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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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Particularly Quotes (21 quotes)

Although I must say that research problems I worked on were frequently the result of serendipity and often grew out of my interest in some species or some environment which I found to be particularly appealing—marine birds and tropical islands for example.
Bartholomew, April 1993, unpublished remarks when receiving the Miller Award from the Cooper Ornithological Society.
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I always love geology. In winter, particularly, it is pleasant to listen to theories about the great mountains one visited in the summer; or about the Flood or volcanoes; about great catastrophes or about blisters; above all about fossils … Everywhere there are hypotheses, but nowhere truths; many workmen, but no experts; priests, but no God. In these circumstances each man can bring his hypothesis like a candle to a burning altar, and on seeing his candle lit declare ‘Smoke for smoke, sir, mine is better than yours’. It is precisely for this reason that I love geology.
In Nouvelles Genevoises (1910), 306. First edition, 1841.
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I am particularly fond of (Emmanuel Mendes da Costa’s) Natural History of Fossils because treatise, more than any other work written in English, records a short episode expressing one of the grand false starts in the history of natural science–and nothing can be quite so informative and instructive as a juicy mistake.
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I have been a sore-headed occupant of a file drawer labeled ‘‘Science Fiction’’; and I would like out, particularly since so many serious critics regularly mistake the drawer for a urinal
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If texts are unified by a central logic of argument, then their pictorial illustrations are integral to the ensemble, not pretty little trifles included only for aesthetic or commercial value. Primates are visual animals, and (particularly in science) illustration has a language and set of conventions all its own.
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If you advertise to tell lies, it will ruin you, but if you advertise to tell the public the truth, and particularly to give information, it will bring you success. I learned early that to tell a man how best to use tires, and to make him want them, was far better than trying to tell him that your tire is the best in the world. If you believe that yours is, let your customer find it out.
As quoted by H.M. Davidson, in System: The Magazine of Business (Apr 1922), 41, 446.
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Malaria which is almost unknown in the north of Europe is however of great importance in the south of the Continent particularly in Greece and Italy; these fevers in many of the localities become the dominant disease and the forms become more grave.
From Nobel Lecture (11 Dec 1907), 'Protozoa as Causes of Diseases', collected in Nobel Lectures, Physiology or Medicine 1901-1921 (1967, 1999), 264.
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Mathematics, among all school subjects, is especially adapted to further clearness, definite brevity and precision in expression, although it offers no exercise in flights of rhetoric. This is due in the first place to the logical rigour with which it develops thought, avoiding every departure from the shortest, most direct way, never allowing empty phrases to enter. Other subjects excel in the development of expression in other respects: translation from foreign languages into the mother tongue gives exercise in finding the proper word for the given foreign word and gives knowledge of laws of syntax, the study of poetry and prose furnish fit patterns for connected presentation and elegant form of expression, composition is to exercise the pupil in a like presentation of his own or borrowed thoughtsand their development, the natural sciences teach description of natural objects, apparatus and processes, as well as the statement of laws on the grounds of immediate sense-perception. But all these aids for exercise in the use of the mother tongue, each in its way valuable and indispensable, do not guarantee, in the same manner as mathematical training, the exclusion of words whose concepts, if not entirely wanting, are not sufficiently clear. They do not furnish in the same measure that which the mathematician demands particularly as regards precision of expression.
In Anleitung zum mathematischen Unterricht in höheren Schulen (1906), 17.
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Modern Physics impresses us particularly with the truth of the old doctrine which teaches that there are realities existing apart from our sense-perceptions, and that there are problems and conflicts where these realities are of greater value for us than the richest treasures of the world of experience.
In The Universe in the Light of Modern Physics (1931), 107.
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My mother, my dad and I left Cuba when I was two [January, 1959]. Castro had taken control by then, and life for many ordinary people had become very difficult. My dad had worked [as a personal bodyguard for the wife of Cuban president Batista], so he was a marked man. We moved to Miami, which is about as close to Cuba as you can get without being there. It’s a Cuba-centric society. I think a lot of Cubans moved to the US thinking everything would be perfect. Personally, I have to say that those early years were not particularly happy. A lot of people didn’t want us around, and I can remember seeing signs that said: “No children. No pets. No Cubans.” Things were not made easier by the fact that Dad had begun working for the US government. At the time he couldn’t really tell us what he was doing, because it was some sort of top-secret operation. He just said he wanted to fight against what was happening back at home. [Estefan’s father was one of the many Cuban exiles taking part in the ill-fated, anti-Castro Bay of Pigs invasion to overthrow dictator Fidel Castro.] One night, Dad disappered. I think he was so worried about telling my mother he was going that he just left her a note. There were rumours something was happening back home, but we didn’t really know where Dad had gone. It was a scary time for many Cubans. A lot of men were involved—lots of families were left without sons and fathers. By the time we found out what my dad had been doing, the attempted coup had taken place, on April 17, 1961. Intitially he’d been training in Central America, but after the coup attempt he was captured and spent the next wo years as a political prisoner in Cuba. That was probably the worst time for my mother and me. Not knowing what was going to happen to Dad. I was only a kid, but I had worked out where my dad was. My mother was trying to keep it a secret, so she used to tell me Dad was on a farm. Of course, I thought that she didn’t know what had really happened to him, so I used to keep up the pretence that Dad really was working on a farm. We used to do this whole pretending thing every day, trying to protect each other. Those two years had a terrible effect on my mother. She was very nervous, just going from church to church. Always carrying her rosary beads, praying her little heart out. She had her religion, and I had my music. Music was in our family. My mother was a singer, and on my father’s side there was a violinist and a pianist. My grandmother was a poet.
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Obviously we biologists should fit our methods to our materials. An interesting response to this challenge has been employed particularly by persons who have entered biology from the physical sciences or who are distressed by the variability in biology; they focus their research on inbred strains of genetically homogeneous laboratory animals from which, to the maximum extent possible, variability has been eliminated. These biologists have changed the nature of the biological system to fit their methods. Such a bold and forthright solution is admirable, but it is not for me. Before I became a professional biologist, I was a boy naturalist, and I prefer a contrasting approach; to change the method to fit the system. This approach requires that one employ procedures which allow direct scientific utilization of the successful long-term evolutionary experiments which are documented by the fascinating diversity and variability of the species of animals which occupy the earth. This is easy to say and hard to do.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 232.
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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 history of most fossil species includes two features particularly inconsistent with gradualism: 1. Stasis. Most species exhibit no directional change during their tenure on earth. They appear in the fossil record looking much the same as when they disappear; morphological change is usually limited and directionless. 2. Sudden appearance. In any local area, a species does not arise gradually by the steady transformation of its ancestors; it appears all at once and ‘fully formed.’
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The student should not lose any opportunity of exercising himself in numerical calculation and particularly in the use of logarithmic tables. His power of applying mathematics to questions of practical utility is in direct proportion to the facility which he possesses in computation.
In Study and Difficulties of Mathematics (1902), chap. 12.
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The surgeon is a man of action. By temperament and by training he prefers to serve the sick by operating on them, and he inwardly commiserates with a patient so unfortunate as to have a disease not suited to surgical treatment. Young surgeons, busy mastering the technicalities of the art, are particularly alert to seize every legitimate opportunity to practice technical maneuvers, the more complicated the better.
American Journal of Surgery.
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There is something particularly human about using tools; the first and most important tool being language.
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 125.
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They are a fairly aggressive conservation organization that was started to protect the great whales particularly, but in general all marine life around the world. So those are the people I’m trying to attach my name to.
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This brings me to the final point of my remarks, the relation between creativity and aging, a topic with which I have had substantial experience. Scientific research, until it has gone through the grueling and sometimes painful process of publication, is just play, and play is characteristic of young vertebrates, particularly young mammals. In some ways, scientific creativity is related to the exuberant behavior of young mammals. Indeed, creativity seems to be a natural characteristic of young humans. If one is fortunate enough to be associated with a university, even as one ages, teaching allows one to contribute to, and vicariously share, in the creativity of youth.”
In 'Integrative Biology: An Organismic Biologist’s Point of View', Integrative and Comparative Biology (2005), 45, 331.
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To emphasize this opinion that mathematicians would be unwise to accept practical issues as the sole guide or the chief guide in the current of their investigations, ... let me take one more instance, by choosing a subject in which the purely mathematical interest is deemed supreme, the theory of functions of a complex variable. That at least is a theory in pure mathematics, initiated in that region, and developed in that region; it is built up in scores of papers, and its plan certainly has not been, and is not now, dominated or guided by considerations of applicability to natural phenomena. Yet what has turned out to be its relation to practical issues? The investigations of Lagrange and others upon the construction of maps appear as a portion of the general property of conformal representation; which is merely the general geometrical method of regarding functional relations in that theory. Again, the interesting and important investigations upon discontinuous two-dimensional fluid motion in hydrodynamics, made in the last twenty years, can all be, and now are all, I believe, deduced from similar considerations by interpreting functional relations between complex variables. In the dynamics of a rotating heavy body, the only substantial extension of our knowledge since the time of Lagrange has accrued from associating the general properties of functions with the discussion of the equations of motion. Further, under the title of conjugate functions, the theory has been applied to various questions in electrostatics, particularly in connection with condensers and electrometers. And, lastly, in the domain of physical astronomy, some of the most conspicuous advances made in the last few years have been achieved by introducing into the discussion the ideas, the principles, the methods, and the results of the theory of functions. … the refined and extremely difficult work of Poincare and others in physical astronomy has been possible only by the use of the most elaborate developments of some purely mathematical subjects, developments which were made without a thought of such applications.
In Presidential Address British Association for the Advancement of Science, Section A, (1897), Nature, 56, 377.
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To the east was our giant neighbor Makalu, unexplored and unclimbed, and even on top of Everest the mountaineering instinct was sufficient strong to cause me to spend some moments conjecturing as to whether a route up that mountain might not exist. Far away across the clouds the great bulk of Kangchenjunga loomed on the horizon. To the west, Cho Oyu, our old adversary from 1952, dominated the scene and we could see the great unexplored ranges of Nepal stretching off into the distance. The most important photograph, I felt, was a shot down the north ridge, showing the North Col and the old route that had been made famous by the struggles of those great climbers of the 1920s and 1930s. I had little hope of the results being particularly successful, as I had a lot of difficulty in holding the camera steady in my clumsy gloves, but I felt that they would at least serve as a record. After some ten minutes of this, I realized that I was becoming rather clumsy-fingered and slow-moving, so I quickly replaced my oxygen set and experience once more the stimulating effect of even a few liters of oxygen. Meanwhile, Tenzing had made a little hole in the snow and in it he placed small articles of food – a bar of chocolate, a packet of biscuits and a handful of lollies. Small offerings, indeed, but at least a token gifts to the gods that all devoted Buddhists believe have their home on this lofty summit. While we were together on the South Col two days before, Hunt had given me a small crucifix that he had asked me to take to the top. I, too, made a hole in the snow and placed the crucifix beside Tenzing’s gifts.
As quoted in Whit Burnett, The Spirit of Adventure: The Challenge (1955), 349.
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Whenever I get gloomy with the state of the world, I think about the arrivals gate at Heathrow Airport. General opinion’s starting to make out that we live in a world of hatred and greed, but I don’t see that. It seems to me that love is everywhere. Often it’s not particularly dignified or newsworthy, but it’s always there - fathers and sons, mothers and daughters, husbands and wives, boyfriends, girlfriends, old friends. When the planes hit the Twin Towers, as far as I know none of the phone calls from the people on board were messages of hate or revenge - they were all messages of love. If you look for it, I’ve got a sneaky feeling you’ll find that love actually is all around.
Movie
Love Actually (Prime Minister)
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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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