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Home > Category Index for Science Quotations > Category Index S > Category: Scale

Scale Quotes (63 quotes)

A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales.
Cited as from Fractals: Form, Chance, and Dimension (1977), by J.W. Cannon, in review of The Fractal Geometry of Nature (1982) in The American Mathematical Monthly (Nov 1984), 91, No. 9, 594.
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A million years is a short time—the shortest worth messing with for most problems. You begin tuning your mind to a time scale that is the planet’s time scale. For me, it is almost unconscious now and is a kind of companionship with the earth.
In Basin and Range (1981), 134.
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A scientist without imagination is a butcher with dull knives and out-worn scales.
In Kahlil Gibran: The Collected Works (207), 204.
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As our researches have made clear, an animal high in the organic scale only reaches this rank by passing through all the intermediate states which separate it from the animals placed below it. Man only becomes man after traversing transitional organisatory states which assimilate him first to fish, then to reptiles, then to birds and mammals.
Annales des Sciences Naturelles (1834), 2 (ii), 248. Trans. in E. S. Russell, Form and Function (1916), 82.
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Because of the way it came into existence, the solar system has only one-way traffic—like Piccadilly Circus. … If we want to make a model to scale, we must take a very tiny object, such as a pea, to represent the sun. On the same scale the nine planets will be small seeds, grains of sand and specks of dust. Even so, Piccadilly Circus is only just big enough to contain the orbit of Pluto. … The whole of Piccadilly Circus was needed to represent the space of the solar system, but a child can carry the whole substance of the model in its hand. All the rest is empty space.
In The Stars in Their Courses (1931, 1954), 49-50 & 89.
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Curves that have no tangents are the rule. … Those who hear of curves without tangents, or of functions without derivatives, often think at first that Nature presents no such complications. … The contrary however is true. … Consider, for instance, one of the white flakes that are obtained by salting a solution of soap. At a distance its contour may appear sharply defined, but as we draw nearer its sharpness disappears. The eye can no longer draw a tangent at any point. … The use of a magnifying glass or microscope leaves us just as uncertain, for fresh irregularities appear every time we increase the magnification. … An essential characteristic of our flake … is that we suspect … that any scale involves details that absolutely prohibit the fixing of a tangent.
(1906). As quoted “in free translation” in Benoit B. Mandelbrot, The Fractal Geometry of Nature (1977, 1983), 7.
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Doubtless the reasoning faculty, the mind, is the leading and characteristic attribute of the human race. By the exercise of this, man arrives at the properties of the natural bodies. This is science, properly and emphatically so called. It is the science of pure mathematics; and in the high branches of this science lies the truly sublime of human acquisition. If any attainment deserves that epithet, it is the knowledge, which, from the mensuration of the minutest dust of the balance, proceeds on the rising scale of material bodies, everywhere weighing, everywhere measuring, everywhere detecting and explaining the laws of force and motion, penetrating into the secret principles which hold the universe of God together, and balancing worlds against worlds, and system against system. When we seek to accompany those who pursue studies at once so high, so vast, and so exact; when we arrive at the discoveries of Newton, which pour in day on the works of God, as if a second fiat had gone forth from his own mouth; when, further, we attempt to follow those who set out where Newton paused, making his goal their starting-place, and, proceeding with demonstration upon demonstration, and discovery upon discovery, bring new worlds and new systems of worlds within the limits of the known universe, failing to learn all only because all is infinite; however we may say of man, in admiration of his physical structure, that “in form and moving he is express and admirable,” it is here, and here without irreverence, we may exclaim, “In apprehension how like a god!” The study of the pure mathematics will of course not be extensively pursued in an institution, which, like this [Boston Mechanics’ Institute], has a direct practical tendency and aim. But it is still to be remembered, that pure mathematics lie at the foundation of mechanical philosophy, and that it is ignorance only which can speak or think of that sublime science as useless research or barren speculation.
In Works (1872), Vol. 1, 180.
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Evolution on the large scale unfolds, like much of human history, as a succession of dynasties.
In The Diversity of Life (1999), 94.
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For a stone, when it is examined, will be found a mountain in miniature. The fineness of Nature’s work is so great, that, into a single block, a foot or two in diameter, she can compress as many changes of form and structure, on a small scale, as she needs for her mountains on a large one; and, taking moss for forests, and grains of crystal for crags, the surface of a stone, in by far the plurality of instances, is more interesting than the surface of an ordinary hill; more fantastic in form and incomparably richer in colour—the last quality being, in fact, so noble in most stones of good birth (that is to say, fallen from the crystalline mountain ranges).
Modern Painters, 4, Containing part 5 of Mountain Beauty (1860), 311.
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Fractals are patterns which occur on many levels. This concept can be applied to any musical parameter. I make melodic fractals, where the pitches of a theme I dream up are used to determine a melodic shape on several levels, in space and time. I make rhythmic fractals, where a set of durations associated with a motive get stretched and compressed and maybe layered on top of each other. I make loudness fractals, where the characteristic loudness of a sound, its envelope shape, is found on several time scales. I even make fractals with the form of a piece, its instrumentation, density, range, and so on. Here I’ve separated the parameters of music, but in a real piece, all of these things are combined, so you might call it a fractal of fractals.
Interview (1999) on The Discovery Channel. As quoted by Benoit B. Manelbrot and Richard Hudson in The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward (2010), 133.
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I grew up in Brooklyn, New York … a city neighborhood that included houses, lampposts, walls, and bushes. But with an early bedtime in the winter, I could look out my window and see the stars, and the stars were not like anything else in my neighborhood. [At age 5] I didn’t know what they were.
[At age 9] my mother … said to me, “You have a library card now, and you know how to read. Take the streetcar to the library and get a book on stars.” … I stepped up to the big librarian and asked for a book on stars. … I sat down and found out the answer, which was something really stunning.
I found out that the stars are glowing balls of gas. I also found out that the Sun is a star but really close and that the stars are all suns except really far away I didn’t know any physics or mathematics at that time, but I could imagine how far you’d have to move the Sun away from us till it was only as bright as a star. It was in that library, reading that book, that the scale of the universe opened up to me. There was something beautiful about it.
At that young age, I already knew that I’d be very happy if I could devote my life to finding out more about the stars and the planets that go around them. And it’s been my great good fortune to do just that.
Quoted in interview with Jack Rightmyer, in 'Stars in His Eyes', Highlights For Children (1 Jan 1997). Ages as given in Tom Head (ed.), Conversations with Carl Sagan (2006), x.
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I had this experience at the age of eight. My parents gave me a microscope. I don’t recall why, but no matter. I then found my own little world, completely wild and unconstrained, no plastic, no teacher, no books, no anything predictable. At first I did not know the names of the water-drop denizens or what they were doing. But neither did the pioneer microscopists. Like them, I graduated to looking at butterfly scales and other miscellaneous objects. I never thought of what I was doing in such a way, but it was pure science. As true as could be of any child so engaged, I was kin to Leeuwenhoek, who said that his work “was not pursued in order to gain the praise I now enjoy, but chiefly from a craving after knowledge, which I notice resides in me more that most other men.”
In The Creation: An Appeal to Save Life on Earth (2010), 143-144.
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If I’m concerned about what an electron does in an amorphous mass then I become an electron. I try to have that picture in my mind and to behave like an electron, looking at the problem in all its dimensions and scales.
Quoted in Timothy L. O’Brien, 'Not Invented here: Are U.S. Innovators Losing Their Competitive Edge?', New York Times (13 Nov 2005), B6.
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In a class I was taking there was one boy who was much older than the rest. He clearly had no motive to work. I told him that, if he could produce for me, accurately to scale, drawings of the pieces of wood required to make a desk like the one he was sitting at, I would try to persuade the Headmaster to let him do woodwork during the mathematics hours—in the course of which, no doubt, he would learn something about measurement and numbers. Next day, he turned up with this task completed to perfection. This I have often found with pupils; it is not so much that they cannot do the work, as that they see no purpose in it.
In Mathematician's Delight (1943), 52.
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In design, people like Buckminster Fuller amazed me at the levels at which he could think. He could think molecularly. And he could think at the almost galactic scale. And the idea that somebody could actually talk about molecules and talk about buildings and structures and talk about space just amazed me. As I get older–I’ll be 60 next year–what I’ve discovered is that I find myself in those three realms too.
In interview with Kerry A. Dolan, 'William McDonough On Cradle-to-Cradle Design', Forbes (4 Aug 2010)
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In geologists’ own lives, the least effect of time is that they think in two languages, function on two different scales. … “A million years is a short time—the shortest worth messing with for most problems.”
In Basin and Range (1981), 134.
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In the real changes which animals undergo during their embryonic growth, in those external transformations as well as in those structural modifications within the body, we have a natural scale to measure the degree or the gradation of those full grown animals which corresponds in their external form and in their structure, to those various degrees in the metamorphoses of animals, as illustrated by embryonic changes, a real foundation for zoological classification.
From Lecture 4, collected in Twelve Lectures on Comparative Embryology: Delivered Before the Lowell Institute in Boston: December and January 1848-9 (1849), 29.
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It is a scale of proportions which makes the bad difficult and the good easy.
…...
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It would appear... that moral phenomena, when observed on a great scale, are found to resemble physical phenomena; and we thus arrive, in inquiries of this kind, at the fundamental principle, that the greater the number of individuals observed, the more do individual peculiarities, whether physical or moral, become effaced, and leave in a prominent point of view the general facts, by virtue of which society exists and is preserved.
A Treatise on Man and the Development of his Faculties (1842). Reprinted with an introduction by Solomon Diamond (1969), 6.
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Look Nature thro’, ’tis neat Gradation all.
By what minute Degrees her Scale ascends!
Each middle Nature join’d at each Extreme,
To that above it join’d, to that beneath.
The Complaint: or, Night-Thoughts on Life, Death, and Immortality (1742, 1750), Night 6, 140.
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Magnitude may be compared to the power output in kilowatts of a [radio] broadcasting station; local intensity, on the Mercalli or similar scale, is then comparable to the signal strength noted on a receiver at a given locality. Intensity, like signal strength, will generally fall off with distance from the source; it will also depend on local conditions at the point of observation, and to some extent on the conditions along the path from source to that point.
From interview in the Earthquake Information Bulletin (Jul-Aug 1971), 3, No. 4, as abridged in article on USGS website.
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Mars tugs at the human imagination like no other planet. With a force mightier than gravity, it attracts the eye to its shimmering red presence in the clear night sky. It is like a glowing ember in a field of ethereal lights, projecting energy and promise. It inspires visions of an approachable world. The mind vaults to thoughts of what might have been (if Mars were a litter closer to the warming Sun) and of what could be (if humans were one day to plant colonies there). Mysterious Mars, alluring Mars, fourth planet from the Sun: so far away and yet, on a cosmic scale, so very near.
…...
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Medicine is a social science, and politics is nothing else but medicine on a large scale.
From the original German “Die Medicin ist eine sociale Wissenschaft, und die Politik ist weiter nichts, als Medicin im Grossen.” In his weekly medical newspaper, 'Der Armenarzt' (Poor Doctor), Die Medizinische Reform, (3 Nov 1848), 3, No. 18, 125. As translated in Henry Ernest Sigerist, Medicine and Human Welfare, (1941) 93.
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My picture of the world is drawn in perspective and not like a model to scale. The foreground is occupied by human beings and the stars are all as small as three-penny bits. I don't really believe in astronomy, except as a complicated description of part of the course of human and possibly animal sensation. I apply my perspective not merely to space but also to time. In time the world will cool and everything will die; but that is a long time off still and its present value at compound discount is almost nothing.
From a paper read to the Apostles, a Cambridge discussion society (1925). In 'The Foundations of Mathematics' (1925), collected in Frank Plumpton Ramsey and D.H. Mellor (ed.), Philosophical Papers (1990), Epilogue, 249. Citation to the paper, in Nils-Eric Sahlin, The Philosophy of F.P. Ramsey (1990), 225.
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My sense is that the most under-appreciated–and perhaps most under-researched–linkages between forests and food security are the roles that forest-based ecosystem services play in underpinning sustainable agricultural production. Forests regulate hydrological services including the quantity, quality, and timing of water available for irrigation. Forest-based bats and bees pollinate crops. Forests mitigate impacts of climate change and extreme weather events at the landscape scale.
In 'Forests and food security: What we know and need to know', Forest News online blog by the Center for International Forestry Research (20 Apr 2011).
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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 it is a well-known principle of zoological evolution that an isolated region, if large and sufficiently varied in its topography, soil, climate and vegetation, will give rise to a diversified fauna according to the law of adaptive radiation from primitive and central types. Branches will spring off in all directions to take advantage of every possible opportunity of securing food. The modifications which animals undergo in this adaptive radiation are largely of mechanical nature, they are limited in number and kind by hereditary, stirp or germinal influences, and thus result in the independent evolution of similar types in widely-separated regions under the law of parallelism or homoplasy. This law causes the independent origin not only of similar genera but of similar families and even of our similar orders. Nature thus repeats herself upon a vast scale, but the similarity is never complete and exact.
'The Geological and Faunal Relations of Europe and America during the Tertiary Period and the Theory of the Successive Invasions of an African Fauna', Science (1900), 11, 563-64.
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O truth of the earth! O truth of things! I am determin’d to press my way toward you;
Sound your voice! I scale mountains, or dive in the sea after you.
In poem, 'Great are the Myths', Leaves of Grass (1867), 292.
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On the most usual assumption, the universe is homogeneous on the large scale, i.e. down to regions containing each an appreciable number of nebulae. The homogeneity assumption may then be put in the form: An observer situated in a nebula and moving with the nebula will observe the same properties of the universe as any other similarly situated observer at any time.
From 'Review of Cosmology,', Monthly Notices of the Royal Astronomical Society (1948), 107-8; as quoted and cited in Hermann Friedmann, Wissenschaft und Symbol, Biederstein (1949), 472.
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Once you go from 10 people to 100, you already don’t know who everyone is. So at that stage you might as well keep growing, to get the advantages of scale.
As quoted, without citation, in Can Akdeniz, Fast MBA (2014), 281.
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One of my inventions was a large thermometer made of an iron rod, … The expansion and contraction of this rod was multiplied by a series of levers … so that the slightest change in the length of the rod was instantly shown on a dial about three feet wide multiplied about thirty-two thousand times. The zero-point was gained by packing the rod in wet snow. The scale was so large that … the temperature read while we were ploughing in the field below the house.
From The Story of My Boyhood and Youth (1913), 258-259. One of the inventions made while growing up on his father’s farm, before he left the year after he was 21.
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Our plenteous streams a various race supply,
The bright-eye Perch with fins of Tyrian dye,
The silver Eel, in shining volumes roll’d,
The yellow Carp, in scales bedropp’d with gold,
Swift Trouts, diversified with crimson stains,
And Pykes, the Tyrants of the wat’ry plains.
In poem, 'Windsor Forest', collected in The Works of Mr. Alexander Pope (1718), 51.
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Phenomena unfold on their own appropriate scales of space and time and may be invisible in our myopic world of dimensions assessed by comparison with human height and times metered by human lifespans. So much of accumulating importance at earthly scales ... is invisible by the measuring rod of a human life. So much that matters to particles in the microscopic world of molecules ... either averages out to stability at our scale or simply stands below our limits of perception.
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Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.
In The Man who Knew Infinity: A Life of the Genius Ramanujan (1975), 226.
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Saturated with that speculative spirit then pervading the Greek mind, he [Pythagoras] endeavoured to discover some principle of homogeneity in the universe. Before him, the philosophers of the Ionic school had sought it in the matter of things; Pythagoras looked for it in the structure of things. He observed the various numerical relations or analogies between numbers and the phenomena of the universe. Being convinced that it was in numbers and their relations that he was to find the foundation to true philosophy, he proceeded to trace the origin of all things to numbers. Thus he observed that musical strings of equal lengths stretched by weights having the proportion of 1/2, 2/3, 3/4, produced intervals which were an octave, a fifth and a fourth. Harmony, therefore, depends on musical proportion; it is nothing but a mysterious numerical relation. Where harmony is, there are numbers. Hence the order and beauty of the universe have their origin in numbers. There are seven intervals in the musical scale, and also seven planets crossing the heavens. The same numerical relations which underlie the former must underlie the latter. But where number is, there is harmony. Hence his spiritual ear discerned in the planetary motions a wonderful “Harmony of spheres.”
In History of Mathematics (1893), 67.
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Science is often regarded as the most objective and truth-directed of human enterprises, and since direct observation is supposed to be the favored route to factuality, many people equate respectable science with visual scrutiny–just the facts ma’am, and palpably before my eyes. But science is a battery of observational and inferential methods, all directed to the testing of propositions that can, in principle, be definitely proven false ... At all scales, from smallest to largest, quickest to slowest, many well-documented conclusions of science lie beyond the strictly limited domain of direct observation. No one has ever seen an electron or a black hole, the events of a picosecond or a geological eon.
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See, thro' this air, this ocean, and this earth,
All matter quick, and bursting into birth.
Above, how high progressive life may go!
Around, how wide! how deep extend below!
Vast chain of being, which from God began,
Natures ethereal, human, angel, man,
Beast, bird, fish, insect! what no eye can see,
No glass can reach! from Infinite to thee,
From thee to Nothing—On superior pow'rs
Were we to press, inferior might on ours:
Or in the full creation leave a void,
Where, one step broken, the great scale's destroy'd:
From Nature's chain whatever link you strike,
Tenth or ten thousandth, breaks the chain alike.
'An Essay on Man' (1733-4), Epistle I. In John Butt (ed.), The Poems of Alexander Pope (1965), 513.
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So far as modern science is concerned, we have to abandon completely the idea that by going into the realm of the small we shall reach the ultimate foundations of the universe. I believe we can abandon this idea without any regret. The universe is infinite in all directions, not only above us in the large but also below us in the small. If we start from our human scale of existence and explore the content of the universe further and further, we finally arrive, both in the large and in the small, at misty distances where first our senses and then even our concepts fail us.
To the German Society of Scientists and Physicists, Braunschweig, Germany (Sep 1896). As quoted in Anton Z. Capri, Quips, Quotes, and Quanta: An Anecdotal History of Physics (2011), 20. Wiechert was reporting his measurement of the mass of the moving particles in a cathode ray beam (electrons).
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Sooner or later in every talk, [David] Brower describes the creation of the world. He invites his listeners to consider the six days of Genesis as a figure of speech for what has in fact been 4 billion years. On this scale, one day equals something like six hundred and sixty-six million years, and thus, all day Monday and until Tuesday noon, creation was busy getting the world going. Life began Tuesday noon, and the beautiful organic wholeness of it developed over the next four days. At 4 p.m. Saturday, the big reptiles came on. At three minutes before midnight on the last day, man appeared. At one-fourth of a second before midnight Christ arrived. At one-fortieth of a second before midnight, the Industrial Revolution began. We are surrounded with people who think that what we have been doing for that one-fortieth of a second can go on indefinitely. They are considered normal, but they are stark. raving mad.
In Encounters with the Archdruid (1971), 79-80.
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Technology is an inherent democratizer. Because of the evolution of hardware and software, you’re able to scale up almost anything you can think up. … We’ll have to see if in our lifetime that means that everybody has more or less tools that are of equal power.
Guest Lecture, UC Berkeley, 'Search Engines, Technology, and Business' (3 Oct 2005). At 10:37 in the YouTube video.
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The argument of the ‘long view’ may be correct in some meaninglessly abstract sense, but it represents a fundamental mistake in categories and time scales. Our only legitimate long view extends to our children and our children’s children’s children–hundreds or a few thousands of years down the road. If we let the slaughter continue, they will share a bleak world with rats, dogs, cockroaches, pigeons, and mosquitoes. A potential recovery millions of years later has no meaning at our appropriate scale.
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The Babylonian and Assyrian civilizations have perished; Hammurabi, Sargon and Nebuchadnezzar are empty names; yet Babylonian mathematics is still interesting, and the Babylonian scale of 60 is still used in Astronomy.
In A Mathematician's Apology (1940, 2012), 80.
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The biologist can push it back to the original protist, and the chemist can push it back to the crystal, but none of them touch the real question of why or how the thing began at all. The astronomer goes back untold million of years and ends in gas and emptiness, and then the mathematician sweeps the whole cosmos into unreality and leaves one with mind as the only thing of which we have any immediate apprehension. Cogito ergo sum, ergo omnia esse videntur. All this bother, and we are no further than Descartes. Have you noticed that the astronomers and mathematicians are much the most cheerful people of the lot? I suppose that perpetually contemplating things on so vast a scale makes them feel either that it doesn’t matter a hoot anyway, or that anything so large and elaborate must have some sense in it somewhere.
As co-author with Robert Eustace, The Documents in the Case (1930), 72.
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The essence of life is statistical improbability on a colossal scale.
In The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe Without Design (1986), 317.
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The next difficulty is in the economical production of small lights by electricity. This is what is commonly meant by the phrase, ‘dividing the electric light.’ Up to the present time, and including Mr. Edison’s latest experiments, it appears that this involves an immense loss of efficiency. Next comes the difficulty of distributing on any large scale the immense electric currents which would be needed.
In 'A Scientific View of It: Prof. Henry Morton Not Sanguine About Edison’s Success', New York Times (28 Dec 1879), 1.
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The process of natural selection has been summed up in the phrase “survival of the fittest.” This, however, tells only part of the story. “Survival of the existing” in many cases covers more of the truth. For in hosts of cases the survival of characters rests not on any special usefulness or fitness, but on the fact that individuals possessing these characters have inhabited or invaded a certain area. The principle of utility explains survivals among competing structures. It rarely accounts for qualities associated with geographic distribution.
The nature of animals which first colonize a district must determine what the future fauna will be. From their specific characters, which are neither useful nor harmful, will be derived for the most part the specific characters of their successors.
It is not essential to the meadow lark that he should have a black blotch on the breast or the outer tail-feather white. Yet all meadow larks have these characters just as all shore larks have the tiny plume behind the ear. Those characters of the parent stock, which may be harmful in the new relations, will be eliminated by natural selection. Those especially helpful will be intensified and modified, but the great body of characters, the marks by which we know the species, will be neither helpful nor hurtful. These will be meaningless streaks and spots, variations in size of parts, peculiar relations of scales or hair or feathers, little matters which can neither help nor hurt, but which have all the persistence heredity can give.
Foot-notes to Evolution. A Series of Popular Addresses on the Evolution of Life (1898), 218.
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The routine produces. But each day, nevertheless, when you try to get started you have to transmogrify, transpose yourself; you have to go through some kind of change from being a normal human being, into becoming some kind of slave.
I simply don’t want to break through that membrane. I’d do anything to avoid it. You have to get there and you don’t want to go there because there’s so much pressure and so much strain and you just want to stay on the outside and be yourself. And so the day is a constant struggle to get going.
And if somebody says to me, You’re a prolific writer—it seems so odd. It’s like the difference between geological time and human time. On a certain scale, it does look like I do a lot. But that’s my day, all day long, sitting there wondering when I’m going to be able to get started. And the routine of doing this six days a week puts a little drop in a bucket each day, and that’s the key. Because if you put a drop in a bucket every day, after three hundred and sixty-five days, the bucket’s going to have some water in it.
https://www.theparisreview.org/interviews/5997/john-mcphee-the-art-of-nonfiction-no-3-john-mcphee
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The rudest numerical scales, such as that by which the mineralogists distinguish different degrees of hardness, are found useful. The mere counting of pistils and stamens sufficed to bring botany out of total chaos into some kind of form. It is not, however, so much from counting as from measuring, not so much from the conception of number as from that of continuous quantity, that the advantage of mathematical treatment comes. Number, after all, only serves to pin us down to a precision in our thoughts which, however beneficial, can seldom lead to lofty conceptions, and frequently descend to pettiness.
On the Doctrine of Chances, with Later Reflections (1878), 61-2.
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The science of optics, like every other physical science, has two different directions of progress, which have been called the ascending and the descending scale, the inductive and the deductive method, the way of analysis and of synthesis. In every physical science, we must ascend from facts to laws, by the way of induction and analysis; and we must descend from laws to consequences, by the deductive and synthetic way. We must gather and group appearances, until the scientific imagination discerns their hidden law, and unity arises from variety; and then from unity must reduce variety, and force the discovered law to utter its revelations of the future.
In On a General Method of Expressing the Paths of Light, & of the Planets, by the Coefficients of a Characteristic Function (1833), 7-8. [The spelling as “groupe” in the original text, has her been corrected to “group” to avoid an intrusive “sic”.]
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The tropical rain forests of the world harbor the majority of the planet’s species, yet this wealth of species is being quickly spent. While the exact numbers of species involved and the rate of forest clearing are still under debate, the trend is unmistakable—the richest terrestrial biome is being altered at a scale unparalleled in geologic history.
In The Fragmented Forest: Island Biogeography Theory and the Preservation of Biotic Diversity (1984),
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The world is full of signals that we don’t perceive. Tiny creatures live in a different world of unfamiliar forces. Many animals of our scale greatly exceed our range of perception for sensations familiar to us ... What an imperceptive lot we are. Surrounded by so much, so fascinating and so real, that we do not see (hear, smell, touch, taste) in nature, yet so gullible and so seduced by claims for novel power that we mistake the tricks of mediocre magicians for glimpses of a psychic world beyond our ken. The paranormal may be a fantasy; it is certainly a haven for charlatans. But ‘parahuman’ powers of perception lie all about us in birds, bees, and bacteria.
…...
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There are things out there that are very simple and you never think would work. … Wikipedia is one of those that it would never occur to me that something like that would work. … But it does work. … People who have taken fairly simple ideas, … at a certain scale and after they gain a certain amount of momentum, they can really take off and work. And that’s really an amazing thing.
Guest Lecture, UC Berkeley, 'Search Engines, Technology, and Business' (3 Oct 2005). At 1:13 in the YouTube video.
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There is common misapprehension that the magnitude scale is itself some kind of instrument or apparatus. Visitors will ask to “see the scale,” and are disconcerted by being referred to tables and charts used for applying the scale to readings taken from the seismograms.
From interview with Henry Spall, as in an abridged version of Earthquake Information Bulletin (Jan-Feb 1980), 12, No. 1, that was on the USGS website.
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There is no absolute scale of size in the Universe, for it is boundless towards the great and also boundless towards the small.
As restated by D'Arcy Wentworth Thompson, in On Growth and Form (1917, 1959), 24. Note that Thompson does not uses quotation marks when he gives this as what “Oliver Heaviside used to say.”
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This theme of mutually invisible life at widely differing scales bears an important implication for the ‘culture wars’ that supposedly now envelop our universities and our intellectual discourse in general ... One side of this false dichotomy features the postmodern relativists who argue that all culturally bound modes of perception must be equally valid, and that no factual truth therefore exists. The other side includes the benighted, old-fashioned realists who insist that flies truly have two wings, and that Shakespeare really did mean what he thought he was saying. The principle of scaling provides a resolution for the false parts of this silly dichotomy. Facts are facts and cannot be denied by any rational being. (Often, facts are also not at all easy to determine or specify–but this question raises different issues for another time.) Facts, however, may also be highly scale dependent–and the perceptions of one world may have no validity or expression in the domain of another. The one-page map of Maine cannot recognize the separate boulders of Acadia, but both provide equally valid representations of a factual coastline.
The World as I See It (1999)
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We are in a position similar to that of a mountaineer who is wandering over uncharted spaces, and never knows whether behind the peak which he sees in front of him and which he tries to scale there may not be another peak still beyond and higher up.
In Max Planck and James Vincent Murphy (trans.), Where is Science Going?, (1932), 200.
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We developed a computer program, based on tests of a quarter-scale model of the lunar module, and we ran the program through some 400 different [moon] landing conditions.
From interview with Technology Review, quoted in Douglas Martin, 'Joseph Gavin, Who Helped Put First Man on Moon, Dies at 90', New York Times (4 Nov 2010).
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We only have to look around us to see how complexity ... and psychic “temperature” are still rising: and rising no longer on the scale of the individual but now on that of the planet. This indication is so familiar to us that we cannot but recognize the objective, experiential, reality of a directionally controlled transformation of the Noosphere “as a whole.”
In Teilhard de Chardin and René Hague (trans.), The Heart of Matter (1950, 1978), 38. His term Noosphere refers to the collective sphere of human consciousness.
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What is art
But life upon the larger scale, the higher,
When, graduating up in a spiral line
Of still expanding and ascending gyres,
It pushed toward the intense significance
Of all things, hungry for the Infinite?
From poem, 'Aurora Leigh' (1856), Book 4. In Elizabeth Barrett Browning and Harriet Waters Preston (ed.), The Complete Poetical Works of Mrs. Browning (1900), 323.
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When asked what it was like to set about proving something, the mathematician likened proving a theorem to seeing the peak of a mountain and trying to climb to the top. One establishes a base camp and begins scaling the mountain’s sheer face, encountering obstacles at every turn, often retracing one’s steps and struggling every foot of the journey. Finally when the top is reached, one stands examining the peak, taking in the view of the surrounding countryside and then noting the automobile road up the other side!
Space-filler in The Two-Year College Mathematics Journal (Nov 1980), 11, No. 5, 295.
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With crystals we are in a situation similar to an attempt to investigate an optical grating merely from the spectra it produces... But a knowledge of the positions and intensities of the spectra does not suffice for the determination of the structure. The phases with which the diffracted waves vibrate relative to one another enter in an essential way. To determine a crystal structure on the atomic scale, one must know the phase differences between the different interference spots on the photographic plate, and this task may certainly prove to be rather difficult.
Physikalische Zeitschrift (1913), 14. Translated in Walter Moore, Schrödinger. Life and Thought (1989), 73.
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Your remarks upon chemical notation with the variety of systems which have arisen, &c., &c., had almost stirred me up to regret publicly that such hindrances to the progress of science should exist. I cannot help thinking it a most unfortunate thing that men who as experimentalists & philosophers are the most fitted to advance the general cause of science & knowledge should by promulgation of their own theoretical views under the form of nomenclature, notation, or scale, actually retard its progress.
Letter to William Whewell (21 Feb 1831). In Isaac Todhunter, William Whewell, An Account of his Writings (1876), Vol. 1., 307. Faraday may have been referring to a paper by Whewell published in the Journal of the Royal Institution of England (1831), 437-453.
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“That’s another thing we’ve learned from your Nation,” said Mein Herr, “map-making. But we’ve carried it much further than you. What do you consider the largest map that would be really useful?”
“About six inches to the mile.”
“Only six inches!” exclaimed Mein Herr. “We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all! We actually made a map of the country, on the scale of a mile to the mile!
“Have you used it much?” I enquired.
“It has never been spread out, yet,” said Mein Herr: “the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly as well.”
From Sylvie and Bruno Concluded (1893), 169.
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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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- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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