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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Exactly Quotes (13 quotes)

Bei solchen chemischen Untersuchungen, die man zersetzende oder zergliedernde nennt, kommt es zunächst darauf an, zu ermitteln, mit welchen Stoffen man es zu thun hat, oder um chemisch zu reden, welche Stoffe in einem bestimmten Gemenge oder Gemisch enthalten sind. Hierzu bedient man sich sogenannter gegenwirkender Mittel, d. h. Stoffe, die bestimmte Eigenschaften und Eigenthümlichkeiten besitzen und die man aus Ueberlieferung oder eigner Erfahrung genau kennt, so daß die Veränderungen, welche sie bewirken oder erleiden, gleichsam die Sprache sind, mit der sie reden und dadurch dem Forscher anzeigen, daß der und der bestimmte Stoff in der fraglichen Mischung enthalten sei.
In the case of chemical investigations known as decompositions or analyses, it is first important to determine exactly what ingredients you are dealing with, or chemically speaking, what substances are contained in a given mixture or composite. For this purpose we use reagents, i.e., substances that possess certain properties and characteristics, which we well know from references or personal experience, such that the changes which they bring about or undergo, so to say the language that they speak thereby inform the researcher that this or that specific substance is present in the mixture in question.
From Zur Farben-Chemie Musterbilder für Freunde des Schönen und zum Gebrauch für Zeichner, Maler, Verzierer und Zeugdrucker [On Colour Chemistry...] (1850), Introduction. Translation tweaked by Webmaster from version in Herbert and W. Roesky and Klaud Möckel, translated from the original German by T.N. Mitchell and W.E. Russey, Chemical Curiosities: Spectacular Experiments and Inspired Quotes (1996), 1.
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A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment.
In 'Chance', Science et Méthode (1908). Quoted in Richard Kautz, Chaos: The Science of Predictable Random Motion (2011), 167 as translated in Science and Method by F. Maitland (1918).
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I waited for Rob and, linking arms, we took our final steps together onto the rooftop of the world. It was 8.15 am on 24 May 2004; there was nowhere higher on the planet that we could go, the world lay at our feet. Holding each other tightly, we tried to absorb where we were. To be standing here, together, exactly three years since Rob’s cancer treatment, was nothing short of a miracle. Standing on top of Everest was more than just climbing a mountain - it was a gift of life. With Pemba and Nawang we crowded together, wrapping our arms around each other. They had been more than Sherpas, they had been our guardian angels.
Jo Gambi
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In psychoanalysis, only the fee is exactly what it seems to be.
City Aphorisms (1984).
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In the year 1692, James Bernoulli, discussing the logarithmic spiral [or equiangular spiral, ρ = αθ] … shows that it reproduces itself in its evolute, its involute, and its caustics of both reflection and refraction, and then adds: “But since this marvellous spiral, by such a singular and wonderful peculiarity, pleases me so much that I can scarce be satisfied with thinking about it, I have thought that it might not be inelegantly used for a symbolic representation of various matters. For since it always produces a spiral similar to itself, indeed precisely the same spiral, however it may be involved or evolved, or reflected or refracted, it may be taken as an emblem of a progeny always in all things like the parent, simillima filia matri. Or, if it is not forbidden to compare a theorem of eternal truth to the mysteries of our faith, it may be taken as an emblem of the eternal generation of the Son, who as an image of the Father, emanating from him, as light from light, remains ὁμοούσιος with him, howsoever overshadowed. Or, if you prefer, since our spira mirabilis remains, amid all changes, most persistently itself, and exactly the same as ever, it may be used as a symbol, either of fortitude and constancy in adversity, or, of the human body, which after all its changes, even after death, will be restored to its exact and perfect self, so that, indeed, if the fashion of Archimedes were allowed in these days, I should gladly have my tombstone bear this spiral, with the motto, ‘Though changed, I arise again exactly the same, Eadem numero mutata resurgo.’”
In 'The Uses of Mathesis', Bibliotheca Sacra, Vol. 32, 516-516. [The Latin phrase “simillima filia matri” roughly translates as “the daughter resembles the mother”. “Spira mirabilis” is Latin for “marvellous spiral”. The Greek word (?µ???s???) translates as “consubstantial”, meaning of the same substance or essence (used especially of the three persons of the Trinity in Christian theology). —Webmaster]
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It would appear that Deductive and Demonstrative Sciences are all, without exception, Inductive Sciences: that their evidence is that of experience, but that they are also, in virtue of the peculiar character of one indispensable portion of the general formulae according to which their inductions are made, Hypothetical Sciences. Their conclusions are true only upon certain suppositions, which are, or ought to be, approximations to the truth, but are seldom, if ever, exactly true; and to this hypothetical character is to be ascribed the peculiar certainty, which is supposed to be inherent in demonstration.
In System of Logic, Bk. 2, chap. 6, 1.
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Nearly every subject has a shadow, or imitation. It would, I suppose, be quite possible to teach a deaf and dumb child to play the piano. When it played a wrong note, it would see the frown of its teacher, and try again. But it would obviously have no idea of what it was doing, or why anyone should devote hours to such an extraordinary exercise. It would have learnt an imitation of music. and it would fear the piano exactly as most students fear what is supposed to be mathematics.
In Mathematician's Delight (1943), 8.
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The significant chemicals of living tissue are rickety and unstable, which is exactly what is needed for life.
As shown, without citation, in Randy Moore, Writing to Learn Science (1997), 226.
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The telegraph is a kind of very long cat. You pull his tail in New York and he is mewing in Los Angeles. Radio operates in exactly the same way, except there is no cat.
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There is a popular cliché ... which says that you cannot get out of computers any more than you have put in..., that computers can only do exactly what you tell them to, and that therefore computers are never creative. This cliché is true only in a crashingly trivial sense, the same sense in which Shakespeare never wrote anything except what his first schoolteacher taught him to write—words.
In The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe Without Design (1966, 1986), 64. Excerpted in Richard Dawkins, ‘Creation and Natural Selection’. New Scientist (25 Sep 1986), 111, 38.
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There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened.
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There will always be dreams grander or humbler than your own, but there will never be a dream exactly like your own...for you are unique and more wondrous than you know!
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You see, wire telegraph is a kind of a very, very long cat. You pull his tail in New York and his head is meowing in Los Angeles. Do you understand this? And radio operates exactly the same way: you send signals here, they receive them there. The only difference is that there is no cat.
When asked to describe radio
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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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