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Home > Category Index for Science Quotations > Category Index D > Category: Distribution

Distribution Quotes (50 quotes)

Conclusions
I. A curve has been found representing the frequency distribution of standard deviations of samples drawn from a normal population.
II. A curve has been found representing the frequency distribution of values of the means of such samples, when these values are measured from the mean of the population in terms of the standard deviation of the sample…
IV. Tables are given by which it can be judged whether a series of experiments, however short, have given a result which conforms to any required standard of accuracy or whether it is necessary to continue the investigation.
'The Probable Error of a Mean', Biometrika, 1908, 6, 25.
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I. Animals have an electricity peculiar to themselves to which the name animal electricity is given.
II. The organs in which animal electricity acts above all others, and by which it is distributed throughout the whole body, are the nerves, and the most important organ of secretion is the brain.
Thierische Elektricitäund Reizbarkeit. Ein Beytrag zu den neuesten Entdeckungen üdiese Gegenstä(1795), 329. Quoted and trans. in Edwin Clarke and C. D. O'Malley, The Human Brain and Spinal Cord (1968), 180.
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A first step in the study of civilization is to dissect it into details, and to classify these in their proper groups. Thus, in examining weapons, they are to be classed under spear, club, sling, bow and arrow, and so forth; among textile arts are to be ranged matting, netting, and several grades of making and weaving threads; myths are divided under such headings as myths of sunrise and sunset, eclipse-myths, earthquake-myths, local myths which account for the names of places by some fanciful tale, eponymic myths which account for the parentage of a tribe by turning its name into the name of an imaginary ancestor; under rites and ceremonies occur such practices as the various kinds of sacrifice to the ghosts of the dead and to other spiritual beings, the turning to the east in worship, the purification of ceremonial or moral uncleanness by means of water or fire. Such are a few miscellaneous examples from a list of hundreds … To the ethnographer, the bow and arrow is the species, the habit of flattening children’s skulls is a species, the practice of reckoning numbers by tens is a species. The geographical distribution of these things, and their transmission from region to region, have to be studied as the naturalist studies the geography of his botanical and zoological species.
In Primitive Culture (1871), Vol. 1, 7.
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A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life.
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 113. Note that Hardy wrote these words while World War II was raging.
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Accordingly the primordial state of things which I picture is an even distribution of protons and electrons, extremely diffuse and filling all (spherical) space, remaining nearly balanced for an exceedingly long time until its inherent instability prevails. We shall see later that the density of this distribution can be calculated; it was about one proton and electron per litre. There is no hurry for anything to begin to happen. But at last small irregular tendencies accumulate, and evolution gets under way. The first stage is the formation of condensations ultimately to become the galaxies; this, as we have seen, started off an expansion, which then automatically increased in speed until it is now manifested to us in the recession of the spiral nebulae.
As the matter drew closer together in the condensations, the various evolutionary processes followed—evolution of stars, evolution of the more complex elements, evolution of planets and life.
The Expanding Universe (1933), 56-57.
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And invention must still go on for it is necessary that we should completely control our circumstances. It is not sufficient that there should [only] be organization capable of providing food and shelter for all and organization to effect its proper distribution.
Aphorism listed Frederick Seitz, The Cosmic Inventor: Reginald Aubrey Fessenden (1866-1932) (1999), 54, being Transactions of the American Philosophical Society, Held at Philadelphia For Promoting Useful Knowledge, Vol. 86, Pt. 6.
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Any experiment may be regarded as forming an individual of a 'population' of experiments which might be performed under the same conditions. A series of experiments is a sample drawn from this population.
Now any series of experiments is only of value in so far as it enables us to form a judgment as to the statistical constants of the population to which the experiments belong. In a great number of cases the question finally turns on the value of a mean, either directly, or as the mean difference between the two qualities.
If the number of experiments be very large, we may have precise information as to the value of the mean, but if our sample be small, we have two sources of uncertainty:— (I) owing to the 'error of random sampling' the mean of our series of experiments deviates more or less widely from the mean of the population, and (2) the sample is not sufficiently large to determine what is the law of distribution of individuals.
'The Probable Error of a Mean', Biometrika, 1908, 6, 1.
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As for me ... I would much rather be a perfected ape than a degraded Adam. Yes, if it is shown to me that my humble ancestors were quadrupedal animals, arboreal herbivores, brothers or cousins of those who were also the ancestors of monkeys and apes, far from blushing in shame for my species because of its genealogy and parentage, I will be proud of all that evolution has accomplished, of the continuous improvement which takes us up to the highest order, of the successive triumphs that have made us superior to all of the other species ... the splendid work of progress.
I will conclude in saying: the fixity of species is almost impossible, it contradicts the mode of succession and of the distribution of species in the sequence of extant and extinct creatures. It is therefore extremely likely that species are variable and are subject to evolution. But the causes, the mechanisms of this evolution are still unknown.
'Discussion sur la Machoire Humaine de la Naulette (Belgique)', Bulletin de la Societé d'Anthropologie de Paris, 2nd Series, I (1866), 595. Trans. Erik Trinkaus and Pat Shipman, The Neanderthals: Changing the Image of Mankind (1993), 103-4.
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By virtue of the way it has organized its technological base, contemporary industrial society tends to be totalitarian. For 'totalitarian' is not only a terroristic political coordination of society, but also a non-terroristic economic-technical coordination which operates through the manipulation of needs by vested interests. It thus precludes the emergence of an effective opposition against the whole. Not only a specific form of government or party rule makes for totalitarianism, but also a specific system of production and distribution which may well be compatible with a 'pluralism' of parties, newspapers, 'countervailing powers,' etc.
One Dimensional Man (1964), 3.
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Electricity is doing for the distribution of energy what the railroads have done for the distribution of materials.
As quoted in 'C.P. Steinmetz Dies In Sudden Relapse', New York Times (27 Oct 1923), 1.
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Entropy theory, on the other hand, is not concerned with the probability of succession in a series of items but with the overall distribution of kinds of items in a given arrangement.
In Entropy and Art: An Essay on Disorder and Order (1974), 19.
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How many and how curious problems concern the commonest of the sea-snails creeping over the wet sea-weed! In how many points of view may its history be considered! There are its origin and development, the mystery of its generation, the phenomena of its growth, all concerning each apparently insignificant individual; there is the history of the species, the value of its distinctive marks, the features which link it with the higher and lower creatures, the reason why it takes its stand where we place it in the scale of creation, the course of its distribution, the causes of its diffusion, its antiquity or novelty, the mystery (deepest of mysteries) of its first appearance, the changes of the outline of continents and of oceans which have taken place since its advent, and their influence on its own wanderings.
On the Natural History of European Seas. In George Wilson and Archibald Geikie, Memoir of Edward Forbes F.R.S. (1861), 547-8.
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Human societies increased the abundance and distribution of useful species. This can also be used to preserve the forest, I think. We can use this as an opportunity to reduce the impacts of deforestation. Now we have huge plantations of soybeans that are destroying the Amazon—while in the forest we have lots of plants that can be used while maintaining the forest as it is.
As quoted in Robinson Meyer, 'The Amazon Rainforest Was Profoundly Changed by Ancient Humans', The Atlantic (2 Mar 2017).
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I have a peculiar theory about radium, and I believe it is the correct one. I believe that there is some mysterious ray pervading the universe that is fluorescing to it. In other words, that all its energy is not self-constructed but that there is a mysterious something in the atmosphere that scientists have not found that is drawing out those infinitesimal atoms and distributing them forcefully and indestructibly.
Quoted in 'Edison Fears Hidden Perils of the X-Rays', New York World (3 Aug 1903), 1.
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I have always consistently opposed high-tension and alternating systems of electric lighting, not only on account of danger, but because of their general unreliability and unsuitability for any general system of distribution.
In 'The Dangers of Electric Lighting', North American Review (Nov 1889), 149, No. 396, 633.
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If E is considered to be a continuously divisible quantity, this distribution is possible in infinitely many ways. We consider, however—this is the most essential point of the whole calculation—E to be composed of a well-defined number of equal parts and use thereto the constant of nature h = 6.55 ×10-27 erg sec. This constant multiplied by the common frequency ν of the resonators gives us the energy element ε in erg, and dividing E by ε we get the number P of energy elements which must be divided over the N resonators.
[Planck’s constant, as introduced in 1900; subsequently written e = hν.]
In 'On the theory of the energy distribution law of the normal spectrum', in D. ter Haar and Stephen G. Brush, trans., Planck’s Original Papers in Quantum Physics (1972), 40.
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Investigating the conditions under which mutations occur … requires studies of mutation frequency under various methods of handling the organisms. As yet, extremely little has been done along this line. That is because, in the past, a mutation was considered a windfall, and the expression “mutation frequency” would have seemed a contradiction in terms. To attempt to study it would have seemed as absurd as to study the conditions affecting the distribution of dollar bills on the sidewalk. You were simply fortunate if you found one. … Of late, however, we may say that certain very exceptional banking houses have been found, in front of which the dollars fall more frequently—in other words, specially mutable genes have been discovered, that are beginning to yield abundant data at the hands of Nilsson-Ehle, Zeleny, Emerson, Anderson and others.
In 'Variation Due to Change in the Individual Gene', The American Naturalist (Jan-Feb 1922), 56, No. 642, 44.
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It is as true now, as it was in the days when Werner first drew his far-reaching inferences before his charmed listeners, that on the characteristic phenomena and varying distribution of the grand mineral masses of the rock-formations, almost all that concerns the relative habitability of a land depends.
In 'The Relations of Geology', Scottish Geographical Magazine (Aug 1902), 19, No. 8, 409.
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It is for such inquiries the modern naturalist collects his materials; it is for this that he still wants to add to the apparently boundless treasures of our national museums, and will never rest satisfied as long as the native country, the geographical distribution, and the amount of variation of any living thing remains imperfectly known. He looks upon every species of animal and plant now living as the individual letters which go to make up one of the volumes of our earth’s history; and, as a few lost letters may make a sentence unintelligible, so the extinction of the numerous forms of life which the progress of cultivation invariably entails will necessarily render obscure this invaluable record of the past. It is, therefore, an important object, which governments and scientific institutions should immediately take steps to secure, that in all tropical countries colonised by Europeans the most perfect collections possible in every branch of natural history should be made and deposited in national museums, where they may be available for study and interpretation. If this is not done, future ages will certainly look back upon us as a people so immersed in the pursuit of wealth as to be blind to higher considerations. They will charge us with having culpably allowed the destruction of some of those records of Creation which we had it in our power to preserve; and while professing to regard every living thing as the direct handiwork and best evidence of a Creator, yet, with a strange inconsistency, seeing many of them perish irrecoverably from the face of the earth, uncared for and unknown.
In 'On the Physical Geography of the Malay Archipelago', Journal of the Royal Geographical Society (1863), 33, 234.
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It is interesting to note how many fundamental terms which the social sciences are trying to adopt from physics have as a matter of historical fact originated in the social field. Take, for instance, the notion of cause. The Greek aitia or the Latin causa was originally a purely legal term. It was taken over into physics, developed there, and in the 18th century brought back as a foreign-born kind for the adoration of the social sciences. The same is true of the concept of law of nature. Originally a strict anthropomorphic conception, it was gradually depersonalized or dehumanized in the natural sciences and then taken over by the social sciences in an effort to eliminate final causes or purposes from the study of human affairs. It is therefore not anomalous to find similar transformations in the history of such fundamental concepts of statistics as average and probability. The concept of average was developed in the Rhodian laws as to the distribution of losses in maritime risks. After astronomers began to use it in correcting their observations, it spread to other physical sciences; and the prestige which it thus acquired has given it vogue in the social field. The term probability, as its etymology indicates, originates in practical and legal considerations of probing and proving.
The Statistical View of Nature (1936), 327-8.
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It is tautological to say that an organism is adapted to its environment. It is even tautological to say that an organism is physiologically adapted to its environment. However, just as in the case of many morphological characters, it is unwarranted to conclude that all aspects of the physiology of an organism have evolved in reference to a specific milieu. It is equally gratuitous to assume that an organism will inevitably show physiological specializations in its adaptation to a particular set of conditions. All that can be concluded is that the functional capacities of an organism are sufficient to have allowed persistence within its environment. On one hand, the history of an evolutionary line may place serious constraints upon the types of further physiological changes that are readily feasible. Some changes might require excessive restructuring of the genome or might involve maladaptive changes in related functions. On the other hand, a taxon which is successful in occupying a variety of environments may be less impressive in individual physiological capacities than one with a far more limited distribution.
In W.R. Dawson, G.A. Bartholomew, and A.F. Bennett, 'A Reappraisal of the Aquatic Specializations of the Galapagos Marine Iguana (Amblyrhynchus cristatus)', Evolution (1977), 31, 891.
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It usually develops that after much laborious and frustrating effort the investigator of environmental physiology succeeds in proving that the animal in question can actually exist where it lives. It is always somewhat discouraging for an investigator to realize that his efforts can be made to appear so trite, but this statement does not belittle the ecological physiologist. If his data assist the understanding of the ways in which an animal manages to live where it does, he makes an important contribution to the study of distribution, for the present is necessarily a key to the past.”
From 'The role of physiology in the distribution of terrestrial vertebrates', collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 84.
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Much of the geographical work of the past hundred years... has either explicitly or implicitly taken its inspiration from biology, and in particular Darwin. Many of the original Darwinians, such as Hooker, Wallace, Huxley, Bates, and Darwin himself, were actively concerned with geographical exploration, and it was largely facts of geographical distribution in a spatial setting which provided Darwin with the germ of his theory.
'Darwin's Impact on Geography', Annals of the Association of American Geographers (1966), 56, 683.
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Nature prefers the more probable states to the less probable because in nature processes take place in the direction of greater probability. Heat goes from a body at higher temperature to a body at lower temperature because the state of equal temperature distribution is more probable than a state of unequal temperature distribution.
'The Atomic Theory of Matter', third lecture at Columbia University (1909), in Max Planck and A. P. Wills (trans.), Eight Lectures on Theoretical Physics (1915), 44.
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Of all the works of civilization that interfere with the natural water distribution system, irrigation has been by far the most pervasive and powerful. (1992)
Al Gore
Earth in the Balance: Ecology and the Human Spirit (2006), 111.
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Of the nucleosides from deoxyribonucleic acids, all that was known with any certainty [in the 1940s] was that they were 2-deoxy-­D-ribosides of the bases adenine, guanine, thymine and cytosine and it was assumed that they were structurally analogous to the ribonucleosides. The chemistry of the nucleotides—the phosphates of the nucleosides—was in a correspondingly primitive state. It may well be asked why the chemistry of these groups of compounds was not further advanced, particularly since we recognize today that they occupy a central place in the history of the living cell. True, their full significance was for a long time unrecognized and emerged only slowly as biochemical research got into its stride but I think a more important reason is to be found in the physical properties of compounds of the nucleotide group. As water-soluble polar compounds with no proper melting points they were extremely difficult to handle by the classic techniques of organic chemistry, and were accordingly very discouraging substances to early workers. It is surely no accident that the major advances in the field have coincided with the appearance of new experimental techniques such as paper and ion-exchange chromatography, paper electrophoresis, and countercurrent distribution, peculiarly appropriate to the compounds of this group.
In 'Synthesis in the Study of Nucleotides', Nobel Lecture, 11 December 1957. In Nobel Lectures: Chemistry 1942-1962 (1964), 524.
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Quantitative work shows clearly that natural selection is a reality, and that, among other things, it selects Mendelian genes, which are known to be distributed at random through wild populations, and to follow the laws of chance in their distribution to offspring. In other words, they are an agency producing variation of the kind which Darwin postulated as the raw material on which selection acts.
'Natural Selection', Nature, 1929, 124, 444.
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Since an organism is inseparable from its environment, any person who attempts to understand an organism’s distribution must keep constantly in mind that the item being studied is neither a stuffed skin, a pickled specimen, nor a dot on a map. It is not even the live organism held in the hand, caged in a laboratory, or seen in the field. It is a complex interaction between a self-sustaining physicochemical system and the environment. An obvious corollary is that to know the organism it is necessary to know its environment.
From 'The role of physiology in the distribution of terrestrial vertebrates', collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 83.
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Sir how pitiable is it to reflect, that altho you were so fully convinced of the benevolence of the Father of mankind, and of his equal and impartial distribution of those rights and privileges which he had conferred upon them, that you should at the Same time counteract his mercies, in detaining by fraud and violence so numerous a part of my brethren under groaning captivity and cruel oppression, that you should at the Same time be found guilty of that most criminal act, which you professedly detested in others, with respect to yourselves.
In Letter to Thomas Jefferson (19 Aug 1791). In John Hazlehurst Boneval Latrobe, Memoir of Benjamin Banneker: Read Before the Maryland Historical Society, at the Monthly Meeting, May 1, 1845 (1845), 15-16.
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The capital ... shall form a fund, the interest of which shall be distributed annually as prizes to those persons who shall have rendered humanity the best services during the past year. ... One-fifth to the person having made the most important discovery or invention in the science of physics, one-fifth to the person who has made the most eminent discovery or improvement in chemistry, one-fifth to the one having made the most important discovery with regard to physiology or medicine, one-fifth to the person who has produced the most distinguished idealistic work of literature, and one-fifth to the person who has worked the most or best for advancing the fraternization of all nations and for abolishing or diminishing the standing armies as well as for the forming or propagation of committees of peace.
From will (27 Nov 1895), in which he established the Nobel Prizes, as translated in U.S. Dept. of Commerce, Consular Reports, Issues 156-159 (1897), 331.
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The conception of correspondence plays a great part in modern mathematics. It is the fundamental notion in the science of order as distinguished from the science of magnitude. If the older mathematics were mostly dominated by the needs of mensuration, modern mathematics are dominated by the conception of order and arrangement. It may be that this tendency of thought or direction of reasoning goes hand in hand with the modern discovery in physics, that the changes in nature depend not only or not so much on the quantity of mass and energy as on their distribution or arrangement.
In History of European Thought in the Nineteenth Century (1903), Vol. 2, 736.
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The contributions of physiological knowledge to an understanding of distribution are necessarily inferential. Distribution is a historical phenomenon, and the data ordinarily obtained by students of physiology are essentially instantaneous. However, every organism has a line of ancestors which extends back to the beginning of life on earth and which, during this immensity of time, has invariably been able to avoid, to adapt to, or to compensate for environmental changes.
From 'The role of physiology in the distribution of terrestrial vertebrates', collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 84.
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The laws and conditions of the production of wealth partake of the character of physical truths. There is nothing optional or arbitrary in them ... It is not so with the Distribution of Wealth. That is a matter of human institution solely. The things once there, mankind, individually or collectively, can do with them as they like.
Principles of Political Economy (1848), Book 2, 199.
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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 ravages committed by man subvert the relations and destroy the balance which nature had established between her organized and her inorganic creations; and she avenges herself upon the intruder, by letting loose upon her defaced provinces destructive energies hitherto kept in check by organic forces destined to be his best auxiliaries, but which he has unwisely dispersed and driven from the field of action. When the forest is gone, the great reservoir of moisture stored up in its vegetable mould is evaporated, and returns only in deluges of rain to wash away the parched dust into which that mould has been converted. The well-wooded and humid hills are turned to ridges of dry rock, which encumbers the low grounds and chokes the watercourses with its debris, and–except in countries favored with an equable distribution of rain through the seasons, and a moderate and regular inclination of surface–the whole earth, unless rescued by human art from the physical degradation to which it tends, becomes an assemblage of bald mountains, of barren, turfless hills, and of swampy and malarious plains. There are parts of Asia Minor, of Northern Africa, of Greece, and even of Alpine Europe, where the operation of causes set in action by man has brought the face of the earth to a desolation almost as complete as that of the moon; and though, within that brief space of time which we call “the historical period,” they are known to have been covered with luxuriant woods, verdant pastures, and fertile meadows, they are now too far deteriorated to be reclaimable by man, nor can they become again fitted for human use, except through great geological changes, or other mysterious influences or agencies of which we have no present knowledge, and over which we have no prospective control. The earth is fast becoming an unfit home for its noblest inhabitant, and another era of equal human crime and human improvidence, and of like duration with that through which traces of that crime and that improvidence extend, would reduce it to such a condition of impoverished productiveness, of shattered surface, of climatic excess, as to threaten the depravation, barbarism, and perhaps even extinction of the species.
Man and Nature, (1864), 42-3.
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The reactions follow a pattern, which is valid for the blood of all humans... Basically, in fact, there are four different types of human blood, the so-called blood groups. The number of the groups follows from the fact that the erythrocytes evidently contain substances (iso-agglutinogens) with two different structures, of which both may be absent, or one or both present, in the erythrocytes of a person. This alone would still not explain the reactions; the active substances of the sera, the iso-agglutinins, must also be present in a specific distribution. This is actually the case, since every serum contains those agglutinins which react with the agglutinogens not present in the cells—a remarkable phenomenon, the cause of which is not yet known for certain.
'On Individual Differences in Human Blood', Nobel Lecture (11 Dec 1930). In Nobel Lectures: Physiology or Medicine 1922-1941 (1965), 235.
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The situation with regard to insulin is particularly clear. In many parts of the world diabetic children still die from lack of this hormone. ... [T]hose of us who search for new biological facts and for new and better therapeutic weapons should appreciate that one of the central problems of the world is the more equitable distribution and use of the medical and nutritional advances which have already been established. The observations which I have recently made in parts of Africa and South America have brought this fact very forcible to my attention.
'Studies on Diabetes and Cirrhosis', Proceedings, American Philosophical Society (1952) 96, No. 1, 29.
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The stone that Dr. Johnson once kicked to demonstrate the reality of matter has become dissipated in a diffuse distribution of mathematical probabilities. The ladder that Descartes, Galileo, Newton, and Leibniz erected in order to scale the heavens rests upon a continually shifting, unstable foundation.
Mathematics in Western Culture (1953), 382.
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The word “electromagnetic” which is used to characterize the phenomena produced by the conducting wires of the voltaic pile, … were those which M. Oersted discovered, exhibited by an electric current and a magnet. I have determined to use the word electrodynamic in order to unite under a common name all these phenomena, and particularly to designate those which I have observed between two voltaic conductors. It expresses their true character, that of being produced by electricity in motion: while the electric attractions and repulsions, which have been known for a long time, are electrostatic phenomena produced by the unequal distribution of electricity at rest in the bodies in which they are observed.
New terminology introduced in 'Experiments on the New Electrodynamical Phenomena', Annales de Chemie et de Physique (1822), Series 2, Vol. 20, 60. As translated in Dagobert David Runes (ed.), A Treasury of World Science (1962), 5.
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There is no other article for individual use so universally known or widely distributed. In my travels I have found [the safety razor] in the most northern town in Norway and in the heart of the Sahara Desert.
In The Gillette Blade (1926), 1 No 2, 36. In Patricia Harris and David Lyon, 1001 Greatest Things Ever Said About Massachusetts (2007), 385.
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These facts shaw that mitosis is due to the co-ordinate play of an extremely complex system of forces which are as yet scarcely comprehended. Its purpose is, however, as obvious as its physiological explanation is difficult. It is the end of mitosis to divide every part of the chromatin of the mother-cell equally between the daughter-nuclei. All the other operations are tributary to this. We may therefore regard the mitotic figure as essentially an apparatus for the distribution of the hereditary substance, and in this sense as the especial instrument of inheritance.
The Cell in Development and Inheritance (1896), 86.
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To take one of the simplest cases of the dissipation of energy, the conduction of heat through a solid—consider a bar of metal warmer at one end than the other and left to itself. To avoid all needless complication, of taking loss or gain of heat into account, imagine the bar to be varnished with a substance impermeable to heat. For the sake of definiteness, imagine the bar to be first given with one half of it at one uniform temperature, and the other half of it at another uniform temperature. Instantly a diffusing of heat commences, and the distribution of temperature becomes continuously less and less unequal, tending to perfect uniformity, but never in any finite time attaining perfectly to this ultimate condition. This process of diffusion could be perfectly prevented by an army of Maxwell’s ‘intelligent demons’* stationed at the surface, or interface as we may call it with Prof. James Thomson, separating the hot from the cold part of the bar.
* The definition of a ‘demon’, according to the use of this word by Maxwell, is an intelligent being endowed with free will, and fine enough tactile and perceptive organisation to give him the faculty of observing and influencing individual molecules of matter.
In 'The Kinetic Theory of the Dissipation of Energy', Nature (1874), 9, 442.
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To the extent that remaining old-growth Douglas fir ecosystems possess unique structural and functional characteristics distinct from surrounding managed forests, the analogy between forest habitat islands and oceanic islands applies. Forest planning decision variables such as total acreage to be maintained, patch size frequency distribution, spatial distribution of patches, specific locations, and protective measures all need to be addressed.
In The Fragmented Forest: Island Biogeography Theory and the Preservation of Biotic Diversity (1984), 6.
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Two forms or species are sympatric, if they occur together, that is if their areas of distribution overlap or coincide. Two forms (or species) are allapatric, if they do not occur together, that is if they exclude each other geographically. The term allopatric is primarily useful in denoting geographic representatives.
Systematics and the Origin of Species: From the Viewpoint of a Zoologist (1942), 148-9.
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We must make the following remark: a proof, that after a certain time t1, the spheres must necessarily be mixed uniformly, whatever may be the initial distribution of states, cannot be given. This is in fact a consequence of probability theory, for any non-uniform distribution of states, no matter how improbable it may be, is still not absolutely impossible. Indeed it is clear that any individual uniform distribution, which might arise after a certain time from some particular initial state, is just as improbable as an individual non-uniform distribution; just as in the game of Lotto, any individual set of five numbers is as improbable as the set 1, 2, 3, 4, 5. It is only because there are many more uniform distributions than non-uniform ones that the distribution of states will become uniform in the course of time. One therefore cannot prove that, whatever may be the positions and velocities of the spheres at the beginning, the distributions must become uniform after a long time; rather one can only prove that infinitely many more initial states will lead to a uniform one after a definite length of time than to a non-uniform one. Loschmidt's theorem tells us only about initial states which actually lead to a very non-uniform distribution of states after a certain time t1; but it does not prove that there are not infinitely many more initial conditions that will lead to a uniform distribution after the same time. On the contrary, it follows from the theorem itself that, since there are infinitely many more uniform distributions, the number of states which lead to uniform distributions after a certain time t1, is much greater than the number that leads to non-uniform ones, and the latter are the ones that must be chosen, according to Loschmidt, in order to obtain a non-uniform distribution at t1.
From 'On the Relation of a General Mechanical Theorem to the Second Law of Thermodynamics' (1877), in Stephen G. Brush (ed.), Selected Readings in Physics (1966), Vol. 2, Irreversible Processes, 191-2.
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When there are two independent causes of variability capable of producing in an otherwise uniform population distributions with standard deviations s1 and s2, it is found that the distribution, when both causes act together, has a standard deviation vs12 + s22. It is therefore desirable in analysing the causes of variability to deal with the square of the standard deviation as the measure of variability. We shall term this quantity the Variance of the normal population to which it refers, and we may now ascribe to the constituent causes fractions or percentages of the total variance which they together produce.
'The Correlation between Relatives on the Supposition of Mendelian Inheritance,' Transactions of the Royal Society of Edinburgh, 1918, 52, 399.
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Why are atoms so small? ... Many examples have been devised to bring this fact home to an audience, none of them more impressive than the one used by Lord Kelvin: Suppose that you could mark the molecules in a glass of water, then pour the contents of the glass into the ocean and stir the latter thoroughly so as to distribute the marked molecules uniformly throughout the seven seas; if you then took a glass of water anywhere out of the ocean, you would find in it about a hundred of your marked molecules.
What is life?: the Physical Aspect of the Living Cell (1944). Collected in What is Life? with Mind And Matter & Autobiographical Sketches (1967, 1992), 6-7.
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[My favourite fellow of the Royal Society is the Reverend Thomas Bayes, an obscure 18th-century Kent clergyman and a brilliant mathematician who] devised a complex equation known as the Bayes theorem, which can be used to work out probability distributions. It had no practical application in his lifetime, but today, thanks to computers, is routinely used in the modelling of climate change, astrophysics and stock-market analysis.
Quoted in Max Davidson, 'Bill Bryson: Have faith, science can solve our problems', Daily Telegraph (26 Sep 2010)
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[The chemical bond] First, it is related to the disposition of two electrons (remember, no one has ever seen an electron!): next, these electrons have their spins pointing in opposite directions (remember, no one can ever measure the spin of a particular electron!): then, the spatial distribution of these electrons is described analytically with some degree of precision (remember, there is no way of distinguishing experimentally the density distribution of one electron from another!): concepts like hybridization, covalent and ionic structures, resonance, all appear, not one of which corresponds to anything that is directly measurable. These concepts make a chemical bond seem so real, so life-like, that I can almost see it. Then I wake with a shock to the realization that a chemical bond does not exist; it is a figment of the imagination that we have invented, and no more real than the square root of - 1. I will not say that the known is explained in terms of the unknown, for that is to misconstrue the sense of intellectual adventure. There is no explanation: there is form: there is structure: there is symmetry: there is growth: and there is therefore change and life.
Quoted in his obituary, Biographical Memoirs of the Fellows of the Royal Society 1974, 20, 96.
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[T]he phenomena of animal life correspond to one another, whether we compare their rank as determined by structural complication with the phases of their growth, or with their succession in past geological ages; whether we compare this succession with their relative growth, or all these different relations with each other and with the geographical distribution of animals upon the earth. The same series everywhere!
In Essay on Classification (1851), 196.
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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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- 40 -
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