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Home > Category Index for Science Quotations > Category Index N > Category: Negative

Negative Quotes (66 quotes)

... every chemical combination is wholly and solely dependent on two opposing forces, positive and negative electricity, and every chemical compound must be composed of two parts combined by the agency of their electrochemical reaction, since there is no third force. Hence it follows that every compound body, whatever the number of its constituents, can be divided into two parts, one of which is positively and the other negatively electrical.
Essai sur la théorie des proportions chemiques (1819), 98. Quoted by Henry M. Leicester in article on Bessel in Charles Coulston Gillespie (editor), Dictionary of Scientific Biography (1981), Vol. 2, 94.
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[Concerning] phosphorescent bodies, and in particular to uranium salts whose phosphorescence has a very brief duration. With the double sulfate of uranium and potassium ... I was able to perform the following experiment: One wraps a Lumière photographic plate with a bromide emulsion in two sheets of very thick black paper, such that the plate does not become clouded upon being exposed to the sun for a day. One places on the sheet of paper, on the outside, a slab of the phosphorescent substance, and one exposes the whole to the sun for several hours. When one then develops the photographic plate, one recognizes that the silhouette of the phosphorescent substance appears in black on the negative. If one places between the phosphorescent substance and the paper a piece of money or a metal screen pierced with a cut-out design, one sees the image of these objects appear on the negative. One can repeat the same experiments placing a thin pane of glass between the phosphorescent substance and the paper, which excludes the possibility of chemical action due to vapors which might emanate from the substance when heated by the sun's rays. One must conclude from these experiments that the phosphorescent substance in question emits rays which pass through the opaque paper and reduces silver salts.
[Although the sun is irrelevant, and he misinterprets the role of phosphorescence, he has discovered the effect of radioactivity.]
Read at French Academy of Science (24 Feb 1896). In Comptes Rendus (1896), 122, 420. As translated by Carmen Giunta on the Classic Chemistry web site.
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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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[Reading a cartoon story,] the boy favored reading over reality. Adults might have characterized him in any number of negative ways—as uninquisitive, uninvolved, apathetic about the world around him and his place in it. I’ve often wondered: Are many adults much different when they read the scriptures of their respective faiths?
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 117.
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Are coral reefs growing from the depths of the oceans? ... [The] reply is a simple negative; and a single fact establishes its truth. The reef-forming coral zoophytes, as has been shown, cannot grow at greater depths than 100 or 120 feet; and therefore in seas deeper than this, the formation or growth of reefs over the bottom is impossible.
On Coral Reefs and Islands (1853), 138.
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Negative Capability, that is when man is capable of being in uncertainties, Mysteries, doubts, without any irritable reaching after fact & reason—Coleridge, for instance, would let go by a fine isolated verisimilitude caught from the Penetralium of mystery, from being incapable of remaining content with half knowledge.
Letter to George and Thomas Keats (21 Dec 1817). In H. E. Rollins (ed.), Letters of John Keats (1958), Vol. 1, 193-4.
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A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: Have you read a work of Shakespeare’s?
The Two Cultures: The Rede Lecture (1959), 15-6.
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Again the message to experimentalists is: Be sensible but don’t be impressed too much by negative arguments. If at all possible, try it and see what turns up. Theorists almost always dislike this sort of approach.
What Mad Pursuit: A Personal View of Scientific Discovery (1988), 113.
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Any opinion as to the form in which the energy of gravitation exists in space is of great importance, and whoever can make his opinion probable will have, made an enormous stride in physical speculation. The apparent universality of gravitation, and the equality of its effects on matter of all kinds are most remarkable facts, hitherto without exception; but they are purely experimental facts, liable to be corrected by a single observed exception. We cannot conceive of matter with negative inertia or mass; but we see no way of accounting for the proportionality of gravitation to mass by any legitimate method of demonstration. If we can see the tails of comets fly off in the direction opposed to the sun with an accelerated velocity, and if we believe these tails to be matter and not optical illusions or mere tracks of vibrating disturbance, then we must admit a force in that direction, and we may establish that it is caused by the sun if it always depends upon his position and distance.
Letter to William Huggins (13 Oct 1868). In P. M. Hannan (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 1862-1873, 451-2.
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Applied research generates improvements, not breakthroughs. Great scientific advances spring from pure research. Even scientists renowned for their “useful” applied discoveries often achieved success only when they abandoned their ostensible applied-science goal and allowed their minds to soar—as when Alexander Fleming, “just playing about,” refrained from throwing away green molds that had ruined his experiment, studied them, and discovered penicillin. Or when C. A. Clarke, a physician affiliated with the University of Liverpool, became intrigued in the 1950s by genetically created color patterns that emerged when he cross-bred butterflies as a hobby. His fascination led him—“by the pleasant route of pursuing idle curiosity”—to the successful idea for preventing the sometimes fatal anemia that threatened babies born of a positive-Rhesus-factor father and a negative-Rhesus-factor mother.
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 214-215.
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As mineralogy constitutes a part of chemistry, it is clear that this arrangement [of minerals] must derive its principles from chemistry. The most perfect mode of arrangement would certainly be to allow bodies to follow each other according to the order of their electro-chemical properties, from the most electro-negative, oxygen, to the most electro-positive, potassium; and to place every compound body according to its most electro-positive ingredient.
An Attempt to Establish a Pure Scientific System of Mineralogy (1814), trans. J. Black, 48.
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Atoms are not indivisible, for negatively electrified particles can be torn from them by the action of electrical forces.
In Recollections and Reflections (1936), 338.
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Atoms have a nucleus, made of protons and neutrons bound together. Around this nucleus shells of electrons spin, and each shell is either full or trying to get full, to balance with the number of protons—to balance the number of positive and negative charges. An atom is like a human heart, you see.
The Lunatics (1988). In Gary Westfahl, Science Fiction Quotations: From the Inner Mind to the Outer Limits (2006), 323.
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But I shall certainly admit a system as empirical or scientific only if it is capable of being tested by experience. These considerations suggest that not the verifiability but the falsifiability of a system is to be taken as a criterion of demarcation. In other words: I shall not require of a scientific system that it shall be capable of being singled out, once and for all, in a positive sense; but I shall require that its logical form shall be such that it can be singled out, by means of empirical tests, in a negative sense: it must be possible for an empirical scientific system to be refuted by experience. (1959)
The Logic of Scientific Discovery: Logik Der Forschung (1959, 2002), 18.
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Concentrate only on the achievements, and ignore the mistakes. When judging a mathematician you should only integrate f+ (the positive part of his function) and ignore the negative part. Perhaps this should apply more generally to all evaluations of your fellow men.
On his philosophy of writing letters of recommendation. As given in essay, Ronald Coifman and Robert S. Strichartz, 'The School of Antoni Zygmund', collected in Peter Duren (ed.), A Century of Mathematics in America (1989), 348. The authors acknowledge students of Zygmund provided personal recollections to them for the essay in general. Webmaster speculates the quote is from a student recollection, and not necessarily verbatim.
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Confined to its true domain, mathematical reasoning is admirably adapted to perform the universal office of sound logic: to induce in order to deduce, in order to construct. … It contents itself to furnish, in the most favorable domain, a model of clearness, of precision, and consistency, the close contemplation of which is alone able to prepare the mind to render other conceptions also as perfect as their nature permits. Its general reaction, more negative than positive, must consist, above all, in inspiring us everywhere with an invincible aversion for vagueness, inconsistency, and obscurity, which may always be really avoided in any reasoning whatsoever, if we make sufficient effort.
In Synthèse Subjective (1856), 98. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 202-203. From the original French, “Bornée à son vrai domaine, la raison mathématique y peut admirablement remplir l’office universel de la saine logique: induire pour déduire, afin de construire. … Elle se contente de former, dans le domaine le plus favorable, un type de clarté, de précision, et de consistance, dont la contemplation familière peut seule disposer l’esprit à rendre les autres conceptions aussi parfaites que le comporte leur nature. Sa réaction générale, plus négative que positive, doit surtout consister à nous inspirer partout une invincible répugnance pour le vague, l’incohérence, et l’obscurité, que nous pouvons réellement éviter envers des pensées quelconques, si nous y faisons assez d’efforts.”
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Descartes said, “I think; therefore I am.” The philosophic evolutionist reverses and negatives the epigram. He says, “I am not; therefore I cannot think.”
In Orthodoxy (1918, 2008), 25.
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Does there truly exist an insuperable contradiction between religion and science? Can religion be superseded by science? The answers to these questions have, for centuries, given rise to considerable dispute and, indeed, bitter fighting. Yet, in my own mind there can be no doubt that in both cases a dispassionate consideration can only lead to a negative answer. What complicates the solution, however, is the fact that while most people readily agree on what is meant by ‘science,’ they are likely to differ on the meaning of ‘religion.’
…...
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Erasmus Darwin held that every so often you should try a damn-fool experiment. He played the trombone to his tulips. This particular result was, in fact, negative.
In 'The Mathematician’s Art of Work' (1967), collected in Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 194. Webmaster has looked for a primary source to verify this statement and so far has found none. Can you help?
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Everything in nature is bipolar, or has a positive and a negative pole.
From essay, 'Character', collected in Ralph Waldo Emerson and J.E. Cabot (ed.), Emerson's Complete Works: Essays, Second Series (1884), Vol. 3, 96.
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He saw virus particles shaped like snakes, in negative images. They were white cobras tangled among themselves, like the hair of Medusa. They were the face of nature herself, the obscene goddess revealed naked. This life form thing was breathtakingly beautiful. As he stared at it, he found himself being pulled out of the human world into a world where moral boundaries blur and finally dissolve completely. He was lost in wonder and admiration, even though he knew that he was the prey.
The Hot Zone
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How would we express in terms of the statistical theory the marvellous faculty of a living organism, by which it delays the decay into thermodynamical equilibrium (death)? … It feeds upon negative entropy … Thus the device by which an organism maintains itself stationary at a fairly high level of orderliness (= fairly low level of entropy) really consists in continually sucking orderliness from its environment.
In 'Organization Maintained by Extracting “Order” from the Environment', What is Life? : The Physical Aspect of the Living Cell (1944), 74.
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I cannot separate land and sea: to me they interfinger like a pattern in a moss agate, positive and negative shapes irrevocably interlocked. My knowledge of this peninsula depends on that understanding: of underwater canyons that are continuations of the land, of the shell fossils far inland that measure continuations of the sea in eons past.
…...
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I have taken the stand that nobody can be always wrong, but it does seem to me that I have approximated so highly that I am nothing short of a negative genius.
Wild Talents (1932). In The Complete Books of Charles Fort (1975), 1037.
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I require a term to express those bodies which can pass to the electrodes, or, as they are usually called, the poles. Substances are frequently spoken of as being electro-negative, or electro-positive, according as they go under the supposed influence of a direct attraction to the positive or negative pole. But these terms are much too significant for the use to which I should have to put them; for though the meanings are perhaps right, they are only hypothetical, and may be wrong; and then, through a very imperceptible, but still very dangerous, because continual, influence, they do great injury to science, by contracting and limiting the habitual view of those engaged in pursuing it. I propose to distinguish these bodies by calling those anions which go to the anode of the decomposing body; and those passing to the cathode, cations; and when I have occasion to speak of these together, I shall call them ions.
Philosophical Transactions of the Royal Society of London, 1834, 124, 79.
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I told him that for a modern scientist, practicing experimental research, the least that could be said, is that we do not know. But I felt that such a negative answer was only part of the truth. I told him that in this universe in which we live, unbounded in space, infinite in stored energy and, who knows, unlimited in time, the adequate and positive answer, according to my belief, is that this universe may, also, possess infinite potentialities.
Nobel Lecture, The Coming Age of the Cell, 12 Dec 1974
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I used to wonder how it comes about that the electron is negative. Negative-positive—these are perfectly symmetric in physics. There is no reason whatever to prefer one to the other. Then why is the electron negative? I thought about this for a long time and at last all I could think was 'It won the fight!'
Quoted in George Wald, 'The Origin of Optical Activity', Annals of the New York Academy of Sciences (1957), 60, 352-68.
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Imaginary numbers are a fine and wonderful refuge of the divine spirit almost an amphibian between being and non-being. (1702)
[Alternate translation:] The Divine Spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and not-being, which we call the imaginary root of negative unity.
Quoted in Félix Klein, Elementary Mathematics From an Advanced Standpoint: Arithmetic, Algebra, Analysis (1924), 56. Alternate translation as quoted in Tobias Dantzig, Number, the Language of Science: a Critical Survey Written for the Cultured Non-Mathematician (1930), 204
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Imagine a person with a gift of ridicule [He might say] First that a negative quantity has no logarithm; secondly that a negative quantity has no square root; thirdly that the first non-existent is to the second as the circumference of a circle is to the diameter.
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In my experience most mathematicians are intellectually lazy and especially dislike reading experimental papers. He (René Thom) seemed to have very strong biological intuitions but unfortunately of negative sign.
In What Mad Pursuit: A Personal View of Scientific Discovery (1988), 136.
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In the tissues generally, and in such a cavity as the abdomen, the pressure is everywhere and practically always very nearly atmospheric, and must be so, because the integuments give way very easily to any excess of pressure, whether positive or negative.
In The Anatomy and Physiology of Capillaries (1922), 244.
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Indeed, nothing more beautifully simplifying has ever happened in the history of science than the whole series of discoveries culminating about 1914 which finally brought practically universal acceptance to the theory that the material world contains but two fundamental entities, namely, positive and negative electrons, exactly alike in charge, but differing widely in mass, the positive electron—now usually called a proton—being 1850 times heavier than the negative, now usually called simply the electron.
Time, Matter and Values (1932), 46. Cited in Karl Raimund Popper and William Warren Bartley (ed.), Quantum Theory and theSchism in Physics (1992), 37.
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Isolated facts and experiments have in themselves no value, however great their number may be. They only become valuable in a theoretical or practical point of view when they make us acquainted with the law of a series of uniformly recurring phenomena, or, it may be, only give a negative result showing an incompleteness in our knowledge of such a law, till then held to be perfect.
'The Aim and Progress of Physical Science' (1869). Trans. E. Atkinson, Popular Lectures on Scientific Subjects (1873), 369.
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It has been demonstrated that a species of penicillium produces in culture a very powerful antibacterial substance which affects different bacteria in different degrees. Generally speaking it may be said that the least sensitive bacteria are the Gram-negative bacilli, and the most susceptible are the pyogenic cocci ... In addition to its possible use in the treatment of bacterial infections penicillin is certainly useful... for its power of inhibiting unwanted microbes in bacterial cultures so that penicillin insensitive bacteria can readily be isolated.
'On the Antibacterial Action of Cultures of a Penicillium, with Special Reference to their Use in the Isolation of B. Influenzae', British Journal of Experimental Pathology, 1929, 10, 235-6.
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It is very desirable to have a word to express the Availability for work of the heat in a given magazine; a term for that possession, the waste of which is called Dissipation. Unfortunately the excellent word Entropy, which Clausius has introduced in this connexion, is applied by him to the negative of the idea we most naturally wish to express. It would only confuse the student if we were to endeavour to invent another term for our purpose. But the necessity for some such term will be obvious from the beautiful examples which follow. And we take the liberty of using the term Entropy in this altered sense ... The entropy of the universe tends continually to zero.
Sketch of Thermodynamics (1868), 100-2.
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It would take a civilization far more advanced than ours, unbelievably advanced, to begin to manipulate negative energy to create gateways to the past. But if you could obtain large quantities of negative energy—and that's a big “IF”—then you could create a time machine that apparently obeys Einstein's equation and perhaps the laws of quantum theory.
Quoted by J.R. Minkel in 'Borrowed Time: Interview with Michio Kaku', Scientific American (23 Nov 2003).
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Keep in mind that new ideas are commonplace, and almost always wrong. Most flashes of insight lead nowhere; statistically, they have a half-life of hours or maybe days. Most experiments to follow up the surviving insights are tedious and consume large amounts of time, only to yield negative or (worse!) ambiguous results.
In Consilience: The Unity of Knowledge (1998, 1999), 60
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Mathematics, indeed, is the very example of brevity, whether it be in the shorthand rule of the circle, c = πd, or in that fruitful formula of analysis, e = -1, —a formula which fuses together four of the most important concepts of the science,—the logarithmic base, the transcendental ratio π, and the imaginary and negative units.
In 'The Poetry of Mathematics', The Mathematics Teacher (May 1926), 19, No. 5, 293.
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Natural Science treats of motion and force. Many of its teachings remain as part of an educated man's permanent equipment in life.
Such are:
(a) The harder you shove a bicycle the faster it will go. This is because of natural science.
(b) If you fall from a high tower, you fall quicker and quicker and quicker; a judicious selection of a tower will ensure any rate of speed.(c) If you put your thumb in between two cogs it will go on and on, until the wheels are arrested, by your suspenders. This is machinery.
(d) Electricity is of two kinds, positive and negative. The difference is, I presume, that one kind comes a little more expensive, but is more durable; the other is a cheaper thing, but the moths get into it.
In Literary Lapses (1918), 130.
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Negative facts when considered alone never teach us anything.
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One never finds fossil bones bearing no resemblance to human bones. Egyptian mummies, which are at least three thousand years old, show that men were the same then. The same applies to other mummified animals such as cats, dogs, crocodiles, falcons, vultures, oxen, ibises, etc. Species, therefore, do not change by degrees, but emerged after the new world was formed. Nor do we find intermediate species between those of the earlier world and those of today's. For example, there is no intermediate bear between our bear and the very different cave bear. To our knowledge, no spontaneous generation occurs in the present-day world. All organized beings owe their life to their fathers. Thus all records corroborate the globe's modernity. Negative proof: the barbaritY of the human species four thousand years ago. Positive proof: the great revolutions and the floods preserved in the traditions of all peoples.
'Note prese al Corso di Cuvier. Corso di Geologia all'Ateneo nel 1805', quoted in Pietro Corsi, The Age of Lamarck, trans. J. Mandelbaum (1988), 183.
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One of the attractions of mathematics … that had a great impact on my choosing a career—I wanted a career where I didn’t have to work with other people … to work in an area where I compete only with myself and didn’t have to deal with the negative aspects of competition.
In 'A Personal Profile of Karen K. Uhlenbeck', collected in Susan Ambrose et al., Journeys of Women in Science and Engineering, No Universal Constants (1999).
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One of the most immediate consequences of the electrochemical theory is the necessity of regarding all chemical compounds as binary substances. It is necessary to discover in each of them the positive and negative constituents... No view was ever more fitted to retard the progress of organic chemistry. Where the theory of substitution and the theory of types assume similar molecules, in which some of the elements can be replaced by others without the edifice becoming modified either in form or outward behaviour, the electrochemical theory divides these same molecules, simply and solely, it may be said, in order to find in them two opposite groups, which it then supposes to be combined with each other in virtue of their mutual electrical activity... I have tried to show that in organic chemistry there exist types which are capable, without destruction, of undergoing the most singular transformations according to the nature of the elements.
Traité de Chemie Appliquée aux Arts, Vol. I (1828), 53. Trans. J. R. Partington, A History of Chemistry, Vol. 4, 366.
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Producing food for 6.2 billion people, adding a population of 80 million more a year, is not simple. We better develop an ever improved science and technology, including the new biotechnology, to produce the food that’s needed for the world today. In response to the fraction of the world population that could be fed if current farmland was convered to organic-only crops: “We are 6.6 billion people now. We can only feed 4 billion. I don’t see 2 billion volunteers to disappear.” In response to extreme critics: “These are utopian people that live on Cloud 9 and come into the third world and cause all kinds of confusion and negative impacts on the developing countries.”
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Pursuit of the objective of maximum species diversity or even maximum species richness could lead to serious negative consequences if taken literally.
In The Fragmented Forest: Island Biogeography Theory and the Preservation of Biotic Diversity (1984), 106.
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Research programmes, besides their negative heuristic, are also characterized by their positive heuristic.
In 'Falsification and the Methodology of Scientific Research Programmes', in I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science, London 1965 (1970), Vol. 4, 134.
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Science is the study of the admitted laws of existence, which cannot prove a universal negative about whether those laws could ever be suspended by something admittedly above them. It is as if we were to say that a lawyer was so deeply learned in the American Constitution that he knew there could never be a revolution in America..
From 'The Early Bird in History',The Thing: Why I Am Catholic (1929), 207. In Collected Works (1990), Vol. 3, 296.
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Some beliefs may be subject to such instant, brutal and unambiguous rejection. For example: no left-coiling periwinkle has ever been found among millions of snails examined. If I happen to find one during my walk on Nobska beach tomorrow morning, a century of well nurtured negative evidence will collapse in an instant.
'A Foot Soldier for Evolution', In Eight Little Piggies (1994), 452.
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Strict conservation of energy in the elementary process had thus been confirmed also by a negative experiment.
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Suppose the results of a line of study are negative. It might save a lot of otherwise wasted money to know a thing won’t work. But how do you accurately evaluate negative results? ... The power plant in [the recently developed streamline trains] is a Diesel engine of a type which was tried out many [around 25] years ago and found to be a failure. … We didn’t know how to build them. The principle upon which it operated was sound. [Since then much has been] learned in metallurgy [and] the accuracy with which parts can be manufactured
When this type of engine was given another chance it was an immediate success [because now] an accuracy of a quarter of a tenth of a thousandth of an inch [prevents high-pressure oil leaks]. … If we had taken the results of past experience without questioning the reason for the first failure, we would never have had the present light-weight, high-speed Diesel engine which appears to be the spark that will revitalize the railroad business.
'Industrial Prospecting', an address to the Founder Societies of Engineers (20 May 1935). In National Research Council, Reprint and Circular Series of the National Research Council (1933), No. 107, 2-3.
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Surely something is wanting in our conception of the universe. We know positive and negative electricity, north and south magnetism, and why not some extra terrestrial matter related to terrestrial matter, as the source is to the sink. … Worlds may have formed of this stuff, with element and compounds possessing identical properties with our own, indistinguishable from them until they are brought into each other’s vicinity. … Astronomy, the oldest and most juvenile of the sciences, may still have some surprises in store. May anti-matter be commended to its care! … Do dreams ever come true?
[Purely whimsical prediction long before the 1932 discovery of the positron, the antiparticle of the electron.]
'Potential Matter—A Holiday Dream', Letter to the Editor, Nature (18 Aug 1898), 58, No. 1503, 367. Quoted in Edward Robert Harrison, Cosmology: the Science of the Universe (2000), 433.
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That this subject [of imaginary magnitudes] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral units, instead of positive, negative and imaginary (or even impossible), such an obscurity would have been out of the question.
Theoria Residiorum Biquadraticorum, Commentario secunda', Werke (1863), Vol. 2. Quoted in Robert Edouard Moritz, Memorabilia Mathematica (1914), 282.
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The cause, then, philosophically speaking, is the sum total of the conditions, positive and negative, taken together; the whole of the contingencies of every description, which being realized, the consequent invariably follows.
A System of Logic, Ratiocinative and Inductive (1858), 200.
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The geometrical problems and theorems of the Greeks always refer to definite, oftentimes to rather complicated figures. Now frequently the points and lines of such a figure may assume very many different relative positions; each of these possible cases is then considered separately. On the contrary, present day mathematicians generate their figures one from another, and are accustomed to consider them subject to variation; in this manner they unite the various cases and combine them as much as possible by employing negative and imaginary magnitudes. For example, the problems which Apollonius treats in his two books De sectione rationis, are solved today by means of a single, universally applicable construction; Apollonius, on the contrary, separates it into more than eighty different cases varying only in position. Thus, as Hermann Hankel has fittingly remarked, the ancient geometry sacrifices to a seeming simplicity the true simplicity which consists in the unity of principles; it attained a trivial sensual presentability at the cost of the recognition of the relations of geometric forms in all their changes and in all the variations of their sensually presentable positions.
In 'Die Synthetische Geometrie im Altertum und in der Neuzeit', Jahresbericht der Deutschen Mathematiker Vereinigung (1902), 2, 346-347. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112. The spelling of the first “Apollonius” has been corrected from “Appolonius” in the original English text. From the original German, “Die geometrischen Probleme und Sätze der Griechen beziehen sich allemal auf bestimmte, oft recht komplizierte Figuren. Nun können aber die Punkte und Linien einer solchen Figur häufig sehr verschiedene Lagen zu einander annehmen; jeder dieser möglichen Fälle wird alsdann für sich besonders erörtert. Dagegen lassen die heutigen Mathematiker ihre Figuren aus einander entstehen und sind gewohnt, sie als veränderlich zu betrachten; sie vereinigen so die speziellen Fälle und fassen sie möglichst zusammen unter Benutzung auch negativer und imaginärer Gröfsen. Das Problem z. B., welches Apollonius in seinen zwei Büchern de sectione rationis behandelt, löst man heutzutage durch eine einzige, allgemein anwendbare Konstruktion; Apollonius selber dagegen zerlegt es in mehr als 80 nur durch die Lage verschiedene Fälle. So opfert, wie Hermann Hankel treffend bemerkt, die antike Geometrie einer scheinbaren Einfachheit die wahre, in der Einheit der Prinzipien bestehende; sie erreicht eine triviale sinnliche Anschaulichkeit auf Kosten der Erkenntnis vom Zusammenhang geometrischer Gestalten in aller Wechsel und in aller Veränderlichkeit ihrer sinnlich vorstellbaren Lage.”
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The imaginary expression √(-a) and the negative expression -b, have this resemblance, that either of them occurring as the solution of a problem indicates some inconsistency or absurdity. As far as real meaning is concerned, both are imaginary, since 0 - a is as inconceivable as √(-a).
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The most startling result of Faraday’s Law is perhaps this. If we accept the hypothesis that the elementary substances are composed of atoms, we cannot avoid concluding that electricity also, positive as well as negative, is divided into definite elementary portions, which behave like atoms of electricity.
Faraday Lecture (1881). In 'On the Modern Development of Faraday's Conception of Electricity', Journal of the Chemical Society 1881, 39, 290. It is also stated in the book by Laurie M. Brown, Abraham Pais and Brian Pippard, Twentieth Century P, Vol. 1, 52, that this is 'a statement which explains why in subsequent years the quantity e was occasionally referred to in German literature as das Helmholtzsche Elementarquantum'.
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The negative cautions of science are never popular. If the experimentalist would not commit himself, the social philosopher, the preacher, and the pedagogue tried the harder to give a short-cut answer.
In Coming of Age in Samoa (1928, 2001), 4.
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The same algebraic sum of positive and negative charges in the nucleus, when the arithmetical sum is different, gives what I call “isotopes” or “isotopic elements,” because they occupy the same place in the periodic table. They are chemically identical, and save only as regards the relatively few physical properties which depend upon atomic mass directly, physically identical also. Unit changes of this nuclear charge, so reckoned algebraically, give the successive places in the periodic table. For any one “place” or any one nuclear charge, more than one number of electrons in the outer-ring system may exist, and in such a case the element exhibits variable valency. But such changes of number, or of valency, concern only the ring and its external environment. There is no in- and out-going of electrons between ring and nucleus.
Concluding paragraph of 'Intra-atomic Charge', Nature (1913), 92, 400. Collected in Alfred Romer, Radiochemistry and the Discovery of Isotopes (1970), 251-252.
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The universality of parasitism as an offshoot of the predatory habit negatives the position taken by man that it is a pathological phenomenon or a deviation from the normal processes of nature. The pathological manifestations are only incidents in a developing parasitism. As human beings intent on maintaining man's domination over nature we may regard parasitism as pathological insofar as it becomes a drain upon human resources. In our efforts to protect ourselves we may make every kind of sacrifice to limit, reduce, and even eliminate parasitism as a factor in human life. Science attempts to define the terms on which this policy of elimination may or may not succeed. We must first of all thoroughly understand the problem, put ourselves in possession of all the facts in order to estimate the cost. Too often it has been assumed that parasitism was abnormal and that it needed only a slight force to reestablish what was believed to be a normal equilibrium without parasitism. On the contrary, biology teaches us that parasitism is a normal phenomenon and if we accept this view we shall be more ready to pay the price of freedom as a permanent and ever recurring levy of nature for immunity from a condition to which all life is subject. The greatest victory of man over nature in the physical realm would undoubtedly be his own delivery from the heavy encumbrance of parasitism with which all life is burdened.
Parasitism and Disease (1934), 4.
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There are something like ten million million million million million million million million million million million million million million (1 with eighty zeroes after it) particles in the region of the universe that we can observe. Where did they all come from? The answer is that, in quantum theory, particles can be created out of energy in the form of particle/antiparticle pairs. But that just raises the question of where the energy came from. The answer is that the total energy of the universe is exactly zero. The matter in the universe is made out of positive energy. However, the matter is all attracting itself by gravity. Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart, because you have to expend energy to separate them against the gravitational force that is pulling them together. Thus, in a sense, the gravitational field has negative energy. In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.
A Brief History of Time: From the Big Bang to Black Holes (1988), 129.
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There is little difference in people, but that little difference makes a big difference. The little difference is attitude. The big difference is weather it is positive or negative.
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There is no bandit so powerful as Nature. [The interaction of the positive and the negative principles, which produces the visible universe.] In the whole universe there is no escape from it.
Chuang Tzu: Mystic, Moralist and Social Reformer (1889), trans. Herbert A. Giles, 303. The brackets indicate a sentence printed as a paragraph in smaller type size.
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This is one of the greatest advantages of modern geometry over the ancient, to be able, through the consideration of positive and negative quantities, to include in a single enunciation the several cases which the same theorem may present by a change in the relative position of the different parts of a figure. Thus in our day the nine principal problems and the numerous particular cases, which form the object of eighty-three theorems in the two books De sectione determinata of Appolonius constitute only one problem which is resolved by a single equation.
In Histoire de la Géométrie, chap. 1, sect. 35.
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Tyndall declared that he saw in Matter the promise and potency of all forms of life, and with his Irish graphic lucidity made a picture of a world of magnetic atoms, each atom with a positive and a negative pole, arranging itself by attraction and repulsion in orderly crystalline structure. Such a picture is dangerously fascinating to thinkers oppressed by the bloody disorders of the living world. Craving for purer subjects of thought, they find in the contemplation of crystals and magnets a happiness more dramatic and less childish than the happiness found by mathematicians in abstract numbers, because they see in the crystals beauty and movement without the corrupting appetites of fleshly vitality.
In Back to Methuselah: A Metabiological Pentateuch (1921), lxi-lxii.
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We must regard it rather as an accident that the Earth (and presumably the whole solar system) contains a preponderance of negative electrons and positive protons. It is quite possible that for some of the stars it is the other way about.
(1902)
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You can try many different conditions, but if you get a negative result, you never know if you’re getting closer or farther away.
Concerning his research for identification of transcription factors. As quoted in Farooq Ahmed, 'Profile of Gregg L. Semenza', Proceedings of the National Academy of Sciences of the United States of America (17 Aug 2010), 107, No. 33, 14522.
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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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