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Who said: “Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.”
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Angle Quotes (15 quotes)

Question: Show how the hypothenuse face of a right-angled prism may be used as a reflector. What connection is there between the refractive index of a medium and the angle at which an emergent ray is totally reflected?
Answer: Any face of any prism may be used as a reflector. The con nexion between the refractive index of a medium and the angle at which an emergent ray does not emerge but is totally reflected is remarkable and not generally known.
Genuine student answer* to an Acoustics, Light and Heat paper (1880), Science and Art Department, South Kensington, London, collected by Prof. Oliver Lodge. Quoted in Henry B. Wheatley, Literary Blunders (1893), 182-3, Question 29. (*From a collection in which Answers are not given verbatim et literatim, and some instances may combine several students' blunders.)
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Thomasina: Every week I plot your equations dot for dot, x’s against y’s in all manner of algebraical relation, and every week they draw themselves as commonplace geometry, as if the world of forms were nothing but arcs and angles. God’s truth, Septimus, if there is an equation for a curve like a bell, there must be an equation for one like a bluebell, and if a bluebell, why not a rose? Do we believe nature is written in numbers?
Septimus: We do.
Thomasina: Then why do your shapes describe only the shapes of manufacture?
Septimus: I do not know.
Thomasina: Armed thus, God could only make a cabinet.
In the play, Acadia (1993), Scene 3, 37.
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Are the atoms of the dextroacid (tartaric) grouped in the spirals of a right-hand helix or situated at the angles of an irregular tetrahedron, or arranged in such or such particular unsymmetrical fashion? We are unable to reply to these questions. But there can be no reason for doubting that the grouping of the atoms has an unsymmetrical arrangement with a non-superimposable image. It is not less certain that the atoms of the laevo-acid realize precisely an unsymmetrical arrangement of the inverse of the above.
Leηons de Chemie (1860), 25.
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If you have an idea that you wish your audience to carry away, turn it upside down and inside out, rephrasing it from different angles. Remember that the form in which the thing may appear best to you may not impress half your audience.
Advice to the writer of his first paper for presentation at a scientific meeting. As expressed in quotation marks by Charles Thom in 'Robert Almer Harper', National Academy Biographical Memoirs (1948), 25, 233-234. Also, in Thom's words, “[Harper] added that a miscellaneous audience can not he expected to carry away a lot of separate facts but one good idea, well pictured out, will be remembered by some of them.”
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In flying, the probability of survival is inversely proportional to the angle of arrival.
Quoted in Richard H. Enns, George McGuire, Computer Algebra Recipes for Classical Mechanics (2003), 37.
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It is natural for man to relate the units of distance by which he travels to the dimensions of the globe that he inhabits. Thus, in moving about the earth, he may know by the simple denomination of distance its proportion to the whole circuit of the earth. This has the further advantage of making nautical and celestial measurements correspond. The navigator often needs to determine, one from the other, the distance he has traversed from the celestial arc lying between the zeniths at his point of departure and at his destination. It is important, therefore, that one of these magnitudes should be the expression of the other, with no difference except in the units. But to that end, the fundamental linear unit must be an aliquot part of the terrestrial meridian. ... Thus, the choice of the metre was reduced to that of the unity of angles.
Lecture at the Ιcole Normale to the Year III (Apr 1795), Oeuvres Completes de Laplace (1878-1912), Vol. 14, 141. In Charles Coulston Gillispie, Dictionary of Scientific Biography (1978), Vol. 15, 335.
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Of all the constituents of the human body, bone is the hardest, the driest, the earthiest, and the coldest; and, excepting only the teeth, it is devoid of sensation. God, the great Creator of all things, formed its substance to this specification with good reason, intending it to be like a foundation for the whole body; for in the fabric of the human body bones perform the same function as do walls and beams in houses, poles in tents, and keels and ribs in boats.
Bones Differentiated by Function
Some bones, by reason of their strength, form as it were props for the body; these include the tibia, the femur, the spinal vertebrae, and most of the bony framework. Others are like bastions, defense walls, and ramparts, affording natural protection to other parts; examples are the skull, the spines and transverse processes of the vertebrae, the breast bone, the ribs. Others stand in front of the joints between certain bones, to ensure that the joint does not move too loosely or bend to too acute an angle. This is the function of the tiny bones, likened by the professors of anatomy to the size of a sesame seed, which are attached to the second internode of the thumb, the first internode of the other four fingers and the first internodes of the five toes. The teeth, on the other hand, serve specifically to cut, crush, pound and grind our food, and similarly the two ossicles in the organ of hearing perform a specifically auditory function.
From De Humani Corporis Fabrica Libri Septem: (1543), Book I, 1, as translated by William Frank Richardson, in 'Nature of Bone; Function of Bones', On The Fabric of the Human Body: Book I: The Bones and Cartilages (1998), 1.
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She has the sort of body you go to see in marble. She has golden hair. Quickly, deftly, she reaches with both hands behind her back and unclasps her top. Setting it on her lap, she swivels ninety degrees to face the towboat square. Shoulders back, cheeks high, she holds her pose without retreat. In her ample presentation there is defiance of gravity. There is no angle of repose. She is a siren and these are her songs.
…...
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The divisions of science are not like different lines that meet in one angle, but rather like the branches of trees that join in one trunk.
The Works of Francis Bacon (1815), Vol. 6, 68.
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The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. Nevertheless, it has been found that there are apparent exceptions to most of these laws, and this is particularly true when the observations are pushed to a limit, i.e., whenever the circumstances of experiment are such that extreme cases can be examined. Such examination almost surely leads, not to the overthrow of the law, but to the discovery of other facts and laws whose action produces the apparent exceptions. As instances of such discoveries, which are in most cases due to the increasing order of accuracy made possible by improvements in measuring instruments, may be mentioned: first, the departure of actual gases from the simple laws of the so-called perfect gas, one of the practical results being the liquefaction of air and all known gases; second, the discovery of the velocity of light by astronomical means, depending on the accuracy of telescopes and of astronomical clocks; third, the determination of distances of stars and the orbits of double stars, which depend on measurements of the order of accuracy of one-tenth of a second-an angle which may be represented as that which a pin's head subtends at a distance of a mile. But perhaps the most striking of such instances are the discovery of a new planet or observations of the small irregularities noticed by Leverrier in the motions of the planet Uranus, and the more recent brilliant discovery by Lord Rayleigh of a new element in the atmosphere through the minute but unexplained anomalies found in weighing a given volume of nitrogen. Many other instances might be cited, but these will suffice to justify the statement that “our future discoveries must be looked for in the sixth place of decimals.”
In Light Waves and Their Uses (1903), 23-4. Michelson had some years earlier referenced “an eminent physicist” that he did not name who had “remarked that the future truths of physical science are to be looked for in the sixth place of decimals,” near the end of his Convocation Address at the Dedication of the Ryerson Physical Laboratory at the University of Chicago, 'Some of the Objects and Methods of Physical Science' (4 Jul 1894), published in University of Chicago Quarterly Calendar (Aug 1894), 3, No.2, 15. Also
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The X-ray spectrometer opened up a new world. It proved to be a far more powerful method of analysing crystal structure…. One could examine the various faces of a crystal in succession, and by noting the angles at which and the intensity with which they reflected the X-rays, one could deduce the way in which the atoms were arranged in sheets parallel to these faces. The intersections of these sheets pinned down the positions of the atoms in space.… It was like discovering an alluvial gold field with nuggets lying around waiting to be picked up.… It was a glorious time when we worked far into every night with new worlds unfolding before us in the silent laboratory.
In The History of X-ray Analysis (1943), 9.
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There are many modes of thinking about the world around us and our place in it. I like to consider all the angles from which we might gain perspective on our amazing universe and the nature of existence.
With co-author Kenneth William Ford Geons, Black Holes, and Quantum Foam: A Life in Physics (1998, 2010), 153.
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To the exact descriptions he gave of the crystalline forms, he added the measure of their angles, and, which was essential, showed that these angles were constant for each variety. In one word, his crystallography was the fruit of an immense work, almost entirely new and most precious in its usefulness.<[About Jean-Baptiste Romι de l’Isle.]
(1795). As quoted in Andrι Authier, Early Days of X-ray Crystallography (2013), 313.
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Years ago I used to worry about the degree to which I specialized. Vision is limited enough, yet I was not really working on vision, for I hardly made contact with visual sensations, except as signals, nor with the nervous pathways, nor the structure of the eye, except the retina. Actually my studies involved only the rods and cones of the retina, and in them only the visual pigments. A sadly limited peripheral business, fit for escapists. But it is as though this were a very narrow window through which at a distance, one can only see a crack of light. As one comes closer the view grows wider and wider, until finally looking through the same narrow window one is looking at the universe. It is like the pupil of the eye, an opening only two to three millimetres across in daylight, but yielding a wide angle of view, and manoeuvrable enough to be turned in all directions. I think this is always the way it goes in science, because science is all one. It hardly matters where one enters, provided one can come closer, and then one does not see less and less, but more and more, because one is not dealing with an opaque object, but with a window.
In Scientific American, 1960s, attributed.
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[The] structural theory is of extreme simplicity. It assumes that the molecule is held together by links between one atom and the next: that every kind of atom can form a definite small number of such links: that these can be single, double or triple: that the groups may take up any position possible by rotation round the line of a single but not round that of a double link: finally that with all the elements of the first short period [of the periodic table], and with many others as well, the angles between the valencies are approximately those formed by joining the centre of a regular tetrahedron to its angular points. No assumption whatever is made as to the mechanism of the linkage. Through the whole development of organic chemistry this theory has always proved capable of providing a different structure for every different compound that can be isolated. Among the hundreds of thousands of known substances, there are never more isomeric forms than the theory permits.
Presidential Address to the Chemical Society (16 Apr 1936), Journal of the Chemical Society (1936), 533.
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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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