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41 group
1) группа, ансамбль || групповой- roughing mill group2) совокупность; комплект3) группировка || группировать(ся)5) класс; категория || классифицировать; категоризировать6) хим. остаток7) сгусток; скопление8) узел9) матем. группа- absolute free group - absolute homotopy group - absolutely irreducible group - absolutely simple group - additively written group - adele group - adelic group - algebraically compact group - algebraically simple group - almost connected group - almost cyclic group - almost ordered group - almost periodic group - almost simple group - alternating form group - cancellative group - cellular homology group - characteristically simple group - complementing group - completely anisotropic group - completely discontinuous group - completely divisible group - completely indecomposable group - completely integrally closed group - deficient group - direct homology group - direct indecomposable group - doubly transitive group - finitely defined group - finitely generated group - finitely presented group - finitely related group - first homology group - first homotopy group - freely generated group - full linear group - full orthogonal group - full rotation group - full symmetric group - full unimodular group - group of classes of algebras - group of covering transformations - group of finite rank - group of infinite order - group of infinite rank - group of inner automorphisms - group of linear equivalence - group of linear forms - group of linear manifold - group of principal ideles - group of real line - group of recursive permutations - group of right quotients - idele class group - linearly ordered group - linearly transitive group - locally bicompact group - locally closed group - locally compact group - locally connected group - locally cyclic group - locally defined group - locally embeddable group - locally finite group - locally free group - locally infinite group - locally nilpotent group - locally normal group - locally solvable group - multiply primitive group - multiply transitive group - nonsolvable group - n-th homotopy group - ordered pair group - principal congruence group - properly orthogonal group - properly unimodular group - pure projective group - pure rotation group - pure simple group - quasipure projective group - quotient divisible group - residually nilpotent group - restricted holonomy group - sharply transitive group - simply ordered group - simply reducible group - simply transitive group - singular cogomology group - singular homology group - solvable group - stable group - strictly transitive group - strongly polycyclic group - subsolvable group - supersolvable group - totally ordered group - totally projective group - totally reducible group - triply transitive group - unitary symmetry group - unitary transformation group - value group - weak homology group - weakly mixing groupgroup with multiple operators — группа с многоместными операторами, мультиоператорная группа
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42 image
1) изображение || изображать(ся)2) оотображение || отображать(ся)3) образ; облик4) снимок, кадр5) вид, отпечаток, оттиск7) геол. характеристика формы осадочной частицы•to image into — матем. отображать(ся)
to image onto — матем. в отображать(ся) на
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43 kernel
1) зерно, зёрнышко2) керн3) матем. кернфункция4) сердцевина; ядро•kernel on the left — алг. ядро слева
kernel on the right — алг. ядро справа
kernel with a summable square — алг. ядро с суммируемым квадратом
- intrinsically singular kernel - kernel of a linear operator - kernel of a singular integral - kernel of a summation method - kernel of integral operator - kernel of integral transformation - locally finite kernel - nonpositive definite kernel - proper covariance kernelkernel with a weak singularity — алг. ядро со слабой особенностью
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44 lattice
1) плетение2) решётка, сетка || решетчатый3) пространственная решётка, структура•- almost contact lattice - almost tangent lattice - completely regular lattice - locally convex lattice - locally distributive lattice - locally modular lattice - lower semimodular lattice - metrically simple lattice - relatively pseudocomplemented lattice - structurally regular lattice - topologically dense lattice -
45 relation
1) зависимость, (взаимо)связь2) отношение; соотношение4) геол. условия залегания•- almost universal relation - cause-effect relation - generalized semigroup relation - logically irreducible relation - parametrically definable relation - partial ordering relation - recursively enumerable relation - recursively invariant relation - recursively representable relation - strongly definable relation - weakly symmetric relation -
46 rule
1) правило, норма; норматив || устанавливать правила или нормы2) строит. прав'ило3) линейка || линовать, разлиновывать4) правление || управлять, руководить, командовать5) мат. закон6) графить, разграфлять•set closed under rule — множество, замкнутое относительно операции
- blind man's ruleto lay down the rule — формулировать [устанавливать] правило
- box rule- cut rule- em rule- slow-in- sum rule- three sigma rule -
47 transformation
трансформация, трансформирование; превращение; преобразование- completely reducible transformation - convexity preserving transformation - identity transformation - inverted transformation - locally isomorphic transformation - locally linear transformation - locally quadratic transformation - normal transformation of binomial distribution - probability integral transformation - proper birational transformation - recursive transformation - uniform probability transformation - uniformly continuous transformation - uniformly regular transformation - weakly compact transformation - weakly completely continuous transformation - weakly mixing transformation - weakly open transformation - weakly separable transformation -
48 pit
1. n яма, ямка; впадина; углубление2. n воен. ровик, одиночный окоп; ячейка; гнездоmachine-gun pit — пулемётный окоп, пулемётная ячейка
rifle pit — стрелковая ячейка, одиночный окоп
3. n шахта; рудник; шахтный ствол; карьер, разрез; копь4. n выемка; котлован5. n колодец; шурфtest pit — пробный шурф, разведочная скважина
6. n метал. литейная ямаpit dwelling — примитивное жилище — яма с крышей из веток
pit retting — мочило, яма для мочки
7. n тех. смотровая канава; ремонтная яма8. n яма для хранения овощей9. n силосная яма10. n выгребная яма11. n яма для сжигания древесного угля12. n парник13. n гурт14. n могила15. n авт. часто заправочно-ремонтный пункт16. n волчья яма, западня17. n ловушка, западня; неожиданная или непредвиденная опасность18. n преисподняя, адthe yawning pit — зияющая бездна, ад
bottomless pit — ад, преисподняя
19. n анат. ямка, углубление20. n оспина, рябина21. n метал. раковина22. n партер,23. n арена петушиных, собачьих боёв24. n амер. часть биржевого зала, отведённая для торговли определённым товаром25. n арх. тюрьма; темница26. n бот. пора27. n спорт. яма для прыжков28. n игровой залpit broker — брокер срочной товарной биржи, работающий в биржевом зале
29. n род шумной карточной игры30. n площадка, куда скатываются кегли31. n тех. загрузочный бункер или воронкаhe who digs a pit for others falls in himself — не рой яму другому, сам в неё попадёшь
32. v класть, складывать, закладывать в яму для хранения33. v рыть ямы34. v делать ямки; оставлять следы, отметины35. v стравливать36. v натравливать37. v бороться; противостоять38. v мед. оставлять след на коже39. v останавливаться на заправочно-ремонтном пункте40. v покрываться коррозией41. n амер. фруктовая косточка42. v амер. вынимать косточкиСинонимический ряд:1. cavity (noun) burrow; cavity; crater; furrow; hole2. core (noun) core; kernel; nut; pip; seed; stone3. excavation (noun) excavation; pitfall; trap; well4. hell (noun) abyss; barathrum; blazes; Gehenna; hades; hell; inferno; netherworld; pandemonium; perdition; Sheol; Tophet5. hollow (noun) dent; depression; hollow; indentation6. sink (noun) cesspool; sink7. dent (verb) dent; gouge; indent; pock8. oppose (verb) counter; match; oppose; play off; vieАнтонимический ряд:fruit; mound -
49 early
early ['ɜ:lɪ]matinal ⇒ 1 (a) premier ⇒ 1 (b) en avance ⇒ 1 (c), 2 (c) de bonne heure ⇒ 1 (c), 2 (a), 2 (c) précoce ⇒ 1 (d)∎ I had an early breakfast j'ai déjeuné de bonne heure;∎ to get off to an early start partir de bonne heure;∎ the early shuttle to London le premier avion pour Londres;∎ it's too early to get up il est trop tôt pour se lever;∎ it's earlier than I thought il est plus tôt que je ne pensais;∎ to be an early riser être matinal ou un lève-tôt;∎ very early in the morning très tôt;∎ early morning call appel m matinal;∎ could you give me an early call at 6:30? pouvez-vous me réveiller à 6 heures 30?;∎ early morning tea thé m du matin;∎ early morning walk promenade f matinale(b) (belonging to the beginning of a period of time → machine, film, poem) premier; (→ Edwardian, Victorian etc) du début de l'époque;∎ in the early afternoon/spring/fifties au début de l'après-midi/du printemps/des années cinquante;∎ in the early nineteenth century au début du XIXème siècle;∎ the earlier applicants were better than the later ones les premiers candidats étaient meilleurs que les derniers;∎ when was that? - early September quand était-ce? - début septembre;∎ from the earliest days of the century depuis le tout début du siècle;∎ British it's early days yet (difficult to be definite) il est trop tôt pour se prononcer; (might yet be worse, better) il est encore tôt;∎ from the earliest times depuis le début des temps;∎ I need an early night je dois me coucher de bonne heure;∎ a couple of early nights wouldn't do you any harm cela ne te ferait pas de mal de te coucher de bonne heure pendant quelques jours;∎ it's too early to tell il est trop tôt pour se prononcer, on ne peut encore rien dire;∎ the earliest human artefacts les premiers objets fabriqués par l'homme;∎ the early Roman Empire l'Empire romain naissant;∎ an early 18th-century form of democracy une forme de démocratie propre au début du XVIIIème siècle;∎ the early American settlers les premiers pionniers américains;∎ an early Picasso une des premières œuvres de Picasso;∎ he's in his early twenties il a une vingtaine d'années;∎ in his early youth quand il était très jeune;∎ a man in early middle age un homme d'une quarantaine d'années;∎ from an early age dès l'enfance;∎ at an early age de bonne heure, très jeune;∎ he received his early education in Paris il reçut sa première éducation à Paris;∎ my earliest recollections mes souvenirs les plus lointains;∎ early reports from the front indicate that… les premières nouvelles du front semblent indiquer que…;∎ in the early stages of the project dans une phase initiale du projet∎ to be early (person, train, flight, winter) être en avance;∎ I am half an hour early je suis en avance d'une demi-heure;∎ let's have an early lunch déjeunons de bonne heure;∎ you're too early vous arrivez trop tôt, vous êtes en avance;∎ Easter is early this year Pâques est de bonne heure cette année∎ early beans haricots mpl de primeur;∎ early vegetables/fruit/produce primeurs fpl;∎ we're having an early winter l'hiver est précoce(e) (relating to the future → reply) prochain;∎ at an early date de bonne heure;∎ at an earlier date plus tôt;∎ we need an early meeting il faut que nous nous réunissions bientôt;∎ Commerce at your earliest convenience dans les meilleurs délais;∎ what is your earliest possible delivery date? quelle est votre première possibilité de livraison?;∎ give us the earliest possible notice avertissez-nous le plus tôt possible2 adverb(a) (in the morning → rise, leave) tôt, de bonne heure;∎ let's set off as early as we can mettons-nous en route le plus tôt possible;∎ how early should I get there? à quelle heure dois-je y être?∎ early in the evening/in the afternoon tôt le soir/(dans) l'après-midi;∎ early in the year/winter au début de l'année/de l'hiver;∎ as early as the tenth century dès le dixième siècle;∎ I can't make it earlier than 2.30 je ne peux pas avant 14 heures 30;∎ what's the earliest you can make it? (be here) quand pouvez-vous être ici?;∎ early on tôt;∎ early on it was apparent that… il est vite apparu que…;∎ early on in June au début du mois de juin;∎ earlier on plus tôt∎ I want to leave early tonight (from work) je veux partir de bonne heure ce soir;∎ shop/post early for Christmas faites vos achats/postez votre courrier à l'avance pour Noël∎ this flower blooms very early cette fleur s'épanouit très précocement∎ at the earliest au plus tôt;∎ we can't deliver earlier than Friday nous ne pouvons pas livrer avant vendredi►► Marketing early adopter réceptif m précoce, adopteur m précoce;early American = style de mobilier et d'architecture du début du XIXème siècle;∎ proverb the early bird catches the worm (it's good to get up early) le monde appartient à ceux qui se lèvent tôt; (it's good to arrive early) les premiers arrivés sont les mieux servis;American Commerce early bird special = dans un restaurant, prix avantageux accordés aux clients qui consomment avant une certaine heure;the early Church l'Église f primitive;∎ it's early closing today (for all shops) les magasins ferment de bonne heure aujourd'hui; (for this shop) on ferme de bonne heure aujourd'hui;British Politics Early Day Motion = proposition de loi dont la discussion n'est pas à l'ordre du jour, présentée par un député qui recherche l'appui de collègues de façon à attirer l'attention du parlement sur une question;early English gothique m anglais primitif;Marketing early follower suiveur m immédiat;Early Learning Centre = chaîne de magasins de jouets d'éveil, en Grande-Bretagne;Marketing early majority majorité f innovatrice;Art the early masters les primitifs mpl;early music (baroque) musique f ancienne;Finance early redemption amortissement m anticipé;early retirement retraite f anticipée;∎ to take early retirement prendre sa retraite anticipée, partir en retraite anticipéeⓘ Here's one I made earlier L'émission éducative britannique Blue Peter, diffusée sur le petit écran depuis de nombreuses années, comprend souvent des séquences de travaux manuels et de cuisine. Les animateurs présentent toujours le produit fini à la caméra en prononçant les mots here's one I made earlier ("en voici un que j'ai confectionné au préalable"). On utilise cette phrase de façon humoristique lorsqu'on montre à quelqu'un une chose que l'on a réalisée. -
50 De Forest, Lee
SUBJECT AREA: Broadcasting, Electronics and information technology, Photography, film and optics, Recording, Telecommunications[br]b. 26 August 1873 Council Bluffs, Iowa, USAd. 30 June 1961 Hollywood, California, USA[br]American electrical engineer and inventor principally known for his invention of the Audion, or triode, vacuum tube; also a pioneer of sound in the cinema.[br]De Forest was born into the family of a Congregational minister that moved to Alabama in 1879 when the father became President of a college for African-Americans; this was a position that led to the family's social ostracism by the white community. By the time he was 13 years old, De Forest was already a keen mechanical inventor, and in 1893, rejecting his father's plan for him to become a clergyman, he entered the Sheffield Scientific School of Yale University. Following his first degree, he went on to study the propagation of electromagnetic waves, gaining a PhD in physics in 1899 for his thesis on the "Reflection of Hertzian Waves from the Ends of Parallel Wires", probably the first US thesis in the field of radio.He then joined the Western Electric Company in Chicago where he helped develop the infant technology of wireless, working his way up from a modest post in the production area to a position in the experimental laboratory. There, working alone after normal working hours, he developed a detector of electromagnetic waves based on an electrolytic device similar to that already invented by Fleming in England. Recognizing his talents, a number of financial backers enabled him to set up his own business in 1902 under the name of De Forest Wireless Telegraphy Company; he was soon demonstrating wireless telegraphy to interested parties and entering into competition with the American Marconi Company.Despite the failure of this company because of fraud by his partners, he continued his experiments; in 1907, by adding a third electrode, a wire mesh, between the anode and cathode of the thermionic diode invented by Fleming in 1904, he was able to produce the amplifying device now known as the triode valve and achieve a sensitivity of radio-signal reception much greater than possible with the passive carborundum and electrolytic detectors hitherto available. Patented under the name Audion, this new vacuum device was soon successfully used for experimental broadcasts of music and speech in New York and Paris. The invention of the Audion has been described as the beginning of the electronic era. Although much development work was required before its full potential was realized, the Audion opened the way to progress in all areas of sound transmission, recording and reproduction. The patent was challenged by Fleming and it was not until 1943 that De Forest's claim was finally recognized.Overcoming the near failure of his new company, the De Forest Radio Telephone Company, as well as unsuccessful charges of fraudulent promotion of the Audion, he continued to exploit the potential of his invention. By 1912 he had used transformer-coupling of several Audion stages to achieve high gain at radio frequencies, making long-distance communication a practical proposition, and had applied positive feedback from the Audion output anode to its input grid to realize a stable transmitter oscillator and modulator. These successes led to prolonged patent litigation with Edwin Armstrong and others, and he eventually sold the manufacturing rights, in retrospect often for a pittance.During the early 1920s De Forest began a fruitful association with T.W.Case, who for around ten years had been working to perfect a moving-picture sound system. De Forest claimed to have had an interest in sound films as early as 1900, and Case now began to supply him with photoelectric cells and primitive sound cameras. He eventually devised a variable-density sound-on-film system utilizing a glow-discharge modulator, the Photion. By 1926 De Forest's Phonofilm had been successfully demonstrated in over fifty theatres and this system became the basis of Movietone. Though his ideas were on the right lines, the technology was insufficiently developed and it was left to others to produce a system acceptable to the film industry. However, De Forest had played a key role in transforming the nature of the film industry; within a space of five years the production of silent films had all but ceased.In the following decade De Forest applied the Audion to the development of medical diathermy. Finally, after spending most of his working life as an independent inventor and entrepreneur, he worked for a time during the Second World War at the Bell Telephone Laboratories on military applications of electronics.[br]Principal Honours and DistinctionsInstitute of Electronic and Radio Engineers Medal of Honour 1922. President, Institute of Electronic and Radio Engineers 1930. Institute of Electrical and Electronics Engineers Edison Medal 1946.Bibliography1904, "Electrolytic detectors", Electrician 54:94 (describes the electrolytic detector). 1907, US patent no. 841,387 (the Audion).1950, Father of Radio, Chicago: WIlcox \& Follett (autobiography).De Forest gave his own account of the development of his sound-on-film system in a series of articles: 1923. "The Phonofilm", Transactions of the Society of Motion Picture Engineers 16 (May): 61–75; 1924. "Phonofilm progress", Transactions of the Society of Motion Picture Engineers 20:17–19; 1927, "Recent developments in the Phonofilm", Transactions of the Society of Motion Picture Engineers 27:64–76; 1941, "Pioneering in talking pictures", Journal of the Society of Motion Picture Engineers 36 (January): 41–9.Further ReadingG.Carneal, 1930, A Conqueror of Space (biography).I.Levine, 1964, Electronics Pioneer, Lee De Forest (biography).E.I.Sponable, 1947, "Historical development of sound films", Journal of the Society of Motion Picture Engineers 48 (April): 275–303 (an authoritative account of De Forest's sound-film work, by Case's assistant).W.R.McLaurin, 1949, Invention and Innovation in the Radio Industry.C.F.Booth, 1955, "Fleming and De Forest. An appreciation", in Thermionic Valves 1904– 1954, IEE.V.J.Phillips, 1980, Early Radio Detectors, London: Peter Peregrinus.KF / JW -
51 Zeiss, Carl
SUBJECT AREA: Photography, film and optics[br]b. 11 September 1816 Weimar, Thuringia, Germanyd. 3 December 1888 Jena, Saxony, Germany[br]German lens manufacturer who introduced scientific method to the production of compound microscopes and made possible the production of the first anastigmatic photographic objectives.[br]After completing his early education in Weimar, Zeiss became an apprentice to the engineer Dr Frederick Koerner. As part of his training, Zeiss was required to travel widely and he visited Vienna, Berlin, Stuttgart and Darmstadt to study his trade. In 1846 he set up a business of his own, an optical workshop in Jena, where he began manufacturing magnifying glasses and microscopes. Much of his work was naturally for the university there and he had the co-operation of some of the University staff in the development of precision instruments. By 1858 he was seeking to make more expensive compound microscopes, but he found the current techniques primitive and laborious. He decided that it was necessary to introduce scientific method to the design of the optics, and in 1866 he sought the advice of a professor of physics at the University of Jena, Ernst Abbe (1840–1905). It took Zeiss until 1869 to persuade Abbe to join his company, and two difficult years were spent working on the calculations before success was achieved. Within a few more years the Zeiss microscope had earned a worldwide reputation for quality. Abbe became a full partner in the Zeiss business in 1875. In 1880 Abbe began an association with Friedrich Otte Schott that was to lead to the establishment of the famous Jena glass works in 1884. With the support of the German government, Jena was to become the centre of world production of new optical glasses for photographic objectives.In 1886 the distinguished mathematician and optician Paul Rudolph joined Zeiss at Jena. After Zeiss's death, Rudolph went on to use the characteristics of the new glass to calculate the first anastigmatic lenses. Immediately successful and widely imitated, the anastigmats were also the first of a long series of Zeiss photographic objectives that were to be at the forefront of lens design for years to come. Abbe took over the management of the company and developed it into an internationally famous organization.[br]Further ReadingL.W.Sipley, 1965, Photography's Great Inventors, Philadelphia (a brief biography). J.M.Eder, 1945, History of Photography, trans. E.Epstean, New York.K.J.Hume, 1980, A History of Engineering Metrology, London, 122–32 (includes a short account of Carl Zeiss and his company).JW / RTS -
52 Knowledge
It is indeed an opinion strangely prevailing amongst men, that houses, mountains, rivers, and, in a word, all sensible objects, have an existence, natural or real, distinct from their being perceived by the understanding. But, with how great an assurance and acquiescence soever this principle may be entertained in the world, yet whoever shall find in his heart to call it into question may, if I mistake not, perceive it to involve a manifest contradiction. For, what are the forementioned objects but things we perceive by sense? and what do we perceive besides our own ideas or sensations? and is it not plainly repugnant that any one of these, or any combination of them, should exist unperceived? (Berkeley, 1996, Pt. I, No. 4, p. 25)It seems to me that the only objects of the abstract sciences or of demonstration are quantity and number, and that all attempts to extend this more perfect species of knowledge beyond these bounds are mere sophistry and illusion. As the component parts of quantity and number are entirely similar, their relations become intricate and involved; and nothing can be more curious, as well as useful, than to trace, by a variety of mediums, their equality or inequality, through their different appearances.But as all other ideas are clearly distinct and different from each other, we can never advance farther, by our utmost scrutiny, than to observe this diversity, and, by an obvious reflection, pronounce one thing not to be another. Or if there be any difficulty in these decisions, it proceeds entirely from the undeterminate meaning of words, which is corrected by juster definitions. That the square of the hypotenuse is equal to the squares of the other two sides cannot be known, let the terms be ever so exactly defined, without a train of reasoning and enquiry. But to convince us of this proposition, that where there is no property, there can be no injustice, it is only necessary to define the terms, and explain injustice to be a violation of property. This proposition is, indeed, nothing but a more imperfect definition. It is the same case with all those pretended syllogistical reasonings, which may be found in every other branch of learning, except the sciences of quantity and number; and these may safely, I think, be pronounced the only proper objects of knowledge and demonstration. (Hume, 1975, Sec. 12, Pt. 3, pp. 163-165)Our knowledge springs from two fundamental sources of the mind; the first is the capacity of receiving representations (the ability to receive impressions), the second is the power to know an object through these representations (spontaneity in the production of concepts).Through the first, an object is given to us; through the second, the object is thought in relation to that representation.... Intuition and concepts constitute, therefore, the elements of all our knowledge, so that neither concepts without intuition in some way corresponding to them, nor intuition without concepts, can yield knowledge. Both may be either pure or empirical.... Pure intuitions or pure concepts are possible only a priori; empirical intuitions and empirical concepts only a posteriori. If the receptivity of our mind, its power of receiving representations in so far as it is in any way affected, is to be called "sensibility," then the mind's power of producing representations from itself, the spontaneity of knowledge, should be called "understanding." Our nature is so constituted that our intuitions can never be other than sensible; that is, it contains only the mode in which we are affected by objects. The faculty, on the other hand, which enables us to think the object of sensible intuition is the understanding.... Without sensibility, no object would be given to us; without understanding, no object would be thought. Thoughts without content are empty; intuitions without concepts are blind. It is therefore just as necessary to make our concepts sensible, that is, to add the object to them in intuition, as to make our intuitions intelligible, that is to bring them under concepts. These two powers or capacities cannot exchange their functions. The understanding can intuit nothing, the senses can think nothing. Only through their union can knowledge arise. (Kant, 1933, Sec. 1, Pt. 2, B74-75 [p. 92])Metaphysics, as a natural disposition of Reason is real, but it is also, in itself, dialectical and deceptive.... Hence to attempt to draw our principles from it, and in their employment to follow this natural but none the less fallacious illusion can never produce science, but only an empty dialectical art, in which one school may indeed outdo the other, but none can ever attain a justifiable and lasting success. In order that, as a science, it may lay claim not merely to deceptive persuasion, but to insight and conviction, a Critique of Reason must exhibit in a complete system the whole stock of conceptions a priori, arranged according to their different sources-the Sensibility, the understanding, and the Reason; it must present a complete table of these conceptions, together with their analysis and all that can be deduced from them, but more especially the possibility of synthetic knowledge a priori by means of their deduction, the principles of its use, and finally, its boundaries....This much is certain: he who has once tried criticism will be sickened for ever of all the dogmatic trash he was compelled to content himself with before, because his Reason, requiring something, could find nothing better for its occupation. Criticism stands to the ordinary school metaphysics exactly in the same relation as chemistry to alchemy, or as astron omy to fortune-telling astrology. I guarantee that no one who has comprehended and thought out the conclusions of criticism, even in these Prolegomena, will ever return to the old sophistical pseudo-science. He will rather look forward with a kind of pleasure to a metaphysics, certainly now within his power, which requires no more preparatory discoveries, and which alone can procure for reason permanent satisfaction. (Kant, 1891, pp. 115-116)Knowledge is only real and can only be set forth fully in the form of science, in the form of system. Further, a so-called fundamental proposition or first principle of philosophy, even if it is true, it is yet none the less false, just because and in so far as it is merely a fundamental proposition, merely a first principle. It is for that reason easily refuted. The refutation consists in bringing out its defective character; and it is defective because it is merely the universal, merely a principle, the beginning. If the refutation is complete and thorough, it is derived and developed from the nature of the principle itself, and not accomplished by bringing in from elsewhere other counter-assurances and chance fancies. It would be strictly the development of the principle, and thus the completion of its deficiency, were it not that it misunderstands its own purport by taking account solely of the negative aspect of what it seeks to do, and is not conscious of the positive character of its process and result. The really positive working out of the beginning is at the same time just as much the very reverse: it is a negative attitude towards the principle we start from. Negative, that is to say, in its one-sided form, which consists in being primarily immediate, a mere purpose. It may therefore be regarded as a refutation of what constitutes the basis of the system; but more correctly it should be looked at as a demonstration that the basis or principle of the system is in point of fact merely its beginning. (Hegel, 1910, pp. 21-22)Knowledge, action, and evaluation are essentially connected. The primary and pervasive significance of knowledge lies in its guidance of action: knowing is for the sake of doing. And action, obviously, is rooted in evaluation. For a being which did not assign comparative values, deliberate action would be pointless; and for one which did not know, it would be impossible. Conversely, only an active being could have knowledge, and only such a being could assign values to anything beyond his own feelings. A creature which did not enter into the process of reality to alter in some part the future content of it, could apprehend a world only in the sense of intuitive or esthetic contemplation; and such contemplation would not possess the significance of knowledge but only that of enjoying and suffering. (Lewis, 1946, p. 1)"Evolutionary epistemology" is a branch of scholarship that applies the evolutionary perspective to an understanding of how knowledge develops. Knowledge always involves getting information. The most primitive way of acquiring it is through the sense of touch: amoebas and other simple organisms know what happens around them only if they can feel it with their "skins." The knowledge such an organism can have is strictly about what is in its immediate vicinity. After a huge jump in evolution, organisms learned to find out what was going on at a distance from them, without having to actually feel the environment. This jump involved the development of sense organs for processing information that was farther away. For a long time, the most important sources of knowledge were the nose, the eyes, and the ears. The next big advance occurred when organisms developed memory. Now information no longer needed to be present at all, and the animal could recall events and outcomes that happened in the past. Each one of these steps in the evolution of knowledge added important survival advantages to the species that was equipped to use it.Then, with the appearance in evolution of humans, an entirely new way of acquiring information developed. Up to this point, the processing of information was entirely intrasomatic.... But when speech appeared (and even more powerfully with the invention of writing), information processing became extrasomatic. After that point knowledge did not have to be stored in the genes, or in the memory traces of the brain; it could be passed on from one person to another through words, or it could be written down and stored on a permanent substance like stone, paper, or silicon chips-in any case, outside the fragile and impermanent nervous system. (Csikszentmihalyi, 1993, pp. 56-57)Historical dictionary of quotations in cognitive science > Knowledge
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53 Science
It is a common notion, or at least it is implied in many common modes of speech, that the thoughts, feelings, and actions of sentient beings are not a subject of science.... This notion seems to involve some confusion of ideas, which it is necessary to begin by clearing up. Any facts are fitted, in themselves, to be a subject of science, which follow one another according to constant laws; although those laws may not have been discovered, nor even to be discoverable by our existing resources. (Mill, 1900, B. VI, Chap. 3, Sec. 1)One class of natural philosophers has always a tendency to combine the phenomena and to discover their analogies; another class, on the contrary, employs all its efforts in showing the disparities of things. Both tendencies are necessary for the perfection of science, the one for its progress, the other for its correctness. The philosophers of the first of these classes are guided by the sense of unity throughout nature; the philosophers of the second have their minds more directed towards the certainty of our knowledge. The one are absorbed in search of principles, and neglect often the peculiarities, and not seldom the strictness of demonstration; the other consider the science only as the investigation of facts, but in their laudable zeal they often lose sight of the harmony of the whole, which is the character of truth. Those who look for the stamp of divinity on every thing around them, consider the opposite pursuits as ignoble and even as irreligious; while those who are engaged in the search after truth, look upon the other as unphilosophical enthusiasts, and perhaps as phantastical contemners of truth.... This conflict of opinions keeps science alive, and promotes it by an oscillatory progress. (Oersted, 1920, p. 352)Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone. (Einstein & Infeld, 1938, p. 27)A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. (Planck, 1949, pp. 33-34)[Original quotation: "Eine neue wissenschaftliche Wahrheit pflegt sich nicht in der Weise durchzusetzen, dass ihre Gegner ueberzeugt werden und sich as belehrt erklaeren, sondern vielmehr dadurch, dass die Gegner allmaehlich aussterben und dass die heranwachsende Generation von vornherein mit der Wahrheit vertraut gemacht ist." (Planck, 1990, p. 15)]I had always looked upon the search for the absolute as the noblest and most worth while task of science. (Planck, 1949, p. 46)If you cannot-in the long run-tell everyone what you have been doing, your doing has been worthless. (SchroЁdinger, 1951, pp. 7-8)Even for the physicist the description in plain language will be a criterion of the degree of understanding that has been reached. (Heisenberg, 1958, p. 168)The old scientific ideal of episteґmeґ-of absolutely certain, demonstrable knowledge-has proved to be an idol. The demand for scientific objectivity makes it inevitable that every scientific statement must remain tentative forever. It may indeed be corroborated, but every corroboration is relative to other statements which, again, are tentative. Only in our subjective experiences of conviction, in our subjective faith, can we be "absolutely certain." (Popper, 1959, p. 280)The layman, taught to revere scientists for their absolute respect for the observed facts, and for the judiciously detached and purely provisional manner in which they hold scientific theories (always ready to abandon a theory at the sight of any contradictory evidence) might well have thought that, at Miller's announcement of this overwhelming evidence of a "positive effect" [indicating that the speed of light is not independent from the motion of the observer, as Einstein's theory of relativity demands] in his presidential address to the American Physical Society on December 29th, 1925, his audience would have instantly abandoned the theory of relativity. Or, at the very least, that scientists-wont to look down from the pinnacle of their intellectual humility upon the rest of dogmatic mankind-might suspend judgment in this matter until Miller's results could be accounted for without impairing the theory of relativity. But no: by that time they had so well closed their minds to any suggestion which threatened the new rationality achieved by Einstein's world-picture, that it was almost impossible for them to think again in different terms. Little attention was paid to the experiments, the evidence being set aside in the hope that it would one day turn out to be wrong. (Polanyi, 1958, pp. 12-13)The practice of normal science depends on the ability, acquired from examplars, to group objects and situations into similarity sets which are primitive in the sense that the grouping is done without an answer to the question, "Similar with respect to what?" (Kuhn, 1970, p. 200)Science in general... does not consist in collecting what we already know and arranging it in this or that kind of pattern. It consists in fastening upon something we do not know, and trying to discover it. (Collingwood, 1972, p. 9)Scientific fields emerge as the concerns of scientists congeal around various phenomena. Sciences are not defined, they are recognized. (Newell, 1973a, p. 1)This is often the way it is in physics-our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. I do not think it is possible really to understand the successes of science without understanding how hard it is-how easy it is to be led astray, how difficult it is to know at any time what is the next thing to be done. (Weinberg, 1977, p. 49)Science is wonderful at destroying metaphysical answers, but incapable of providing substitute ones. Science takes away foundations without providing a replacement. Whether we want to be there or not, science has put us in a position of having to live without foundations. It was shocking when Nietzsche said this, but today it is commonplace; our historical position-and no end to it is in sight-is that of having to philosophize without "foundations." (Putnam, 1987, p. 29)Historical dictionary of quotations in cognitive science > Science
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