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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Home > Category Index for Science Quotations > Category Index O > Category: Occasion

Occasion Quotes (23 quotes)

An inventor is an opportunist, one who takes occasion by the hand; who, having seen where some want exists, successfully applies the right means to attain the desired end. The means may be largely, or even wholly, something already known, or there may be a certain originality or discovery in the means employed. But in every case the inventor uses the work of others. If I may use a metaphor, I should liken him to the man who essays the conquest of some virgin alp. At the outset he uses the beaten track, and, as he progresses in the ascent, he uses the steps made by those who have preceded him, whenever they lead in the right direction; and it is only after the last footprints have died out that he takes ice-axe in hand and cuts the remaining steps, few or many, that lift him to the crowning height which is his goal.
In Kenneth Raydon Swan, Sir Joseph Swan (1946), 44.
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Bad times have a scientific value. These are occasions a good learner would not miss.
In 'Considerations by the Way', The Conduct of Life (1860) collected in The Works of Ralph Waldo Emerson: Comprising His Essays, Lectures, Poems and Orations (1882), Vol. 2, 420.
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During seasons of great pestilence men have often believed the prophecies of crazed fanatics, that the end of the world was come. Credulity is always greatest in times of calamity. Prophecies of all sorts are rife on such occasions, and are readily believed, whether for good or evil.
From Memoirs of Extraordinary Popular Delusions (1841), Vol. 1, 170.
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Even on the most solemn occasions I got away without wearing socks and hid that lack of civilisation in high boots.
…...
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I have mentioned mathematics as a way to settle in the mind a habit of reasoning closely and in train; not that I think it necessary that all men should be deep mathematicians, but that, having got the way of reasoning which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge, as they shall have occasion. For in all sorts of reasoning, every single argument should be managed as a mathematical demonstration; the connection and dependence of ideas should be followed till the mind is brought to the source on which it bottoms, and observes the coherence all along; …
In The Conduct of the Understanding, Sect. 7.
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I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary—being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived. And these are the causes that operate in perfect harmony. Each new scientific conception gives occasion to new applications of deductive reasoning; but those applications may be only possible through the methods and the processes which belong to an earlier stage.
Explaining his choice for the exposition in historical order of the topics in A Treatise on Differential Equations (1859), Preface, v-vi.
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If it were possible for a metaphysician to be a golfer, he might perhaps occasionally notice that his ball, instead of moving forward in a vertical plane (like the generality of projectiles, such as brickbats and cricket balls), skewed away gradually to the right. If he did notice it, his methods would naturally lead him to content himself with his caddies’s remark-“ye heeled that yin,” or “Ye jist sliced it.” … But a scientific man is not to be put off with such flimsy verbiage as that. He must know more. What is “Heeling”, what is “slicing”, and why would either operation (if it could be thoroughly carried out) send a ball as if to cover point, thence to long slip, and finally behind back-stop? These, as Falstaff said, are “questions to be asked.”
In 'The Unwritten Chapter on Golf, Nature (1887), 36, 502.
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If on occasion Mr. Casson exhibits an insularity of judgment when it comes to the evaluation of the contribution made by various men to the development of modern anthropology, he may be forgiven upon the ground that, where anthropology is concerned, he is only following an old English custom!
In 'Review: The Discovery of Man by Stanley Casson', Isis (Jun 1941), 33, No. 2, 302.
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It is said that the composing of the Lilavati was occasioned by the following circumstance. Lilavati was the name of the author’s daughter, concerning whom it appeared, from the qualities of the ascendant at her birth, that she was destined to pass her life unmarried, and to remain without children. The father ascertained a lucky hour for contracting her in marriage, that she might be firmly connected and have children. It is said that when that hour approached, he brought his daughter and his intended son near him. He left the hour cup on the vessel of water and kept in attendance a time-knowing astrologer, in order that when the cup should subside in the water, those two precious jewels should be united. But, as the intended arrangement was not according to destiny, it happened that the girl, from a curiosity natural to children, looked into the cup, to observe the water coming in at the hole, when by chance a pearl separated from her bridal dress, fell into the cup, and, rolling down to the hole, stopped the influx of water. So the astrologer waited in expectation of the promised hour. When the operation of the cup had thus been delayed beyond all moderate time, the father was in consternation, and examining, he found that a small pearl had stopped the course of the water, and that the long-expected hour was passed. In short, the father, thus disappointed, said to his unfortunate daughter, I will write a book of your name, which shall remain to the latest times—for a good name is a second life, and the ground-work of eternal existence.
In Preface to the Persian translation of the Lilavati by Faizi (1587), itself translated into English by Strachey and quoted in John Taylor (trans.) Lilawati, or, A Treatise on Arithmetic and Geometry by Bhascara Acharya (1816), Introduction, 3. [The Lilavati is the 12th century treatise on mathematics by Indian mathematician, Bhaskara Acharya, born 1114.]
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Literature is made upon any occasion that a challenge is put to the legal apparatus by conscience in touch with humanity.
In Chicago: A City on the Make (1951, 1983), 81.
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Many quite nefarious ideologies pass for common sense. For decades of American history, it was common sense in some quarters for white people to own slaves and for women not to vote. … If common sense sometimes preserves the social status quo, and that status quo sometimes treats unjust social hierarchies as natural, it makes good sense on such occasions to find ways of challenging common sense.
In 'A “Bad Writer” Bites Back', The New York Times (20 Mar 1999), A15.
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Mathematical rigor is like clothing; in its style it ought to suit the occasion, and it diminishes comfort and restrains freedom of movement if it is either too loose or too tight.
In Differential Equations: With Applications and Historical Notes (1972), ix.
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Newton lectured now and then to the few students who chose to hear him; and it is recorded that very frequently he came to the lecture-room and found it empty. On such occasions he would remain fifteen minutes, and then, if no one came, return to his apartments.
In 'Sir Isaac Newton', People’s Book of Biography: Or, Short Lives of the Most Interesting Persons of All Ages and Countries (1868), 250.
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On certain occasions, the eyes of the mind can supply the want of the most powerful telescopes, and lead to astronomical discoveries of the highest importance.
In François Arago, trans. by William Henry Smyth, Baden Powell and Robert Grant, 'Laplace', Biographies of Distinguished Scientific Men (1859), Vol. 1, 347. This comment refers to the ability of a mathematician to describe a circumstance before an actual observation confirms it.
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On two occasions I have been asked [by members of Parliament], “Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?” I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.
In 'Difference Engine No. 1', Passages from the Life of a Philosopher (1864), Chap. 5, 59.
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Statistical analysis in cases involving small numbers can be particularly helpful because on many occasions intuition can be highly misleading.
In essay 'Statistical Proof of Employment Discrimination', collected in Judith M. Tanur et al. (eds.), Statistics, a Guide to the Unknown (3rd ed., 1989), 83.
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The bell ringing for church, we went thither immediately, and with hearts full of gratitude, returned sincere thanks to God for the mercies we had received: were I a Roman Catholic, perhaps I should on this occasion vow to build a chapel to some saint, but as I am not, if I were to vow at all, it should be to build a light-house. [Upon narrowly missing a shipwreck on the Scilly rocks.]
[Frequently seen summarized as, though not Franklin's own wording: Lighthouses are more helpful than churches.
Letter written at Falmouth, England (17 Jul 1757) to Deborah Read Franklin (common-law wife). Quoted in Benjamin Franklin and William Temple Franklin, The Works of Dr. Benjamin Franklin (1818), 175 footnote added by W.T. Franklin.
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The Greeks in the first vigour of their pursuit of mathematical truth, at the time of Plato and soon after, had by no means confined themselves to those propositions which had a visible bearing on the phenomena of nature; but had followed out many beautiful trains of research concerning various kinds of figures, for the sake of their beauty alone; as for instance in their doctrine of Conic Sections, of which curves they had discovered all the principal properties. But it is curious to remark, that these investigations, thus pursued at first as mere matters of curiosity and intellectual gratification, were destined, two thousand years later, to play a very important part in establishing that system of celestial motions which succeeded the Platonic scheme of cycles and epicycles. If the properties of conic sections had not been demonstrated by the Greeks and thus rendered familiar to the mathematicians of succeeding ages, Kepler would probably not have been able to discover those laws respecting the orbits and motions of planets which were the occasion of the greatest revolution that ever happened in the history of science.
In History of Scientific Ideas, Bk. 9, chap. 14, sect. 3.
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The origin of a science is usually to be sought for not in any systematic treatise, but in the investigation and solution of some particular problem. This is especially the case in the ordinary history of the great improvements in any department of mathematical science. Some problem, mathematical or physical, is proposed, which is found to be insoluble by known methods. This condition of insolubility may arise from one of two causes: Either there exists no machinery powerful enough to effect the required reduction, or the workmen are not sufficiently expert to employ their tools in the performance of an entirely new piece of work. The problem proposed is, however, finally solved, and in its solution some new principle, or new application of old principles, is necessarily introduced. If a principle is brought to light it is soon found that in its application it is not necessarily limited to the particular question which occasioned its discovery, and it is then stated in an abstract form and applied to problems of gradually increasing generality.
Other principles, similar in their nature, are added, and the original principle itself receives such modifications and extensions as are from time to time deemed necessary. The same is true of new applications of old principles; the application is first thought to be merely confined to a particular problem, but it is soon recognized that this problem is but one, and generally a very simple one, out of a large class, to which the same process of investigation and solution are applicable. The result in both of these cases is the same. A time comes when these several problems, solutions, and principles are grouped together and found to produce an entirely new and consistent method; a nomenclature and uniform system of notation is adopted, and the principles of the new method become entitled to rank as a distinct science.
In A Treatise on Projections (1880), Introduction, xi. Published as United States Coast and Geodetic Survey, Treasury Department Document, No. 61.
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There are many occasions when the muscles that form the lips of the mouth move the lateral muscles that are joined to them, and there are an equal number of occasions when these lateral muscles move the lips of this mouth, replacing it where it cannot return of itself, because the function of muscle is to pull and not to push except in the case of the genitals and the tongue.
'Anatomy', in The Notebooks of Leonardoda Vinci, trans. E. MacCurdy (1938), Vol. 1, 152.
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Those who intend to practise Midwifery, ought first of all to make themselves masters of anatomy, and acquire a competent knowledge in surgery and physic; because of their connections with the obstetric art, if not always, at least in many cases. He ought to take the best opportunities he can find of being well instructed; and of practising under a master, before he attempts to deliver by himself. ... He should also embrace every occasion of being present at real labours, ... he will assist the poor as well as the rich, behaving always with charity and compassion.
In A Treatise on the Theory and Practice of Midwifery (1766), 440-441.
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What we have to discover for ourselves leaves behind in our mind a pathway that can be used on another occasion.
Aphorism 26 in Notebook C (1772-1773), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 36.
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Whoever wishes to acquire a deep acquaintance with Nature must observe that there are analogies which connect whole branches of science in a parallel manner, and enable us to infer of one class of phenomena what we know of another. It has thus happened on several occasions that the discovery of an unsuspected analogy between two branches of knowledge has been the starting point for a rapid course of discovery.
Principles of Science: A Treatise on Logic and Scientific Method (1874, 2nd ed., 1913), 631.
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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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