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Home > Category Index for Science Quotations > Category Index R > Category: Ratio

Ratio Quotes (39 quotes)

A distinguished writer [Siméon Denis Poisson] has thus stated the fundamental definitions of the science:
“The probability of an event is the reason we have to believe that it has taken place, or that it will take place.”
“The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible” (equally like to happen).
From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary. Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.
An Investigation of the Laws of Thought (1854), 243-244. The Poisson quote is footnoted as from Recherches sur la Probabilité des Jugemens.
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A great surgeon performs operations for stone by a single method; later he makes a statistical summary of deaths and recoveries, and he concludes from these statistics that the mortality law for this operation is two out of five. Well, I say that this ratio means literally nothing scientifically and gives us no certainty in performing the next operation; for we do not know whether the next case will be among the recoveries or the deaths. What really should be done, instead of gathering facts empirically, is to study them more accurately, each in its special determinism. We must study cases of death with great care and try to discover in them the cause of mortal accidents so as to master the cause and avoid the accidents.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 137-138. (Note that Bernard overlooks how the statistical method can be useful: a surgeon announcing a mortality rate of 40% invites comparison. A surgeon with worse outcomes should adopt this method. If a surgeon has a better results, that method should be adopted.)
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After I had addressed myself to this very difficult and almost insoluble problem, the suggestion at length came to me how it could be solved with fewer and much simpler constructions than were formerly used, if some assumptions (which are called axioms) were granted me. They follow in this order.
There is no one center of all the celestial circles or spheres.
The center of the earth is not the center of the universe, but only of gravity and of the lunar sphere.
All the spheres revolve about the sun as their mid-point, and therefore the sun is the center of the universe.
The ratio of the earth's distance from the sun to the height of the firmament is so much smaller than the ratio of the earth's radius to its distance from the sun that the distance from the earth to the sun is imperceptible in comparison with the height of the firmament.
Whatever motion appears in the firmament arises not from any motion of the firmament, but from the earth's motion. The earth together with its circumjacent elements performs a complete rotation on its fixed poles in a daily motion, while the firmament and highest heaven abide unchanged.
What appears to us as motions of the sun arise not from its motion but from the motion of the earth and our sphere, with which we revolve about the sun like any other planet. The earth has, then, more than one motion.
The apparent retrograde and direct motion of the planets arises not from their motion but from the earth's. The motion of the earth alone, therefore, suffices to explain so many apparent inequalities in the heavens.
'The Commentariolus', in Three Copernican Treatises (c.1510), trans. E. Rosen (1939), 58-9.
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All that we can do, is to keep steadily in mind that each organic being is striving to increase at a geometrical ratio; that each at some period of its life, during some season of the year, during each generation or at intervals, has to struggle for life, and to suffer great destruction. When we reflect on this struggle, we may console ourselves with the full belief, that the war of nature is not incessant, that no fear is felt, that death is generally prompt, and that the vigorous, the healthy, and the happy survive and multiply.
From On the Origin of Species by Means of Natural Selection; or, The Preservation of Favoured Races in the Struggle for Life (1861), 76.
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All those who think it paradoxical that so great a weight as the earth should not waver or move anywhere seem to me to go astray by making their judgment with an eye to their own affects and not to the property of the whole. For it would not still appear so extraordinary to them, I believe, if they stopped to think that the earth's magnitude compared to the whole body surrounding it is in the ratio of a point to it. For thus it seems possible for that which is relatively least to be supported and pressed against from all sides equally and at the same angle by that which is absolutely greatest and homogeneous.
Ptolemy
'The Almagest 1', in Ptolemy: the Almagest; Nicolaus Copernicus: On the Revolutions of the Heavenly Spheres; Johannes Kepler: Epitome of Copernican Astronomy: IV - V The Harmonies of the World: V, trans. R. Catesby Taliaferro (1952), 11.
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Among nonclassical ions the ratio of conceptual difficulty to molecular weight reaches a maximum with the cyclopropylcarbinyl-cyclobutyl system.
Nonclassical Ions (1965), 272.
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An event experienced is an event perceived, digested, and assimilated into the substance of our being, and the ratio between the number of cases seen and the number of cases assimilated is the measure of experience.
Address, opening of 1932-3 session of U.C.H. Medical School (4 Oct 1932), 'Art and Science in medicine', The Collected Papers of Wilfred Trotter, FRS (1941), 98.
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Compounds of gaseous substances with each other are always formed in very simple ratios, so that representing one of the terms by unity, the other is 1, 2, or at most 3 ... The apparent contraction of volume suffered by gas on combination is also very simply related to the volume of one of them.
Mémoires de la Société d' Arcueil, 1809, 2, 233-4. Trans. Foundations of the Molecular Theory, Alembic Club Reprint, no. 4 (1950), 24.
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Consider the plight of a scientist of my age. I graduated from the University of California at Berkeley in 1940. In the 41 years since then the amount of biological information has increased 16 fold; during these 4 decades my capacity to absorb new information has declined at an accelerating rate and now is at least 50% less than when I was a graduate student. If one defines ignorance as the ratio of what is available to be known to what is known, there seems no alternative to the conclusion that my ignorance is at least 25 times as extensive as it was when I got my bachelor’s degree. Although I am sure that my unfortunate condition comes as no surprise to my students and younger colleagues, I personally find it somewhat depressing. My depression is tempered, however, by the fact that all biologists, young or old, developing or senescing, face the same melancholy situation because of an interlocking set of circumstances.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 228.
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De Morgan was explaining to an actuary what was the chance that a certain proportion of some group of people would at the end of a given time be alive; and quoted the actuarial formula, involving p [pi], which, in answer to a question, he explained stood for the ratio of the circumference of a circle to its diameter. His acquaintance, who had so far listened to the explanation with interest, interrupted him and exclaimed, “My dear friend, that must be a delusion, what can a circle have to do with the number of people alive at a given time?”
In Mathematical Recreations and Problems (1896), 180; See also De Morgan’s Budget of Paradoxes (1872), 172.
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For any two portions of fire, small or great, will exhibit the same ratio of solid to void; but the upward movement of the greater is quicker than that of the less, just as the downward movement of a mass of gold or lead, or of any other body endowed with weight, is quicker in proportion to its size.
Aristotle
On the Heavens, 309b, 11-5. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. I, 505.
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I was led to the conclusion that at the most extreme dilutions all salts would consist of simple conducting molecules. But the conducting molecules are, according to the hypothesis of Clausius and Williamson, dissociated; hence at extreme dilutions all salt molecules are completely disassociated. The degree of dissociation can be simply found on this assumption by taking the ratio of the molecular conductivity of the solution in question to the molecular conductivity at the most extreme dilution.
Letter to Van’t Hoff, 13 April 1887. In J. R. Partington, A History of Chemistry (1961), Vol. 4, 678.
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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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In a lot of scientists, the ratio of wonder to skepticism declines in time. That may be connected with the fact that in some fields—mathematics, physics, some others—the great discoveries are almost entirely made by youngsters.
Quoted in interview with magazine staff, Psychology Today (Jan 1996).
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In fact, the thickness of the Earth's atmosphere, compared with the size of the Earth, is in about the same ratio as the thickness of a coat of shellac on a schoolroom globe is to the diameter of the globe. That's the air that nurtures us and almost all other life on Earth, that protects us from deadly ultraviolet light from the sun, that through the greenhouse effect brings the surface temperature above the freezing point. (Without the greenhouse effect, the entire Earth would plunge below the freezing point of water and we'd all be dead.) Now that atmosphere, so thin and fragile, is under assault by our technology. We are pumping all kinds of stuff into it. You know about the concern that chlorofluorocarbons are depleting the ozone layer; and that carbon dioxide and methane and other greenhouse gases are producing global warming, a steady trend amidst fluctuations produced by volcanic eruptions and other sources. Who knows what other challenges we are posing to this vulnerable layer of air that we haven't been wise enough to foresee?
In 'Wonder and Skepticism', Skeptical Enquirer (Jan-Feb 1995), 19, No. 1.
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In general I would be cautious against … plays of fancy and would not make way for their reception into scientific astronomy, which must have quite a different character. Laplace’s cosmogenic hypotheses belong in that class. Indeed, I do not deny that I sometimes amuse myself in a similar manner, only I would never publish the stuff. My thoughts about the inhabitants of celestial bodies, for example, belong in that category. For my part, I am (contrary to the usual opinion) convinced … that the larger the cosmic body, the smaller are the inhabitants and other products. For example, on the sun trees, which in the same ratio would be larger than ours, as the sun exceeds the earth in magnitude, would not be able to exist, for on account of the much greater weight on the surface of the sun, all branches would break themselves off, in so far as the materials are not of a sort entirely heterogeneous with those on earth.
Letter to Heinrich Schumacher (7 Nov 1847). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 411.
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In the discussion of the. energies involved in the deformation of nuclei, the concept of surface tension of nuclear matter has been used and its value had been estimated from simple considerations regarding nuclear forces. It must be remembered, however, that the surface tension of a charged droplet is diminished by its charge, and a rough estimate shows that the surface tension of nuclei, decreasing with increasing nuclear charge, may become zero for atomic numbers of the order of 100. It seems therefore possible that the uranium nucleus has only small stability of form, and may, after neutron capture, divide itself into two nuclei of roughly equal size (the precise ratio of sizes depending on liner structural features and perhaps partly on chance). These two nuclei will repel each other and should gain a total kinetic energy of c. 200 Mev., as calculated from nuclear radius and charge. This amount of energy may actually be expected to be available from the difference in packing fraction between uranium and the elements in the middle of the periodic system. The whole 'fission' process can thus be described in an essentially classical way, without having to consider quantum-mechanical 'tunnel effects', which would actually be extremely small, on account of the large masses involved.
[Co-author with Otto Robert Frisch]
Lise Meitner and O. R. Frisch, 'Disintegration of Uranium by Neutrons: a New Type of Nuclear Reaction', Nature (1939), 143, 239.
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It has been found experimentally that the ratio of the amounts of adenine to thymine, and the ratio of guanine to cytosine, are always very close to unity for deoxyribose nucleic acid.
[Co-author with Francis Crick]
In 'Molecular Structure of Nucleic Acids', Nature (1953), 171, 737.
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It is interesting to contemplate an entangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us. These laws, taken in the largest sense, being Growth with Reproduction; Inheritance which is almost implied by reproduction; Variability from the indirect and direct action of the external conditions of life, and from use and disuse; a Ratio of Increase so high as to lead to a Struggle for Life, and as a consequence to Natural Selection, entailing Divergence of Character and the Extinction of less-improved forms. Thus, from the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows. There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.
Concluding remarks in final chapter, The Origin of Species (1859), 490. In the second edition, Darwin changed “breathed” to “breathed by the Creator”.
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Kepler’s laws, although not rigidly true, are sufficiently near to the truth to have led to the discovery of the law of attraction of the bodies of the solar system. The deviation from complete accuracy is due to the facts, that the planets are not of inappreciable mass, that, in consequence, they disturb each other's orbits about the Sun, and, by their action on the Sun itself, cause the periodic time of each to be shorter than if the Sun were a fixed body, in the subduplicate ratio of the mass of the Sun to the sum of the masses of the Sun and Planet; these errors are appreciable although very small, since the mass of the largest of the planets, Jupiter, is less than 1/1000th of the Sun's mass.
In Isaac Newton and Percival Frost (ed.) Newton’s Principia: Sections I, II, III (1863), 216.
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Laplace would have found it child's-play to fix a ratio of progression in mathematical science between Descartes, Leibnitz, Newton and himself
The Education of Henry Adams: An Autobiography? (1918), 491.
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Let me tell you how at one time the famous mathematician Euclid became a physician. It was during a vacation, which I spent in Prague as I most always did, when I was attacked by an illness never before experienced, which manifested itself in chilliness and painful weariness of the whole body. In order to ease my condition I took up Euclid’s Elements and read for the first time his doctrine of ratio, which I found treated there in a manner entirely new to me. The ingenuity displayed in Euclid’s presentation filled me with such vivid pleasure, that forthwith I felt as well as ever.
Selbstbiographie (1875), 20. In Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 146.
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Lord Kelvin was so satisfied with this triumph of science that he declared himself to be as certain of the existence of the ether as a man can be about anything.... “When you can measure what you are speaking about, and express it in numbers, you know something about it....” Thus did Lord Kelvin lay down the law. And though quite wrong, this time he has the support of official modern Science. It is NOT true that when you can measure what you are speaking about, you know something about it. The fact that you can measure something doesn't even prove that that something exists.... Take the ether, for example: didn't they measure the ratio of its elasticity to its density?
In Science is a Sacred Cow (1950), 69-70; 85.
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Mankind has always drawn from outside sources of energy. This island was the first to harness coal and steam. But our present sources stand in the ratio of a million to one, compared with any previous sources. The release of atomic energy will change the whole structure of society.
Address to New Europe Group meeting on the third anniversary of the Hiroshima bomb. Quoted in New Europe Group, In Commemoration of Professor Frederick Soddy (1956), 7.
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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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Newton was probably responsible for the concept that there are seven primary colours in the spectrum—he had a strong interest in musical harmonies and, since there are seven distinct notes in the musical scale, he divided up the spectrum into spectral bands with widths corresponding to the ratios of the small whole numbers found in the just scale.
In 'Light and Colour', Trevor Lamb and Janine Bourriau, Colour: Art & Science (1995), 72.
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Now of the difficulties bound up with the public in which we doctors work, I hesitate to speak in a mixed audience. Common sense in matters medical is rare, and is usually in inverse ratio to the degree of education.
'Teaching and Thinking' (1894). In Aequanimitas with Other Addresses to Medical Students, Nurses and Practitioners of Medicine (1904), 131.
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Population, when unchecked, goes on doubling itself every twenty-five years, or increases in a geometrical ratio. … The means of subsistence, under circumstances the most favorable to human industry, could not possibly be made to increase faster than in an arithmetical ratio.
In An Essay on the Principle of Population: (new ed. 1803), Vol. 1, 5 and 7.
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Thomas Robert Malthus quote Population…increases in a geometrical ratio
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Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio. A slight acquaintance with numbers will show the immensity of the first power in comparison of the second.
An Essay on the Principle of Population (1798), 1st edition, 14. As cited in James Bonar, Parson Malthus (1881), 18.
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The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible, or all of which have the same chance.
In 'Règles générales des probabilités', Recherches sur la Probabilités des Jugemens (1837), Chap. 1, 31, as translated in George Boole, An Investigation of the Laws of Thought (1854), 244. From the original French, “La mesure de la probabilité d'un événement, est le rapport du nombre de cas favorables à cet événement, au nombre total de cas favorables ou contraires, et tous également possibles, ou qui ont tous une même chance.”
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The power of my [steam] engine rises in a geometrical proportion, while the consumption of fuel has only an arithmetical ratio; in such proportion that every time I added one fourth more to the consumption of fuel, the powers of the engine were doubled.
From 'On the Origin of Steam Boats and Steam Wagons', Thomas Cooper (ed.), The Emporium of Arts and Sciences (Feb 1814), 2, No. 2, 211-212.
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The ratio between supervisory and producing personnel is always highest where the intellectuals are in power. In a Communist country it takes half the population to supervise the other half.
In The Temper of Our Time (1967), 70.
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The results serve to disprove the tetranucleotide hypothesis. It is, however, noteworthy—whether this is more than accidental, cannot yet be said—that in all desoxypentose nucleic acids examined thus far the molar ratios of total purines to total pyrimidines, and also of adenine to thymine and of guanine to cytosine, were not far from 1.
'Chemical Specificity of Nucleic Acids and Mechanism of their Enzymatic Degradation', Experientia, 1950, 6, 206.
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The risk of developing carcinoma of the lung increases steadily as the amount smoked increases. If the risk among non-smokers is taken as unity and the resulting ratios in the three age groups in which a large number of patients were interviewed (ages 45 to 74) are averaged, the relative risks become 6, 19, 26, 49, and 65 when the number of cigarettes smoked a day are 3, 10, 20, 35, and, say, 60—that is, the mid-points of each smoking group. In other words, on the admittedly speculative assumptions we have made, the risk seems to vary in approximately simple proportion with the amount smoked.
William Richard Shaboe Doll and Austin Bradford Hill (1897-1991 British medical statistician) 'Smoking and Carcinoma of the Lung', British Medical Journal, 1950, ii, 746.
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This very important property of rods, and indeed also of each kind of cone, this limitation of output to a single dimension of change, may be called the Principle of Univariance and stated thus: “The output of a receptor depends upon its quantum catch, but not upon what quanta are caught.” … Young's theory of colour vision may now be stated in terms of cone pigments. “There are three classes of cone each containing a different visual pigment. The output of each cone is univariant, depending simply upon the quantum catch of its pigment. Our sensation of colour depends upon the ratios of these three cone outputs.”
Principle of Univariance, concerning color vision, as stated in Lecture to a meeting of the Physiological Society at Chelsea College, London (17 Apr 1970), and reported in 'Pigments and Signals in Colour Vision', The Journal of Physiology (1972), 220 No. 3, 4P.
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To regulate something always requires two opposing factors. You cannot regulate by a single factor. To give an example, the traffic in the streets could not be controlled by a green light or a red light alone. It needs a green light and a red light as well. The ratio between retine and promine determines whether there is any motion, any growth, or not. Two different inclinations have to be there in readiness to make the cells proliferate.
In Ralph W. Moss, Free Radical (1988), 186.
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[Archimedes] is said to have requested his friends and relations that when he was dead, they would place over his tomb a sphere containing a cylinder, inscribing it with the ratio which the containing solid bears to the contained.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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… There can be no doubt about faith and not reason being the ultima ratio. Even Euclid, who has laid himself as little open to the charge of credulity as any writer who ever lived, cannot get beyond this. He has no demonstrable first premise. He requires postulates and axioms which transcend demonstration, and without which he can do nothing. His superstructure indeed is demonstration, but his ground his faith. Nor again can he get further than telling a man he is a fool if he persists in differing from him. He says “which is absurd,” and declines to discuss the matter further. Faith and authority, therefore, prove to be as necessary for him as for anyone else.
In The Way of All Flesh (1917), 319-320.
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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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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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Euclid
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- 80 -
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Bible
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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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- 10 -
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