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1 essentially singular point
Математика: существенно особая точкаУниверсальный англо-русский словарь > essentially singular point
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2 essentially singular point
English-russian dictionary of physics > essentially singular point
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3 essentially singular point
мат. существенно особая точкаEnglish-Russian scientific dictionary > essentially singular point
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4 point
1) точка2) балл, очко3) деление (шкалы); румб; лимб4) заострение, остриё, острый конец || заострять, затачивать5) полигр. пункт ( единица измерения в типографской системе мер)6) пост, пункт, место7) мыс8) наконечник9) предмет11) указывать•about a point — мат. в окрестности точки
point at infinity — мат. несобственный элемент, бесконечно удалённая точка
point covers a line — т. граф. вершина покрывает ребро
point in infinity — мат. точка в бесконечности
winding number of curve with respect to point — мат. порядок кривой относительно точки (число оборотов вектора, соединяющего данную точку с точкой кривой при обходе кривой)
right two points — мор. на два румба вправо
with a point as a center — мат. с центром в точке…
- bisecting point of a segment - conditionally stable point - division point - essentially singular point - general point - generic point - horizontal control point - infinitely remote point point - material point - minimal fixed point - negatively stable point - nonessential singular point - optimum point - piercing point of a line - point of greatest concentration - positively normal point - positively stable point - right singular point - single mass point - strongly recurrent point - strongly singular point - triply rational point - uniplanar double point - unstable nodal point - upper significance pointwith respect to point — мат. относительно точки
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5 function
1) функция, действие || функционировать; действовать- essential functions - routine function - safety-related functions2) функциональное назначение; роль- circuit function - intrinsic function - metering function - primary function - robot function - planning function - service function - support function4) функциональный узел ( машины)5) матем. функциональная зависимость, функция- absolutely additive function - absolutely bounded function - absolutely continuous function - absolutely integrable function - absolutely monotone function - absolutely summable function - absolutely symmetric function - almost complex function - almost continuous function - almost convex function - almost everywhere defined function - almost everywhere finite function - almost invariant function - almost periodic function - almost recursive function - almost separably-valued function - almost separating function - almost universal function - analytically independent function - analytically representable function - approximately differentiable function - asymptotically differentiable function - asymptotically finite function - asymptotically uniformly optimal function - bounded below function - cellwise continuous function - circumferentially mean p-valent function - comparison function - complementary error function - complete analytic function - completely additive function - completely computable function - completely monotone function - completely multiplicative function - completely productive function - completely subadditive function - completely symmetrical function - completely undefined function - complex hyperbolic function - conditional risk function - countably multiplicative function - countably valued function - covariant function - cumulative distribution function - cumulative frequency function - deficiency function - double limit function - doubly periodic function - doubly recursive function - effectively computable function - effectively constant function - effectively decidable function - effectively variable function - elementarily symmetric function - entire function of maximum type - entire function of mean type - entire function of potential type - entire function of zero type - entire rational function - essentially increasing function - essentially integrable function - essentially real function - essentially smooth function - everywhere differentiable function - everywhere smooth function - expansible function - explicitly definable function - exponentially convex function - exponentially decreasing function - exponentially increasing function - exponentially multiplicative function - exponentially vanishing function - finitely mean valent function - finitely measurable function - function of appropriate behavior - function of bounded characteristic - function of bounded type - function of bounded variation - function of complex variable - function of exponential type - function of finite genus - function of finite variation - function of fractional order - function of infinite type - function of integral order - function of maximal type - function of minimal type - function of mixed variables - function of normal type - function of number theory - function of one variable - function of rapid descent - function of rapid growth - function of real variable - general universal function - geometric carrier function - implicitly definable function - incomplete dibeta function - incomplete gamma function - incomplete tribeta function - incompletely defined function - inductively defined function - inductively integrable function - infinitely divisible function - infinitely many-valued function - integral logarithmic function - inverse trigonometric function - inverted beta function - iterative function - joint correlation function - joint density function - linearly separable function - locally bounded function - locally constant function - locally holomorphic function - locally homogeneous function - locally integrable function - locally negligible function - locally regular function - locally summable function - logarithmic generating function - logarithmic integral function - logarithmically infinite function - logarithmically plurisubharmonic function - logarithmically subharmonic function - lower semicontinuous function - monotone non-decreasing function - monotone non-increasing function - multiply periodic function - multiply recursive function - negative definite function - negative infinite function - nontangentially bounded function - normalized function - normed function - nowhere continuous function - nowhere differentiable function - nowhere monotonic function - n-times differentiable function - n-tuply periodic function - numeralwise expressible function - numeralwise representable function - numerical function - numerically valued function - oblate spheroidal function - operating characteristic function - optimal policy function - parametrically definable function - partially symmetric function - piecewise constant function - piecewise continuously differentiable function - piecewise linear function - piecewise monotonic function - piecewise polynomial function - piecewise quadratic function - piecewise regular function - piecewise smooth function - pointwise approximated function - positive homogeneous function - positive infinite function - positive monotone function - positive monotonic function - positive semidefinite function - potentially calculable function - potentially recursive function - power series function - probability generating function - quadratically summable function - rapidly damped function - rapidly decreasing function - rapidly oscillatory function - recursively continuous function - recursively convergent function - recursively defined function - recursively differentiable function - recursively divergent function - recursively extensible function - relative distribution function - relative frequency function - representing function - reproducing kernel function - residual function - residue function - scalarwise integrable function - scalarwise measurable function - sectionally smooth function - simply periodic function - singly recursive function - slowly increasing function - slowly oscillating function - slowly varying function - smoothly varying function - solid spherical harmonic function - solid zonal harmonic function - steadily increasing function - stopped random function - strictly convex function - strictly decreasing function - strictly increasing function - strictly integrable function - strictly monotone function - strongly differentiable function - strongly holomorphic function - strongly integrable function - strongly measurable function - strongly plurisubharmonic function - totally additive function - totally continuous function - totally measurable function - totally multiplicative function - totally positive function - triangular function - uniformly best decision function - uniformly bounded function - uniformly definable function - uniformly differentiable function - uniformly homotopic function - uniformly integrable function - uniformly limited function - uniformly measurable function - uniformly smooth function - unit step function - unitary divisor function - upper measurable function - upper semicontinuous function - weakly analytic function - weakly continuous function - weakly differentiable function - weakly holomorphic function - weakly measurable function - weakly singular function - weighted random functiondomain of a function — область определения функции, область изменения независимой переменной
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6 sequence
1) очерёдность; порядок следования3) геол. стратиграфический разрез4) серия, комплекс•- absolutely divergent sequence - absolutely limited sequence - absolutely summable sequence - absolutely unbiased sequence - adjusted homology sequence - asymptotically convergent sequence - asymptotically isotropic sequence - asymptotically lattice sequence - compactly divergent sequence - completely reversible sequence - conditionally divergent sequence - decimal geometric sequence - delicately divergent sequence - discretely convergent sequence - essentially convergent sequence - essentially finite sequence - essentially periodic sequence - everywhere dense sequence - infinitely large sequence - infinitely proceeding sequence - infinitely small sequence - integral stationary sequence - inverse sequence - inverted sequence - linearly independent sequence - locally convergent sequence - metrically convergent sequence - metrically transitive sequence - monotonically decreasing sequence - monotonically increasing sequence - never increasing sequence - numerical sequence - projectively realizable sequence - properly divergent sequence - rapid acquisition sequence - rapidly decreasing sequence - rapidly increasing sequence - recursively defined sequence - recursively divergent sequence - recursively enumerable sequence - relatively compact sequence - sequence of prime numbers - sequence of principal indices - slowly decreasing sequence - slowly increasing sequence - slowly oscillating sequence - stochastically compact sequence - stochastically stable sequence - strictly increasing sequence - strictly measurable sequence - strictly monotonic sequence - strongly convergent sequence - strongly downward sequence - strongly stationary sequence - strongly summable sequence - totally increasing sequence - totally monotone sequence - two-taile sequence - two-way infinite sequence - unconditionally divergent sequence - uniformly divergent sequence - uniformly integrable sequence - weakly convergent sequence -
7 Language
Philosophy is written in that great book, the universe, which is always open, right before our eyes. But one cannot understand this book without first learning to understand the language and to know the characters in which it is written. It is written in the language of mathematics, and the characters are triangles, circles, and other figures. Without these, one cannot understand a single word of it, and just wanders in a dark labyrinth. (Galileo, 1990, p. 232)It never happens that it [a nonhuman animal] arranges its speech in various ways in order to reply appropriately to everything that may be said in its presence, as even the lowest type of man can do. (Descartes, 1970a, p. 116)It is a very remarkable fact that there are none so depraved and stupid, without even excepting idiots, that they cannot arrange different words together, forming of them a statement by which they make known their thoughts; while, on the other hand, there is no other animal, however perfect and fortunately circumstanced it may be, which can do the same. (Descartes, 1967, p. 116)Human beings do not live in the object world alone, nor alone in the world of social activity as ordinarily understood, but are very much at the mercy of the particular language which has become the medium of expression for their society. It is quite an illusion to imagine that one adjusts to reality essentially without the use of language and that language is merely an incidental means of solving specific problems of communication or reflection. The fact of the matter is that the "real world" is to a large extent unconsciously built on the language habits of the group.... We see and hear and otherwise experience very largely as we do because the language habits of our community predispose certain choices of interpretation. (Sapir, 1921, p. 75)It powerfully conditions all our thinking about social problems and processes.... No two languages are ever sufficiently similar to be considered as representing the same social reality. The worlds in which different societies live are distinct worlds, not merely the same worlds with different labels attached. (Sapir, 1985, p. 162)[A list of language games, not meant to be exhaustive:]Giving orders, and obeying them- Describing the appearance of an object, or giving its measurements- Constructing an object from a description (a drawing)Reporting an eventSpeculating about an eventForming and testing a hypothesisPresenting the results of an experiment in tables and diagramsMaking up a story; and reading itPlay actingSinging catchesGuessing riddlesMaking a joke; and telling itSolving a problem in practical arithmeticTranslating from one language into anotherLANGUAGE Asking, thanking, cursing, greeting, and praying-. (Wittgenstein, 1953, Pt. I, No. 23, pp. 11 e-12 e)We dissect nature along lines laid down by our native languages.... The world is presented in a kaleidoscopic flux of impressions which has to be organized by our minds-and this means largely by the linguistic systems in our minds.... No individual is free to describe nature with absolute impartiality but is constrained to certain modes of interpretation even while he thinks himself most free. (Whorf, 1956, pp. 153, 213-214)We dissect nature along the lines laid down by our native languages.The categories and types that we isolate from the world of phenomena we do not find there because they stare every observer in the face; on the contrary, the world is presented in a kaleidoscopic flux of impressions which has to be organized by our minds-and this means largely by the linguistic systems in our minds.... We are thus introduced to a new principle of relativity, which holds that all observers are not led by the same physical evidence to the same picture of the universe, unless their linguistic backgrounds are similar or can in some way be calibrated. (Whorf, 1956, pp. 213-214)9) The Forms of a Person's Thoughts Are Controlled by Unperceived Patterns of His Own LanguageThe forms of a person's thoughts are controlled by inexorable laws of pattern of which he is unconscious. These patterns are the unperceived intricate systematizations of his own language-shown readily enough by a candid comparison and contrast with other languages, especially those of a different linguistic family. (Whorf, 1956, p. 252)It has come to be commonly held that many utterances which look like statements are either not intended at all, or only intended in part, to record or impart straightforward information about the facts.... Many traditional philosophical perplexities have arisen through a mistake-the mistake of taking as straightforward statements of fact utterances which are either (in interesting non-grammatical ways) nonsensical or else intended as something quite different. (Austin, 1962, pp. 2-3)In general, one might define a complex of semantic components connected by logical constants as a concept. The dictionary of a language is then a system of concepts in which a phonological form and certain syntactic and morphological characteristics are assigned to each concept. This system of concepts is structured by several types of relations. It is supplemented, furthermore, by redundancy or implicational rules..., representing general properties of the whole system of concepts.... At least a relevant part of these general rules is not bound to particular languages, but represents presumably universal structures of natural languages. They are not learned, but are rather a part of the human ability to acquire an arbitrary natural language. (Bierwisch, 1970, pp. 171-172)In studying the evolution of mind, we cannot guess to what extent there are physically possible alternatives to, say, transformational generative grammar, for an organism meeting certain other physical conditions characteristic of humans. Conceivably, there are none-or very few-in which case talk about evolution of the language capacity is beside the point. (Chomsky, 1972, p. 98)[It is] truth value rather than syntactic well-formedness that chiefly governs explicit verbal reinforcement by parents-which renders mildly paradoxical the fact that the usual product of such a training schedule is an adult whose speech is highly grammatical but not notably truthful. (R. O. Brown, 1973, p. 330)he conceptual base is responsible for formally representing the concepts underlying an utterance.... A given word in a language may or may not have one or more concepts underlying it.... On the sentential level, the utterances of a given language are encoded within a syntactic structure of that language. The basic construction of the sentential level is the sentence.The next highest level... is the conceptual level. We call the basic construction of this level the conceptualization. A conceptualization consists of concepts and certain relations among those concepts. We can consider that both levels exist at the same point in time and that for any unit on one level, some corresponding realizate exists on the other level. This realizate may be null or extremely complex.... Conceptualizations may relate to other conceptualizations by nesting or other specified relationships. (Schank, 1973, pp. 191-192)The mathematics of multi-dimensional interactive spaces and lattices, the projection of "computer behavior" on to possible models of cerebral functions, the theoretical and mechanical investigation of artificial intelligence, are producing a stream of sophisticated, often suggestive ideas.But it is, I believe, fair to say that nothing put forward until now in either theoretic design or mechanical mimicry comes even remotely in reach of the most rudimentary linguistic realities. (Steiner, 1975, p. 284)The step from the simple tool to the master tool, a tool to make tools (what we would now call a machine tool), seems to me indeed to parallel the final step to human language, which I call reconstitution. It expresses in a practical and social context the same understanding of hierarchy, and shows the same analysis by function as a basis for synthesis. (Bronowski, 1977, pp. 127-128)t is the language donn eґ in which we conduct our lives.... We have no other. And the danger is that formal linguistic models, in their loosely argued analogy with the axiomatic structure of the mathematical sciences, may block perception.... It is quite conceivable that, in language, continuous induction from simple, elemental units to more complex, realistic forms is not justified. The extent and formal "undecidability" of context-and every linguistic particle above the level of the phoneme is context-bound-may make it impossible, except in the most abstract, meta-linguistic sense, to pass from "pro-verbs," "kernals," or "deep deep structures" to actual speech. (Steiner, 1975, pp. 111-113)A higher-level formal language is an abstract machine. (Weizenbaum, 1976, p. 113)Jakobson sees metaphor and metonymy as the characteristic modes of binarily opposed polarities which between them underpin the two-fold process of selection and combination by which linguistic signs are formed.... Thus messages are constructed, as Saussure said, by a combination of a "horizontal" movement, which combines words together, and a "vertical" movement, which selects the particular words from the available inventory or "inner storehouse" of the language. The combinative (or syntagmatic) process manifests itself in contiguity (one word being placed next to another) and its mode is metonymic. The selective (or associative) process manifests itself in similarity (one word or concept being "like" another) and its mode is metaphoric. The "opposition" of metaphor and metonymy therefore may be said to represent in effect the essence of the total opposition between the synchronic mode of language (its immediate, coexistent, "vertical" relationships) and its diachronic mode (its sequential, successive, lineal progressive relationships). (Hawkes, 1977, pp. 77-78)It is striking that the layered structure that man has given to language constantly reappears in his analyses of nature. (Bronowski, 1977, p. 121)First, [an ideal intertheoretic reduction] provides us with a set of rules"correspondence rules" or "bridge laws," as the standard vernacular has it-which effect a mapping of the terms of the old theory (T o) onto a subset of the expressions of the new or reducing theory (T n). These rules guide the application of those selected expressions of T n in the following way: we are free to make singular applications of their correspondencerule doppelgangers in T o....Second, and equally important, a successful reduction ideally has the outcome that, under the term mapping effected by the correspondence rules, the central principles of T o (those of semantic and systematic importance) are mapped onto general sentences of T n that are theorems of Tn. (P. Churchland, 1979, p. 81)If non-linguistic factors must be included in grammar: beliefs, attitudes, etc. [this would] amount to a rejection of the initial idealization of language as an object of study. A priori such a move cannot be ruled out, but it must be empirically motivated. If it proves to be correct, I would conclude that language is a chaos that is not worth studying.... Note that the question is not whether beliefs or attitudes, and so on, play a role in linguistic behavior and linguistic judgments... [but rather] whether distinct cognitive structures can be identified, which interact in the real use of language and linguistic judgments, the grammatical system being one of these. (Chomsky, 1979, pp. 140, 152-153)23) Language Is Inevitably Influenced by Specific Contexts of Human InteractionLanguage cannot be studied in isolation from the investigation of "rationality." It cannot afford to neglect our everyday assumptions concerning the total behavior of a reasonable person.... An integrational linguistics must recognize that human beings inhabit a communicational space which is not neatly compartmentalized into language and nonlanguage.... It renounces in advance the possibility of setting up systems of forms and meanings which will "account for" a central core of linguistic behavior irrespective of the situation and communicational purposes involved. (Harris, 1981, p. 165)By innate [linguistic knowledge], Chomsky simply means "genetically programmed." He does not literally think that children are born with language in their heads ready to be spoken. He merely claims that a "blueprint is there, which is brought into use when the child reaches a certain point in her general development. With the help of this blueprint, she analyzes the language she hears around her more readily than she would if she were totally unprepared for the strange gabbling sounds which emerge from human mouths. (Aitchison, 1987, p. 31)Looking at ourselves from the computer viewpoint, we cannot avoid seeing that natural language is our most important "programming language." This means that a vast portion of our knowledge and activity is, for us, best communicated and understood in our natural language.... One could say that natural language was our first great original artifact and, since, as we increasingly realize, languages are machines, so natural language, with our brains to run it, was our primal invention of the universal computer. One could say this except for the sneaking suspicion that language isn't something we invented but something we became, not something we constructed but something in which we created, and recreated, ourselves. (Leiber, 1991, p. 8)Historical dictionary of quotations in cognitive science > Language
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8 Computers
The brain has been compared to a digital computer because the neuron, like a switch or valve, either does or does not complete a circuit. But at that point the similarity ends. The switch in the digital computer is constant in its effect, and its effect is large in proportion to the total output of the machine. The effect produced by the neuron varies with its recovery from [the] refractory phase and with its metabolic state. The number of neurons involved in any action runs into millions so that the influence of any one is negligible.... Any cell in the system can be dispensed with.... The brain is an analogical machine, not digital. Analysis of the integrative activities will probably have to be in statistical terms. (Lashley, quoted in Beach, Hebb, Morgan & Nissen, 1960, p. 539)It is essential to realize that a computer is not a mere "number cruncher," or supercalculating arithmetic machine, although this is how computers are commonly regarded by people having no familiarity with artificial intelligence. Computers do not crunch numbers; they manipulate symbols.... Digital computers originally developed with mathematical problems in mind, are in fact general purpose symbol manipulating machines....The terms "computer" and "computation" are themselves unfortunate, in view of their misleading arithmetical connotations. The definition of artificial intelligence previously cited-"the study of intelligence as computation"-does not imply that intelligence is really counting. Intelligence may be defined as the ability creatively to manipulate symbols, or process information, given the requirements of the task in hand. (Boden, 1981, pp. 15, 16-17)The task is to get computers to explain things to themselves, to ask questions about their experiences so as to cause those explanations to be forthcoming, and to be creative in coming up with explanations that have not been previously available. (Schank, 1986, p. 19)In What Computers Can't Do, written in 1969 (2nd edition, 1972), the main objection to AI was the impossibility of using rules to select only those facts about the real world that were relevant in a given situation. The "Introduction" to the paperback edition of the book, published by Harper & Row in 1979, pointed out further that no one had the slightest idea how to represent the common sense understanding possessed even by a four-year-old. (Dreyfus & Dreyfus, 1986, p. 102)A popular myth says that the invention of the computer diminishes our sense of ourselves, because it shows that rational thought is not special to human beings, but can be carried on by a mere machine. It is a short stop from there to the conclusion that intelligence is mechanical, which many people find to be an affront to all that is most precious and singular about their humanness.In fact, the computer, early in its career, was not an instrument of the philistines, but a humanizing influence. It helped to revive an idea that had fallen into disrepute: the idea that the mind is real, that it has an inner structure and a complex organization, and can be understood in scientific terms. For some three decades, until the 1940s, American psychology had lain in the grip of the ice age of behaviorism, which was antimental through and through. During these years, extreme behaviorists banished the study of thought from their agenda. Mind and consciousness, thinking, imagining, planning, solving problems, were dismissed as worthless for anything except speculation. Only the external aspects of behavior, the surface manifestations, were grist for the scientist's mill, because only they could be observed and measured....It is one of the surprising gifts of the computer in the history of ideas that it played a part in giving back to psychology what it had lost, which was nothing less than the mind itself. In particular, there was a revival of interest in how the mind represents the world internally to itself, by means of knowledge structures such as ideas, symbols, images, and inner narratives, all of which had been consigned to the realm of mysticism. (Campbell, 1989, p. 10)[Our artifacts] only have meaning because we give it to them; their intentionality, like that of smoke signals and writing, is essentially borrowed, hence derivative. To put it bluntly: computers themselves don't mean anything by their tokens (any more than books do)-they only mean what we say they do. Genuine understanding, on the other hand, is intentional "in its own right" and not derivatively from something else. (Haugeland, 1981a, pp. 32-33)he debate over the possibility of computer thought will never be won or lost; it will simply cease to be of interest, like the previous debate over man as a clockwork mechanism. (Bolter, 1984, p. 190)t takes us a long time to emotionally digest a new idea. The computer is too big a step, and too recently made, for us to quickly recover our balance and gauge its potential. It's an enormous accelerator, perhaps the greatest one since the plow, twelve thousand years ago. As an intelligence amplifier, it speeds up everything-including itself-and it continually improves because its heart is information or, more plainly, ideas. We can no more calculate its consequences than Babbage could have foreseen antibiotics, the Pill, or space stations.Further, the effects of those ideas are rapidly compounding, because a computer design is itself just a set of ideas. As we get better at manipulating ideas by building ever better computers, we get better at building even better computers-it's an ever-escalating upward spiral. The early nineteenth century, when the computer's story began, is already so far back that it may as well be the Stone Age. (Rawlins, 1997, p. 19)According to weak AI, the principle value of the computer in the study of the mind is that it gives us a very powerful tool. For example, it enables us to formulate and test hypotheses in a more rigorous and precise fashion than before. But according to strong AI the computer is not merely a tool in the study of the mind; rather the appropriately programmed computer really is a mind in the sense that computers given the right programs can be literally said to understand and have other cognitive states. And according to strong AI, because the programmed computer has cognitive states, the programs are not mere tools that enable us to test psychological explanations; rather, the programs are themselves the explanations. (Searle, 1981b, p. 353)What makes people smarter than machines? They certainly are not quicker or more precise. Yet people are far better at perceiving objects in natural scenes and noting their relations, at understanding language and retrieving contextually appropriate information from memory, at making plans and carrying out contextually appropriate actions, and at a wide range of other natural cognitive tasks. People are also far better at learning to do these things more accurately and fluently through processing experience.What is the basis for these differences? One answer, perhaps the classic one we might expect from artificial intelligence, is "software." If we only had the right computer program, the argument goes, we might be able to capture the fluidity and adaptability of human information processing. Certainly this answer is partially correct. There have been great breakthroughs in our understanding of cognition as a result of the development of expressive high-level computer languages and powerful algorithms. However, we do not think that software is the whole story.In our view, people are smarter than today's computers because the brain employs a basic computational architecture that is more suited to deal with a central aspect of the natural information processing tasks that people are so good at.... hese tasks generally require the simultaneous consideration of many pieces of information or constraints. Each constraint may be imperfectly specified and ambiguous, yet each can play a potentially decisive role in determining the outcome of processing. (McClelland, Rumelhart & Hinton, 1986, pp. 3-4)Historical dictionary of quotations in cognitive science > Computers
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9 solution
1) раствор2) растворение3) мат. решение- completely unstable solution - neutrally stable solution - particular solution - pure strategy solution - solution of equation - uniformly stable solutionsolution by inspection — решение подбором, решение проверкой
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