicate how it is to be applied in practice—the mode of operation of these principles. The theory, when mastered, gives us a certain kind of knowledge. Thus we say, for example, there are three forms of fevers and nine constitutions. The practice of medicine is not the work which the physician carries out, but is that branch of medical knowledge which, when acquired, enables one to form an opinion upon which to base the proper plan of treatment.
'The Definition of Medicine', in The Canon of Medicine, adapted by L. Bakhtiar (1999), 10.
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The theory of the earth is the science which describes and explains changes that the terrestrial globe has undergone from its beginning until today, and which allows the prediction of those it shall undergo in the future. The only way to understand these changes and their causes is to study the present-day state of the globe in order to gradually reconstruct its earlier stages, and to develop probable hypotheses on its future state. Therefore, the present state of the earth is the only solid base on which the theory can rely.
In Albert V. Carozzi, 'Forty Years of Thinking in Front of the Alps: Saussure's (1796) Unpublished Theory of the Earth', Earth Sciences History (1989), 8 136.
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The tree of life should perhaps be called the coral of life, base of branches dead; so that passages cannot be seen—this again offers contradiction to constant succession of germs in progress.
P. H. Barrett et al. (eds.), Charles Darwin's Notebooks1836-1844: Geology, Transmutation of the Species, Metaphysical Enquiries, (1987), Notebook B, 25-6.
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There is no certainty where one can neither apply any of the mathematical sciences nor any of those which are based upon the mathematical sciences.
(G 96 v.) In Edward McCurdy (ed., trans.), Leonardo da Vinci’s Note-Books: Arranged and Rendered into English (1908), 54. Also translated elsewhere as, “No knowledge can be certain if it is not based upon mathematics or upon some other knowledge which is itself based upon the mathematical sciences.”
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There is no field of biological inquiry in which the influence of the Origin of Species is not traceable; the foremost men of science in every country are either avowed champions of its leading doctrines, or at any rate abstain from opposing them; a host of young and ardent investigators seek for and find inspiration and guidance in Mr. Darwin’s great work; and the general doctrine of Evolution, to one side of which it gives expression, finds in the phenomena of biology a firm base of operations whence it may conduct its conquest of the whole realm of nature.
From Lecture (19 Mar 1880) delivered at the Royal Institute 'The Coming of Age of The Origin of Species', printed in John Michels (ed.), Science (3 Jul 1880), 1, 15.
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There is no sharp boundary line separating the reactions of the immune bodies from chemical processes between crystalloids, just as in nature there exists every stage between crystalloid and colloid. The nearer the colloid particle approximates to the normal electrolyte, the nearer its compounds must obviously come to conforming to the law of simple stoichiometric proportions, and the compounds themselves to simple chemical compounds. At this point, it should be recalled that Arrhenius has shown that the quantitative relationship between toxin and antitoxin is very similar to that between acid and base.
Landsteiner and Nicholas von Jagic, 'Uber Reaktionen anorganischer Kolloide und Immunkorper', Münchener medizinischer Wochenschrift (1904), 51, 1185-1189. Trans. Pauline M. H. Mazumdar.
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These machines [used in the defense of the Syracusans against the Romans under Marcellus] he [Archimedes] had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with king Hiero’s desire and request, some time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of people in general. Eudoxus and Archytas had been the first originators of this far-famed and highly-prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams. As, for example, to solve the problem, so often required in constructing geometrical figures, given the two extremes, to find the two mean lines of a proportion, both these mathematicians had recourse to the aid of instruments, adapting to their purpose certain curves and sections of lines. But what with Plato’s indignation at it, and his invectives against it as the mere corruption and annihilation of the one good of geometry,—which was thus shamefully turning its back upon the unembodied objects of pure intelligence to recur to sensation, and to ask help (not to be obtained without base supervisions and depravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as a military art.
In John Dryden (trans.), Life of Marcellus.
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This is the element that distinguishes applied science from basic. Surprise is what makes the difference. When you are organized to apply knowledge, set up targets, produce a usable product, you require a high degree of certainty from the outset. All the facts on which you base protocols must be reasonably hard facts with unambiguous meaning. The challenge is to plan the work and organize the workers so that it will come out precisely as predicted. For this, you need centralized authority, elaborately detailed time schedules, and some sort of reward system based on speed and perfection. But most of all you need the intelligible basic facts to begin with, and these must come from basic research. There is no other source. In basic research, everything is just the opposite. What you need at the outset is a high degree of uncertainty; otherwise it isn’t likely to be an important problem. You start with an incomplete roster of facts, characterized by their ambiguity; often the problem consists of discovering the connections between unrelated pieces of information. You must plan experiments on the basis of probability, even bare possibility, rather than certainty.
The Planning of Science, The Lives of a Cell: Notes of a Biology Watcher, (1974) .
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Thus, remarkably, we do not know the true number of species on earth even to the nearest order of magnitude. My own guess, based on the described fauna and flora and many discussions with entomologists and other specialists, is that the absolute number falls somewhere between five and thirty million.
Conservation for the 21st Century
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To turn Karl [Popper]'s view on its head, it is precisely the abandonment of critical discourse that marks the transition of science. Once a field has made the transition, critical discourse recurs only at moments of crisis when the bases of the field are again in jeopardy. Only when they must choose between competing theories do scientists behave like philosophers.
'Logic of Discovery or Psychology of Research', in I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge (1970), 6-7.
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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 developed a computer program, based on tests of a quarter-scale model of the lunar module, and we ran the program through some 400 different [moon] landing conditions.
From interview with Technology Review, quoted in Douglas Martin, 'Joseph Gavin, Who Helped Put First Man on Moon, Dies at 90', New York Times (4 Nov 2010).
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We were very privileged to leave on the Moon a plaque ... saying, ‘For all Mankind’. Perhaps in the third millennium a wayward stranger will read the plaque at Tranquility Base. We’ll let history mark that this was the age in which that became a fact. I was struck this morning in New York by a proudly waved but uncarefully scribbled sign. It said, ‘Through you we touched the Moon.’ It was our privilege today to touch America. I suspect perhaps the most warm, genuine feeling that all of us could receive came through the cheers and shouts and, most of all, the smiles of our fellow Americans. We hope and think that those people shared our belief that this is the beginning of a new era—the beginning of an era when man understands the universe around him, and the beginning of the era when man understands himself.
Acceptance speech (13 Aug 1969), upon receiving the Medal of Freedom as a member of the first manned moon-landing mission. In James R. Hansen, First Man: The Life of Neil A. Armstrong (2005), 569.
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What intellectual phenomenon can be older, or more oft repeated, than the story of a large research program that impaled itself upon a false central assumption accepted by all practitioners? Do we regard all people who worked within such traditions as dishonorable fools? What of the scientists who assumed that the continents were stable, that the hereditary material was protein, or that all other galaxies lay within the Milky Way? These false and abandoned efforts were pursued with passion by brilliant and honorable scientists. How many current efforts, now commanding millions of research dollars and the full attention of many of our best scientists, will later be exposed as full failures based on false premises?
…...
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When asked what it was like to set about proving something, the mathematician likened proving a theorem to seeing the peak of a mountain and trying to climb to the top. One establishes a base camp and begins scaling the mountain’s sheer face, encountering obstacles at every turn, often retracing one’s steps and struggling every foot of the journey. Finally when the top is reached, one stands examining the peak, taking in the view of the surrounding countryside and then noting the automobile road up the other side!
Space-filler in The Two-Year College Mathematics Journal (Nov 1980), 11, No. 5, 295.
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When someone says his conclusions are objective, he means that they are based on prejudices which many other people share.
In The Decline and Fall of Science (1976), 3.
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Why is it so very important to know that the lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal!
In Letter (29 May 1898), at age almost 18, to Mrs. Lawrence Hutton, excerpted in The Story of My Life: With her Letters (1887-1901) (1903, 1921), 242.
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You cannot do without one specialty. You must have some base-line to measure the work and attainments of others. For a general view of the subject, study the history of the sciences. Broad knowledge of all Nature has been the possession of no naturalist except Humboldt, and general relations constituted his specialty.
Lecture at a teaching laboratory on Penikese Island, Buzzard's Bay. Quoted from the lecture notes by David Starr Jordan, Science Sketches (1911), 146.
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You may drink the ocean dry; you may uproot from its base the mountain Meru: you may swallow fire. But more difficult than all these, oh Good One! is control over the mind.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 258.
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Your Grace will no doubt have learnt from the weekly reports of one Marco Antonio Bragadini, called Mamugnano. … He is reported to be able to turn base metal into gold… . He literally throws gold about in shovelfuls. This is his recipe: he takes ten ounces of quicksilver, puts it into the fire, and mixes it with a drop of liquid, which he carries in an ampulla. Thus it promptly turns into good gold. He has no other wish but to be of good use to his country, the Republic. The day before yesterday he presented to the Secret Council of Ten two ampullas with this liquid, which have been tested in his absence. The first test was found to be successful and it is said to have resulted in six million ducats. I doubt not but that this will appear mighty strange to your Grace.
'The Famous Alchemist Bragadini. From Vienna on the 1st day of November 1589'. As quoted in George Tennyson Matthews (ed.) News and Rumor in Renaissance Europe: The Fugger Newsletters (1959), 173. A handwritten collection of news reports (1568-1604) by the powerful banking and merchant house of Fugger in Ausburg.
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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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