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Today in Science History - Quickie Quiz
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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Home > Category Index for Science Quotations > Category Index S > Category: Structure

Structure Quotes (365 quotes)

“Progress” was synonymous with distance from nature. The adults, who set the pace of progress from nature, were so absorbed by their own ability to invent and to alter the existing world, that they hurried headlong, with no design for the ultimate structure. A man-made environment was the obvious goal, but who was the responsible architect? No one in my country. Not even the king of Great Britain or the president of America. Each inventor and producer who worked on building tomorrow’s world just threw in a brick or a cogwheel wherever he cared to, and it was up to us of the next generation to find out what the result would be.
In Ch. 1, 'Farewell to Civilization', Fatu-Hiva (1974), 4.
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[About the structure of DNA] [T]he whole business was like a child's toy that you could buy at the dime store, all built in this wonderful way that you could explain in Life magazine so that really a five-year-old can understand what's going on...This was the greatest surprise for everyone.
Quoted in Horace Freeland Judson, Eighth Day of Creation (1979)
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[Certain students] suppose that because science has penetrated the structure of the atom it can solve all the problems of the universe. ... They are known in every ... college as the most insufferable, cocksure know-it-alls. If you want to talk to them about poetry, they are likely to reply that the "emotive response" to poetry is only a conditioned reflex .... If they go on to be professional scientists, their sharp corners are rubbed down, but they undergo no fundamental change. They most decidedly are not set apart from the others by their intellectual integrity and faith, and their patient humility in front of the facts of nature.... They are uneducated, in the fullest sense of the word, and they certainly are no advertisement for the claims of science teachers.
In Science is a Sacred Cow (1950), 18-19.
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[Herschel and Humboldt] stirred up in me a burning zeal to add even the most humble contribution to the noble structure of Natural Science. No one or a dozen other books influenced me nearly so much as these two. I copied out from Humboldt long passages about Teneriffe and read them aloud on one of [my walking excursions].
Autobiographies, (eds.) Michael Neve and Sharon Messenger (2002), Penguin edn., 36.
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[I doubt that in today's world, I and Francis Crick would ever have had our Eureka moment.] I recently went to my staircase at Clare College, Cambridge and there were women there! he said, with an enormous measure of retrospective sexual frustration. There have been a lot of convincing studies recently about the loss of productivity in the Western male. It may be that entertainment culture now is so engaging that it keeps people satisfied. We didn't have that. Science was much more fun than listening to the radio. When you are 16 or 17 and in that inherently semi-lonely period when you are deciding whether to be an intellectual, many now don't bother.
(Response when asked how he thought the climate of scientific research had changed since he made his discovery of the structure of life in 1953.)
Quoted by Tim Adams in 'The New Age of Ignorance', The Observer (30 Jun 2007).
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[It] is not the nature of things for any one man to make a sudden, violent discovery; science goes step by step and every man depends on the work of his predecessors. When you hear of a sudden unexpected discovery—a bolt from the blue—you can always be sure that it has grown up by the influence of one man or another, and it is the mutual influence which makes the enormous possibility of scientific advance. Scientists are not dependent on the ideas of a single man, but on the combined wisdom of thousands of men, all thinking of the same problem and each doing his little bit to add to the great structure of knowledge which is gradually being erected.
Concluding remark in Lecture ii (1936) on 'Forty Years of Physics', revised and prepared for publication by J.A. Ratcliffe, collected in Needham and Pagel (eds.), Background to Modern Science: Ten Lectures at Cambridge Arranged by the History of Science Committee, (1938), 73-74. Note that the words as prepared for publication may not be verbatim as spoken in the original lecture by the then late Lord Rutherford.
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[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. … They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That’s what mathematics is to me.
From interview with Donald J. Albers. In John H. Ewing and Frederick W. Gehring, Paul Halmos Celebrating 50 Years of Mathematics (1991), 13.
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[Mercurial medicines] affect the human constitution in a peculiar manner, taking, so to speak, an iron grasp of all its systems, and penetrating even to the bones, by which they not only change the healthy action of its vessels, and general structure, but greatly impair and destroy its energies; so that their abuse is rarely overcome. When the tone of the stomach, intestines, or nervous system generally, has been once injured by this mineral ... it could seldom be restored.
Quoted in Wooster Beach, A Treatise on Anatomy, Physiology, and Health (1848), 177.
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[Molecular biology] is concerned particularly with the forms of biological molecules and with the evolution, exploitation and ramification of these forms in the ascent to higher and higher levels of organisation. Molecular biology is predominantly three-dimensional and structural—which does not mean, however, that it is merely a refinement of morphology. It must at the same time inquire into genesis and function.
From Harvey lecture (1951). As cited by John Law in 'The Case of X-ray Protein Crystallography', collected in Gerard Lemaine (ed.), Perspectives on the Emergence of Scientific Disciplines, 1976, 141.
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[Our work on the structure of DNA] was fairly fast, but you know, we were lucky. One must remember, it was based on the X-ray work done here in London started off by Morris Wilkins and carried on by Rosalind Franklin, and we wouldn’t have got to the stage of at least having a molecular model, if it hadn't been for their work.
Quoted and cited from BBC radio (1999) in transcript of Australian ABC radio program PM (30 Jul 2004) on the ABC website.
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[Professor Pauling] confesses that he had harboured the feeling that sooner or later he would be the one to get the DNA structure; and although he was pleased with the double-helix, he ‘rather wished the idea had been his’.
‘The Need to Understand’, New Scientist (1971), 50, 755.
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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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[The ancient monuments] were all dwarfs in size and pigmies in spirit beside this mighty Statue of Liberty, and its inspiring thought. Higher than the monument in Trafalgar Square which commemorates the victories of Nelson on the sea; higher than the Column Vendome, which perpetuates the triumphs of Napoleon on the land; higher than the towers of the Brooklyn Bridge, which exhibit the latest and greatest results of science, invention, and industrial progress, this structure rises toward the heavens to illustrate an idea ... which inspired the charter in the cabin of the Mayflower and the Declaration of Independence from the Continental Congress.
Speech at unveiling of the Statue of Liberty, New York. In E.S. Werner (ed.), Werner's Readings and Recitations (1908), 107.
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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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[The octopus has] an amazing skin, because there are up to 20 million of these chromatophore pigment cells and to control 20 million of anything is going to take a lot of processing power. ... These animals have extraordinarily large, complicated brains to make all this work. ... And what does this mean about the universe and other intelligent life? The building blocks are potentially there and complexity will arise. Evolution is the force that's pushing that. I would expect, personally, a lot of diversity and a lot of complicated structures. It may not look like us, but my personal view is that there is intelligent life out there.
From transcript of PBS TV program Nova episode 'Origins: Where are the Aliens?' (2004).
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[The] structural theory is of extreme simplicity. It assumes that the molecule is held together by links between one atom and the next: that every kind of atom can form a definite small number of such links: that these can be single, double or triple: that the groups may take up any position possible by rotation round the line of a single but not round that of a double link: finally that with all the elements of the first short period [of the periodic table], and with many others as well, the angles between the valencies are approximately those formed by joining the centre of a regular tetrahedron to its angular points. No assumption whatever is made as to the mechanism of the linkage. Through the whole development of organic chemistry this theory has always proved capable of providing a different structure for every different compound that can be isolated. Among the hundreds of thousands of known substances, there are never more isomeric forms than the theory permits.
Presidential Address to the Chemical Society (16 Apr 1936), Journal of the Chemical Society (1936), 533.
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[About gorillas] You take these fine, regal animals. How many (human) fathers have the same sense of paternity? How many human mothers are more caring? The family structure is unbelievably strong.
As quoted in article from Times Wire Services, 'Naturalist Dian Fossey Slain at Camp in Rwanda: American Was Expert on Mountain Gorillas; Assailants Hunted', Los Angeles Times (29 Dec 1985).
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[When asked “Dr. Einstein, why is it that when the mind of man has stretched so far as to discover the structure of the atom we have been unable to devise the political means to keep the atom from destroying us?”] That is simple, my friend. It is because politics is more difficult than physics.
Einstein’s answer to a conferee at a meeting at Princeton, N.J. (Jan 1946), as recalled by Greenville Clark in 'Letters to the Times', in New York Times (22 Apr 1955), 24.
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Branches or types are characterized by the plan of their structure,
Classes, by the manner in which that plan is executed, as far as ways and means are concerned,
Orders, by the degrees of complication of that structure,
Families, by their form, as far as determined by structure,
Genera, by the details of the execution in special parts, and
Species, by the relations of individuals to one another and to the world in which they live, as well as by the proportions of their parts, their ornamentation, etc.
Essay on Classification (1857). Contributions to the Natural History of the United States of America (1857), Vol. I, 170.
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La nature veut que dans certains temps les hommes se succèdent les uns aux autres par le moyen de la mort; il leur est permis de se défendre contr’elle jusqu’à un certain point; mais passé cela, on aura beau faire de nouvelles découvertes dans l’Anatomie, on aura beau pénétrer de plus en plus dans les secrets de la structure du corps humain, on ne prendra point la Nature pour dupe, on mourra comme à l’ordinaire.
Nature intends that at fixed periods men should succeed each other by the instrumentality of death. They are allowed to keep it at bay up to a certain point; but when that is passed, it will be of no use to make new discoveries in anatomy, or to penetrate more and more into the secrets of the structure of the human body; we shall never outwit nature, we shall die as usual.
In 'Dialogue 5: Dialogues De Morts Anciens', Nouveaux Dialogues des Morts (2nd Ed., 1683), Vol. 1, 154-155. As translated in Craufurd Tait Ramage, Beautiful Thoughts from French and Italian Authors (1866), 113.
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~~[Unverified]~~ Through steady observation and a meaningful contact with the divined order of the world’s structure, arranged by God’s wisdom,–who would not be guided to admire the Builder who creates all!
As quoted, without citation, in Adam Mabry, Life and Doctrine: How the Truth and Grace of Christian Story Change Everything (2001, 2014), 17. Also seen, without citation, in Katherine Katsanis, 'In This Age of Science And Technology, How Can we Accept The Reality of Miracles?', Orthodox Observer (Sep 1997), 21, attributed to Nikolai Copernicus. As yet, Webmaster cannot identify a trustworthy primary source, is therefore presently skeptical, and meanwhile labels the quote as unverified.
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1839—The fermentation satire
THE MYSTERY OF ALCOHOLIC FERMENTATION RESOLVED
(Preliminary Report by Letter) Schwindler
I am about to develop a new theory of wine fermentation … Depending on the weight, these seeds carry fermentation to completion somewhat less than as in the beginning, which is understandable … I shall develop a new theory of wine fermentation [showing] what simple means Nature employs in creating the most amazing phenomena. I owe it to the use of an excellent microscope designed by Pistorius.
When brewer’s yeast is mixed with water the microscope reveals that the yeast dissolves into endless small balls, which are scarcely 1/800th of a line in diameter … If these small balls are placed in sugar water, it can be seen that they consist of the eggs of animals. As they expand, they burst, and from them develop small creatures that multiply with unbelievable rapidity in a most unheard of way. The form of these animals differs from all of the 600 types described up until now. They possess the shape of a Beinsdorff still (without the cooling apparatus). The head of the tube is a sort of proboscis, the inside of which is filled with fine bristles 1/2000th of a line long. Teeth and eyes are not discernible; however, a stomach, intestinal canal, anus (a rose red dot), and organs for secretion of urine are plainly discernible. From the moment they are released from the egg one can see these animals swallow the sugar from the solution and pass it to the stomach. It is digested immediately, a process recognized easily by the resultant evacuation of excrements. In a word, these infusors eat sugar, evacuate ethyl alcohol from the intestinal canal, and carbon dioxide from the urinary organs. The bladder, in the filled state, has the form of a champagne bottle; when empty, it is a small button … As soon as the animals find no more sugar present, they eat each other up, which occurs through a peculiar manipulation; everything is digested down to the eggs which pass unchanged through the intestinal canal. Finally, one again fermentable yeast, namely the seed of the animals, which remain over.
In 'Das entriithselle Geheimiss der geisligen Giihrung', Annalen der Pharmacie und Chemie (1839), 29, 100-104; adapted from English translalion by Ralph E. Oesper, The Human Side of Scientists (1975), 203-205.
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A cell has a history; its structure is inherited, it grows, divides, and, as in the embryo of higher animals, the products of division differentiate on complex lines. Living cells, moreover, transmit all that is involved in their complex heredity. I am far from maintaining that these fundamental properties may not depend upon organisation at levels above any chemical level; to understand them may even call for different methods of thought; I do not pretend to know. But if there be a hierarchy of levels we must recognise each one, and the physical and chemical level which, I would again say, may be the level of self-maintenance, must always have a place in any ultimate complete description.
'Some Aspects of Biochemistry', The Irish Journal of Medical Science (1932), 79, 346.
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A complete theory of evolution must acknowledge a balance between ‘external’ forces of environment imposing selection for local adaptation and ‘internal’ forces representing constraints of inheritance and development. Vavilov placed too much emphasis on internal constraints and downgraded the power of selection. But Western Darwinians have erred equally in practically ignoring (while acknowledging in theory) the limits placed on selection by structure and development–what Vavilov and the older biologists would have called ‘laws of form.’
…...
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A good psychologist has to be able to distinguish strongly between problems of process, which are causal, and problems of structure, which are analytic and descriptive. In particular the statistics adequate for the latter are not sufficient for the former.
From archive recording (3 Jun 1959) with to John C. Kenna, giving his recollection of his farewell speech to Cambridge Psychological Society (4 Mar 1952), in which he gave a summary of points he considered to be basic requirements for a good experimental psychologist. Point 5 of 7, from transcription of recording held at British Psychological Society History of Psychology Centre, London, as abridged on thepsychologist.bps.org.uk website.
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A great advantage of X-ray analysis as a method of chemical structure analysis is its power to show some totally unexpected and surprising structure with, at the same time, complete certainty.
In 'X-ray Analysis of Complicated Molecules', Nobel Lecture (11 Dec 1964). In Nobel Lectures: Chemistry 1942-1962 (1964), 83.
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A man's own addition to what he learns is cement to bind an otherwise loose heap of stones into a structure of unity, strength, and use.
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 180.
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A scientific observation is always a committed observation. It confirms or denies one’s preconceptions, one’s first ideas, one’s plan of observation. It shows by demonstration. It structures the phenomenon. It transcends what is close at hand. It reconstructs the real after having reconstructed its representation.
In The New Scientific Spirit (1934).
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According to my derivative hypothesis, a change takes place first in the structure of the animal, and this, when sufficiently advanced, may lead to modifications of habits… . “Derivation” holds that every species changes, in time, by virtue of inherent tendencies thereto. “Natural Selection” holds that no such change can take place without the influence of altered external circumstances educing or selecting such change… . The hypothesis of “natural selection” totters on the extension of a conjectural condition, explanatory of extinction to the majority of organisms, and not known or observed to apply to the origin of any species.
In On the Anatomy of Vertebrates (1868), Vol. 3, 808.
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According to the older view, for every single effect of a serum, there was a separate substance, or at least a particular chemical group... A normal serum contained as many different haemagglutinins as it agglutinated different cells. The situation was undoubtedly made much simpler if, to use the Ehrlich terminology... the separate haptophore groups can combine with an extremely large number of receptors in stepwise differing quantities as a stain does with different animal tissues, though not always with the same intensity. A normal serum would therefore visibly affect such a large number of different blood cells... not because it contained countless special substances, but because of the colloids of the serum, and therefore of the agglutinins by reason of their chemical constitution and the electrochemical properties resulting from it. That this manner of representation is a considerable simplification is clear; it also opens the way to direct experimental testing by the methods of structural chemistry.
'Die Theorien der Antikorperbildung ... ', Wiener klinische Wöchenschrift (1909), 22, 1623-1631. Trans. Pauline M. H. Mazumdar.
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Adrenalin does not excite sympathetic ganglia when applied to them directly, as does nicotine. Its effective action is localised at the periphery. The existence upon plain muscle of a peripheral nervous network, that degenerates only after section of both the constrictor and inhibitory nerves entering it, and not after section of either alone, has been described. I find that even after such complete denervation, whether of three days' or ten months' duration, the plain muscle of the dilatator pupillae will respond to adrenalin, and that with greater rapidity and longer persistence than does the iris whose nervous relations are uninjured. Therefore it cannot be that adrenalin excites any structure derived from, and dependent for its persistence on, the peripheral neurone. But since adrenalin does not evoke any reaction from muscle that has at no time of its life been innervated by the sympathetic, the point at which the stimulus of the chemical excitant is received, and transformed into what may cause the change of tension of the muscle fibre, is perhaps a mechanism developed out of the muscle cell in response to its union with the synapsing sympathetic fibre, the function of which is to receive and transform the nervous impulse. Adrenalin might then be the chemical stimulant liberated on each occasion when the impulse arrives at the periphery.
'On the Action of Adrenalin', Proceedings of the Physiological Society, 21 May 1904, in The Journal of Physiology 1904, 31, xxi.
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After a duration of a thousand years, the power of astrology broke down when, with Copernicus, Kepler, and Galileo, the progress of astronomy overthrew the false hypothesis upon which the entire structure rested, namely the geocentric system of the universe. The fact that the earth revolves in space intervened to upset the complicated play of planetary influences, and the silent stars, related to the unfathomable depths of the sky, no longer made their prophetic voices audible to mankind. Celestial mechanics and spectrum analysis finally robbed them of their mysterious prestige.
Franz Cumont, translated by J.B. Baker, Astrology and Religion Among the Greeks and Romans (1912, 2007), 6.
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After the discovery of spectral analysis no one trained in physics could doubt the problem of the atom would be solved when physicists had learned to understand the language of spectra. So manifold was the enormous amount of material that has been accumulated in sixty years of spectroscopic research that it seemed at first beyond the possibility of disentanglement. An almost greater enlightenment has resulted from the seven years of Röntgen spectroscopy, inasmuch as it has attacked the problem of the atom at its very root, and illuminates the interior. What we are nowadays hearing of the language of spectra is a true 'music of the spheres' in order and harmony that becomes ever more perfect in spite of the manifold variety. The theory of spectral lines will bear the name of Bohr for all time. But yet another name will be permanently associated with it, that of Planck. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei.
Atombau und Spektrallinien (1919), viii, Atomic Structure and Spectral Lines, trans. Henry L. Brose (1923), viii.
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Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghost-like character of the real variable.
In Science and Philosophy (1948), 116.
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All of our experience indicates that life can manifest itself only in a concrete form, and that it is bound to certain substantial loci. These loci are cells and cell formations. But we are far from seeking the last and highest level of understanding in the morphology of these loci of life. Anatomy does not exclude physiology, but physiology certainly presupposes anatomy. The phenomena that the physiologist investigates occur in special organs with quite characteristic anatomical arrangements; the various morphological parts disclosed by the anatomist are the bearers of properties or, if you will, of forces probed by the physiologist; when the physiologist has established a law, whether through physical or chemical investigation, the anatomist can still proudly state: This is the structure in which the law becomes manifest.
In 'Cellular-Pathologie', Archiv für pathologische Anatomie und Physiologie und fur klinische Medizin (1855), 8, 19, as translated in LellandJ. Rather, 'Cellular Pathology', Disease, Life, and Man: Selected Essays by Rudolf Virchow (1958), 84.
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All the human culture, all the results of art, science and technology that we see before us today, are almost exclusively the creative product of the Aryan. This very fact admits of the not unfounded inference that he alone was the founder of all higher humanity, therefore representing the prototype of all that we understand by the word 'man.' He is the Prometheus of mankind from whose shining brow the divine spark of genius has sprung at all times, forever kindling anew that fire of knowledge which illuminated the night of silent mysteries and thus caused man to climb the path to mastery over the other beings of the earth ... It was he who laid the foundations and erected the walls of every great structure in human culture.
Mein Kampf (1925-26), American Edition (1943), 290. In William Lawrence Shirer, The Rise and Fall of the Third Reich (1990), 86-87.
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Although we may be at a loss to explain the nature of that substance in the nerves, by whose intervention the mind seems enabled to act upon the muscles; and though we may be unacquainted with the intimate structure of those fibres upon which this substance operates, yet we have no room to doubt that voluntary motion is produced by the immediate energy of the mind; manifold experience convincing us, that though there be required certain conditions in the body in order to its performance, it is nevertheless owing to the will.
In An Essay on the Vital and Other Involuntary Motions of Animals (1751), 2.
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An aromatic compound may be defined as a cyclic compound with a large resonance energy where all the annular atoms take part in a single conjugated system.
Electronic Theory of Organic Chemistry (1949), 160.
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As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries—not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer. For my part I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conception only as cultural posits. The myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience.
From A Logical Point of View (1953), 44. [Note: “qua” means “in the character or role of,” thus “qua lay physicist” means “in the role of lay physicist,” or perhaps even (?) “putting on my lay physicist hat.” —Webmaster]
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As I have already mentioned, wherever cells are formed, this tough fluid precedes the first solid structures that indicate the presence of future cells. Moreover, we must assume that this substance furnishes the material for the formation of the nucleus and of the primitive sac, not only because these structures are closely apposed to it, but also because,they react to iodine in the same way. We must assume also that the organization of this substance is the process that inaugurates the formation of new cells. It therefore seems justifiable for me to propose a name that refers to its physiological function: I propose the word protoplasma.
H. Mohl, Botanisch Zeitung (1846), 4, col. 73, trans. Henry Harris, The Birth of the Cell (1999), 75.
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As long as our brain is a mystery, the universe, the reflection of the structure of the brain will also be a mystery.
In Charlas de Café: pensamientos, anécdotas y confidencias (1920,1967), 276. (Café Chats: Thoughts, Anecdotes and Confidences). As translated in Roger Carpenter and Benjamin Redd, Neurophysiology: A Conceptual Approach (2012), 5th ed., 16. From the original Spanish, “Mientras nuestro cerebro sea un arcano, el universo reflejo de su estructura también será un misterio.”
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Astrophysicists closing in on the grand structure of matter and emptiness in the universe are ruling out the meatball theory, challenging the soap bubble theory, and putting forward what may be the strongest theory of all: that the cosmos is organized like a sponge.
'Rethinking Clumps and Voids in the Universe', New York Times (9 Nov 1986), A1.
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Astrophysicists have the formidable privilege of having the largest view of the Universe; particle detectors and large telescopes are today used to study distant stars, and throughout space and time, from the infinitely large to the infinitely small, the Universe never ceases to surprise us by revealing its structures little by little.
In Black Holes (1992), xv.
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Basic research at universities comes in two varieties: research that requires big bucks and research that requires small bucks. Big bucks research is much like government research and in fact usually is government research but done for the government under contract. Like other government research, big bucks academic research is done to understand the nature and structure of the universe or to understand life, which really means that it is either for blowing up the world or extending life, whichever comes first. Again, that's the government's motivation. The universities' motivation for conducting big bucks research is to bring money in to support professors and graduate students and to wax the floors of ivy-covered buildings. While we think they are busy teaching and learning, these folks are mainly doing big bucks basic research for a living, all the while priding themselves on their terrific summer vacations and lack of a dress code.
Smalls bucks research is the sort of thing that requires paper and pencil, and maybe a blackboard, and is aimed primarily at increasing knowledge in areas of study that don't usually attract big bucks - that is, areas that don't extend life or end it, or both. History, political science, and romance languages are typically small bucks areas of basic research. The real purpose of small bucks research to the universities is to provide a means of deciding, by the quality of their small bucks research, which professors in these areas should get tenure.
Accidental Empires (1992), 78.
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Because intelligence is our own most distinctive feature, we may incline to ascribe superior intelligence to the basic primate plan, or to the basic plan of the mammals in general, but this point requires some careful consideration. There is no question at all that most mammals of today are more intelligent than most reptiles of today. I am not going to try to define intelligence or to argue with those who deny thought or consciousness to any animal except man. It seems both common and scientific sense to admit that ability to learn, modification of action according to the situation, and other observable elements of behavior in animals reflect their degrees of intelligence and permit us, if only roughly, to compare these degrees. In spite of all difficulties and all the qualifications with which the expert (quite properly) hedges his conclusions, it also seems sensible to conclude that by and large an animal is likely to be more intelligent if it has a larger brain at a given body size and especially if its brain shows greater development of those areas and structures best developed in our own brains. After all, we know we are intelligent, even though we wish we were more so.
In The Meaning of Evolution: A Study of the History of Life and of its Significance for Man (1949), 78.
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Being the most striking manifestation of the art of metal structures by which our engineers have shown in Europe, it [the Eiffel Tower] is one of the most striking of our modern national genius.
English version by Webmaster using Google Translate, from the original French, “Étant la plus saisissante manifestation de l’art des constructions métalliques par lesquelles nos ingénieurs se sont illustrés en Europe, elle est une des formes les plus frappantes de notre génie national moderne.” From interview of Eiffel by Paul Bourde, in the newspaper Le Temps (14 Feb 1887). Reprinted in 'Au Jour le Jour: Les Artistes Contre la Tour Eiffel', Gazette Anecdotique, Littéraire, Artistique et Bibliographique (Feb 1887), 126, and in Gustave Eiffel, Travaux Scientifiques Exécutés à la Tour de 300 Mètres de 1889 à 1900 (1900), 14. Also quoted in review of the Gustave Eiffel’s book La Tour Eiffel (1902), in Nature (30 Jan 1902), 65, 292.
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Biologists have long attempted by chemical means to induce in higher organisms predictable and specific changes which thereafter could be transmitted in series as hereditary characters. Among microorganisms the most striking example of inheritable and specific alterations in cell structure and function that can be experimentally induced and are reproducible under well defined and adequately controlled conditions is the transformation of specific types of Pneumococcus.
Oswald T. Avery (1877-1955), Colin Macleod (1909-72) and Maclyn McCarty (1911-2005), 'Studies on the Chemical Nature of the Substance Inducing Transformation of Pneumococcal Types', Journal of Experimental Medicine 1944, 79, 137.
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Biology today is moving in the direction of chemistry. Much of what is understood in the field is based on the structure of molecules and the properties of molecules in relation to their structure. If you have that basis, then biology isn’t just a collection of disconnected facts.
From interview with Neil A. Campbell, in 'Crossing the Boundaries of Science', BioScience (Dec 1986), 36, No. 11, 737.
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Borel makes the amusing supposition of a million monkeys allowed to play upon the keys of a million typewriters. What is the chance that this wanton activity should reproduce exactly all of the volumes which are contained in the library of the British Museum? It certainly is not a large chance, but it may be roughly calculated, and proves in fact to be considerably larger than the chance that a mixture of oxygen and nitrogen will separate into the two pure constituents. After we have learned to estimate such minute chances, and after we have overcome our fear of numbers which are very much larger or very much smaller than those ordinarily employed, we might proceed to calculate the chance of still more extraordinary occurrences, and even have the boldness to regard the living cell as a result of random arrangement and rearrangement of its atoms. However, we cannot but feel that this would be carrying extrapolation too far. This feeling is due not merely to a recognition of the enormous complexity of living tissue but to the conviction that the whole trend of life, the whole process of building up more and more diverse and complex structures, which we call evolution, is the very opposite of that which we might expect from the laws of chance.
The Anatomy of Science (1926), 158-9.
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Built up of carbon, hydrogen, oxygen, nitrogen, together with traces of a few other elements, yet of a complexity of structure that has hitherto resisted all attempts at complete analysis, protoplasm is at once the most enduring and the most easily destroyed of substances; its molecules are constantly breaking down to furnish the power for the manifestations of vital phenomena, and yet, through its remarkable property of assimilation, a power possessed by nothing else upon earth, it constantly builds up its substance anew from the surrounding medium.
In History of the Human Body (1919), 1.
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But I think that in the repeated and almost entire changes of organic types in the successive formations of the earth—in the absence of mammalia in the older, and their very rare appearance (and then in forms entirely. unknown to us) in the newer secondary groups—in the diffusion of warm-blooded quadrupeds (frequently of unknown genera) through the older tertiary systems—in their great abundance (and frequently of known genera) in the upper portions of the same series—and, lastly, in the recent appearance of man on the surface of the earth (now universally admitted—in one word, from all these facts combined, we have a series of proofs the most emphatic and convincing,—that the existing order of nature is not the last of an uninterrupted succession of mere physical events derived from laws now in daily operation: but on the contrary, that the approach to the present system of things has been gradual, and that there has been a progressive development of organic structure subservient to the purposes of life.
'Address to the Geological Society, delivered on the Evening of the 18th of February 1831', Proceedings of the Geological Society (1834), 1, 305-6.
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But many of our imaginations and investigations of nature are futile, especially when we see little living animals and see their legs and must judge the same to be ten thousand times thinner than a hair of my beard, and when I see animals living that are more than a hundred times smaller and am unable to observe any legs at all, I still conclude from their structure and the movements of their bodies that they do have legs... and therefore legs in proportion to their bodies, just as is the case with the larger animals upon which I can see legs... Taking this number to be about a hundred times smaller, we therefore find a million legs, all these together being as thick as a hair from my beard, and these legs, besides having the instruments for movement, must be provided with vessels to carry food.
Letter to N. Grew, 27 Sep 1678. In The Collected Letters of Antoni van Leeuwenhoek (1957), Vol. 2, 391.
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By considering the embryological structure of man - the homologies which he presents with the lower animals - the rudiments which he retains - and the reversions to which he is liable, we can partly recall in imagination the former condition of our early progenitors; and we can approximately place them in their proper position in the zoological series. We thus learnt that man is descended from a hairy quadruped, furnished with a tail and pointed ears, probably arboreal in its habit, and an inhabitant of the Old World. This creature, if its whole structure had been examined by a naturalist, would have been classed among the Quadrumana, as surely as would be the common and still more ancient progenitor of the Old and New World monkeys.
The Descent of Man (1871), Vol. 2, 389.
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Can one think that because we are engineers, beauty does not preoccupy us or that we do not try to build beautiful, as well as solid and long lasting structures? Aren’t the genuine functions of strength always in keeping with unwritten conditions of harmony? … Besides, there is an attraction, a special charm in the colossal to which ordinary theories of art do not apply.
As translated in Henry Petroski, Remaking the World: Adventures in Engineering (1998), 173. From the original French in interview of Eiffel by Paul Bourde, in the newspaper Le Temps (14 Feb 1887). Quoted in 'Au Jour le Jour: Les Artistes Contre la Tour Eiffel', Gazette Anecdotique, Littéraire, Artistique et Bibliographique (Feb 1887), 126, and in Gustave Eiffel, Travaux Scientifiques Exécutés à la Tour de 300 Mètres de 1889 à 1900 (1900), 14. “Parce que nous sommes des ingénieurs, croit-on donc que la beauté ne nous préoccupe pas dans nos constructions et qu'en même temps que nous faisons solide et durable nous ne nous efforçons pas rletfaire élégant? Est-ce que les véritables conditions de la force ne sont pas toujours conformes aux conditions secrètes de l'harmonie?.… Il y a du reste dans le colossal une attraction, un charme propre auxquels les théories d'art ordinaires ne sont guère applicables.
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Cell genetics led us to investigate cell mechanics. Cell mechanics now compels us to infer the structures underlying it. In seeking the mechanism of heredity and variation we are thus discovering the molecular basis of growth and reproduction. The theory of the cell revealed the unity of living processes; the study of the cell is beginning to reveal their physical foundations.
Recent Advances in Cytology (1937), 562.
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Chess combines the beauty of mathematical structure with the recreational delights of a competitive game.
In 'Preface', Mathematics, Magic, and Mystery (1956), ix.
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Classes and concepts may, however, also be conceived as real objects, namely classes as “pluralities of things” or as structures consisting of a plurality of things and concepts as the properties and relations of things existing independently of our definitions and constructions. It seems to me that the assumption of such objects is quite as legitimate as the assumption of physical bodies and there is quite as much reason to believe in their existence. They are in the same sense necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions…
In 'Russell's Mathematical Logic', in P.A. Schilpp (ed.), The Philosophy of Bertrand Russell (1944), Vol. 1, 137.
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Consider the very roots of our ability to discern truth. Above all (or perhaps I should say “underneath all”), common sense is what we depend on—that crazily elusive, ubiquitous faculty we all have to some degree or other. … If we apply common sense to itself over and over again, we wind up building a skyscraper. The ground floor of the structure is the ordinary common sense we all have, and the rules for building news floors are implicit in the ground floor itself. However, working it all out is a gigantic task, and the result is a structure that transcends mere common sense.
In Metamagical Themas: Questing for the Essence of Mind and Pattern (1985), 93–94.
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Disease is an abnormal state of the body which primarily and independently produces a disturbance in the normal functions of the body. It may be an abnormality of temperament or form (structure). Symptom is a manifestation of some abnormal state in the body. It may be harmful as a colic pain or harmless as the flushing of cheeks in peripneumonia.
Avicenna
'A Discussion of the Cause of Disease and Symptoms', in The Canon of Medicine, adapted by L. Bakhtiar (1999), 171.
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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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During my stay in London I resided for a considerable time in Clapham Road in the neighbourhood of Clapham Common... One fine summer evening I was returning by the last bus 'outside' as usual, through the deserted streets of the city, which are at other times so full of life. I fell into a reverie (Träumerei), and 10, the atoms were gambolling before my eyes! Whenever, hitherto, these diminutive beings had appeared to me, they had always been in motion: but up to that time I had never been able to discern the nature of their motion. Now, however, I saw how, frequently, two smaller atoms united to form a pair: how the larger one embraced the two smaller ones: how still larger ones kept hold of three or even four of the smaller: whilst the whole kept whirling in a giddy dance. I saw how the larger ones formed a chain, dragging the smaller ones after them but only at the ends of the chain. I saw what our past master, Kopp, my highly honoured teacher and friend has depicted with such charm in his Molekular-Welt: but I saw it long before him. The cry of the conductor 'Clapham Road', awakened me from my dreaming: but I spent part of the night in putting on paper at least sketches of these dream forms. This was the origin of the 'Structural Theory'.
Kekule at Benzolfest in Berichte (1890), 23, 1302.
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During the half-century that has elapsed since the enunciation of the cell-theory by Schleiden and Schwann, in 1838-39, it has became ever more clearly apparent that the key to all ultimate biological problems must, in the last analysis, be sought in the cell. It was the cell-theory that first brought the structure of plants and animals under one point of view by revealing their common plan of organization. It was through the cell-theory that Kolliker and Remak opened the way to an understanding of the nature of embryological development, and the law of genetic continuity lying at the basis of inheritance. It was the cell-­theory again which, in the hands of Virchaw and Max Schultze, inaugurated a new era in the history of physiology and pathology, by showing that all the various functions of the body, in health and in disease, are but the outward expression of cell­-activities. And at a still later day it was through the cell-theory that Hertwig, Fol, Van Beneden, and Strasburger solved the long-standing riddle of the fertilization of the egg, and the mechanism of hereditary transmission. No other biological generalization, save only the theory of organic evolution, has brought so many apparently diverse phenomena under a common point of view or has accomplished more far the unification of knowledge. The cell-theory must therefore be placed beside the evolution-theory as one of the foundation stones of modern biology.
In The Cell in Development and Inheritance (1896), 1.
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Each nerve cell receives connections from other nerve cells at six sites called synapses. But here is an astonishing fact—there are about one million billion connections in the cortical sheet. If you were to count them, one connection (or synapse) per second, you would finish counting some thirty-two million years after you began. Another way of getting a feeling for the numbers of connections in this extraordinary structure is to consider that a large match-head’s worth of your brain contains about a billion connections. Notice that I only mention counting connections. If we consider how connections might be variously combined, the number would be hyperastronomical—on the order of ten followed by millions of zeros. (There are about ten followed by eighty zero’s worth of positively charged particles in the whole known universe!)
Bright and Brilliant Fire, On the Matters of the Mind (1992), 17.
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Embryology will often reveal to us the structure, in some degree obscured, of the prototype of each great class.
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Energy is the measure of that which passes from one atom to another in the course of their transformations. A unifying power, then, but also, because the atom appears to become enriched or exhausted in the course of the exchange, the expression of structure.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 42. Originally published in French as Le Phénomene Humain (1955).
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Engineering is the application of scientific and mathematical principles to practical ends such as the design, manufacture, and operation of efficient and economical structures, machines, processes, and systems.
In Bernice Zeldin Schacter, Issues and Dilemmas of Biotechnology: A Reference Guide (1999), 1, citing the American Heritage Dictionary, 2nd College Edition.
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Engineering is the art or science of utilizing, directing or instructing others in the utilization of the principles, forces, properties and substance of nature in the production, manufacture, construction, operation and use of things ... or of means, methods, machines, devices and structures ...
(1920}
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Enough for me the mystery of the eternity of life, and the inkling of the marvellous structure of reality, together with the single-hearted endeavour to comprehend a portion, be it never so tiny, of the reason that manifests itself in nature.
In Alan Harris (ed.), The World As I See It (1934), 242.
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Entropy theory is indeed a first attempt to deal with global form; but it has not been dealing with structure. All it says is that a large sum of elements may have properties not found in a smaller sample of them.
In Entropy and Art: An Essay on Disorder and Order (1974), 21.
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Every complete set of chromosomes contains the full code; so there are, as a rule, two copies of the latter in the fertilized egg cell, which forms the earliest stage of the future individual. In calling the structure of the chromosome fibres a code-script we mean that the all-penetrating mind, once conceived by Laplace, to which every causal connection lay immediately open, could tell from their structure whether the egg would develop, under suitable conditions, into a black cock or into a speckled hen, into a fly or a maize plant, a rhododendron, a beetle, a mouse or a woman. To which we may add, that the appearances of the egg cells are very often remarkably similar; and even when they are not, as in the case of the comparatively gigantic eggs of birds and reptiles, the difference is not so much in the relevant structures as in the nutritive material which in these cases is added for obvious reasons.
But the term code-script is, of course, too narrow. The chromosome structures are at the same time instrumental in bringing about the development they foreshadow. They are law-code and executive power?or, to use another simile, they are architect's plan and builder’s craft-in one.
In What is Life? : The Physical Aspect of the Living Cell (1944), 20-21.
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Every dream will reveal itself as a psychological structure, full of significance.
First sentence of Chapter 1, 'The Scientific Literature on the Problems of the Dream, The Interpretation of Dreams (1900) as translated by A.A. Brill (1913), 1.
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Every living being is also a fossil. Within it, all the way down to the microscopic structure of its proteins, it bears the traces if not the stigmata of its ancestry.
In Jacques Monod and Austryn Wainhouse (trans.), Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology (1972), 160.
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Everybody now wants to discover universal laws which will explain the structure and behavior of the nucleus of the atom. But actually our knowledge of the elementary particles that make up the nucleus is tiny. The situation calls for more modesty. We should first try to discover more about these elementary particles and about their laws. Then it will be the time for the major synthesis of what we really know, and the formulation of the universal law.
As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 74.
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Evolution is a theory of organic change, but it does not imply, as many people assume, that ceaseless flux is the irreducible state of nature and that structure is but a temporary incarnation of the moment. Change is more often a rapid transition between stable states than a continuous transformation at slow and steady rates. We live in a world of structure and legitimate distinction. Species are the units of nature’s morphology.
…...
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Exact science and its practical movements are no checks on the greatest poet, but always his encouragement and support … The sailor and traveller, the anatomist, chemist, astronomer, geologist, phrenologist, spiritualist, mathematician, historian and lexicographer are not poets, but they are the lawgivers of poets and their construction underlies the structure of every perfect poem.
In Walt Whitman and William Michael Rossetti (ed.), 'Preface to the First Edition of Leaves of Grass', Poems By Walt Whitman (1868), 46.
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Facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts. Facts do not go away while scientists debate rival theories for explaining them. Einstein's theory of gravitation replaced Newton's, but apples did not suspend themselves in mid-air pending the outcome.
'Evolution as Fact and Theory', in Hen's Teeth and Horse's Toes (1983, 1994), Chap. 19.
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Few scientists acquainted with the chemistry of biological systems at the molecular level can avoid being inspired. Evolution has produced chemical compounds exquisitely organized to accomplish the most complicated and delicate of tasks. Many organic chemists viewing crystal structures of enzyme systems or nucleic acids and knowing the marvels of specificity of the immune systems must dream of designing and synthesizing simpler organic compounds that imitate working features of these naturally occurring compounds.
In 'The Design of Molecular Hosts, Guests, and Their Complexes', Nobel Lecture, 8 December 1987. In Nobel Lectures: Chemistry 1981-1990 (1992), 419.
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First they said my [cyclol] structure [of proteins] couldn’t exist. Then when it was found in Nature they said it couldn’t be synthesized in a laboratory. Then when it was synthesized they said it wasn’t important in any way.
Quoted in Maureen M. Julian in G. Kass­Simon and Patricia Farnes (eds.), Women of Science (1990), 368.
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Food is the burning question in animal society, and the whole structure and activities of the community are dependent upon questions of food-supply.
(1960)
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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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For Christmas, 1939, a girl friend gave me a book token which I used to buy Linus Pauling's recently published Nature of the Chemical Bond. His book transformed the chemical flatland of my earlier textbooks into a world of three-dimensional structures.
'What Holds Molecules Together', in I Wish I'd Made You Angry Earlier (1998), 165.
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Fossils, be it understood, are given botanical names and spoken of as if they were species, but they are merely the bits, however wonderfully preserved, of extinct beings: we are apt to forget in the explicit elegance of the structures made by cell-walls, that it is the living protoplasm which is plant life and makes species.
In The Life of Plants (1964, 2002), 177.
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Fractal is a word invented by Mandelbrot to bring together under one heading a large class of objects that have [played] … an historical role … in the development of pure mathematics. A great revolution of ideas separates the classical mathematics of the 19th century from the modern mathematics of the 20th. Classical mathematics had its roots in the regular geometric structures of Euclid and the continuously evolving dynamics of Newton. Modern mathematics began with Cantor’s set theory and Peano’s space-filling curve. Historically, the revolution was forced by the discovery of mathematical structures that did not fit the patterns of Euclid and Newton. These new structures were regarded … as “pathological,” .… as a “gallery of monsters,” akin to the cubist paintings and atonal music that were upsetting established standards of taste in the arts at about the same time. The mathematicians who created the monsters regarded them as important in showing that the world of pure mathematics contains a richness of possibilities going far beyond the simple structures that they saw in Nature. Twentieth-century mathematics flowered in the belief that it had transcended completely the limitations imposed by its natural origins.
Now, as Mandelbrot points out, … Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.
From 'Characterizing Irregularity', Science (12 May 1978), 200, No. 4342, 677-678. Quoted in Benoit Mandelbrot, The Fractal Geometry of Nature (1977, 1983), 3-4.
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Freudian psychoanalytical theory is a mythology that answers pretty well to Levi-Strauss's descriptions. It brings some kind of order into incoherence; it, too, hangs together, makes sense, leaves no loose ends, and is never (but never) at a loss for explanation. In a state of bewilderment it may therefore bring comfort and relief … give its subject a new and deeper understanding of his own condition and of the nature of his relationship to his fellow men. A mythical structure will be built up around him which makes sense and is believable-in, regardless of whether or not it is true.
From 'Science and Literature', The Hope of Progress: A Scientist Looks at Problems in Philosophy, Literature and Science (1973), 29.
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From all we have learnt about the structure of living matter, we must be prepared to find it working in a manner that cannot be reduced to the ordinary laws of physics. And that not on the ground that there is any “new force” or what not, directing the behavior of the single atoms within a living organism, but because the construction is different from anything we have yet tested in the physical laboratory.
What is Life? (1956), 74.
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From the intensity of the spots near the centre, we can infer that the protein molecules are relatively dense globular bodies, perhaps joined together by valency bridges, but in any event separated by relatively large spaces which contain water. From the intensity of the more distant spots, it can be inferred that the arrangement of atoms inside the protein molecule is also of a perfectly definite kind, although without the periodicities characterising the fibrous proteins. The observations are compatible with oblate spheroidal molecules of diameters about 25 A. and 35 A., arranged in hexagonal screw-axis. ... At this stage, such ideas are merely speculative, but now that a crystalline protein has been made to give X-ray photographs, it is clear that we have the means of checking them and, by examining the structure of all crystalline proteins, arriving at a far more detailed conclusion about protein structure than previous physical or chemical methods have been able to give.
'X-Ray Photographs of Crystalline Pepsin', Nature (1934), 133, 795.
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From thus meditating on the great similarity of the structure of the warm-blooded animals, and at the same time of the great changes they undergo both before and after their nativity; and by considering in how minute a portion of time many of the changes of animals above described have been produced; would it be too bold to imagine that, in the great length of time since the earth began to exist, perhaps millions of ages before the commencement of the history of mankind would it be too bold to imagine that all warm-blooded animals have arisen from one living filament, which THE GREAT FIRST CAUSE endued with animality, with the power of acquiring new parts, attended with new propensities, directed by irritations, sensations, volitions and associations, and thus possessing the faculty of continuing to improve by its own inherent activity, and of delivering down these improvements by generation to its posterity, world without end!
Zoonomia, Or, The Laws of Organic Life, in three parts (1803), Vol. 1, 397.
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Games are among the most interesting creations of the human mind, and the analysis of their structure is full of adventure and surprises. Unfortunately there is never a lack of mathematicians for the job of transforming delectable ingredients into a dish that tastes like a damp blanket.
In J.R. Newman (ed.), 'Commentary on Games and Puzzles', The World of Mathematics (1956), Vol. 4, 2414.
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Geology is the science which investigates the successive changes that have taken place in the organic and inorganic kingdoms of nature; it enquires into the causes of these changes, and the influence which they have exerted in modifying the surface and external structure of our planet.
Principles of Geology (1830-3), Vol. 1, 1.
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Given a situation, a system with a Leerstelle [a gap], whether a given completion (Lueckenfuellung) does justice to the structure, is the “right” one, is often determined by the structure of the system, the situation. There are requirements, structurally determined; there are possible in pure cases unambiguous decisions as to which completion does justice to the situation, which does not, which violates the requirements and the situation.
From 'Some Problems in the Theory of Ethics', collected in Mary Henle (ed.), Documents of Gestalt Psychology (1961), 36.
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He who designs an unsafe structure or an inoperative machine is a bad Engineer; he who designs them so that they are safe and operative, but needlessly expensive, is a poor Engineer, and … he who does the best work at lowest cost sooner or later stands at the top of his profession.
From Address on 'Industrial Engineering' at Purdue University (24 Feb 1905). Reprinted by Yale & Towne Mfg Co of New York and Stamford, Conn. for the use of students in its works.
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Hence, a generative grammar must be a system of rules that can iterate to generate an indefinitely large number of structures. This system of rules can be analyzed into the three major components of a generative grammar: the syntactic, phonological, and semantic components... the syntactic component of a grammar must specify, for each sentence, a deep structure that determines its semantic interpretation and a surface structure that determines its phonetic interpretation. The first of these is interpreted by the semantic component; the second, by the phonological component.
Aspects of the Theory of Syntax (1965), 15-6.
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Historians constantly rewrite history, reinterpreting (reorganizing) the records of the past. So, too, when the brain's coherent responses become part of a memory, they are organized anew as part of the structure of consciousness. What makes them memories is that they become part of that structure and thus form part of the sense of self; my sense of self derives from a certainty that my experiences refer back to me, the individual who is having them. Hence the sense of the past, of history, of memory, is in part the creation of the self.
The Strange, Familiar, and Forgotten: An Anatomy of Consciousness (1995), 87.
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History employs evolution to structure biological events in time.
The Flamingo's Smile (1987), 18.
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However far the mathematician’s calculating senses seem to be separated from the audacious flight of the artist’s imagination, these manifestations refer to mere instantaneous images, which have been arbitrarily torn from the operation of both. In designing new theories, the mathematician needs an equally bold and inspired imagination as creative as the artist, and in carrying out the details of a work the artist must unemotionally reckon all the resources necessary for the success of the parts. Common to both is the fabrication, the creation of the structure from the intellect.
From Die Entwickelung der Mathematik im Zusammenhange mit der Ausbreitung der Kultur (1893), 4. Translated by Webmaster using online resources. From the original German, “Wie weit auch der rechnende Verstand des Mathematikers von dem kühnen Fluge der Phantasie des Künstlers getrennt zu sein scheint, so bezeichnen diese Ausdrücke doch blosse Augenblicksbilder, die willkürlich aus der Thätigkeit Beider herausgerissen sind. Bei dem Entwurfe neuer Theorieen bedarf der Mathematiker einer ebenso kühnen und schöpferischen Phantasie wie der schaffende Künstler, und bei der Ausführung der Einzelheiten eines Werkes muss auch der Künstler kühl alle Mittel berechnen, welche zum Gelingen der Theile erforderlich sind. Gemeinsam ist Beiden die Hervorbringung, die Erzeugung der Gebilde aus dem Geiste.”
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However, if we consider that all the characteristics which have been cited are only differences in degree of structure, may we not suppose that this special condition of organization of man has been gradually acquired at the close of a long period of time, with the aid of circumstances which have proved favorable? What a subject for reflection for those who have the courage to enter into it!
In Recherches sur l'Organization des corps vivans (1802), as translated in Alpheus Spring Packard, Lamarck, the Founder of Evolution: His Life and Work (1901), 363. Packard's italics.
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Human personality resembles a coral reef: a large hard/dead structure built and inhabited by tiny soft/live animals. The hard/dead part of our personality consists of habits, memories, and compulsions and will probably be explained someday by some sort of extended computer metaphor. The soft/live part of personality consists of moment-to-moment direct experience of being. This aspect of personality is familiar but somewhat ineffable and has eluded all attempts at physical explanation.
Quoted in article 'Nick Herbert', in Gale Cengage Learning, Contemporary Authors Online (2002).
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Hyper-selectionism has been with us for a long time in various guises; for it represents the late nineteenth century’s scientific version of the myth of natural harmony–all is for the best in the best of all possible worlds (all structures well designed for a definite purpose in this case). It is, indeed, the vision of foolish Dr. Pangloss, so vividly satirized by Voltaire in Candide–the world is not necessarily good, but it is the best we could possibly have.
…...
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I am afraid all we can do is to accept the paradox and try to accommodate ourselves to it, as we have done to so many paradoxes lately in modern physical theories. We shall have to get accustomed to the idea that the change of the quantity R, commonly called the 'radius of the universe', and the evolutionary changes of stars and stellar systems are two different processes, going on side by side without any apparent connection between them. After all the 'universe' is an hypothesis, like the atom, and must be allowed the freedom to have properties and to do things which would be contradictory and impossible for a finite material structure.
Kosmos (1932), 133.
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I am delighted that I have found a new reaction to demonstrate even to the blind the structure of the interstitial stroma of the cerebral cortex. I let the silver nitrate react with pieces of brain hardened in potassium dichromate. I have already obtained magnificent results and hope to do even better in the future.
Letter to Nicolo Manfredi, 16 Feb 1873. Archive source. Quoted in Paolo Mazzarello, The Hidden Structure: A Scientific Biography of Camillo Golgi, trans. and ed. Henry A. Buchtel and Aldo Badiani (1999), 63.
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I am of the decided opinion, that mathematical instruction must have for its first aim a deep penetration and complete command of abstract mathematical theory together with a clear insight into the structure of the system, and doubt not that the instruction which accomplishes this is valuable and interesting even if it neglects practical applications. If the instruction sharpens the understanding, if it arouses the scientific interest, whether mathematical or philosophical, if finally it calls into life an esthetic feeling for the beauty of a scientific edifice, the instruction will take on an ethical value as well, provided that with the interest it awakens also the impulse toward scientific activity. I contend, therefore, that even without reference to its applications mathematics in the high schools has a value equal to that of the other subjects of instruction.
In 'Ueber das Lehrziel im mathemalischen Unterricht der höheren Realanstalten', Jahresbericht der Deutschen Mathematiker Vereinigung, 2, 192. (The Annual Report of the German Mathematical Association. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 73.
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I am satisfied with the mystery of life’s eternity and with a knowledge, a sense, of the marvelous structure of existence–as well as the humble attempt to understand even a tiny portion of the Reason that manifests itself in nature.
…...
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I believe that, as men occupied with the study and treatment of disease, we cannot have too strong a conviction that the problems presented to us are physical problems, which perhaps we may never solve, but still admitting of solution only in one way, namely, by regarding them as part of an unbroken series, running up from the lowest elementary conditions of matter to the highest composition of organic structure.
From Address (7 Aug 1868), the Hunterian Oration, 'Clinical Observation in Relation to medicine in Modern Times' delivered to a meeting of the British Medical Association, Oxford. Collected in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), 4.
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I cannot imagine a God who rewards and punishes the objects of his creation, whose purposes are modeled after our own–a God, in short, who is but a reflection of human frailty. Neither can I believe that the individual survives the death of his body, although feeble souls harbor such thoughts through fear or ridiculous egotism. It is enough for me to contemplate the mystery of conscious life perpetuating itself through all eternity, to reflect upon the marvelous structure of the universe which we can dimly perceive, and to try humbly to comprehend even an infinitesimal part of the intelligence manifested in nature.
From 'What I Believe: Living Philosophies XIII', Forum and Century (Oct 1930), 84, No. 4, 194. Article in full, reprinted in Edward H. Cotton (ed.), Has Science Discovered God? A Symposium of Modern Scientific Opinion (1931), 97.
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I consider the differences between man and animals in propensities, feelings, and intellectual faculties, to be the result of the same cause as that which we assign for the variations in other functions, viz. difference of organization; and that the superiority of man in rational endowments is not greater than the more exquisite, complicated, and perfectly developed structure of his brain, and particularly of his ample cerebral hemispheres, to which the rest of the animal kingdom offers no parallel, nor even any near approximation, is sufficient to account for.
Lectures on Physiology, Zoology, and the Natural History of Man (1819), 237.
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I definitely deny that any pathological process, i.e. any life-process taking place under unfavourable circumstances, is able to call forth qualitatively new formations lying beyond the customary range of forms characteristic of the species. All pathological formations are either degenerations, transformations, or repetitions of typical physiological structures.
In 'Cellular-Pathologie', Archiv für pathologische Anatomie und Physiologie und fur klinische Medizin (1855), 8, 13-14, as translated in LellandJ. Rather, 'Cellular Pathology', Disease, Life, and Man: Selected Essays by Rudolf Virchow (1958), 81.
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I don’t know whether there is a finite set of basic laws of physics or whether there are infinite sets of structure like an infinite set of Chinese boxes. Will the electron turn out to have an interior structure? I wish I knew!
In Kendrick Frazier, 'A Mind at Play: An Interview with Martin Gardner', Skeptical Inquirer (Mar/Apr 1998), 37.
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I don’t think it is proper at all to take the position that C. P. Snow has: namely, that the science—the knowledge, the mathematical side of life—runs in an opposite direction to the life of spontaneous humanistic action. They supplement each other. In literature, for instance, writing sonnets: it takes a lot of practice to make that kind of structure become something that just pours out, but when it does pour out, it is possible to say things that cannot be said without the sonnet form. Form and expression are very close together.
In Diane K. Osbon (ed.), A Joseph Campbell Companion: Reflections on the Art of Living (Collected Works of Joseph Campbell) (1991, 1995), 261.
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I have destroyed almost the whole race of frogs, which does not happen in that savage Batrachomyomachia of Homer. For in the anatomy of frogs, which, by favour of my very excellent colleague D. Carolo Fracassato, I had set on foot in order to become more certain about the membranous substance of the lungs, it happened to me to see such things that not undeservedly I can better make use of that [saying] of Homer for the present matter—
“I see with my eyes a work trusty and great.”
For in this (frog anatomy) owing to the simplicity of the structure, and the almost complete transparency of the vessels which admits the eye into the interior, things are more clearly shown so that they will bring the light to other more obscure matters.
De Pulmonibus (1661), trans. James Young, Proceedings of the Royal Society of Medicine (1929-30), 23, 7.
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I have no patience with attempts to identify science with measurement, which is but one of its tools, or with any definition of the scientist which would exclude a Darwin, a Pasteur or a Kekulé. The scientist is a practical man and his are practical aims. He does not seek the ultimate but the proximate. He does not speak of the last analysis but rather of the next approximation. His are not those beautiful structures so delicately designed that a single flaw may cause the collapse of the whole. The scientist builds slowly and with a gross but solid kind of masonry. If dissatisfied with any of his work, even if it be near the very foundations, he can replace that part without damage to the remainder. On the whole, he is satisfied with his work, for while science may never be wholly right it certainly is never wholly wrong; and it seems to be improving from decade to decade.
The Anatomy of Science (1926), 6-7.
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I have paid special attention to those Properties of the Positive Rays which seem to throw light on the problems of the structure of molecules and atoms and the question of chemical combination … I am convinced that as yet we are only at the beginning of the harvest of results which will elucidate the process of chemical combination, and thus bridge over the most serious gap which now exists between Physics and Chemistry.
Rays of Positive Electricity and their Application to Chemical Analyses (1921), v.
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I heard … xenon was a good anesthesia. … I thought, “How can xenon, which doesn’t form any chemical compounds, serve as a general anesthetic? … I lay awake at night for a few minutes before going to sleep, and during the next couple of weeks each night I would think, “…how do anesthetic agents work?" Then I forgot to do it after a while, but I’d trained my unconscious mind to keep this question alive and to call [it] to my consciousness whenever a new idea turned up…. So seven years went by. [One day I] put my feet up on the desk and started reading my mail, and here was a letter from George Jeffrey … an x-ray crystallographer, on his determination of the structure of a hydrate crystal. Immediately I sat up, took my feet off the desk, and said, “I understand anesthesia!” … I spent a year [and] determined the structure of chloroform hydrate, and then I wrote my paper published in June of 1961.
Interview with George B. Kauffman and Laurie M. Kauffman, in 'Linus Pauling: Reflections', American Scientist (Nov-Dec 1994), 82, No. 6, 522-523.
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I hope that in due time the chemists will justify their proceedings by some large generalisations deduced from the infinity of results which they have collected. For me I am left hopelessly behind and I will acknowledge to you that through my bad memory organic chemistry is to me a sealed book. Some of those here, [August] Hoffman for instance, consider all this however as scaffolding, which will disappear when the structure is built. I hope the structure will be worthy of the labour. I should expect a better and a quicker result from the study of the powers of matter, but then I have a predilection that way and am probably prejudiced in judgment.
Letter to Christian Schönbein (9 Dec 1852), The Letters of Faraday and Schoenbein, 1836-1862 (1899), 209-210.
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I know well there are those who would have the Study of Nature restrained wholly to Observations; without ever proceeding further. But due Consideration, and a deeper Insight into Things, would soon have undeceived and made them sensible of their error. Assuredly, that man who should spend his whole life in amassing together stone, timber, and other materials for building, without ever at the making any use, or raising any fabrick out of them, might well be reputed very fantastic and extravagant. And a like censure would be his due, who should be perpetually heaping up of natural collections without design. building a structure of philosophy out of them, or advancing some propositions that might turn to the benefit and advantage of the world. This is in reality the true and only proper end of collections, of observations, and natural history: and they are of no manner of use or value without it.
In An Attempt Toward a Natural History of the Fossils of England (1729), xiii-xiv.
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I shall conclude, for the time being, by saying that until Philosophers make observations (especially of mountains) that are longer, more attentive, orderly, and interconnected, and while they fail to recognize the two great agents, fire and water, in their distinct affects, they will not be able to understand the causes of the great natural variety in the disposition, structure, and other matter that can be observed in the terrestrial globe in a manner that truly corresponds to the facts and to the phenomena of Nature.
'Aleune Osservazioni Orittologiche fatte nei Monti del Vicentino', Giomale d’Italia, 1769, 5, 411, trans. Ezio Vaccari.
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I should like to compare this rearrangement which the proteins undergo in the animal or vegetable organism to the making up of a railroad train. In their passage through the body parts of the whole may be left behind, and here and there new parts added on. In order to understand fully the change we must remember that the proteins are composed of Bausteine united in very different ways. Some of them contain Bausteine of many kinds. The multiplicity of the proteins is determined by many causes, first through the differences in the nature of the constituent Bausteine; and secondly, through differences in the arrangement of them. The number of Bausteine which may take part in the formation of the proteins is about as large as the number of letters in the alphabet. When we consider that through the combination of letters an infinitely large number of thoughts may be expressed, we can understand how vast a number of the properties of the organism may be recorded in the small space which is occupied by the protein molecules. It enables us to understand how it is possible for the proteins of the sex-cells to contain, to a certain extent, a complete description of the species and even of the individual. We may also comprehend how great and important the task is to determine the structure of the proteins, and why the biochemist has devoted himself with so much industry to their analysis.
'The Chemical Composition of the Cell', The Harvey Lectures (1911), 7, 45.
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I should not like to leave an impression that all structural problems can be settled by X-ray analysis or that all crystal structures are easy to solve. I seem to have spent much more of my life not solving structures than solving them.
In 'X-ray Analysis of Complicated Molecules', Nobel Lecture (11 Dec 1964). In Nobel Lectures: Chemistry 1942-1962 (1964), 88.
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I think that the event which, more than anything else, led me to the search for ways of making more powerful radio telescopes, was the recognition, in 1952, that the intense source in the constellation of Cygnus was a distant galaxy—1000 million light years away. This discovery showed that some galaxies were capable of producing radio emission about a million times more intense than that from our own Galaxy or the Andromeda nebula, and the mechanisms responsible were quite unknown. ... [T]he possibilities were so exciting even in 1952 that my colleagues and I set about the task of designing instruments capable of extending the observations to weaker and weaker sources, and of exploring their internal structure.
From Nobel Lecture (12 Dec 1974). In Stig Lundqvist (ed.), Nobel Lectures, Physics 1971-1980 (1992), 187.
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I think that the formation of [DNA's] structure by Watson and Crick may turn out to be the greatest developments in the field of molecular genetics in recent years.
‘Discussion des rapports de M Pauling’, Rep. Institut International de Chemie Solvay: Conference on Proteins, 6-14 April 1953 (1953), 113.
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I was sitting writing at my textbook but the work did not progress; my thoughts were elsewhere. I turned my chair to the fire and dozed. Again the atoms were gambolling before my eyes. This time the smaller groups kept modestly in the background. My mental eye, rendered more acute by the repeated visions of the kind, could now distinguish larger structures of manifold confirmation: long rows, sometimes more closely fitted together all twining and twisting in snake like motion. But look! What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes. As if by a flash of lightning I awoke; and this time also I spent the rest of the night in working out the rest of the hypothesis. Let us learn to dream, gentlemen, then perhaps we shall find the truth... But let us beware of publishing our dreams till they have been tested by waking understanding.
Kekule at Benzolfest in Berichte (1890), 23, 1302.
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I would ... change the accepted rule that the nature of a complex molecule is determined by the nature, quantity, and position of its elementary component parts, by the following statement: the chemical nature of a complex molecule is determined by the nature of its elementary component parts, their quantity and chemical structure.
'On the Chemical Structure of Substances' 1861.
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Iconography becomes even more revealing when processes or concepts, rather than objects, must be depicted–for the constraint of a definite ‘thing’ cedes directly to the imagination. How can we draw ‘evolution’ or ‘social organization,’ not to mention the more mundane ‘digestion’ or ‘self-interest,’ without portraying more of a mental structure than a physical reality? If we wish to trace the history of ideas, iconography becomes a candid camera trained upon the scholar’s mind.
…...
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If gold medals and prizes were awarded to institutions instead of individuals, the Peter Bent Brigham Hospital of 30 years ago would have qualified. The ruling board and administrative structure of that hospital did not falter in their support of the quixotic objective of treating end-stage renal disease despite a long list of tragic failures that resulted from these early efforts.
In Tore Frängsmyr and Jan E. Lindsten (eds.), Nobel Lectures: Physiology Or Medicine: 1981-1990 (1993), 558.
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If molecules can be structurally identical and yet possess dissimilar properties, this can be explained only on the ground that the difference is due to a different arrangement of the atoms in space.
In Annalen der Chemie (1873), 166, 47, translated in A. Ihde, The Development of Modern Chemistry (1964), 326.
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If the structure that serves as a template (the gene or virus molecule) consists of, say, two parts, which are themselves complementary In structure, then each of these parts can serve as the mould for the production of a replica of the other part, and the complex of two complementary parts thus can serve as the mould for the production of duplicates of itself.
Molecular Architecture and the Processses of Life (1948), 10.
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If the universe is not meaningless, what is its meaning? For me, this meaning is to be found in the structure of the universe, which happens to be such as to produce thought by way of life and mind. Thought, in turn, is a faculty whereby the universe can reflect upon itself, discover its own structure, and apprehend such immanent entities as truth, beauty, goodness, and love. Such is the meaning of the universe, as I see it.
In Vital Dust: Life as a Cosmic Imperative (1995), 301.
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If Watson and I had not discovered the [DNA] structure, instead of being revealed with a flourish it would have trickled out and that its impact would have been far less. For this sort of reason Stent had argued that a scientific discovery is more akin to a work of art than is generally admitted. Style, he argues, is as important as content. I am not completely convinced by this argument, at least in this case.
What Mad Pursuit (1990), 76.
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If we range through the whole territory of nature, and endeavour to extract from each department the rich stores of knowledge and pleasure they respectively contain, we shall not find a more refined or purer source of amusement, or a more interesting and unfailing subject for recreation, than that which the observation and examination of the structure, affinities, and habits of plants and vegetables, afford.
In A Practical Treatise on the Cultivation of the Dahlia (1838), 2.
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If words are not things, or maps are not the actual territory, then, obviously, the only possible link between the objective world and the linguistic world is found in structure, and structure alone.
Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics (1958), 61.
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In all works on Natural History, we constantly find details of the marvellous adaptation of animals to their food, their habits, and the localities in which they are found. But naturalists are now beginning to look beyond this, and to see that there must be some other principle regulating the infinitely varied forms of animal life. It must strike every one, that the numbers of birds and insects of different groups having scarcely any resemblance to each other, which yet feed on the same food and inhabit the same localities, cannot have been so differently constructed and adorned for that purpose alone. Thus the goat-suckers, the swallows, the tyrant fly-catchers, and the jacamars, all use the same kind ‘Of food, and procure it in the same manner: they all capture insects on the wing, yet how entirely different is the structure and the whole appearance of these birds!
In A Narrative of Travels on the Amazon and Rio Negro (1853), 83-84.
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In attempting to understand the elements out of which mental phenomena are compounded, it is of the greatest importance to remember that from the protozoa to man there is nowhere a very wide gap either in structure or in behaviour. From this fact it is a highly probable inference that there is also nowhere a very wide mental gap.
Lecture II, 'Instinct and Habit', The Analysis of Mind
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In clinical investigation the sick individual is at the centre of the picture. The physician must have a deep interest in his patient’s economic and social structure as well as in his physical and psychic state. If attention is not paid to the diagnosis of the person the clinical investigator is apt to fail in studies of the patient’s disease. Without a consideration of the patient as a human being it would have been difficult to have fed patients daily large amounts of liver.
In Nobel Banquet speech (10 Dec 1934). Collected in Gustaf Santesson (ed.) Les Prix Nobel en 1934 (1935).
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In describing a protein it is now common to distinguish the primary, secondary and tertiary structures. The primary structure is simply the order, or sequence, of the amino-acid residues along the polypeptide chains. This was first determined by Sanger using chemical techniques for the protein insulin, and has since been elucidated for a number of peptides and, in part, for one or two other small proteins. The secondary structure is the type of folding, coiling or puckering adopted by the polypeptide chain: the a-helix structure and the pleated sheet are examples. Secondary structure has been assigned in broad outline to a number of librous proteins such as silk, keratin and collagen; but we are ignorant of the nature of the secondary structure of any globular protein. True, there is suggestive evidence, though as yet no proof, that a-helices occur in globular proteins, to an extent which is difficult to gauge quantitatively in any particular case. The tertiary structure is the way in which the folded or coiled polypeptide chains are disposed to form the protein molecule as a three-dimensional object, in space. The chemical and physical properties of a protein cannot be fully interpreted until all three levels of structure are understood, for these properties depend on the spatial relationships between the amino-acids, and these in turn depend on the tertiary and secondary structures as much as on the primary. Only X-ray diffraction methods seem capable, even in principle, of unravelling the tertiary and secondary structures.
Co-author with G. Bodo, H. M. Dintzis, R. G. Parrish, H. Wyckoff, and D. C. Phillips
'A Three-Dimensional Model of the Myoglobin Molecule Obtained by X-ray Analysis', Nature (1958) 181, 662.
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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 high school, when I first heard of entropy, I was attracted to it immediately. They said that in nature all systems are breaking down, and I thought, What a wonderful thing; perhaps I can make some small contribution to this process, myself. And, of course, it’s not just true of nature, it’s true of society as well. If you look carefully, you can see that the social structure is just beginning to break down, just beginning to come apart at the seams.
In Napalm and Silly Putty (2001), 130.
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In its most primitive form, life is, therefore, no longer bound to the cell, the cell which possesses structure and which can be compared to a complex wheel-work, such as a watch which ceases to exist if it is stamped down in a mortar. No, in its primitive form life is like fire, like a flame borne by the living substance;—like a flame which appears in endless diversity and yet has specificity within it;—which can adopt the form of the organic world, of the lank grass-leaf and of the stem of the tree.
Address given at the 1913 meeting of the Koninklijke Akademie van Wetenschappen in Amsterdam. Trans. in G. Van Iterson, Jr, L. E. Den Dooren De Jong and A. J. Kluyver, Martinus Willem Beilerinck: His Life and Work (1940), 120.
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In man, population structure reaches its greatest complexity. Mankind—the human species, Homo sapiens—is the most inclusive Mendelian population, one which inhabits nearly the whole globe.
In Radiation, Genes, and Man (1959), 102.
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In man’s brain the impressions from outside are not merely registered; they produce concepts and ideas. They are the imprint of the external world upon the human brain. Therefore, it is not surprising that, after a long period of searching and erring, some of the concepts and ideas in human thinking should have come gradually closer to the fundamental laws of the world, that some of our thinking should reveal the true structure of atoms and the true movements of the stars. Nature, in the form of man, begins to recognize itself.
In Knowledge and Wonder (1962).
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In most sciences one generation tears down what another has built, and what one has established, another undoes. In mathematics alone each generation adds a new storey to the old structure.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1869), 34. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 14. From the original German, “In den meisten Wissenschaften pflegt eine Generation das niederzureissen, was die andere gebaut, und was jene gesetzt, hebt diese auf. In der Mathematik allein setzt jede Generation ein neues Stockwerk auf den alten Unterbau.”
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In my own field, x-ray crystallography, we used to work out the structure of minerals by various dodges which we never bothered to write down, we just used them. Then Linus Pauling came along to the laboratory, saw what we were doing and wrote out what we now call Pauling's Rules. We had all been using Pauling's Rules for about three or four years before Pauling told us what the rules were.
In The Extension of Man (1972), 116.
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In physics we have dealt hitherto only with periodic crystals. To a humble physicist’s mind, these are very interesting and complicated objects; they constitute one of the most fascinating and complex material structures by which inanimate nature puzzles his wits. Yet, compared with the aperiodic crystal, they are rather plain and dull. The difference in structure is of the same kind as that between an ordinary wallpaper in which the same pattern is repeated again and again in regular periodicity and a masterpiece of embroidery, say a Raphael tapestry, which shows no dull repetition, but an elaborate, coherent, meaningful design traced by the great master.
…...
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In pure mathematics we have a great structure of logically perfect deductions which constitutes an integral part of that great and enduring human heritage which is and should be largely independent of the perhaps temporary existence of any particular geographical location at any particular time. … The enduring value of mathematics, like that of the other sciences and arts, far transcends the daily flux of a changing world. In fact, the apparent stability of mathematics may well be one of the reasons for its attractiveness and for the respect accorded it.
In Fundamentals of Mathematics (1941), 463.
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In scientific study, or, as I prefer to phrase it, in creative scholarship, the truth is the single end sought; all yields to that. The truth is supreme, not only in the vague mystical sense in which that expression has come to be a platitude, but in a special, definite, concrete sense. Facts and the immediate and necessary inductions from facts displace all pre-conceptions, all deductions from general principles, all favourite theories. Previous mental constructions are bowled over as childish play-structures by facts as they come rolling into the mind. The dearest doctrines, the most fascinating hypotheses, the most cherished creations of the reason and of the imagination perish from a mind thoroughly inspired with the scientific spirit in the presence of incompatible facts. Previous intellectual affections are crushed without hesitation and without remorse. Facts are placed before reasonings and before ideals, even though the reasonings and the ideals be more beautiful, be seemingly more lofty, be seemingly better, be seemingly truer. The seemingly absurd and the seemingly impossible are sometimes true. The scientific disposition is to accept facts upon evidence, however absurd they may appear to our pre-conceptions.
The Ethical Functions of Scientific Study: An Address Delivered at the Annual Commencement of the University of Michigan, 28 June 1888, 7-8.
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In structure these little animals were fashioned like a bell, and at the round opening they made such a stir, that the particles in the water thereabout were set in motion thereby. … And though I must have seen quite 20 of these little animals on their long tails alongside one another very gently moving, with outstretcht bodies and straitened-out tails; yet in an instant, as it were, they pulled their bodies and their tails together, and no sooner had they contracted their bodies and tails, than they began to stick their tails out again very leisurely, and stayed thus some time continuing their gentle motion: which sight I found mightily diverting.
[Describing the ciliate Vorticella.]
Letter to the Royal Society, London (25 Dec 1702). In Clifford Dobell (ed.), Anthony van Leewenhoek and his “Little Animals” (1932), 277.
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In the first book I shall describe all the positions of the spheres, along with the motions which I attribute to the Earth, so that the book will contain as it were the general structure of the universe. In the remaining books I relate the motions of the remaining stars, and all the spheres, to the mobility of the Earth, so that it can be thence established how far the motions and appearances of the remaining stars and spheres can be saved, if they are referred to the motions of the Earth.
'To His Holiness Pope Paul III', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans, A. M. Duncan (1976), 26.
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In the light of [current research on atomic structure] the physicists have, I think, some justification for their faith that they are building on the solid rock of fact, and not, as we are often so solemnly warned by some of our scientific brethren, on the shifting sands of imaginative hypothesis.
From Opening Address to the Mathematics and Physics Section at the Annual Meeting of the British Association for the Advancement of Science, Winnipeg. Collected in 'The British Association at Winnipeg', Nature (26 Aug 1909), 81. No. 2078, 263.
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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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In the summer after kindergarten, a friend introduced me to the joys of building plastic model airplanes and warships. By the fourth grade, I graduated to an erector set and spent many happy hours constructing devices of unknown purpose where the main design criterion was to maximize the number of moving parts and overall size. The living room rug was frequently littered with hundreds of metal “girders” and tiny nuts and bolts surrounding half-finished structures. An understanding mother allowed me to keep the projects going for days on end.
Autobiography in Gösta Ekspong (ed.), Nobel Lectures: Physics 1996-2000 (2002), 116.
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In the year 1902 (while I was attempting to explain to an elementary class in chemistry some of the ideas involved in the periodic law) becoming interested in the new theory of the electron, and combining this idea with those which are implied in the periodic classification, I formed an idea of the inner structure of the atom which, although it contained certain crudities, I have ever since regarded as representing essentially the arrangement of electrons in the atom ... In accordance with the idea of Mendeleef, that hydrogen is the first member of a full period, I erroneously assumed helium to have a shell of eight electrons. Regarding the disposition in the positive charge which balanced the electrons in the neutral atom, my ideas were very vague; I believed I inclined at that time toward the idea that the positive charge was also made up of discrete particles, the localization of which determined the localization of the electrons.
Valence and the Structure of Atoms and Molecules (1923), 29-30.
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In using the present in order to reveal the past, we assume that the forces in the world are essentially the same through all time; for these forces are based on the very nature of matter, and could not have changed. The ocean has always had its waves, and those waves have always acted in the same manner. Running water on the land has ever had the same power of wear and transportation and mathematical value to its force. The laws of chemistry, heat, electricity, and mechanics have been the same through time. The plan of living structures has been fundamentally one, for the whole series belongs to one system, as much almost as the parts of an animal to the one body; and the relations of life to light and heat, and to the atmosphere, have ever been the same as now.
In 'Introduction', Manual of Geology: Treating of the Principles of the Science (1863), 7.
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Indeed, while Nature is wonderfully inventive of new structures, her conservatism in holding on to old ones is still more remarkable. In the ascending line of development she tries an experiment once exceedingly thorough, and then the question is solved for all time. For she always takes time enough to try the experiment exhaustively. It took ages to find how to build a spinal column or brain, but when the experiment was finished she had reason to be, and was, satisfied.
In The Whence and Whither of Man; a Brief History of his Origin and Development through Conformity to Environment; being the Morse Lectures of 1895. (1896), 173. The Morse lectureship was founded by Prof. Samuel F.B. Morse in 1865 at Union Theological Seminary, the lectures to deal with “the relation of the Bible to any of the sciences.”
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Innovation is not the product of logical thought, even though the final product is tied to a logical structure.
…...
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It had the old double keyboard, an entirely different set of keys for capitals and figures, so that the paper seemed a long way off, and the machine was as big and solid as a battle cruiser. Typing was then a muscular activity. You could ache after it. If you were not familiar with those vast keyboards, your hand wandered over them like a child lost in a wood. The noise might have been that of a shipyard on the Clyde. You would no more have thought of carrying one of those grim structures as you would have thought of travelling with a piano.
[About his first typewriter.]
English Journey (1934), 122-123.
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It has been recognized that hydrogen bonds restrain protein molecules to their native configurations, and I believe that as the methods of structural chemistry are further applied to physiological problems it will be found that the significance of the hydrogen bond for physiology is greater than that of any other single structural feature.
Nature of the Chemical Bond and the Structure of Molecules and Crystals (1939), 265.
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It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material.
[Concluding remark in the paper by Watson and Crick announcing discovery of the structure of DNA.]
In J.D. Watson and F.H.C. Crick, 'A Structure for Deoxyribose Nucleic Acid,' Letter in Nature (25 Apr 1953), 171, 738. Quoted in Francis Crick, What Mad Pursuit (1990), 66.
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It is frivolous to fix pedantically the date of particular inventions. They have all been invented over and over fifty times. Man is the arch machine, of which all these shifts drawn from himself are toy models. He helps himself on each emergency by copying or duplicating his own structure, just so far as the need is.
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It is natural selection that gives direction to changes, orients chance, and slowly, progressively produces more complex structures, new organs, and new species. Novelties come from previously unseen association of old material. To create is to recombine.
In 'Evolution and Tinkering', Science (10 Jun 1977), 196, 1163.
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It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again; the never-satisfied man is so strange if he has completed a structure, then it is not in order to dwell in it peacefully,but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others.
Letter to Farkas Wolfgang Bolyai (2 Sep 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
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It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
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It is not the organs—that is, the character and form of the animal's bodily parts—that have given rise to its habits and particular structures. It is the habits and manner of life and the conditions in which its ancestors lived that have in the course of time fashioned its bodily form, its organs and qualities.
Attributed.
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It is probable that all heavy matter possesses—latent and bound up with the structure of the atom—a similar quantity of energy to that possessed by radium. If it could be tapped and controlled, what an agent it would be in shaping the world's destiny! The man who puts his hand on the lever by which a parsimonious nature regulates so jealously the output of this store of energy would possess a weapon by which he could destroy the Earth if he chose.
A prescient remark on atomic energy after the discovery of radioactivity, but decades before the harnessing of nuclear fission in an atomic bomb became a reality.
Lecture to the Corps of Royal Engineers, Britain (19040. In Rodney P. Carlisle, Scientific American Inventions and Discoveries (2004), 373.
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It is probable that all organisms now alive are descended from one ancestor, for the following reason. Most of our structural molecules are asymmetrical, as shown by the fact that they rotate the plane of polarized light, and often form asymmetrical crystals. But of the two possible types of any such molecule, related to one another like a right and left boot, only one is found throughout living nature. The apparent exceptions to this rule are all small molecules which are not used in the building of the large structures which display the phenomena of life.
In 'The Origin of Life', The Inequality of Man: And Other Essays (1932), 157.
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It is structure that we look for whenever we try to understand anything. All science is built upon this search; we investigate how the cell is built of reticular material, cytoplasm, chromosomes; how crystals aggregate; how atoms are fastened together; how electrons constitute a chemical bond between atoms. We like to understand, and to explain, observed facts in terms of structure. A chemist who understands why a diamond has certain properties, or why nylon or hemoglobin have other properties, because of the different ways their atoms are arranged, may ask questions that a geologist would not think of formulating, unless he had been similarly trained in this way of thinking about the world.
‘The Place of Chemistry In the Integration of the Sciences’, Main Currents in Modern Thought (1950), 7, 110.
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It is the destiny of wine to be drunk, and it is the destiny of glucose to be oxidized. But it was not oxidized immediately: its drinker kept it in his liver for more than a week, well curled up and tranquil, as a reserve aliment for a sudden effort; an effort that he was forced to make the following Sunday, pursuing a bolting horse. Farewell to the hexagonal structure: in the space of a few instants the skein was unwound and became glucose again, and this was dragged by the bloodstream all the way to a minute muscle fiber in the thigh, and here brutally split into two molecules of lactic acid, the grim harbinger of fatigue: only later, some minutes after, the panting of the lungs was able to supply the oxygen necessary to quietly oxidize the latter. So a new molecule of carbon dioxide returned to the atmosphere, and a parcel of the energy that the sun had handed to the vine-shoot passed from the state of chemical energy to that of mechanical energy, and thereafter settled down in the slothful condition of heat, warming up imperceptibly the air moved by the running and the blood of the runner. 'Such is life,' although rarely is it described in this manner: an inserting itself, a drawing off to its advantage, a parasitizing of the downward course of energy, from its noble solar form to the degraded one of low-temperature heat. In this downward course, which leads to equilibrium and thus death, life draws a bend and nests in it.
The Periodic Table (1975), trans. Raymond Rosenthal (1984), 192-3.
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It is the structure of the universe that has taught this knowledge to man. That structure is an ever existing exhibition of every principle upon which every part of mathematical science is founded. The offspring of this science is mechanics; for mechanics are no other than the principles of science appplied practically.
In The Age of Reason: Being an Investigation of True and Fabulous Theology (27 Jan O.S. 1794), 42.
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It was not alone the striving for universal culture which attracted the great masters of the Renaissance, such as Brunellesco, Leonardo da Vinci, Raphael, Michelangelo and especially Albrecht Dürer, with irresistible power to the mathematical sciences. They were conscious that, with all the freedom of the individual fantasy, art is subject to necessary laws, and conversely, with all its rigor of logical structure, mathematics follows aesthetic laws.
From Lecture (5 Feb 1891) held at the Rathhaus, Zürich, printed as Ueber den Antheil der mathematischen Wissenschaft an der Kultur der Renaissance (1892), 19. (The Contribution of the Mathematical Sciences to the Culture of the Renaissance.) As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 183.
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It was, of course, a lie what you read about my religious convictions, a lie which is being systematically repeated. I do not believe in a personal God and I have never denied this but have expressed it clearly. If something is in me which can be called religious then it is the unbounded admiration for the structure of the world so far as our science can reveal it.
From Letter (24 Mar 1954) in Einstein archives. Quoted by Helen Dukas and Banesh Hoffman, Albert Einstein: The Human Side (1979, 2013), 43. Dukas was Einstein’s personal secretary for 28 years, so she knew his philosophy well.
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Just as a tree constitutes a mass arranged in a definite manner, in which, in every single part, in the leaves as in the root, in the trunk as in the blossom, cells are discovered to be the ultimate elements, so is it also with the forms of animal life. Every animal presents itself as a sum of vital unities, every one of which manifests all the characteristics of life. The characteristics and unity of life cannot be limited to anyone particular spot in a highly developed organism (for example, to the brain of man), but are to be found only in the definite, constantly recurring structure, which every individual element displays. Hence it follows that the structural composition of a body of considerable size, a so-called individual, always represents a kind of social arrangement of parts, an arrangement of a social kind, in which a number of individual existences are mutually dependent, but in such a way, that every element has its own special action, and, even though it derive its stimulus to activity from other parts, yet alone effects the actual performance of its duties.
In Lecture I, 'Cells and the Cellular Theory' (1858), Rudolf Virchow and Frank Chance (trans.) ,Cellular Pathology (1860), 13-14.
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Just as the constant increase of entropy is the basic law of the universe, so it is the basic law of life to be ever more highly structured and to struggle against entropy.
In 'Letter to Dr. Gustáv Husák', Václav Havel: Or Living in Truth (1986), Pt. 1, 23.
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Knowing what we know from X-ray and related studies of the fibrous proteins, how they are built from long polypeptide chains with linear patterns drawn to a grand scale, how these chains can contract and take up different configurations by intramolecular folding, how the chain- groups are penetrated by, and their sidechains react with, smaller co-operating molecules, and finally how they can combine so readily with nucleic acid molecules and still maintain the fibrous configuration, it is but natural to assume, as a first working hypothesis at least, that they form the long scroll on which is written the pattern of life. No other molecules satisfy so many requirements.
William Thomas Astbury and Florence O. Bell. 'Some Recent Developments in the X-Ray Study of Proteins and Related Structures', Cold Spring Harbor Symposia on Quantitative Biology, 1938, 6, 1144.
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Let us ... consider the ovum [egg] as a physical system. Its potentialities are prodigious and one's first impulse is to expect that such vast potentialities would find expression in complexity of structure. But what do we find? The substance is clouded with particles, but these can be centrifuged away leaving it optically structureless but still capable of development.... On the surface of the egg there is a fine membrane, below it fluid of high viscosity, next fluid of relatively low viscosity, and within this the nucleus, which in the resting stage is simply a bag of fluid enclosed in a delicate membrane.... The egg's simplicity is not that of a machine or a crystal, but that of a nebula. Gathered into it are units relatively simple but capable by their combinations of forming a vast number of dynamical systems...
As guest of honour, closing day address (Jun 1928), Sixth Colloid Symposium, Toronto, Canada, 'Living Matter', printed in Harry Boyer Weiser (ed.), Colloid Symposium Monograph (1928), Vol. 6, 15. Quoted in Joseph Needham, Chemical Embryology (1931), Vol. 1, 612-613.
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Let us only imagine that birds had studied their own development and that it was they in turn who investigated the structure of the adult mammal and of man. Wouldn’t their physiological textbooks teach the following? “Those four and two-legged animals bear many resemblances to embryos, for their cranial bones are separated, and they have no beak, just as we do in the first live or six days of incubation; their extremities are all very much alike, as ours are for about the same period; there is not a single true feather on their body, rather only thin feather-shafts, so that we, as fledglings in the nest, are more advanced than they shall ever be … And these mammals that cannot find their own food for such a long time after their birth, that can never rise freely from the earth, want to consider themselves more highly organized than we?”
Über Entwicklungsgeschichte der Thiere: Beobachtung und Reflexion (1828), 203. Trans. Stephen Jay Gould, Ontogeny and Phylogeny (1977), 54.
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Life is a series of definite and successive changes both in structure and in composition, which take place in an individual without destroying its identity.
In Problems of Life and Mind: Second Series: the Physical Basis of Mind (1891), 32.
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Life through many long periods has been manifested in a countless host of varying structures, all circumscribed by one general plan, each appointed to a definite place, and limited to an appointed duration. On the whole the earth has been thus more and more covered by the associated life of plants and animals, filling all habitable space with beings capable of enjoying their own existence or ministering to the enjoyment of others; till finally, after long preparation, a being was created capable of the wonderful power of measuring and weighing all the world of matter and space which surrounds him, of treasuring up the past history of all the forms of life, and considering his own relation to the whole. When he surveys this vast and co-ordinated system, and inquires into its history and origin, can he be at a loss to decide whether it be a work of Divine thought and wisdom, or the fortunate offspring of a few atoms of matter, warmed by the anima mundi, a spark of electricity, or an accidental ray of sunshine?
Life on the Earth: Its Origin and Succession (1860), 216-7.
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Man, whose organization is regarded as the highest, departs from the vertebrate archetype; and it is because the study of anatomy is usually commenced from, and often confined to, his structure, that a knowledge of the archetype has been so long hidden from anatomists.
'The Lexington Papers', The Quarterly Review (1851), 89, 450-1.
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Mankind has always drawn from outside sources of energy. This island was the first to harness coal and steam. But our present sources stand in the ratio of a million to one, compared with any previous sources. The release of atomic energy will change the whole structure of society.
Address to New Europe Group meeting on the third anniversary of the Hiroshima bomb. Quoted in New Europe Group, In Commemoration of Professor Frederick Soddy (1956), 7.
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Mathematical magic combines the beauty of mathematical structure with the entertainment value of a trick.
In 'Preface', Mathematics, Magic, and Mystery (1956), ix. Webmaster checked the actual page, in the 1956 edition, and there Gardner plainly uses the beginning words “Mathematical magic.” On page 113, Gardner credits Royal V. Heath for originating the term “Mathemagic,” used as Heath’s book title in 1933. Anywhere you see the quote incorrectly beginning with “Mathemagical mathematics…” or saying Gardner coined the term “mathemagical” obviously did not check the primary source.
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Mathematicians are only dealing with the structure of reasoning, and they do not really care what they are talking about. They do not even need to know what they are talking about … But the physicist has meaning to all his phrases. … In physics, you have to have an understanding of the connection of words with the real world.
In The Character of Physical Law (1965), 55.
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Mathematicians create by acts of insight and intuition. Logic then sanctions the conquests of intuition. It is the hygiene that mathematics practices to keep its ideas healthy and strong. Moreover, the whole structure rests fundamentally on uncertain ground, the intuition of humans. Here and there an intuition is scooped out and replaced by a firmly built pillar of thought; however, this pillar is based on some deeper, perhaps less clearly defined, intuition. Though the process of replacing intuitions with precise thoughts does not change the nature of the ground on which mathematics ultimately rests, it does add strength and height to the structure.
In Mathematics in Western Culture (1964), 408.
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Mathematicians deal with possible worlds, with an infinite number of logically consistent systems. Observers explore the one particular world we inhabit. Between the two stands the theorist. He studies possible worlds but only those which are compatible with the information furnished by observers. In other words, theory attempts to segregate the minimum number of possible worlds which must include the actual world we inhabit. Then the observer, with new factual information, attempts to reduce the list further. And so it goes, observation and theory advancing together toward the common goal of science, knowledge of the structure and observation of the universe.
Lecture to Sigma Xi, 'The Problem of the Expanding Universe' (1941), printed in Sigma Xi Quarterly (1942), 30, 104-105. Reprinted in Smithsonian Institution Report of the Board of Regents (1943), 97, 123. As cited by Norriss S. Hetherington in 'Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe', Historical Studies in the Physical Sciences (1982), 13, No. 1, 63.
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Mathematics because of its nature and structure is peculiarly fitted for high school instruction [Gymnasiallehrfach]. Especially the higher mathematics, even if presented only in its elements, combines within itself all those qualities which are demanded of a secondary subject.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 40. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 49.
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Mathematics is a structure providing observers with a framework upon which to base healthy, informed, and intelligent judgment. Data and information are slung about us from all directions, and we are to use them as a basis for informed decisions. … Ability to critically analyze an argument purported to be logical, free of the impact of the loaded meanings of the terms involved, is basic to an informed populace.
In 'Mathematics Is an Edifice, Not a Toolbox', Notices of the AMS (Oct 1996), 43, No. 10, 1108.
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Mathematics is not only real, but it is the only reality. That is that entire universe is made of matter, obviously. And matter is made of particles. It’s made of electrons and neutrons and protons. So the entire universe is made out of particles. Now what are the particles made out of? They’re not made out of anything. The only thing you can say about the reality of an electron is to cite its mathematical properties. So there’s a sense in which matter has completely dissolved and what is left is just a mathematical structure.
In 'Gardner on Gardner: JPBM Communications Award Presentation', Focus-The Newsletter of the Mathematical Association of America (Dec 1994), 14, No. 6. Also, first sentence as filler, with citation, after Washek F. Pfeffer, 'A Devil's Platform', The American Mathematical Monthly (Dec 2008), 115, No. 10, 947.
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Mathematics, too, is a language, and as concerns its structure and content it is the most perfect language which exists, superior to any vernacular; indeed, since it is understood by every people, mathematics may be called the language of languages. Through it, as it were, nature herself speaks; through it the Creator of the world has spoken, and through it the Preserver of the world continues to speak.
In Die Mathematik die Fackeltragerin einer neutn Zeit (1889), 5. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 194. From the original German, “Denn auch die Mathematik ist eine Sprache, und zwar nach Bau und Inhalt die vollkommenste Sprache, die es giebt, höher als jede Volkssprache; ja, weil alle Völker sie verstehen, kann sie die Sprache der Sprachen heißen. In ihr spricht sozusagen die Natur selbst, in ihr hat der Schöpfer der Welt geredet und in ihr redet noch immer ihr Erhalter.”
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Mathematics… is the set of all possible self-consistent structures, and there are vastly more logical structures than physical principles.
In 'Conclusion', Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (1995), 328.
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Matter and energy seem granular in structure, and so does “life”, but not so mind.
In Tarner Lecture, at Trinity College, Cambridge (Oct 1956), 'The Arithmetical Paradox: The Oneness of Mind', printed in Mind and Matter (1958), 61. Also collected in What is Life?: With Mind and Matter and Autobiographical Sketches (1992, 2012), 134.
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Medicine is essentially a learned profession. Its literature is ancient, and connects it with the most learned periods of antiquity; and its terminology continues to be Greek or Latin. You cannot name a part of the body, and scarcely a disease, without the use of a classical term. Every structure bears upon it the impress of learning, and is a silent appeal to the student to cultivate an acquaintance with the sources from which the nomenclature of his profession is derived.
From Address (Oct 1874) delivered at Guy’s Hospital, 'On The Study of Medicine', printed in British Medical journal (1874), 2, 425. Collected in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), 11.
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Men cannot help feeling a little ashamed of their cousin-german the Ape. His close yet grotesque and clumsy semblance of the human form is accompanied by no gleams of higher instinct. Our humble friend the dog, our patient fellow-labourer the horse, are nearer to us in this respect. The magnanimous and sagacious elephant, doomed though he be to all fours, is godlike compared with this spitefully ferocious creature. Strangely enough, too, the most repulsive and ferocious of all apekind, the recently discovered Gorilla is, the comparative anatomist assures us, nearest to us all: the most closely allied in structure to the human form.
In 'Our Nearest Relation', All Year Round (28 May 1859), 1, No. 5, 112. Charles Dickens was both the editor and publisher of this magazine. The author of the article remains unknown. The articles were by custom printed without crediting the author. Biographers have been able to use extant office records to identify various authors of other articles, but not this specific one. Dickens and Richard Owen were friends; they read each other’s work. Owen is known to have found at least a little time to write a few articles for Dickens’ magazines. Owen had given a talk at the Royal Institution (4 Feb 1859) titled 'On the Gorilla.' This would suggest why Dickens may have had a definite interest in publishing on this subject, regardless of who in fact wrote the article.
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Men of science belong to two different types—the logical and the intuitive. Science owes its progress to both forms of minds. Mathematics, although a purely logical structure, nevertheless makes use of intuition. Among the mathematicians there are intuitives and logicians, analysts and geometricians. Hermite and Weierstrass were intuitives. Riemann and Bertrand, logicians. The discoveries of intuition have always to be developed by logic.
In Man the Unknown (1935), 123.
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Mistakes are at the very base of human thought feeding the structure like root nodules. If we were not provided with the knack of being wrong, we could never get anything useful done.
In The Medusa and the Snail (1979), 37.
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Modern tree communities in Amazonia are structured to an important extent by a long history of plant domestication by Amazonian peoples.
As quoted in Robinson Meyer, 'The Amazon Rainforest Was Profoundly Changed by Ancient Humans', The Atlantic (2 Mar 2017).
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MOLECULE, n. The ultimate, indivisible unit of matter. It is distinguished from the corpuscle, also the ultimate, indivisible unit of matter, by a closer resemblance to the atom, also the ultimate, indivisible unit of matter. Three great scientific theories of the structure of the universe are the molecular, the corpuscular and the atomic. A fourth affirms, with Haeckel, the condensation or precipitation of matter from ether—whose existence is proved by the condensation or precipitation. The present trend of scientific thought is toward the theory of ions. The ion differs from the molecule, the corpuscle and the atom in that it is an ion. A fifth theory is held by idiots, but it is doubtful if they know any more about the matter than the others.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  220-221.
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Morphological information has provided the greatest single source of data in the formulation and development of the theory of evolution and that even now, when the preponderance of work is experimental, the basis for interpretation in many areas of study remains the form and relationships of structures.
'Morphology, Paleontology, and Evolution', in Sol Tax (ed.), Evolution After Darwin, Vol. 1, The Evolution of Life (1960), 524.
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Most loss of life and property has been due to the collapse of antiquated and unsafe structures, mostly of brick and other masonry. ... There is progress of California toward building new construction according to earthquake-resistant design. We would have less reason to ask for earthquake prediction if this was universal.
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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Much scientific truth proved to be as hypothetical as poetic allegory. The relationshiip of those rod-connected blue and red balls to an actual atomic structure was about the same as the relationship of Christianity to the fish or the Lamb.
Another Roadside Attraction (1990), 240.
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Mutations and chromosomal changes arise in every sufficiently studied organism with a certain finite frequency, and thus constantly and unremittingly supply the raw materials for evolution. But evolution involves something more than origin of mutations. Mutations and chromosomal changes are only the first stage, or level, of the evolutionary process, governed entirely by the laws of the physiology of individuals. Once produced, mutations are injected in the genetic composition of the population, where their further fate is determined by the dynamic regularities of the physiology of populations. A mutation may be lost or increased in frequency in generations immediately following its origin, and this (in the case of recessive mutations) without regard to the beneficial or deleterious effects of the mutation. The influences of selection, migration, and geographical isolation then mold the genetic structure of populations into new shapes, in conformity with the secular environment and the ecology, especially the breeding habits, of the species. This is the second level of the evolutionary process, on which the impact of the environment produces historical changes in the living population.
Genetics and Origin of Species (1937), 13.
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My own prejudices are exactly the opposite of the functionalists’: “If you want to understand function, study structure.” I was supposed to have said in my molecular biology days. (I believe I was sailing at the time.)
What Mad Pursuit: A Personal View of Scientific Discovery (1988), 150.
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Nature has but one plan of operation, invariably the same in the smallest things as well as in the largest, and so often do we see the smallest masses selected for use in Nature, that even enormous ones are built up solely by fitting these together. Indeed, all Nature’s efforts are devoted to uniting the smallest parts of our bodies in such a way that all things whatsoever, however diverse they may be, which coalesce in the structure of living things construct the parts by means of a sort of compendium.
'On the Developmental Process', in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 2, 843.
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Nature is disordered, powerful and chaotic, and through fear of the chaos we impose system on it. We abhor complexity, and seek to simplify things whenever we can by whatever means we have at hand. We need to have an overall explanation of what the universe is and how it functions. In order to achieve this overall view we develop explanatory theories which will give structure to natural phenomena: we classify nature into a coherent system which appears to do what we say it does.
In Day the Universe Changed (1985), 11.
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Nature never “fails.” Nature complies with its own laws. Nature is the law. When Man lacks understanding of Nature’s laws and a Man-contrived structure buckles unexpectedly, it does not fail. It only demonstrates that Man did not understand Nature’s laws and behaviors. Nothing failed. Man’s knowledge or estimating was inadequate.
In "How Little I Know", in Saturday Review (12 Nov 1966), 152. Excerpted in Buckminster Fuller and Answar Dil, Humans in Universe (1983), 31.
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Nature when more shy in one, hath more freely confest and shewn herself in another; and a Fly sometimes hath given greater light towards the true knowledge of the structure and the uses of the Parts in Humane Bodies, than an often repeated dissection of the same might have done … We must not therefore think the meanest of the Creation vile or useless, since that in them in lively Characters (if we can but read) we may find the knowledge of a Deity and ourselves … In every Animal there is a world of wonders; each is a Microcosme or a world in it self.
Phocrena, or the Anatomy of a Porpess, dissected at Gresham College: With a Prreliminary Discourse Concerning Anatomy, and a Natural History of Animals (1680), 2-3.
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Nature, … in order to carry out the marvelous operations [that occur] in animals and plants has been pleased to construct their organized bodies with a very large number of machines, which are of necessity made up of extremely minute parts so shaped and situated as to form a marvelous organ, the structure and composition of which are usually invisible to the naked eye without the aid of a microscope. … Just as Nature deserves praise and admiration for making machines so small, so too the physician who observes them to the best of his ability is worthy of praise, not blame, for he must also correct and repair these machines as well as he can every time they get out of order.
'Reply to Doctor Sbaraglia' in Opera Posthuma (1697), in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 1, 568.
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No collateral science had profited so much by palæontology as that which teaches the structure and mode of formation of the earth’s crust, with the relative position, time, and order of formation of its constituent stratified and unstratified parts. Geology has left her old hand-maiden mineralogy to rest almost wholly on the broad shoulders of her young and vigorous offspring, the science of organic remains.
In article 'Palæontology' contributed to Encyclopædia Britannica (8th ed., 1859), Vol. 17, 91.
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No medieval schoolman has been singled out as a precursor more often than the French scholastic Nicole Oresme.This brilliant scholar has been credited with … the framing of Gresham’s law before Gresham, the invention of analytic geometry before Descartes, with propounding structural theories of compounds before nineteenth century organic chemists, with discovering the law of free fall before Galileo, and with advocating the rotation of the Earth before Copernicus. None of these claims is, in fact, true, although each is based on discussion by Oresme of some penetration and originality …
In Nicole Oresme and the Medieval Geometry of Quantities and Motions (1968).
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No more harmful nonsense exists than the common supposition that deepest insight into great questions about the meaning of life or the structure of reality emerges most readily when a free, undisciplined, and uncluttered (read, rather, ignorant and uneducated) mind soars above mere earthly knowledge and concern.
…...
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No occupation is more worthy of an intelligent and enlightened mind, than the study of Nature and natural objects; and whether we labour to investigate the structure and function of the human system, whether we direct our attention to the classification and habits of the animal kingdom, or prosecute our researches in the more pleasing and varied field of vegetable life, we shall constantly find some new object to attract our attention, some fresh beauties to excite our imagination, and some previously undiscovered source of gratification and delight.
In A Practical Treatise on the Cultivation of the Dahlia (1838), 1-2.
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No physiologist who calmly considers the question in connection with the general truths of his science, can long resist the conviction that different parts of the cerebrum subserve different kinds of mental action. Localization of function is the law of all organization whatever: separateness of duty is universally accompanied with separateness of structure: and it would be marvellous were an exception to exist in the cerebral hemispheres.
The Principles of Psychology (1855), 607.
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No substantial part of the universe is so simple that it can be grasped and controlled without abstraction. Abstraction consists in replacing the part of the universe under consideration by a model of similar but simpler structure. Models, formal and intellectual on the one hand, or material on the other, are thus a central necessity of scientific procedure.
As coauthor with Norbert Wiener in 'The Role of Models in Science', Philosophy of Science (Oct 1945), 12, No. 4, 316.
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Nor can it be supposed that the diversity of chemical structure and process stops at the boundary of the species, and that within that boundary, which has no real finality, rigid uniformity reigns. Such a conception is at variance with any evolutionary conception of the nature and origin of species. The existence of chemical individuality follows of necessity from that of chemical specificity, but we should expect the differences between individuals to be still more subtle and difficult of detection. Indications of their existence are seen, even in man, in the various tints of skin, hair, and eyes, and in the quantitative differences in those portions of the end-products of metabolism which are endogenous and are not affected by diet, such as recent researches have revealed in increasing numbers. Even those idiosyncrasies with regard to drugs and articles of food which are summed up in the proverbial saying that what is one man's meat is another man's poison presumably have a chemical basis.
Inborn Errors of Metabolism: The Croonian Lectures delivered before the Royal College of Physicians of London, in June, 1908 (1909), 2-3.
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Not only do the various components of the cells form a living system, in which the capacity to live, react, and reproduce is dependent on the interactions of all the members of the system; but this living system is identical with the genetic system. The form of life is determined not only by the specific nature of the hereditary units but also by the structure and arrangement of the system. The whole system is more than the sum of its parts, and the effect of each of the components depends on and is influenced by all previous reactions, whose sequence is in turn determined by the whole idiotype.
'Cytoplasmic Inheritance in Epilobium and Its Theoretical Significance', Advances in Genetics (1954), 6, 320.
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Observation by means of the microscope will reveal more wonderful things than those viewed in regard to mere structure and connection: for while the heart is still beating the contrary (i.e., in opposite directions in the different vessels) movement of the blood is observed in the vessels—though with difficulty—so that the circulation of the blood is clearly exposed.
De Pulmonibus (1661), trans. James Young, Proceedings of the Royal Society of Medicine (1929-30), 23, 8.
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Occurrences that other men would have noted only with the most casual interest became for Whitney exciting opportunities to experiment. Once he became disturbed by a scientist's seemingly endless pursuit of irrelevant details in the course of an experiment, and criticized this as being as pointless as grabbing beans out of a pot, recording the numbers, and then analyzing the results. Later that day, after he had gone home, his simile began to intrigue him, and he asked himself whether it would really be pointless to count beans gathered in such a random manner. Another man might well have dismissed this as an idle fancy, but to Whitney an opportunity to conduct an experiment was not to be overlooked. Accordingly, he set a pot of beans beside his bed, and for several days each night before retiring he would take as many beans as he could grasp in one hand and make a note of how many were in the handful. After several days had passed he was intrigued to find that the results were not as unrewarding as he had expected. He found that each handful contained more beans than the one before, indicating that with practice he was learning to grasp more and more beans. “This might be called research in morphology, the science of animal structure,” he mused. “My hand was becoming webbed … so I said to myself: never label a real experiment useless, it may reveal something unthought of but worth knowing.”
'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 358-359.
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