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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Collect Quotes (19 quotes)

I grew up in Japan and Hong Kong and then came to the States. Japan was a huge influence on me because, as a child, I would hear the oxcarts come and collect our sewage at night out of our house from the latrine and then take it off to the farms as fertilizer. And then the food would come back in oxcarts during the day. I always had this sort of “our poop became food” mental model. The idea of “waste equals food” was pretty inculcated, that everything was precious and the systems were coherent and cyclical.
In interview with Kerry A. Dolan, 'William McDonough On Cradle-to-Cradle Design', Forbes (4 Aug 2010)
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I now collect all sorts of itineraries from other travelers from the local companies and am able to fill many a gap in the map between Djur and Bahr el Jebel.
From Letter in August Petermann, Petermann’s Geographische Mittheilungen (1870), 20. As quoted and cited in Kathrin Fritsch, '"You Have Everything Confused And Mixed Up…!" Georg Schweinfurth, Knowledge And Cartography Of Africa In The 19th Century', History in Africa (2009), 36, 93. Fritsch comments, “Thus indigenous African knowledge found its way directly into modern nineteenth-century maps of Africa.”
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In addition, the oil royalties the Federal Government does not collect from big oil will starve the Land and Water Conservation Fund of critical financial resources.
…...
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It appears … [Descartes] has inverted the order of philosophising, … it seemed good to him not to learn from things, but to impose his own laws on things.… First he collected … truths which he thought suitable …; and then gradually advanced to particulars explicable from principles which … he had framed without consulting Nature.
As quoted in B.J.T. Dobbs, The Foundations of Newton's Alchemy (1983), 101. Cited as Osmond’s translation in Percy Herbert Osmond, Isaac Barrow, His Life and Times (1944), 30-31.
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It has been said that no science is established on a firm basis unless its generalisations can be expressed in terms of number, and it is the special province of mathematics to assist the investigator in finding numerical relations between phenomena. After experiment, then mathematics. While a science is in the experimental or observational stage, there is little scope for discerning numerical relations. It is only after the different workers have “collected data” that the mathematician is able to deduce the required generalisation. Thus a Maxwell followed Faraday and a Newton completed Kepler.
In Higher Mathematics for Students of Chemistry and Physics (1902), 3.
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It is for such inquiries the modern naturalist collects his materials; it is for this that he still wants to add to the apparently boundless treasures of our national museums, and will never rest satisfied as long as the native country, the geographical distribution, and the amount of variation of any living thing remains imperfectly known. He looks upon every species of animal and plant now living as the individual letters which go to make up one of the volumes of our earth’s history; and, as a few lost letters may make a sentence unintelligible, so the extinction of the numerous forms of life which the progress of cultivation invariably entails will necessarily render obscure this invaluable record of the past. It is, therefore, an important object, which governments and scientific institutions should immediately take steps to secure, that in all tropical countries colonised by Europeans the most perfect collections possible in every branch of natural history should be made and deposited in national museums, where they may be available for study and interpretation. If this is not done, future ages will certainly look back upon us as a people so immersed in the pursuit of wealth as to be blind to higher considerations. They will charge us with having culpably allowed the destruction of some of those records of Creation which we had it in our power to preserve; and while professing to regard every living thing as the direct handiwork and best evidence of a Creator, yet, with a strange inconsistency, seeing many of them perish irrecoverably from the face of the earth, uncared for and unknown.
In 'On the Physical Geography of the Malay Archipelago', Journal of the Royal Geographical Society (1863), 33, 234.
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It is unquestionably no slight advantage to be placed, at that early stage of life, when the mind collects its facts with greatest avidity, and the curiosity is most active, in localities where there is much to attract observation that has, escaped the notice of others. … I…was born on the Old Red Sandstone [of Scotland].
In front matter, The Old Red Sandstone: Or, New Walks in an Old Field (1851), v.
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Many scientists have spent years collecting information about the effect of human actions on the climate. There’s no question that the climate is changing, I’ve seen it all over the world. And the fact that people can deny that humans have influenced this change in climate is quite frankly absurd.
From Facebook video 10155220356117171 (31 Mar 2017) posted by Dr. Jane Goodall.
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Mathematics … above all other subjects, makes the student lust after knowledge, fills him, as it were, with a longing to fathom the cause of things and to employ his own powers independently; it collects his mental forces and concentrates them on a single point and thus awakens the spirit of individual inquiry, self-confidence and the joy of doing; it fascinates because of the view-points which it offers and creates certainty and assurance, owing to the universal validity of its methods. Thus, both what he receives and what he himself contributes toward the proper conception and solution of a problem, combine to mature the student and to make him skillful, to lead him away from the surface of things and to exercise him in the perception of their essence. A student thus prepared thirsts after knowledge and is ready for the university and its sciences. Thus it appears, that higher mathematics is the best guide to philosophy and to the philosophic conception of the world (considered as a self-contained whole) and of one’s own being.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 40. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 49.
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My interest in Science had many roots. Some came from my mother … while I was in my early teens. She fell in love with science,… [from] classes on the Foundations of Physical Science. … I was infected by [her] professor second hand, through hundreds of hours of conversations at my mother’s knees. It was from my mother that I first learned of Archimedes, Leonardo da Vinci, Galileo, Kepler, Newton, and Darwin. We spent hours together collecting single-celled organisms from a local pond and watching them with a microscope.
From 'Richard E. Smalley: Biographical', collected in Tore Frängsmyr (ed.), Les Prix Nobel: The Nobel Prizes 1996 (1997).
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One cannot collect all the beautiful shells on the beach. One can collect only a few, and they are more beautiful if they are few.
In Gift From the Sea (1955), 114.
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The ideas which these sciences, Geometry, Theoretical Arithmetic and Algebra involve extend to all objects and changes which we observe in the external world; and hence the consideration of mathematical relations forms a large portion of many of the sciences which treat of the phenomena and laws of external nature, as Astronomy, Optics, and Mechanics. Such sciences are hence often termed Mixed Mathematics, the relations of space and number being, in these branches of knowledge, combined with principles collected from special observation; while Geometry, Algebra, and the like subjects, which involve no result of experience, are called Pure Mathematics.
In The Philosophy of the Inductive Sciences (1868), Part 1, Bk. 2, chap. 1, sect. 4.
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The invention of the differential calculus marks a crisis in the history of mathematics. The progress of science is divided between periods characterized by a slow accumulation of ideas and periods, when, owing to the new material for thought thus patiently collected, some genius by the invention of a new method or a new point of view, suddenly transforms the whole subject on to a higher level.
In An Introduction to Mathematics (1911), 217. Whitehead continued by quoting the poet, Percy Shelley, who compared the slow accumulation of thoughts leading to an avalanche following the laying down of a great truth. See the poetic quote beginning, “The sun-awakened avalanche…” on the Percy Shelley Quotations page.
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The professor may choose familiar topics as a starting point. The students collect material, work problems, observe regularities, frame hypotheses, discover and prove theorems for themselves. … the student knows what he is doing and where he is going; he is secure in his mastery of the subject, strengthened in confidence of himself. He has had the experience of discovering mathematics. He no longer thinks of mathematics as static dogma learned by rote. He sees mathematics as something growing and developing, mathematical concepts as something continually revised and enriched in the light of new knowledge. The course may have covered a very limited region, but it should leave the student ready to explore further on his own.
In A Concrete Approach to Abstract Algebra (1959), 1-2.
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The Spaniards plundered Peru for its gold, which the Inca aristocracy had collected as we might collect stamps, with the touch of Midas. Gold for greed, gold for splendor, gold for adornment, gold for reverence, gold for power, sacrificial gold, life-giving gold, gold for tenderness, barbaric gold, voluptuous gold.
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The Superfund legislation set up a system of insurance premiums collected from the chemical industry to clean up toxic wastes. This new program may prove to be as far-reaching and important as any accomplishment of my administration. The reduction of the threat to America's health and safety from thousands of toxic-waste sites will continue to be an urgent but bitterly fought issue—another example for the conflict between the public welfare and the profits of a few private despoilers of our nation's environment.
Keeping Faith: Memoirs of a President (1980), 591.
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Think how busy the squirrels are in October, in every pitch-pine grove all over the state, cutting off the twigs and collecting the cones. While the farmer is digging his potatoes and gathering his corn, he little thinks of this harvest of pine cones which the squirrel is gathering in the neighboring woods still more sedulously than himself.
In Wild Fruits: Thoreau’s Rediscovered Last Manuscript (2000), 269.
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When I was a little over eight years old,… I was sent to a day-school…. [By this time] my taste for natural history, and more especially for collecting, was well developed. I tried to make out the names of plants, and collected all sorts of things, shells, seals, franks, coins, and minerals. The passion for collecting which leads a man to be a systematic naturalist, a virtuoso, or a miser, was very strong in me.
In Charles Darwin and Francis Darwin (ed.), 'Autobiography', The Life and Letters of Charles Darwin (1887, 1896), Vol. 1, 26.
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When I was about 13, I cycled from Leicester to the Lake District and back again, collecting fossils and staying in youth hostels. I was away for three weeks, and my mother and father didn’t know where I was. I doubt many parents would let children do that now.
It is about 200 miles each way between his hometown (Leicester) and the Lake District. As reported by Adam Lusher in 'Sir David Attenborough', Daily Mail (28 Feb 2014).
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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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