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Who said: “I have no satisfaction in formulas unless I feel their arithmetical magnitude.”
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Property Quotes (177 quotes)

Carl Sagan quote A Subject Called Chemistry
Wellington College. CC by-NC 2.0 (source)

…resort to science has rendered modern war so destructive of life and property that it presents a new problem to mankind, such, that unless our civilization shall find some means of making an end to war, war will make an end to our civilization.
America and World Peace (1925), 37. In Edward C. Luck, Mixed Messages: American Politics and International Organization, 1919-1999 (1999), 143.
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[About the mechanical properties of the molecules of a chemical substance being studied:] They could be measured, but that would have taken several months. So someone said, ‘Let’s get Teller in and make him guess the data.’ We got him into a room and locked the door, so no one else could get at him, and he asked questions and did some figuring at the blackboard. He got the answers in about two hours, not entirely accurately, of course, but—as we found out when we got around to verifying them—close enough for the purpose.
Recalls the first time she was ever really awed by mental abilities of Edward Teller. She had joined the Manhattan Project, and needed data on the physical properties of molecules of a certain substance to get started on her assigned task of calculating its chemical properties. As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 61.
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[Mathematics is] the study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols.
Definition of Mathematics in William morris (ed.), American Heritage Dictionary (2000).
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[On gold, silver, mercury, platinum, palladium, rhodium, iridium, osmium:] As in their physical properties so in their chemical properties. Their affinities being weaker, (the noble metals) do not present that variety of combinations, belonging to the more common metals, which renders them so extensively useful in the arts; nor are they, in consequence, so necessary and important in the operations of nature. They do not assist in her hands in breaking down rocks and strata into soil, nor do they help man to make that soil productive or to collect for him its products.
From 13th Lecture in 1818, in Bence Jones, The Life and Letters of Faraday (1870), Vol. 1, 254.
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[On Oxygen, Chlorine, Iodine, Fluorine:] The most important division of ponderable substances seems to be that which represents their electrical energies or their respective inherent states. When the poles of a voltaic apparatus are introduced into a mixture of the simple substances, it is found that four of them go to the positive, while the rest evince their state by passing to the negative pole. As this division coincides with one resulting from a consideration of their most important properties, it is that which I shall adopt as the first.
From 5th Lecture in 1816, in Bence Jones, The Life and Letters of Faraday (1870), Vol. 1, 217-218.
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[On research] It’s got to be fun. I don't think anybody should tell you that he’s slogged his way through 25 years on a problem and there's only one reward at the end, and that's the value of the Hubble constant. That’s a bunch of hooey. The reward is learning all the wonderful properties of the things that don’t work.
As quoted in Obituary, 'Allan Sandage, 84, Astronomer, Dies; Charted Cosmos’s Age and Expansion', New York Times (17 Nov 2010), B19.
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[The famous attack of Sir William Hamilton on the tendency of mathematical studies] affords the most express evidence of those fatal lacunae in the circle of his knowledge, which unfitted him for taking a comprehensive or even an accurate view of the processes of the human mind in the establishment of truth. If there is any pre-requisite which all must see to be indispensable in one who attempts to give laws to the human intellect, it is a thorough acquaintance with the modes by which human intellect has proceeded, in the case where, by universal acknowledgment, grounded on subsequent direct verification, it has succeeded in ascertaining the greatest number of important and recondite truths. This requisite Sir W. Hamilton had not, in any tolerable degree, fulfilled. Even of pure mathematics he apparently knew little but the rudiments. Of mathematics as applied to investigating the laws of physical nature; of the mode in which the properties of number, extension, and figure, are made instrumental to the ascertainment of truths other than arithmetical or geometrical—it is too much to say that he had even a superficial knowledge: there is not a line in his works which shows him to have had any knowledge at all.
In Examination of Sir William Hamilton's Philosophy (1878), 607.
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[The nanotube] brings those properties you cannot get from other organic molecules. And it’s still carbon, so it has organic chemistry. Here is an object that has, to a superlative degree, the aspects that we hold most central to the inorganic world: hardness, toughness, terrific strength, thermal and electrical conductivity. Things you just can’t do with bone and wood. But it’s made out of carbon. It’s something that plays the game at the same level of perfection as molecules and life.
From interview in 'Wires of Wonder', Technology Review (Mar 2001), 104, No. 2, 88.
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[On the use of scopolamine in criminology], If it is permissible for a state to take life, liberty and property because of crime, it can be made legal to obtain information from a suspected criminal by the use of a drug. If the use of bloodhounds is legal, the use of scopolamine can be made legal.
From paper read at the Section on State Medicine and Public Hygiene of the State Medical Association of Texas at El Paso (11 May 1922), 'The Use Of Scopolamine In Criminology', published in Texas State Journal of Medicine (Sep 1922). Reprinted in The American Journal of Police Science (Jul-Aug 1931), 2, No. 4, 328.
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Compounds formed by chemical attraction, possess new properties different from those of their component parts... chemists have long believed that the contrary took place in their combination. They thought, in fact, that the compounds possessed properties intermediate between those of their component parts; so that two bodies, very coloured, very sapid, or insapid, soluble or insoluble, fusible or infusible, fixed or volatile, assumed in chemical combination, a shade or colour, or taste, solubility or volatility, intermediate between, and in some sort composed of, the same properties which were considered in their principles. This is an illusion or error which modern chemistry is highly interested to overthrow.
Quoted in A General System of Chemical Knowledge (1804), Vol. I, trans. W. Nicholson, 102-3.
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Une même expression, dont les géomètres avaient considéré les propriétés abstraites, … représente'aussi le mouvement de la lumière dans l’atmosphère, quelle détermine les lois de la diffusion de la chaleur dans la matière solide, et quelle entre dans toutes les questions principales de la théorie des probabilités.
The same expression whose abstract properties geometers had considered … represents as well the motion of light in the atmosphere, as it determines the laws of diffusion of heat in solid matter, and enters into all the chief problems of the theory of probability.
From Théorie Analytique de la Chaleur (1822), translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.
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Wenn sich für ein neues Fossil kein, auf eigenthümliche Eigenschaften desselben hinweisender, Name auffinden lassen Will; als in welchem Falle ich mich bei dem gegenwärtigen zu befinden gestehe; so halte ich es für besser, eine solche Benennung auszuwählen, die an sich gar nichts sagt, und folglich auch zu keinen unrichtigen Begriffen Anlass geben kann. Diesem zufolge will ich den Namen für die gegenwärtige metallische Substanz, gleichergestalt wie bei dem Uranium geschehen, aus der Mythologie, und zwar von den Ursöhnen der Erde, den Titanen, entlehnen, und benenne also dieses neue Metallgeschlecht: Titanium.
Wherefore no name can be found for a new fossil [element] which indicates its peculiar and characteristic properties (in which position I find myself at present), I think it is best to choose such a denomination as means nothing of itself and thus can give no rise to any erroneous ideas. In consequence of this, as I did in the case of Uranium, I shall borrow the name for this metallic substance from mythology, and in particular from the Titans, the first sons of the earth. I therefore call this metallic genus TITANIUM.
Martin Heinrich Klaproth. Original German edition, Beiträge Zur Chemischen Kenntniss Der Mineralkörper (1795), Vol. 1 , 244. English edition, translator not named, Analytical Essays Towards Promoting the Chemical Knowledge of Mineral Substances (1801), Vol. 1, 210. Klaproth's use of the term fossil associates his knowledge of the metal as from ore samples dug out of a mine.
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A force unconnected with matter, hovering loose over matter, is an utterly empty conception. In nitrogen, carbon, hydrogen, oxygen, in sulphur and phosphorus, their several properties have dwelt from all eternity.
As quoted in Ludwig Büchner, Force and Matter: Or, Principles of the Natural Order of the Universe (1891), 1.
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A man has a very insecure tenure of a property which another can carry away with his eyes. A few months reduced me to the cruel necessity either of destroying my machine, or of giving it to the public. To destroy it, I could not think of; to give up that for which I had laboured so long, was cruel. I had no patent, nor the means of purchasing one. In preference to destroying, I gave it to the public.
[On his inability to keep for himself a profitable income from his invention of the Spinning Mule.]
As quoted in James Mason, The Great Triumphs of Great Men (1875), 579.
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A patent is property carried to the highest degree of abstraction—a right in rem to exclude, without a physical object or content.
Homes-Pollock Letters (1946), edited by Mark DeWolfe Howe, Vol. 1, 53. In Eugene C. Gerhart, Quote it Completely! (1998), 802.
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A right understanding of the words which are names of names, is of great importance in philosophy. The tendency was always strong to believe that whatever receives a name must be an entity or being, having an independent existence of its own; and if no real entity answering to the name could be found, men did not for that reason suppose that none existed, but imagined that it was something peculiarly abstruse and mysterious, too high to be an object of sense. The meaning of all general, and especially of all abstract terms, became in this way enveloped in a mystical haze; and none of these have been more generally misunderstood, or have been a more copious source of futile and bewildering speculation, than some of the words which are names of names. Genus, Species, Universal, were long supposed to be designations of sublime hyperphysical realities; Number, instead of a general name of all numerals, was supposed to be the name, if not of a concrete thing, at least of a single property or attribute.
A footnote by John Stuart Mill, which he added as editor of a new edition of a work by his father, James Mill, Analysis of the Phenomena of the Human Mind (1869), Vol. 2, 5.
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According to Democritus, atoms had lost the qualities like colour, taste, etc., they only occupied space, but geometrical assertions about atoms were admissible and required no further analysis. In modern physics, atoms lose this last property, they possess geometrical qualities in no higher degree than colour, taste, etc. The atom of modern physics can only be symbolized by a partial differential equation in an abstract multidimensional space. Only the experiment of an observer forces the atom to indicate a position, a colour and a quantity of heat. All the qualities of the atom of modern physics are derived, it has no immediate and direct physical properties at all, i.e. every type of visual conception we might wish to design is, eo ipso, faulty. An understanding of 'the first order' is, I would almost say by definition, impossible for the world of atoms.
Philosophic Problems of Nuclear Science, trans. F. C. Hayes (1952), 38.
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All change is relative. The universe is expanding relatively to our common material standards; our material standards are shrinking relatively to the size of the universe. The theory of the “expanding universe” might also be called the theory of the “shrinking atom”. …
:Let us then take the whole universe as our standard of constancy, and adopt the view of a cosmic being whose body is composed of intergalactic spaces and swells as they swell. Or rather we must now say it keeps the same size, for he will not admit that it is he who has changed. Watching us for a few thousand million years, he sees us shrinking; atoms, animals, planets, even the galaxies, all shrink alike; only the intergalactic spaces remain the same. The earth spirals round the sun in an ever-decreasing orbit. It would be absurd to treat its changing revolution as a constant unit of time. The cosmic being will naturally relate his units of length and time so that the velocity of light remains constant. Our years will then decrease in geometrical progression in the cosmic scale of time. On that scale man’s life is becoming briefer; his threescore years and ten are an ever-decreasing allowance. Owing to the property of geometrical progressions an infinite number of our years will add up to a finite cosmic time; so that what we should call the end of eternity is an ordinary finite date in the cosmic calendar. But on that date the universe has expanded to infinity in our reckoning, and we have shrunk to nothing in the reckoning of the cosmic being.
We walk the stage of life, performers of a drama for the benefit of the cosmic spectator. As the scenes proceed he notices that the actors are growing smaller and the action quicker. When the last act opens the curtain rises on midget actors rushing through their parts at frantic speed. Smaller and smaller. Faster and faster. One last microscopic blurr of intense agitation. And then nothing.
In The Expanding Universe (1933) , 90-92.
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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 properties that we designate as activity of the soul, are only the functions of the cerebral substance, and to express ourselves in a coarser way, thought is just about to the brain what bile is to the liver and urine to the kidney. It is absurd to admit an independent soul who uses the cerebellum as an instrument with which he would work as he pleases.
Carl Vogt
As quoted in William Vogt, La Vie d'un Homme, Carl Vogt (1896), 48. Translated by Webmaster, from the original French, “Toutes les propriétés que nous designons sous le nom d’activité de l’âme, ne sont que les fonctions de la substance cérébrale, et pour nous exprimer d’ une façon plus grossière, la pensée est à peu près au cerveau ce que la bile est au foie et l’urine au rein. Il est absurde d’ admettre une âme indépendante qui se serve du cervelet comme d’un instrument avec lequelle travaillerait comme il lui plait.”
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All those who think it paradoxical that so great a weight as the earth should not waver or move anywhere seem to me to go astray by making their judgment with an eye to their own affects and not to the property of the whole. For it would not still appear so extraordinary to them, I believe, if they stopped to think that the earth’s magnitude compared to the whole body surrounding it is in the ratio of a point to it. For thus it seems possible for that which is relatively least to be supported and pressed against from all sides equally and at the same angle by that which is absolutely greatest and homogeneous.
Ptolemy
'The Almagest 1', in Ptolemy: the Almagest; Nicolaus Copernicus: On the Revolutions of the Heavenly Spheres; Johannes Kepler: Epitome of Copernican Astronomy: IV - V The Harmonies of the World: V, trans. R. Catesby Taliaferro (1952), 11.
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Almost all of the material phenomena which occur under terrestrial conditions are recognized as quantum mechanical consequences of the electrical attraction between electrons and nuclei and of the gravitational attraction between massive objects. We should be able, therefore, to express all the relevant magnitudes which characterize the properties of matter in terms of the following six magnitudes: M, m, e, c, G, and h; M is the mass of the proton, m and e are the mass and electrical charge of the electron, c is the light velocity, G is Newton's gravitational constant, and—most importantly—h is the quantum of action.
In 'Of Atoms, Mountains, and Stars: A Study in Qualitative Physics' (21 Feb 1975), Science, 187 No. 4177, 605.
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As Arkwright and Whitney were the demi-gods of cotton, so prolific Time will yet bring an inventor to every plant. There is not a property in nature but a mind is born to seek and find it.
In Fortune of the Republic (1878), 3.
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As physicists have arranged an extensive series of effects under the general term of Heat, so they have named another series Light, and a third they have called Electricity. We find ... that all these principles are capable of being produced through the medium of living bodies, for nearly all animals have the power of evolving heat; many insects, moreover, can voluntarily emit light; and the property of producing electricity is well evinced in the terrible shock of the electric eel, as well as in that of some other creatures. We are indeed in the habit of talking of the Electric fluid, or the Galvanic fluid, but this in reality is nothing but a licence of expression suitable to our finite and material notions.
In the Third Edition of Elements of Electro-Metallurgy: or The Art of Working in Metals by the Galvanic Fluid (1851), 1.
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As regards the co-ordination of all ordinary properties of matter, Rutherford’s model of the atom puts before us a task reminiscent of the old dream of philosophers: to reduce the interpretation of the laws of nature to the consideration of pure numbers.
In Faraday Lecture (1930), Journal of the Chemical Society (Feb 1932), 349. As quoted and cited in Chen Ning Yang, Elementary Particles (1961), 7.
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At the present time all property is personal; the man owns his own ponies and other belongings he has personally acquired; the woman owns her horses, dogs, and all the lodge equipments; children own their own articles; and parents do not control the possessions of their children. There is no family property as we use the term. A wife is as independent as the most independent man in our midst. If she chooses to give away or sell all of her property, there is no one to gainsay her.
Speech on 'The Legal Conditions of Indian Women', delivered to Evening Session (Thur 29 Mar 1888), collected in Report of the International Council of Women: Assembled by the National Woman Suffrage Association, Washington, D.C., U.S. of America, March 25 to April 1, 1888 (1888), Vol. 1, 239-240.
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Available energy is energy which we can direct into any desired channel. Dissipated energy is energy which we cannot lay hold of and direct at pleasure, such as the energy of the confused agitation of molecules which we call heat. Now, confusion, like the correlative term order, is not a property of material things in themselves, but only in relation to the mind which perceives them. A memorandum-book does not, provided it is neatly written, appear confused to an illiterate person, or to the owner who understands it thoroughly, but to any other person able to read it appears to be inextricably confused. Similarly the notion of dissipated energy could not occur to a being who could not turn any of the energies of nature to his own account, or to one who could trace the motion of every molecule and seize it at the right moment. It is only to a being in the intermediate stage, who can lay hold of some forms of energy while others elude his grasp, that energy appears to be passing inevitably from the available to the dissipated state.
'Diffusion', Encyclopaedia Britannica (1878). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 646.
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Bacteria are highly adaptable. They frequently change both morphologically and functionally. Their virulence is also an essentially fluctuating property, that increases or diminishes according to the conditions to which the pathogenic organism is subjected.
In Studies in Immunity (1909), 1.
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Before the promulgation of the periodic law the chemical elements were mere fragmentary incidental facts in nature; there was no special reason to expect the discovery of new elements, and the new ones which were discovered from time to time appeared to be possessed of quite novel properties. The law of periodicity first enabled us to perceive undiscovered elements at a distance which formerly were inaccessible to chemical vision, and long ere they were discovered new elements appeared before our eyes possessed of a number of well-defined properties.
In Faraday Lecture, delivered before the Fellows of the Chemical Society in the Theatre of the Royal Institution (4 Jun 1889), printed in Professor Mendeléeff, 'The Periodic Law of the Chemical Elements', Transactions of the Chemical Society (1889), 55, 648.
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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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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 nothing is more estimable than a physician who, having studied nature from his youth, knows the properties of the human body, the diseases which assail it, the remedies which will benefit it, exercises his art with caution, and pays equal attention to the rich and the poor.
A Philosophical Dictionary: from the French? (2nd Ed.,1824), Vol. 5, 239-240.
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But when it has been shown by the researches of Pasteur that the septic property of the atmosphere depended not on the oxygen, or any gaseous constituent, but on minute organisms suspended in it, which owed their energy to their vitality, it occurred to me that decomposition in the injured part might be avoided without excluding the air, by applying as a dressing some material capable of destroying the life of the floating particles. Upon this principle I have based a practice.
'On the Antiseptic Principle in the Practice of Surgery', The British Medical Journal (1867), ii, 246.
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Certain elements have the property of producing the same crystal form when in combination with an equal number of atoms of one or more common elements, and the elements, from his point of view, can be arranged in certain groups. For convenience I have called the elements belonging to the same group … isomorphous.
Originally published in 'Om Förhållandet emellan chemiska sammansättningen och krystallformen hos Arseniksyrade och Phosphorsyrade Salter', (On the Relation between the Chemical Composition and Crystal Form of Salts of Arsenic and Phosphoric Acids), Kungliga Svenska vetenskapsakademiens handlingar (1821), 4. In F. Szabadváry article on 'Eilhard Mitscherlich' in Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 424; perhaps from J.R. Partington, A History of Chemistry, Vol. 4 (1964), 210.
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Chemistry works with an enormous number of substances, but cares only for some few of their properties; it is an extensive science. Physics on the other hand works with rather few substances, such as mercury, water, alcohol, glass, air, but analyses the experimental results very thoroughly; it is an intensive science. Physical chemistry is the child of these two sciences; it has inherited the extensive character from chemistry. Upon this depends its all-embracing feature, which has attracted so great admiration. But on the other hand it has its profound quantitative character from the science of physics.
In Theories of Solutions (1912), xix.
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Chemists show us that strange property, catalysis, which enables a substance while unaffected itself to incite to union elements around it. So a host, or hostess, who may know but little of those concerned, may, as a social switchboard, bring together the halves of pairs of scissors, men who become life-long friends, men and women who marry and are happy husbands and wives.
From chapter 'Jottings from a Note-book', in Canadian Stories (1918), 179.
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Chlorine is a deadly poison gas employed on European battlefields in World War I. Sodium is a corrosive metal which burns upon contact with water. Together they make a placid and unpoisonous material, table salt. Why each of these substances has the properties it does is a subject called chemistry.
In Broca's Brain: The Romance of Science (1979), 18, footnote.
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Common sense … has the very curious property of being more correct retrospectively than prospectively. It seems to me that one of the principal criteria to be applied to successful science is that its results are almost always obvious retrospectively; unfortunately, they seldom are prospectively. Common sense provides a kind of ultimate validation after science has completed its work; it seldom anticipates what science is going to discover.
Quoted in A. De Reuck, M. Goldsmith and J. Knight (eds.), Decision Making in National Science Policy (1968), 96.
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Curiosity that inborn property of man, daughter of ignorance and mother of knowledge when wonder wakens our minds, has the habit, wherever it sees some extraordinary phenomenon of nature, a comet for example, a sun-dog, or a midday star, of asking straightway what it means.
In The New Science (3rd ed., 1744), Book 1, Para. 189, as translated by Thomas Goddard Bergin and Max Harold Fisch, The New Science of Giambattista Vico (1948), 64.
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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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Each new atom brings something of the personality of its element to the molecule, and this conspiracy of atoms results in a molecule with properties that are richer than those of each atom alone.
In Scientific American Library, Molecules (1987), 13.
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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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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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Euclidean mathematics assumes the completeness and invariability of mathematical forms; these forms it describes with appropriate accuracy and enumerates their inherent and related properties with perfect clearness, order, and completeness, that is, Euclidean mathematics operates on forms after the manner that anatomy operates on the dead body and its members. On the other hand, the mathematics of variable magnitudes—function theory or analysis—considers mathematical forms in their genesis. By writing the equation of the parabola, we express its law of generation, the law according to which the variable point moves. The path, produced before the eyes of the student by a point moving in accordance to this law, is the parabola.
If, then, Euclidean mathematics treats space and number forms after the manner in which anatomy treats the dead body, modern mathematics deals, as it were, with the living body, with growing and changing forms, and thus furnishes an insight, not only into nature as she is and appears, but also into nature as she generates and creates,—reveals her transition steps and in so doing creates a mind for and understanding of the laws of becoming. Thus modern mathematics bears the same relation to Euclidean mathematics that physiology or biology … bears to anatomy.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 38. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112-113.
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Finally, in regard to those who possess the largest shares in the stock of worldly goods, could there, in your opinion, be any police so vigilant and effetive, for the protections of all the rights of person, property and character, as such a sound and comprehensive education and training, as our system of Common Schools could be made to impart; and would not the payment of a sufficient tax to make such education and training universal, be the cheapest means of self-protection and insurance?
Annual Reports of the Secretary of the Board of Education of Massachusetts for the years 1839-1844, Life and Works of Horace Mann (1891), Vol. 3, 100.
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Following the example of Archimedes who wished his tomb decorated with his most beautiful discovery in geometry and ordered it inscribed with a cylinder circumscribed by a sphere, James Bernoulli requested that his tomb be inscribed with his logarithmic spiral together with the words, “Eadem mutata resurgo,” a happy allusion to the hope of the Christians, which is in a way symbolized by the properties of that curve.
From 'Eloge de M. Bernoulli', Oeuvres de Fontenelle, t. 5 (1768), 112. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 143-144. [The Latin phrase, Eadem numero mutata resurgo means as “Though changed, I arise again exactly the same”. —Webmaster]
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For a smart material to be able to send out a more complex signal it needs to be nonlinear. If you hit a tuning fork twice as hard it will ring twice as loud but still at the same frequency. That’s a linear response. If you hit a person twice as hard they’re unlikely just to shout twice as loud. That property lets you learn more about the person than the tuning fork. - When Things Start to Think, 1999.
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Force is no impelling god, no entity separate from the material substratum ; it is inseparable from matter, is one of its eternal indwelling properties.
As quoted in Ludwig Büchner, Force and Matter: Or, Principles of the Natural Order of the Universe (1891), 1.
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Fundamentally, as is readily seen, there exists neither force nor matter. Both are abstractions of things, such as they are, looked at from different standpoints. They complete and presuppose each other. Isolated they are meaningless. … Matter is not a go-cart, to and from which force, like a horse, can be now harnessed, now loosed. A particle of iron is and remains exactly the same thing, whether it shoot through space as a meteoric stone, dash along on the tire of an engine-wheel, or roll in a blood-corpuscle through the veins of a poet. … Its properties are eternal, unchangeable, untransferable.
From the original German text in 'Über die Lebenskraft', Preface to Untersuchungen über tierische Elektrizität (1848), xliii. As translated in Ludwig Büchner, Force and Matter: Or, Principles of the Natural Order of the Universe (1891), 1.
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Generality of points of view and of methods, precision and elegance in presentation, have become, since Lagrange, the common property of all who would lay claim to the rank of scientific mathematicians. And, even if this generality leads at times to abstruseness at the expense of intuition and applicability, so that general theorems are formulated which fail to apply to a single special case, if furthermore precision at times degenerates into a studied brevity which makes it more difficult to read an article than it was to write it; if, finally, elegance of form has well-nigh become in our day the criterion of the worth or worthlessness of a proposition,—yet are these conditions of the highest importance to a wholesome development, in that they keep the scientific material within the limits which are necessary both intrinsically and extrinsically if mathematics is not to spend itself in trivialities or smother in profusion.
In Die Entwickdung der Mathematik in den letzten Jahrhunderten (1884), 14-15.
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He [Heinrich Rose] looked upon the various substances that he was manipulating, as well as their reactions, under a thoroughly familial point of view: they were like so many children entrusted to his tutelage. Every time he explained simple, clear, well-defined phenomena, he assumed a jovial and smiling countenance; on the other hand, he almost got angry at certain mischievous bodies, the properties of which did not obey ordinary laws and troubled general theoretical views; in his eyes, this was unruly behavior.
As his student, about the lectures of Heinrich Rose, as quoted in entry by Stuart Pierson, 'Rose, Heinrich', in Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography (1975), Vol.11, 541, citing Adolphe Remelé, 'Notice biographique sur le Professeur Henri Rose', in Moniteur Scientifique (1864), 2nd ser., 6, 385–389. [Remelé’s italics.]
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How greatly would the heroes and statesmen of antiquity have despised the labours of that man who devoted his life to investigate the properties of the magnet! Little could they anticipate that this humble mineral was destined to change the very form and condition of human society in every quarter of the globe.
In 'Observations on the Study of Mineralogy', The Philosophical Magazine and Journal (Jul 1819), 54, 46. Slightly edited and used by Joseph Henry in 'Introductory Lecture on Chemistry' (Jan-Mar 1832), The Papers of Joseph Henry, Vol. 1, 396.
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However closely we may associate thought with the physical machinery of the brain, the connection is dropped as irrelevant as soon as we consider the fundamental property of thought—that it may be correct or incorrect. …that involves recognising a domain of the other type of law—laws which ought to be kept, but may be broken.
Swarthmore Lecture (1929) at Friends’ House, London, printed in Science and the Unseen World (1929), 57-58.
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Hunting, fishing, drawing, and music occupied my every moment. ... Cares I knew not, and cared naught about them.
[Recalling his time spent at his father's property, Mill Grove, during his first visit to America.]
In John James Audubon and Lucy Audubon (editor), The Life of John James Audubon: the Naturalist (1869), 17.
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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 believe that the useful methods of mathematics are easily to be learned by quite young persons, just as languages are easily learned in youth. What a wondrous philosophy and history underlie the use of almost every word in every language—yet the child learns to use the word unconsciously. No doubt when such a word was first invented it was studied over and lectured upon, just as one might lecture now upon the idea of a rate, or the use of Cartesian co-ordinates, and we may depend upon it that children of the future will use the idea of the calculus, and use squared paper as readily as they now cipher. … When Egyptian and Chaldean philosophers spent years in difficult calculations, which would now be thought easy by young children, doubtless they had the same notions of the depth of their knowledge that Sir William Thomson might now have of his. How is it, then, that Thomson gained his immense knowledge in the time taken by a Chaldean philosopher to acquire a simple knowledge of arithmetic? The reason is plain. Thomson, when a child, was taught in a few years more than all that was known three thousand years ago of the properties of numbers. When it is found essential to a boy’s future that machinery should be given to his brain, it is given to him; he is taught to use it, and his bright memory makes the use of it a second nature to him; but it is not till after-life that he makes a close investigation of what there actually is in his brain which has enabled him to do so much. It is taken because the child has much faith. In after years he will accept nothing without careful consideration. The machinery given to the brain of children is getting more and more complicated as time goes on; but there is really no reason why it should not be taken in as early, and used as readily, as were the axioms of childish education in ancient Chaldea.
In Teaching of Mathematics (1902), 14.
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I like to summarize what I regard as the pedestal-smashing messages of Darwin’s revolution in the following statement, which might be chanted several times a day, like a Hare Krishna mantra, to encourage penetration into the soul: Humans are not the end result of predictable evolutionary progress, but rather a fortuitous cosmic afterthought, a tiny little twig on the enormously arborescent bush of life, which, if replanted from seed, would almost surely not grow this twig again, or perhaps any twig with any property that we would care to call consciousness.
…...
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I then bequeath the whole of my property … to the United States of America, to found at Washington, under the name of the Smithsonian Institution, an establishment for the increase and diffusion of knowledge among men.
From the will of James Smithson written on 23 Oct 1826. (The amount excluded a modest lifetime annuity to a former faithful servant.) Smithson willed his estate firstly to his nephew, but it was to be bequeathed to the U.S. in the case his nephew died without heir—which did come to pass in 1835. Smithson included no further instructions concerning the Smithsonian Institution.
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I think we are beginning to suspect that man is not a tiny cog that doesn’t really make much difference to the running of the huge machine but rather that there is a much more intimate tie between man and the universe than we heretofore suspected. … [Consider if] the particles and their properties are not somehow related to making man possible. Man, the start of the analysis, man, the end of the analysis—because the physical world is, in some deep sense, tied to the human being.
In The Intellectual Digest (Jun 1973), as quoted and cited in Mark Chandos, 'Philosophical Essay: Story Theory", Kosmoautikon: Exodus From Sapiens (2015).
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I’m sure that science can’t ever explain everything and I can give you the reasons for that decision … I believe that scientific knowledge has fractal properties; that no matter how much we learn, whatever is left, however small it may seem, is just as infinitely complex as the whole was to start with. That, I think is the secret of the universe.
In It’s Been a Good Life (2009), 258, cited as from I. Asimov: A Memoir (1994), 481.
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If all the elements are arranged in the order of their atomic weights, a periodic repetition of properties is obtained. This is expressed by the law of periodicity.
Principles of Chemistry (1905), Vol. 2, 17.
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If feeling be not a property of matter, but owing to a superior principle, it must follow, that the motions of the heart, and other muscles of animals, after being separated from their bodies, are to be ascribed to this principle; and that any difficulties which may appear in this matter are owing to our ignorance of the nature of the soul, of the manner of its existence, and of its wonderful union with, and action upon the body.
In An Essay on the Vital and Other Involuntary Motions of Animals (1751), 389-390.
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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 some nuclear properties of the heavy elements had been a little different from what they turned out to be, it might have been impossible to build a bomb.
In Enrico Fermi: Physicist (1970), 149.
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If these d'Hérelle bodies were really genes, fundamentally like our chromosome genes, they would give us an utterly new angle from which to attack the gene problem. They are filterable, to some extent isolable, can be handled in test-tubes, and their properties, as shown by their effects on the bacteria, can then be studied after treatment. It would be very rash to call these bodies genes, and yet at present we must confess that there is no distinction known between the genes and them. Hence we can not categorically deny that perhaps we may be able to grind genes in a mortar and cook them in a beaker after all. Must we geneticists become bacteriologists, physiological chemists and physicists, simultaneously with being zoologists and botanists? Let us hope so.
'Variation Due to Change in the Individual Gene', The American Naturalist (1922), 56, 48-9.
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In destroying the predisposition to anger, science of all kind is useful; but the mathematics possess this property in the most eminent degree.
Quoted in Day, Collacon (no date).
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In my opinion the separation of the c- and ac-stars is the most important advancement in stellar classification since the trials by Vogel and Secchi ... To neglect the c-properties in classifying stellar spectra, I think, is nearly the same thing as if a zoologist, who has detected the deciding differences between a whale and a fish, would continue classifying them together.
Letter to Edward Pickering (22 Jul 1908). In Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 194.
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In the case of chemical investigations known as decompositions or analyses, it is first important to determine exactly what ingredients you are dealing with, or chemically speaking, what substances are contained in a given mixture or composite. For this purpose we use reagents, i.e., substances that possess certain properties and characteristics, which we well know from references or personal experience, such that the changes which they bring about or undergo, so to say the language that they speak thereby inform the researcher that this or that specific substance is present in the mixture in question.
From Zur Farben-Chemie Musterbilder für Freunde des Schönen und zum Gebrauch für Zeichner, Maler, Verzierer und Zeugdrucker [On Colour Chemistry...] (1850), Introduction. Translation tweaked by Webmaster from version in Herbert and W. Roesky and Klaud Möckel, translated by T.N. Mitchell and W.E. Russey, Chemical Curiosities: Spectacular Experiments and Inspired Quotes (1996), 1. From the original German, “Bei solchen chemischen Untersuchungen, die man zersetzende oder zergliedernde nennt, kommt es zunächst darauf an, zu ermitteln, mit welchen Stoffen man es zu thun hat, oder um chemisch zu reden, welche Stoffe in einem bestimmten Gemenge oder Gemisch enthalten sind. Hierzu bedient man sich sogenannter gegenwirkender Mittel, d. h. Stoffe, die bestimmte Eigenschaften und Eigenthümlichkeiten besitzen und die man aus Ueberlieferung oder eigner Erfahrung genau kennt, so daß die Veränderungen, welche sie bewirken oder erleiden, gleichsam die Sprache sind, mit der sie reden und dadurch dem Forscher anzeigen, daß der und der bestimmte Stoff in der fraglichen Mischung enthalten sei.”
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In the present state of our knowledge, it would be useless to attempt to speculate on the remote cause of the electrical energy, or the reason why different bodies, after being brought into contact, should be found differently electrified; its relation to chemical affinity is, however, sufficiently evident. May it not be identical with it, and an essential property of matter?
Bakerian Lecture, 'On Some Chemical Agencies of Electricity', Philosophical Transactions of the Royal Society, 1807, 97, 39.
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In your letter you apply the word imponderable to a molecule. Don’t do that again. It may also be worth knowing that the aether cannot be molecular. If it were, it would be a gas, and a pint of it would have the same properties as regards heat, etc., as a pint of air, except that it would not be so heavy.
Letter to Lewis Campbell (Sep 1874). In Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (1882), 391.
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Isolating mechanisms are biological properties of individuals that prevent the interbreeding of populations that are actually or potentially sympatric.
Animal Species and Evolution (1963), 91.
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It has the property of detonating very violently in certain circumstances. On one occasion a small amount of ether solution of pyroglycerin condensed in a glass bowl. ... When the bowl was heated over a spirit lamp, an extremely violent explosion occurred, which shattered it into small fragments. On another occasion a drop was heated in a test-tube, and exploded with such violence that the glass splinters cut deep into my face and hands, and hurt other people who were standing some distance off in the room.
[Describing early experiments on his discovery of nitroglycerin.]
From speech to the Royal Academy of Turin (1847). In Robert Shaplen, 'Annals of Science, Adventures of a Pacifist,' The New Yorker (15 Mar 1958), 49.
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It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years.
Address at the Franklin Institute (1937). Journal of the Franklin Institute (1937), 224, 277. Also see Paul C. Wensberg, Land's Polaroid: A Company and the Man who Invented It (1987), 31.
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It is above all the duty of the methodical text-book to adapt itself to the pupil’s power of comprehension, only challenging his higher efforts with the increasing development of his imagination, his logical power and the ability of abstraction. This indeed constitutes a test of the art of teaching, it is here where pedagogic tact becomes manifest. In reference to the axioms, caution is necessary. It should be pointed out comparatively early, in how far the mathematical body differs from the material body. Furthermore, since mathematical bodies are really portions of space, this space is to be conceived as mathematical space and to be clearly distinguished from real or physical space. Gradually the student will become conscious that the portion of the real space which lies beyond the visible stellar universe is not cognizable through the senses, that we know nothing of its properties and consequently have no basis for judgments concerning it. Mathematical space, on the other hand, may be subjected to conditions, for instance, we may condition its properties at infinity, and these conditions constitute the axioms, say the Euclidean axioms. But every student will require years before the conviction of the truth of this last statement will force itself upon him.
In Methodisches Lehrbuch der Elementar-Mathemalik (1904), Teil I, Vorwort, 4-5.
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It is admitted by all that a finished or even a competent reasoner is not the work of nature alone; the experience of every day makes it evident that education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history, may be chosen for this purpose. Now of all these, it is desirable to choose the one which admits of the reasoning being verified, that is, in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. When the guiding property of the loadstone was first ascertained, and it was necessary to learn how to use this new discovery, and to find out how far it might be relied on, it would have been thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.
In On the Study and Difficulties of Mathematics (1898), chap. 1.
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It is another property of the human mind that whenever men can form no idea of distant and unknown things, they judge them by what is familiar and at hand.
In The New Science (3rd ed., 1744), Book 1, Para. 122, as translated by Thomas Goddard Bergin and Max Harold Fisch, The New Science of Giambattista Vico (1948, 1984), 60.
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It is curious to observe how differently these great men [Plato and Bacon] estimated the value of every kind of knowledge. Take Arithmetic for example. Plato, after speaking slightly of the convenience of being able to reckon and compute in the ordinary transactions of life, passes to what he considers as a far more important advantage. The study of the properties of numbers, he tells us, habituates the mind to the contemplation of pure truth, and raises us above the material universe. He would have his disciples apply themselves to this study, not that they may be able to buy or sell, not that they may qualify themselves to be shop-keepers or travelling merchants, but that they may learn to withdraw their minds from the ever-shifting spectacle of this visible and tangible world, and to fix them on the immutable essences of things.
Bacon, on the other hand, valued this branch of knowledge only on account of its uses with reference to that visible and tangible world which Plato so much despised. He speaks with scorn of the mystical arithmetic of the later Platonists, and laments the propensity of mankind to employ, on mere matters of curiosity, powers the whole exertion of which is required for purposes of solid advantage. He advises arithmeticians to leave these trifles, and employ themselves in framing convenient expressions which may be of use in physical researches.
In 'Lord Bacon', Edinburgh Review (Jul 1837). Collected in Critical and Miscellaneous Essays: Contributed to the Edinburgh Review (1857), Vol. 1, 394.
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It is more important to know the properties of chlorine than the improprieties of Claudius!
Quoted in D. W. F. Hardie and J. D. Pratt, A History of the Modern Chemical Industry (1966), frontispiece.
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It is strange that we know so little about the properties of numbers. They are our handiwork, yet they baffle us; we can fathom only a few of their intricacies. Having defined their attributes and prescribed their behavior, we are hard pressed to perceive the implications of our formulas.
In James R. Newman (ed.), 'Commentary on The Mysteries of Arithmetic', The World of Mathematics (1956), Vol. 1, 497.
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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 they who hold the secret of the mysterious property of the mind by which error ministers to truth, and truth slowly but irrevocably prevails. Theirs is the logic of discovery, the demonstration of the advance of knowledge and the development of ideas, which as the earthly wants and passions of men remain almost unchanged, are the charter of progress, and the vital spark in history.
Lecture, 'The Study of History' (11 Jun 1895) delivered at Cambridge, published as A Lecture on The Study of History (1895), 54-55.
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It is to geometry that we owe in some sort the source of this discovery [of beryllium]; it is that [science] that furnished the first idea of it, and we may say that without it the knowledge of this new earth would not have been acquired for a long time, since according to the analysis of the emerald by M. Klaproth and that of the beryl by M. Bindheim one would not have thought it possible to recommence this work without the strong analogies or even almost perfect identity that Citizen Haüy found for the geometrical properties between these two stony fossils.
Haüy used the geometry of cleavage to reveal the underlying crystal structure, and thus found the emeral and beryl were geometrically identical. In May Elvira Weeks, The Discovery of the Elements (1934), 153, citing Mellor, Comprehensive Treatise on Inorganic and Theoretical Chemistry (1923), 204-7.
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Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past … I shall use the phrase “time's arrow” to express this one-way property of time which has no analogue in space.
Gifford Lectures (1927), The Nature of The Physical World (1928), 69.
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Let us investigate more closely this property common to animal and plant, this power of producing its likeness, this chain of successive existences of individuals, which constitutes the real existence of the species.
'De la Reproduction en Générale et particulière', Histoire Naturelle, Générale et Particulière, Avec la Description du Cabinet du Roi (1749), Vol. 2, 18. Trans. Phillip R. Sloan.
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Life is girt all round with a zodiac of sciences, the contributions of men who have perished to add their point of light to our sky. ... These road-makers on every hand enrich us. We must extend the area of life and multiply our relations. We are as much gainers by finding a property in the old earth as by acquiring a new planet.
In James Wood, Dictionary of Quotations from Ancient and Modern, English and Foreign Sources (1893), 247:34.
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Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined
In CRC Concise Encyclopedia of Mathematics (1998, 2nd ed. 2002 ), 1862.
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Mathematics is a science of Observation, dealing with reals, precisely as all other sciences deal with reals. It would be easy to show that its Method is the same: that, like other sciences, having observed or discovered properties, which it classifies, generalises, co-ordinates and subordinates, it proceeds to extend discoveries by means of Hypothesis, Induction, Experiment and Deduction.
In Problems of Life and Mind: The Method of Science and its Application (1874), 423-424. [The reals are the relations of magnitude.]
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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, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road. I believe, on the contrary, that there was a long period of tentative work (chiefly still among the Egyptians), and that the change is to be ascribed to a revolution, produced by the happy thought of a single man, whose experiments pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science. The history of that intellectual revolution, which was far more important than the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us. … A new light flashed on the first man who demonstrated the properties of the isosceles triangle (whether his name was Thales or any other name), for he found that he had not to investigate what he saw in the figure, or the mere concepts of that figure, and thus to learn its properties; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.
In Critique of Pure Reason, Preface to the Second Edition, (1900), 690.
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May every young scientist remember … and not fail to keep his eyes open for the possibility that an irritating failure of his apparatus to give consistent results may once or twice in a lifetime conceal an important discovery.
Commenting on the discovery of thoron gas because one of Rutherford’s students had found his measurements of the ionizing property of thorium were variable. His results even seemed to relate to whether the laboratory door was closed or open. After considering the problem, Rutherford realized a radioactive gas was emitted by thorium, which hovered close to the metal sample, adding to its radioactivity—unless it was dissipated by air drafts from an open door. (Thoron was later found to be argon.)
In Barbara Lovett Cline, Men Who Made a New Physics (1987), 21.
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Medicine rests upon four pillars—philosophy, astronomy, alchemy, and ethics. The first pillar is the philosophical knowledge of earth and water; the second, astronomy, supplies its full understanding of that which is of fiery and airy nature; the third is an adequate explanation of the properties of all the four elements—that is to say, of the whole cosmos—and an introduction into the art of their transformations; and finally, the fourth shows the physician those virtues which must stay with him up until his death, and it should support and complete the three other pillars.
Vas Buch Paragranum (c.1529-30), in J. Jacobi (ed.), Paracelsus: Selected Writings (1951), 133-4.
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More than any other product of human scientific culture scientific knowledge is the collective property of all mankind.
In On Aggression (2002), 279.
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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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My Design in this Book is not to explain the Properties of Light by Hypotheses, but to propose and prove them by Reason and Experiments: In order to which, I shall premise the following Definitions and Axioms.
Opticks (1704), Book 1, Part 1, Introduction, 1.
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My experiments proved that the radiation of uranium compounds ... is an atomic property of the element of uranium. Its intensity is proportional to the quantity of uranium contained in the compound, and depends neither on conditions of chemical combination, nor on external circumstances, such as light or temperature.
... The radiation of thorium has an intensity of the same order as that of uranium, and is, as in the case of uranium, an atomic property of the element.
It was necessary at this point to find a new term to define this new property of matter manifested by the elements of uranium and thorium. I proposed the word radioactivity which has since become generally adopted; the radioactive elements have been called radio elements.
In Pierre Curie, with the Autobiographical Notes of Marie Curie, trans. Charlotte and Vernon Kellogg (1923), 96. Also in reprint (2012) 45-46.
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Necessity is not the mother of invention. Knowledge and experiment are its parents. It sometimes happens that successful search is made for unknown materials to fill well-recognized and predetermined requirements. It more often happens that the acquirement of knowledge of the previously unknown properties of a material suggests its trial for some new use. These facts strongly indicate the value of knowledge of properties of materials and indicate a way for research.
Quoted in Guy Suits, 'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 357.
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No irrational exaggeration of the claims of Mathematics can ever deprive that part of philosophy of the property of being the natural basis of all logical education, through its simplicity, abstractness, generality, and freedom from disturbance by human passion. There, and there alone, we find in full development the art of reasoning, all the resources of which, from the most spontaneous to the most sublime, are continually applied with far more variety and fruitfulness than elsewhere;… The more abstract portion of mathematics may in fact be regarded as an immense repository of logical resources, ready for use in scientific deduction and co-ordination.
In Auguste Comte and Harriet Martineau (trans.), Positive Philosophy (1854), Vol. 2, 528-529.
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Numbers … were his friends. In the simplest array of digits [Ramanujan] detected wonderful properties: congruences, symmetries and relationships which had escaped the notice of even the outstandingly gifted theoreticians.
In James R. Newman (ed.), 'Commentary on Srinivasa Ramanujan', The World of Mathematics (1956), Vol. 1, 367.
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Old and new put their stamp to everything in Nature. The snowflake that is now falling is marked by both. The present moment gives the motion and the color of the flake, Antiquity its form and properties. All things wear a lustre which is the gift of the present, and a tarnish of time.
Epigraph for chapter 'Quotation and Originality', in Letters and Social Aims (1875, 1917), 175.
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On the most usual assumption, the universe is homogeneous on the large scale, i.e. down to regions containing each an appreciable number of nebulae. The homogeneity assumption may then be put in the form: An observer situated in a nebula and moving with the nebula will observe the same properties of the universe as any other similarly situated observer at any time.
From 'Review of Cosmology,', Monthly Notices of the Royal Astronomical Society (1948), 107-8; as quoted and cited in Hermann Friedmann, Wissenschaft und Symbol, Biederstein (1949), 472.
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Our conception of a native protein molecule (showing specific properties) is the following. The molecule consists of one polypeptide chain which continues without interruption throughout the molecule (or, in certain cases, of two or more such chains); this chain is folded into a uniquely defined configuration, in which it is held by hydrogen bonds between the peptide nitrogen and oxygen atoms and also between the free amino and carboxyl groups of the diamino and dicarboxyl amino acid residues.
The characteristic specific properties of native proteins we attribute to their uniquely defined configurations.
The denatured protein molecule we consider to be characterized by the absence of a uniquely defined configuration.
[Co-author with American chemist, Linus Pauling (1901-94)]
'On the Structure of Native, Denatured, and Coagulated Proteins', Proceedings of the National Academy of Sciences of the United States of America (1936), 22, 442-3.
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Our science is a drop, our ignorance a sea. Whatever else be certain, this at least is certain—that the world of our present natural knowledge is enveloped in a larger world of some sort of whose residual properties we at present can frame no positive idea.
In Address to Harvard Young Men’s Christian Association, 'Is Life Worth Living?', collected in The Will to Believe and other Essays in Popular Philosophy, (1897, 2006), 54. Published earlier in International Journal of Ethics (Oct 1895).
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Perhaps the problem is the seeming need that people have of making black-and-white cutoffs when it comes to certain mysterious phenomena, such as life and consciousness. People seem to want there to be an absolute threshold between the living and the nonliving, and between the thinking and the “merely mechanical,” ... But the onward march of science seems to force us ever more clearly into accepting intermediate levels of such properties.
‘Shades of Gray Along the Consciousness Continuum’, Fluid Concepts & Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought (1995), 310.
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Physicists speak of the particle representation or the wave representation. Bohr's principle of complementarity asserts that there exist complementary properties of the same object of knowledge, one of which if known will exclude knowledge of the other. We may therefore describe an object like an electron in ways which are mutually exclusive—e.g., as wave or particle—without logical contradiction provided we also realize that the experimental arrangements that determine these descriptions are similarly mutually exclusive. Which experiment—and hence which description one chooses—is purely a matter of human choice.
The Cosmic Code: Quantum Physics as the Language of Nature (1982), 94.
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Positive, objective knowledge is public property. It can be transmitted directly from one person to another, it can be pooled, and it can be passed on from one generation to the next. Consequently, knowledge accumulates through the ages, each generation adding its contribution. Values are quite different. By values, I mean the standards by which we judge the significance of life. The meaning of good and evil, of joy and sorrow, of beauty, justice, success-all these are purely private convictions, and they constitute our store of wisdom. They are peculiar to the individual, and no methods exist by which universal agreement can be obtained. Therefore, wisdom cannot be readily transmitted from person to person, and there is no great accumulation through the ages. Each man starts from scratch and acquires his own wisdom from his own experience. About all that can be done in the way of communication is to expose others to vicarious experience in the hope of a favorable response.
The Nature of Science and Other Lectures (1954), 7.
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Professors in every branch of the sciences, prefer their own theories to truth: the reason is that their theories are private property, but truth is common stock.
Reflection 378, in Lacon: or Many things in Few Words; Addressed to Those Who Think (1820), 169.
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Quantum theory thus reveals a basic oneness of the universe. It shows that we cannot decompose the world into independently existing smallest units. As we penetrate into matter, nature does not show us any isolated “building blocks,” but rather appears as a complicated web of relations between the various parts of the whole. These relations always include the observer in an essential way. The human observer constitute the final link in the chain of observational processes, and the properties of any atomic object can be understood only in terms of the object’s interaction with the observer.
In The Tao of Physics (1975), 68.
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Science and politics become the hobby of, and are cherished only by, the elect few; but religion becomes, through education, the property of all, without reference to station, age, and sex.
From an essay, reprinted as 'The Elect People' in Rev. W. Ayerst The Jews of the Nineteenth Century: A Collection of Essays, Reviews and Historical Notices, Originally Published in the “Jewish Intelligence” (1848) 119.
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Scientific wealth tends to accumulate according to the law of compound interest. Every addition to knowledge of the properties of matter supplies the physical scientist with new instrumental means for discovering and interpreting phenomena of nature, which in their turn afford foundations of fresh generalisations, bringing gains of permanent value into the great storehouse of natural philosophy.
From Inaugural Address of the President to British Association for the Advancement of Science, Edinburgh (2 Aug 1871). Printed in The Chemical News (4 Aug 1871), 24, No. 610., 53.
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Since it is necessary for specific ideas to have definite and consequently as far as possible selected terms, I have proposed to call substances of similar composition and dissimilar properties isomeric, from the Greek ίσομερης (composed of equal parts).
Jahrebericht (1832). As translated in Henry M. Leicester and Herbert S. Klickstein, A Source Book in Chemistry 1400-1900 (1952), 265.
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So far as physics is concerned, time’s arrow is a property of entropy alone.
Gifford Lectures (1927), The Nature of the Physical World (1928), 80.
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Success in the solution of a problem generally depends in a great measure on the selection of the most appropriate method of approaching it; many properties of conic sections (for instance) being demonstrable by a few steps of pure geometry which would involve the most laborious operations with trilinear co-ordinates, while other properties are almost self-evident under the method of trilinear co-ordinates, which it would perhaps be actually impossible to prove by the old geometry.
In Trilinear Coordinates and Other Methods of Modern Analytical Geometry of Two Dimensions (1866), 154.
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The automatic computing engine now being designed at N.P.L. [National Physics Laboratory] is atypical large scale electronic digital computing machine. In a single lecture it will not be possible to give much technical detail of this machine, and most of what I shall say will apply equally to any other machine of this type now being planned. From the point of view of the mathematician the property of being digital should be of greater interest than that of being electronic. That it is electronic is certainly important because these machines owe their high speed to this, and without the speed it is doubtful if financial support for their construction would be forthcoming. But this is virtually all that there is to be said on that subject. That the machine is digital however has more subtle significance. It means firstly that numbers are represented by sequences of digits which can be as long as one wishes. One can therefore work to any desired degree of accuracy. This accuracy is not obtained by more careful machining of parts, control of temperature variations, and such means, but by a slight increase in the amount of equipment in the machine.
Lecture to the London Mathematical Society, 20 February 1947. Quoted in B. E. Carpenter and R. W. Doran (eds.), A. M. Turing's Ace Report of 1946 and Other Papers (1986), 106.
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The basic ideas and simplest facts of set-theoretic topology are needed in the most diverse areas of mathematics; the concepts of topological and metric spaces, of compactness, the properties of continuous functions and the like are often indispensable.
As co-author with H. Hopf, Topologie I (1935), 23. As quoted, translated and cited in Reinhold Remmert, Theory of Complex Functions (1991), 9-10. From the original German, “Die Grundbegriffe und die einfachsten Tatsachen aus der mengentheoretischen Topologie braucht man in sehr verschiedenen Gebieten der Mathematik; die Begriffe des topologischen und des metrischen Raumes, der Kompaktheit, die Eigenschaften stetiger Abbildungen u. dgl. sind oft unentbehrlich.”
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The beginning of civilisation is the discovery of some useful arts, by which men acquire property, comforts, or luxuries. The necessity or desire of preserving them leads to laws and social institutions. The discovery of peculiar arts gives superiority to particular nations ... to subjugate other nations, who learn their arts, and ultimately adopt their manners;— so that in reality the origin as well as the progress and improvement of civil society is founded in mechanical and chemical inventions.
Consolations In Travel; or, the Last Days of a Philosopher (1830), 228.
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The best and safest way of philosophising seems to be, first to enquire diligently into the properties of things, and to establish those properties by experiences [experiments] and then to proceed slowly to hypotheses for the explanation of them. For hypotheses should be employed only in explaining the properties of things, but not assumed in determining them; unless so far as they may furnish experiments.
Letter to the French Jesuit, Gaston Pardies. Translation from the original Latin, as in Richard S. Westfall, Never at Rest: a Biography of Isaac Newton (1983), 242.
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The curiosity remains… to grasp more clearly how the same matter, which in physics and chemistry displays orderly and reproducible and relatively simple properties, arranges itself in the most astounding fashions as soon as it is drawn into the orbit of the living organism. The closer one looks at these performances of matter in living organisms the more impressive the show becomes. The meanest living cell becomes a magic puzzle box full of elaborate and changing molecules.
From 'Life: The Magic Puzzle Box', Transactions of the Connecticut Academy of Arts and Sciences (Dec 1949), 38, 173-190.
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The final result of our researches has widened the class of substances sensitive to light vibrations, until we can propound the fact of such sensitiveness being a general property of all matter.
In Paper (27 Aug 1880) read to the American Association for the Advancement of Science, 'On the Production and Reproduction of Sound by Light'. Printed in The American Journal of Science (Oct 1880), 20, 3rd Ser., No. 118, 305.
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The Greeks in the first vigour of their pursuit of mathematical truth, at the time of Plato and soon after, had by no means confined themselves to those propositions which had a visible bearing on the phenomena of nature; but had followed out many beautiful trains of research concerning various kinds of figures, for the sake of their beauty alone; as for instance in their doctrine of Conic Sections, of which curves they had discovered all the principal properties. But it is curious to remark, that these investigations, thus pursued at first as mere matters of curiosity and intellectual gratification, were destined, two thousand years later, to play a very important part in establishing that system of celestial motions which succeeded the Platonic scheme of cycles and epicycles. If the properties of conic sections had not been demonstrated by the Greeks and thus rendered familiar to the mathematicians of succeeding ages, Kepler would probably not have been able to discover those laws respecting the orbits and motions of planets which were the occasion of the greatest revolution that ever happened in the history of science.
In History of Scientific Ideas, Bk. 9, chap. 14, sect. 3.
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The hybridoma technology was a by-product of basic research. Its success in practical applications is to a large extent the result of unexpected and unpredictable properties of the method. It thus represents another clear-cut example of the enormous practical impact of an investment in research which might not have been considered commercially worthwhile, or of immediate medical relevance. It resulted from esoteric speculations, for curiosity’s sake, only motivated by a desire to understand nature.
From Nobel Lecture (8 Dec 1984), collected in Tore Frängsmyr and Jan Lindsten (eds.), Nobel Lectures in Physiology Or Medicine: 1981-1990 (1993), 267-268.
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The importance of group theory was emphasized very recently when some physicists using group theory predicted the existence of a particle that had never been observed before, and described the properties it should have. Later experiments proved that this particle really exists and has those properties.
Groups in the New Mathematics (1967), 7. Quoted in Rosemary Schmalz, Out of the Mouths of Mathematicians: A Quotation Book for Philomaths (1993), 42.
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The instinct for collecting, which began as in other animals as an adaptive property, could always in man spread beyond reason; it could become a hoarding mania. But in its normal form it provides a means of livelihood at the hunting and collecting stage of human evolution. It is then attached to a variety of rational aptitudes, above all in observing, classifying, and naming plants, animals and minerals, skills diversely displayed by primitive peoples. These skills with an instinctive beginning were the foundation of most of the civilised arts and sciences. Attached to other skills in advanced societies they promote the formation of museums and libraries; detached, they lead to acquisition and classification by eccentric individuals, often without any purpose or value at all.
As quoted in Richard Fifield, 'Cytologist Supreme', New Scientist (16 Apr 1981), 90, No. 1249, 179; citing C.D. Darlington, The Little Universe of Man (1978).
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The intrinsic character of mathematical research and knowledge is based essentially on three properties: first, on its conservative attitude towards the old truths and discoveries of mathematics; secondly, on its progressive mode of development, due to the incessant acquisition of new knowledge on the basis of the old; and thirdly, on its self-sufficiency and its consequent absolute independence.
In Mathematical Essays and Recreations (1898), 87.
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The Mathematician deals with two properties of objects only, number and extension, and all the inductions he wants have been formed and finished ages ago. He is now occupied with nothing but deduction and verification.
In 'On the Educational Value of the Natural History Sciences', Lay Sermons, Addresses and Reviews (1872), 87.
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The most fundamental difference between compounds of low molecular weight and macromolecular compounds resides in the fact that the latter may exhibit properties that cannot be deduced from a close examination of the low molecular weight materials. Not very different structures can be obtained from a few building blocks; but if 10,000 or 100,000 blocks are at hand, the most varied structures become possible, such as houses or halls, whose special structure cannot be predicted from the constructions that are possible with only a few building blocks... Thus, a chromosome can be viewed as a material whose macromolecules possess a well defined arrangement, like a living room in which each piece of furniture has its place and not, as in a warehouse, where the pieces of furniture are placed together in a heap without design.
Quoted, without citation, in Ralph E. Oesper (ed.), The Human Side of Scientists (1975), 175.
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The most important object of Civil Engineering is to improve the means of production and of traffic in states, both for external and internal trade. It is applied in the construction and management of roads, bridges, railroads, aqueducts, canals, river navigation, docks and storehouses, for the convenience of internal intercourse and exchange; and in the construction of ports, harbours, moles, breakwaters and lighthouses; and in the navigation by artificial power for the purposes of commerce. It is applied to the protection of property where natural powers are the sources of injury, as by embankments forthe defence of tracts of country from the encroachments of the sea, or the overflowing of rivers; it also directs the means of applying streams and rivers to use, either as powers to work machines, or as supplies for the use of cities and towns, or for irrigation; as well as the means of removing noxious accumulations, as by the drainage of towns and districts to ... secure the public health.
1828
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The native intellectual powers of men in different times, are not so much the causes of the different success of their labours, as the peculiar nature of the means and artificial resources in their possession‎. Independent of vessels of glass, there could have been no accurate manipulations in common chemistry: the air pump was necessary for live investigation of the properties of gaseous matter; and without the Voltaic apparatus, there was no possibility of examining the relations of electrical polarities to chemical attractions.
In Elements of Chemical Philosophy (1812), Vol. 1, Part 1, 28-29.
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The old Sussex tortoise, that I have mentioned to you so often, is become my property. I dug it out of its winter dormitory in March last, when it was enough awakened to express its resentments by hissing; and, packing it in a box with earth, carried it eighty miles in post-chaises. The rattle and hurry of the journey so perfectly roused it that, when I turned it out on a border, it walked twice down to the bottom of my garden; however, in the evening, the weather being cold, it buried it-self in the loose mound, and continues still concealed … When one reflects on the state of this strange being, it is a matter of wonder to find that Providence should bestow such a profusion of days, such a seeming waste of longevity, on a reptile that appears to relish it so little as to squander more than two-thirds of its existence in joyless stupor, and be lost to all sensation for months together in the profoundest of slumbers.
In Letter to Daines Barrington, (21 Apr 1780) in The Natural History and Antiquities of Selborne (1789), 357.
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The owner of the means of production is in a position to purchase the labor power of the worker. By using the means of production, the worker produces new goods which become the property of the capitalist. The essential point about this process is the relation between what the worker produces and what he is paid, both measured in terms of real value. In so far as the labor contract is free what the worker receives is determined not by the real value of the goods he produces, but by his minimum needs and by the capitalists’ requirements for labor power in relation to the number of workers competing for jobs. It is important to understand that even in theory the payment of the worker is not determined by the value of his product.
…...
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The plant cell, like the animal cell, is a type of laboratory of cellular tissues that organize themselves and develop within its innermost substance; its imperforate walls, to judge from our strongest magnifying instruments, have the property of drawing out by aspiration from the ambient liquid the elements necessary for its elaboration. They thus have the property of acting as a sorter, of admitting certain substances and preventing the passage of others, and consequently of separating the elements of certain combinations in order to admit only a portion of them.
As quoted in article Marc Klein,'François-Vincent Raspail', in Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography (1975). Vol.11, 300.
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The privilege is not allowed even to genius in this world to inspect its own elements, and read its own destiny, and it is perhaps well for mankid that it is so. Could we lift the curtain which hides our future lives, and glance hastily at the misfortunes, the vexations, and the disappointments which await us, we should be discouraged from attempting the performance of even of such deeds as are destined eventually to crown us with honor.
In a book of his reminiscenses, Oliver Hampton Smith, years after his first meeting with Morse, described the inventor - who had by then overcome the initial scepticism over his invention, but instead needed to vigorously defend his exclusive right of property in the magnetic telegraph.
Early Indiana Trials and Sketches (1858), 414.
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The question whether atoms exist or not... belongs rather to metaphysics. In chemistry we have only to decide whether the assumption of atoms is an hypothesis adapted to the explanation of chemical phenomena... whether a further development of the atomic hypothesis promises to advance our knowledge of the mechanism of chemical phenomena... I rather expect that we shall some day find, for what we now call atoms, a mathematico-mechanical explanation, which will render an account of atomic weight, of atomicity, and of numerous other properties of the so-called atoms.
Laboratory (1867), 1, 303.
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The serum, when subjected to heat, coagulates and hardens like egg. This property is one of its striking characteristics; it is attributed to a particular substance which is thereby readily recognizable, and which is called albumine, because it is the one present in egg white, termed albumen.
Système des Connaissances Chimiques (1801), Vol. 5, 117. Trans. Joseph S. Fmton, Proteins, Enzymes, Genes: The Interplay of Chemistry and Biology (1999), 161.
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The skeletal striated muscle cell of amphibia therefore resembles the cardiac striated muscle cell in the property of “all or none” contraction. The difference which renders it possible to obtain 'submaximal' contractions from a whole skeletal muscle but not from a whole heart is not a difference in the functional capabilities of the two types of cell; it depends upon the fact that cardiac muscle cells are connected one with another, whereas skeletal muscle cells are isolated by their sarcolemma. The 'submaximal' contraction of a skeletal muscle is the maximal contraction of less than all its fibres.
'The “All or None” Contraction of the Amphibian Skeletal Muscle Fibre', Journal of Physiology (1909), 38, 133.
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The special vital forces that distinguish living things from the nonliving are emergent, holistic properties, not properties of their physiochemical components. Nor can they be explained in mechanistic terms.
Interview in 'Vital Holistic Phenomena and Properties of Living', The World & I (1986), 1, No. 5-6, 265.
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The subject matter of science has been described as “judgments on which it is possible to obtain universal agreement.” These judgments do not concern individual events, which can be witnessed only by a few persons at most. They are the invariable association of events or properties which are known as the laws of science. Agreement is obtained by observation and experiment—a court of appeal to which men of all races and creeds must submit if they wish to survive.
The Nature of Science and Other Lectures (1954), 8. Norriss S. Hetherington comments parenthetically that the references to court, judgment and appeal may be attributable to his prior experiences as a Rhodes Scholar reading Roman law at Oxford, and to a year’s practice as an attorney in Louisville, Kentucky. As stated in Norriss S. Hetherington, '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, 41.
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The supposed astronomical proofs of the theory [of relativity], as cited and claimed by Einstein, do not exist. He is a confusionist. The Einstein theory is a fallacy. The theory that ether does not exist, and that gravity is not a force but a property of space can only be described as a crazy vagary, a disgrace to our age.
Quoted in Elizabeth Dilling, A "Who's Who" and Handbook of Radicalism for Patriots (1934), 49.
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There are in this world optimists who feel that any symbol that starts off with an integral sign must necessarily denote something that will have every property that they should like an integral to possess. This of course is quite annoying to us rigorous mathematicians; what is even more annoying is that by doing so they often come up with the right answer.
In 'Integrals Devised for Special Purposes', Bulletin of the American Mathematical Society (1963), 69, 611.
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There are many arts and sciences of which a miner should not be ignorant. First there is Philosophy, that he may discern the origin, cause, and nature of subterranean things; for then he will be able to dig out the veins easily and advantageously, and to obtain more abundant results from his mining. Secondly there is Medicine, that he may be able to look after his diggers and other workman ... Thirdly follows astronomy, that he may know the divisions of the heavens and from them judge the directions of the veins. Fourthly, there is the science of Surveying that he may be able to estimate how deep a shaft should be sunk … Fifthly, his knowledge of Arithmetical Science should be such that he may calculate the cost to be incurred in the machinery and the working of the mine. Sixthly, his learning must comprise Architecture, that he himself may construct the various machines and timber work required underground … Next, he must have knowledge of Drawing, that he can draw plans of his machinery. Lastly, there is the Law, especially that dealing with metals, that he may claim his own rights, that he may undertake the duty of giving others his opinion on legal matters, that he may not take another man’s property and so make trouble for himself, and that he may fulfil his obligations to others according to the law.
In De Re Metallica (1556), trans. H.C. and L.H. Hoover (1950), 3-4.
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There are three ruling ideas, three so to say, spheres of thought, which pervade the whole body of mathematical science, to some one or other of which, or to two or all three of them combined, every mathematical truth admits of being referred; these are the three cardinal notions, of Number, Space and Order.
Arithmetic has for its object the properties of number in the abstract. In algebra, viewed as a science of operations, order is the predominating idea. The business of geometry is with the evolution of the properties of space, or of bodies viewed as existing in space.
In 'A Probationary Lecture on Geometry, York British Association Report (1844), Part 2; Collected Mathematical Papers, Vol. 2, 5.
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There are two kinds of biologists, those who are looking to see if there is one thing that can be understood and those who keep saying it is very complicated and that nothing can be understood. ... You must study the simplest system you think has the properties you are interested in.
As quoted, without source, by John R. Platt in 'Science, Strong Inference', Science (16 Oct 1964), 146, No. 3642, 349.
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There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that… or: There is capitalism in so far as… The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.
From 'The Power of Words', collected in Siân Miles (ed.), Simone Weil: An Anthology (2000), 222-223.
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There is no art so difficult as the art of observation: it requires a skillful, sober spirit and a well-trained experience, which can only be acquired by practice; for he is not an observer who only sees the thing before him with his eyes, but he who sees of what parts the thing consists, and in what connexion the parts stand to the whole. One person overlooks half from inattention; another relates more than he sees while he confounds it with that which he figures to himself; another sees the parts of the whole, but he throws things together that ought to be separated. ... When the observer has ascertained the foundation of a phenomenon, and he is able to associate its conditions, he then proves while he endeavours to produce the phenomena at his will, the correctness of his observations by experiment. To make a series of experiments is often to decompose an opinion into its individual parts, and to prove it by a sensible phenomenon. The naturalist makes experiments in order to exhibit a phenomenon in all its different parts. When he is able to show of a series of phenomena, that they are all operations of the same cause, he arrives at a simple expression of their significance, which, in this case, is called a Law of Nature. We speak of a simple property as a Law of Nature when it serves for the explanation of one or more natural phenomena.
'The Study of the Natural Sciences: An Introductory Lecture to the Course of Experimental Chemistry in the University of Munich, for the Winter Session of 1852-53,' as translated and republished in The Medical Times and Gazette (22 Jan 1853), N.S. Vol. 6, 82.
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There is not, we believe, a single example of a medicine having been received permanently into the Materia Medica upon the sole ground of its physical, chemical, or physiological properties. Nearly every one has become a popular remedy before being adopted or even tried by physicians; by far the greater number were first employed in countries which were and are now in a state of scientific ignorance....
Therapeutics and Materia Medica (2006), 31
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There is thus a possibility that the ancient dream of philosophers to connect all Nature with the properties of whole numbers will some day be realized. To do so physics will have to develop a long way to establish the details of how the correspondence is to be made. One hint for this development seems pretty obvious, namely, the study of whole numbers in modern mathematics is inextricably bound up with the theory of functions of a complex variable, which theory we have already seen has a good chance of forming the basis of the physics of the future. The working out of this idea would lead to a connection between atomic theory and cosmology.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 129.
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There may be as many classifications of any series of natural, or of other, bodies, as they have properties or relations to one another, or to other things; or, again, as there are modes in which they may be regarded by the mind: so that, with respect to such classifications as we are here concerned with, it might be more proper to speak of a classification than of the classification of the animal kingdom.
In Lecture (Spring 1863) to the Royal College of Surgeons of England, 'On the Classification of Animals', Lectures on the Elements of Comparative Anatomy (1864), 1.
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There must be some bond of union between mass and the chemical elements; and as the mass of a substance is ultimately expressed (although not absolutely, but only relatively) in the atom, a functional dependence should exist and be discoverable between the individual properties of the elements and their atomic weights. But nothing, from mushrooms to a scientific dependence can be discovered without looking and trying. So I began to look about and write down the elements with their atomic weights and typical properties, analogous elements and like atomic weights on separate cards, and soon this convinced me that the properties of the elements are in periodic dependence upon their atomic weights; and although I had my doubts about some obscure points, yet I have never doubted the universality of this law, because it could not possibly be the result of chance.
Principles of Chemistry (1905), Vol. 2, 18.
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There’s no evolution of single individuals. Evolution is the property of populations.
In transcript of video interview story No. 112, 'What is Life?' on webofstories.com website.
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This is the kingdom of the chemical elements, the substances from which everything tangible is made. It is not an extensive country, for it consists of only a hundred or so regions (as we shall often term the elements), yet it accounts for everything material in our actual world. From the hundred elements that are at the center of our story, all planets, rocks, vegetation, and animals are made. These elements are the basis of the air, the oceans, and the Earth itself. We stand on the elements, we eat the elements, we are the elements. Because our brains are made up of elements, even our opinions are, in a sense, properties of the elements and hence inhabitants of the kingdom.
In 'The Terrain', The Periodic Kingdom: A Journey Into the Land of the Chemical Elements (1995), 3.
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This method is, to define as the number of a class the class of all classes similar to the given class. Membership of this class of classes (considered as a predicate) is a common property of all the similar classes and of no others; moreover every class of the set of similar classes has to the set of a relation which it has to nothing else, and which every class has to its own set. Thus the conditions are completely fulfilled by this class of classes, and it has the merit of being determinate when a class is given, and of being different for two classes which are not similar. This, then, is an irreproachable definition of the number of a class in purely logical terms.
The Principles of Mathematics (1903), 115.
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This property of human languages—their resistance to algorithmic processing— is perhaps the ultimate reason why only mathematics can furnish an adequate language for physics. It is not that we lack words for expressing all this E = mc² and ∫eiS(Φ)DΦ … stuff … , the point is that we still would not be able to do anything with these great discoveries if we had only words for them. … Miraculously, it turns out that even very high level abstractions can somehow reflect reality: knowledge of the world discovered by physicists can be expressed only in the language of mathematics.
In 'Mathematical Knowledge: Internal, Social, And Cultural Aspects', Mathematics As Metaphor: Selected Essays (2007), 5.
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This pure species of air [oxygen] has the property of combining with the blood and … this combination constitutes its red colour.
From 'Expériences sur la respiration des animaux, et sur les changemens qui arrivent à l’air en passant par leur poumon', Histoire de l’Académie Royale des Sciences for 1777 (1780) as translated by Thomas Henry in 'Experiments on the Respiration of Animals on the Changes effected on the Air passing through their Lungs', Essays, on the Effects Produced by Various Processes on Atmospheric Air, etc. (1783), 13-14. Also in John F. Fulton, Selected Readings in the History of Physiology (1930), 125.
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This spontaneous emergence of order at critical points of instability, which is often referred to simply as “emergence,” is one of the hallmarks of life. It has been recognized as the dynamic origin of development, learning, and evolution. In other words, creativity—the generation of new forms—is a key property of all living systems.
From 'Complexity and Life', in Fritjof Capra, Alicia Juarrero, Pedro Sotolongo (eds.) Reframing Complexity: Perspectives From the North and South (2007), 16.
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This theory [the oxygen theory] is not as I have heard it described, that of the French chemists, it is mine (elle est la mienne); it is a property which I claim from my contemporaries and from posterity.
Memoires de Chimie (1805), Vol. 2, 87, trans. M. P. Crosland.
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This very important property of rods, and indeed also of each kind of cone, this limitation of output to a single dimension of change, may be called the Principle of Univariance and stated thus: “The output of a receptor depends upon its quantum catch, but not upon what quanta are caught.” … Young's theory of colour vision may now be stated in terms of cone pigments. “There are three classes of cone each containing a different visual pigment. The output of each cone is univariant, depending simply upon the quantum catch of its pigment. Our sensation of colour depends upon the ratios of these three cone outputs.”
Principle of Univariance, concerning color vision, as stated in Lecture to a meeting of the Physiological Society at Chelsea College, London (17 Apr 1970), and reported in 'Pigments and Signals in Colour Vision', The Journal of Physiology (1972), 220 No. 3, 4P.
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Though much new light is shed by ... studies in radioactivity, the nucleus of the atom, with its hoard of energy, thus continues to present us with a fascinating mystery. ... Our assault on atoms has broken down the outer fortifications. We feel that we know the fundamental rules according to which the outer part of the atom is built. The appearance and properties of the electron atmosphere are rather familiar. Yet that inner citadel, the atomic nucleus, remains unconquered, and we have reason to believe that within this citadel is secreted a great treasure. Its capture may form the main objective of the physicists’ next great drive.
'Assault on Atoms' (Read 23 Apr 1931 at Symposium—The Changing World) Proceedings of the American Philosophical Society (1931), 70, No. 3, 229.
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Thus it might be said, that the vegetable is only the sketch, nor rather the ground-work of the animal; that for the formation of the latter, it has only been requisite to clothe the former with an apparatus of external organs, by which it might be connected with external objects.
From hence it follows, that the functions of the animal are of two very different classes. By the one (which is composed of an habitual succession of assimilation and excretion) it lives within itself, transforms into its proper substance the particles of other bodies, and afterwards rejects them when they are become heterogeneous to its nature. By the other, it lives externally, is the inhabitant of the world, and not as the vegetable of a spot only; it feels, it perceives, it reflects on its sensations, it moves according to their influence, and frequently is enabled to communicate by its voice its desires, and its fears, its pleasures, and its pains.
The aggregate of the functions of the first order, I shall name the organic life, because all organized beings, whether animal or vegetable, enjoy it more or less, because organic texture is the sole condition necessary to its existence. The sum of the functions of the second class, because it is exclusively the property of the animal, I shall denominate the animal life.
Physiological Researches on Life and Death (1815), trans. P. Gold, 22-3.
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To characterize the import of pure geometry, we might use the standard form of a movie-disclaimer: No portrayal of the characteristics of geometrical figures or of the spatial properties of relationships of actual bodies is intended, and any similarities between the primitive concepts and their customary geometrical connotations are purely coincidental.
From 'Geometry and Empirical Science', collected in Carl Hempel and James H. Fetzer (ed.), The Philosophy of Carl G. Hempel: Studies in Science, Explanation, and Rationality (2001), Chap. 2, 24. Also Carl Hempel, 'Geometry and Empirical Science', collected in J.R. Newman (ed.), The World of Mathematics (1956), Vol. 3, 1641.
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To derive two or three general Principles of Motion from Phænomena, and afterwards to tell us how the Properties and Actions of all corporeal Things follow from those manifest Principles, would be a very great step in Philosophy.
From 'Query 31', Opticks (1704, 2nd ed., 1718), 377.
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To emphasize this opinion that mathematicians would be unwise to accept practical issues as the sole guide or the chief guide in the current of their investigations, ... let me take one more instance, by choosing a subject in which the purely mathematical interest is deemed supreme, the theory of functions of a complex variable. That at least is a theory in pure mathematics, initiated in that region, and developed in that region; it is built up in scores of papers, and its plan certainly has not been, and is not now, dominated or guided by considerations of applicability to natural phenomena. Yet what has turned out to be its relation to practical issues? The investigations of Lagrange and others upon the construction of maps appear as a portion of the general property of conformal representation; which is merely the general geometrical method of regarding functional relations in that theory. Again, the interesting and important investigations upon discontinuous two-dimensional fluid motion in hydrodynamics, made in the last twenty years, can all be, and now are all, I believe, deduced from similar considerations by interpreting functional relations between complex variables. In the dynamics of a rotating heavy body, the only substantial extension of our knowledge since the time of Lagrange has accrued from associating the general properties of functions with the discussion of the equations of motion. Further, under the title of conjugate functions, the theory has been applied to various questions in electrostatics, particularly in connection with condensers and electrometers. And, lastly, in the domain of physical astronomy, some of the most conspicuous advances made in the last few years have been achieved by introducing into the discussion the ideas, the principles, the methods, and the results of the theory of functions. … the refined and extremely difficult work of Poincare and others in physical astronomy has been possible only by the use of the most elaborate developments of some purely mathematical subjects, developments which were made without a thought of such applications.
In Presidential Address British Association for the Advancement of Science, Section A, (1897), Nature, 56, 377.
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To have a railroad, there must have been first the discoverers, who found out the properties of wood and iron, fire and water, and their latent power to carry men over the earth; next the organizers, who put these elements together, surveyed the route, planned the structure, set men to grade the hill, to fill the valley, and pave the road with iron bars; and then the administrators, who after all that is done, procure the engines, engineers, conductors, ticket-distributors, and the rest of the “hands;” they buy the coal and see it is not wasted, fix the rates of fare, calculate the savings, and distribute the dividends. The discoverers and organizers often fare hard in the world, lean men, ill-clad and suspected, often laughed at, while the administrator is thought the greater man, because he rides over their graves and pays the dividends, where the organizer only called for the assessments, and the discoverer told what men called a dream. What happens in a railroad happens also in a Church, or a State.
Address at the Melodeon, Boston (5 Mar 1848), 'A Discourse occasioned by the Death of John Quincy Adams'. Collected in Discourses of Politics: The Collected Works of Theodore Parker: Part 4 (1863), 139. Note: Ralph Waldo Emerson earlier used the phrase “pave the road with iron bars,” in Nature (1836), 17.
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To say that mind is a product or function of protoplasm, or of its molecular changes, is to use words to which we can attach no clear conception. You cannot have, in the whole, what does not exist in any of the parts; and those who argue thus should put forth a definite conception of matter, with clearly enunciated properties, and show, that the necessary result of a certain complex arrangement of the elements or atoms of that matter, will be the production of self-consciousness. There is no escape from this dilemma—either all matter is conscious, or consciousness is something distinct from matter, and in the latter case, its presence in material forms is a proof of the existence of conscious beings, outside of, and independent of, what we term matter. The foregoing considerations lead us to the very important conclusion, that matter is essentially force, and nothing but force; that matter, as popularly understood, does not exist, and is, in fact, philosophically inconceivable. When we touch matter, we only really experience sensations of resistance, implying repulsive force; and no other sense can give us such apparently solid proofs of the reality of matter, as touch does. This conclusion, if kept constantly present in the mind, will be found to have a most important bearing on almost every high scientific and philosophical problem, and especially on such as relate to our own conscious existence.
In 'The Limits of Natural Selection as Applied to Man', last chapter of Contributions to the Theory of Natural Selection (1870), 365-366.
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We are concerned to understand the motivation for the development of pure mathematics, and it will not do simply to point to aesthetic qualities in the subject and leave it at that. It must be remembered that there is far more excitement to be had from creating something than from appreciating it after it has been created. Let there be no mistake about it, the fact that the mathematician is bound down by the rules of logic can no more prevent him from being creative than the properties of paint can prevent the artist. … We must remember that the mathematician not only finds the solutions to his problems, he creates the problems themselves.
In A Signpost to Mathematics (1951), 19. As quoted and cited in William L. Schaaf, 'Memorabilia Mathematica', The Mathematics Teacher (Mar 1957), 50, No. 3, 230. Note that this paper incorrectly attributes “A.H. Head”.
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We can no longer afford to consider air and water common property, free to be abused by anyone without regard to the consequences. Instead, we should begin now to treat them as scarce resources, which we are no more free to contaminate than we are free to throw garbage into our neighbor’s yard.
In State of the Union Address (22 Jan 1970).
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We do live in a conceptual trough that encourages such yearning for unknown and romanticized greener pastures of other times. The future doesn’t seem promising, if only because we can extrapolate some disquieting present trends in to further deterioration: pollution, nationalism, environmental destruction, and aluminum bats. Therefore, we tend to take refuge in a rose-colored past ... I do not doubt the salutary, even the essential, properties of this curiously adaptive human trait, but we must also record the down side. Legends of past golden ages become impediments when we try to negotiate our current dilemma.
…...
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We do not know of any enzymes or other chemical defined organic substances having specifically acting auto-catalytic properties such as to enable them to construct replicas of themselves. Neither was there a general principle known that would result in pattern-copying; if there were, the basis of life would be easier to come by. Moreover, there was no evidence to show that the enzymes were not products of hereditary determiners or genes, rather than these genes themselves, and they might even be products removed by several or many steps from the genes, just as many other known substances in the cell must be. However, the determiners or genes themselves must conduct, or at least guide, their own replication, so as to lead to the formation of genes just like themselves, in such wise that even their own mutations become .incorporated in the replicas. And this would probably take place by some kind of copying of pattern similar to that postulated by Troland for the enzymes, but requiring some distinctive chemical structure to make it possible. By virtue of this ability of theirs to replicate, these genes–or, if you prefer, genetic material–contained in the nuclear chromosomes and in whatever other portion of the cell manifests this property, such as the chloroplastids of plants, must form the basis of all the complexities of living matter that have arisen subsequent to their own appearance on the scene, in the whole course of biological evolution. That is, this genetic material must underlie all evolution based on mutation and selective multiplication.
'Genetic Nucleic Acid', Perspectives in Biology and Medicine (1961), 5, 6-7.
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We find that light acquires properties which are relative only to the sides of the ray,–which are the same for the north and south sides of the ray, (using the points of the compass for description’s sake only) and which are different when we go from the north and south to the east or to the west sides of the ray. I shall give the name of poles to these sides of the ray, and shall call polarization the modification which gives to light these properties relative to these poles.
(1811). As quoted in William Whewell, The Philosophy of the Inductive Sciences (1840), 336.
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We have a right to expect that the best trained, the best educated men on the Pacific slope, the Rocky Mountains, and great plains States will take the lead in the preservation and right use of forests, in securing the right use of waters, and in seeing that our land policy is not twisted from its original purpose, but is perpetuated by amendment, by change when such change is necessary in the life of that purpose, the purpose being to turn the public domain into farms each to be the property of the man who actually tills it and makes his home in it.
Address at Leland Stanford, Jr., University, Palo Alto, California, 12 May 1903. Addresses and Presidential Messages of Theodore Roosevelt, 1902-1904 (1904), 198.
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We…know…that the smallest units of many materials are not atoms but molecules, which are groups of atoms, closely bound to each other. If we are to understand the structure of matter, we must understand not only the structure of atoms but also the reason atoms join and form molecules. We must understand what is called the chemical bond, which keeps the atoms together within the molecule, and we must get acquainted with a few typical molecules and their properties. The chemical bond and the properties of molecules are the subjects of chemistry.
In 'The Chemical Bond', Knowledge and Wonder (1962, Rev. ed. 1966), 142.
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What distinguishes the straight line and circle more than anything else, and properly separates them for the purpose of elementary geometry? Their self-similarity. Every inch of a straight line coincides with every other inch, and of a circle with every other of the same circle. Where, then, did Euclid fail? In not introducing the third curve, which has the same property—the screw. The right line, the circle, the screw—the representations of translation, rotation, and the two combined—ought to have been the instruments of geometry. With a screw we should never have heard of the impossibility of trisecting an angle, squaring the circle, etc.
From Letter (15 Feb 1852) to W.R. Hamilton, collected in Robert Perceval Graves, Life of W.R. Hamilton (1889), Vol. 3, 343.
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What is this subject, which may be called indifferently either mathematics or logic? Is there any way in which we can define it? Certain characteristics of the subject are clear. To begin with, we do not, in this subject, deal with particular things or particular properties: we deal formally with what can be said about any thing or any property. We are prepared to say that one and one are two, but not that Socrates and Plato are two, because, in our capacity of logicians or pure mathematicians, we have never heard of Socrates or Plato. A world in which there were no such individuals would still be a world in which one and one are two. It is not open to us, as pure mathematicians or logicians, to mention anything at all, because, if we do so we introduce something irrelevant and not formal.
In Introduction to Mathematical Philosophy (1920), 196-197.
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When carbon (C), Oxygen (o) and hydrogen (H) atoms bond in a certain way to form sugar, the resulting compound has a sweet taste. The sweetness resides neither in the C, nor in the O, nor in the H; it resides in the pattern that emerges from their interaction. It is an emergent property. Moreover, strictly speaking, is not a property of the chemical bonds. It is a sensory experience that arises when the sugar molecules interact with the chemistry of our taste buds, which in turns causes a set of neurons to fire in a certain way. The experience of sweetness emerges from that neural activity.
In The Hidden Connections (2002), 116-117.
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When I was living with the Indians, my hostess, a fine looking woman, who wore numberless bracelets, and rings in her ears and on her fingers, and painted her face like a brilliant sunset, one day gave away a very fine horse. I was surprised, for I knew there had been no family talk on the subject, so I asked: “Will your husband like to have you give the horse away?” Her eyes danced, and, breaking into a peal of laughter, she hastened to tell the story to the other women gathered in the tent, and I became the target of many merry eyes. I tried to explain how a white woman would act, but laughter and contempt met my explanation of the white man’s hold upon his wife’s property.
Speech on 'The Legal Conditions of Indian Women', delivered to Evening Session (Thur 29 Mar 1888), collected in Report of the International Council of Women: Assembled by the National Woman Suffrage Association, Washington, D.C., U.S. of America, March 25 to April 1, 1888 (1888), Vol. 1, 240.
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When the state is shaken to its foundations by internal or external events, when commerce, industry and all trades shall be at a stand, and perhaps on the brink of ruin; when the property and fortune of all are shaken or changed, and the inhabitants of towns look forward with dread and apprehension to the future, then the agriculturalist holds in his hand the key to the money chest of the rich, and the savings-box of the poor; for political events have not the slightest influence on the natural law, which forces man to take into his system, daily, a certain number of ounces of carbon and nitrogen.
Reflecting on events of 1848.
Familiar Letters on Chemistry (1851), 3rd edn., 483.
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While we keep an open mind on this question of vitalism, or while we lean, as so many of us now do, or even cling with a great yearning, to the belief that something other than the physical forces animates the dust of which we are made, it is rather the business of the philosopher than of the biologist, or of the biologist only when he has served his humble and severe apprenticeship to philosophy, to deal with the ultimate problem. It is the plain bounden duty of the biologist to pursue his course unprejudiced by vitalistic hypotheses, along the road of observation and experiment, according to the accepted discipline of the natural and physical sciences. … It is an elementary scientific duty, it is a rule that Kant himself laid down, that we should explain, just as far as we possibly can, all that is capable of such explanation, in the light of the properties of matter and of the forms of energy with which we are already acquainted.
From Presidential Address to Zoological Section of the British Association for the Advancement of Science. As quoted in H.V. Neal, 'The Basis of Individuality in Organisms: A Defense of Vitalism', Science (21 Jul 1916), 44 N.S., No. 1125, 82.
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Why we love science. It’s more than a school subject, or the periodic table, or the properties of waves. It is an approach to the world, a critical way to understand and explore and engage with the world, and then have the capacity to change that world, and to share this accumulated knowledge. It’s a mindset that says we that can use reason and logic and honest inquiry to reach new conclusions and solve big problems.
From remarks at the fifth White House Science Fair, in Press Release (23 Mar 2015).
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With the neutron bomb, which destroys life but not property, capitalism has found the weapon of its dreams.
In 'Money Et Cetera', A Voice Crying in the Wilderness (Vox Clamantis in Deserto) (1989), 100.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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