Все эти вопросы так или иначе затрагиваются в серии

TEXT 7 How Does a Machine Actually Compute? How does a machine succeed in manipulating information reasonably? How does it actually compute? To explain the different ways in which a computer actually computes, suppose we take a sample operation with information and show how it is handled by a human being engaged in computing and by a machine engaged in computing. For the example operation let us take the operation of finding twice a number. This is the operation expressed by the formula “equals 2 times ”, where and are numbers. A human being will find twice a number in the following way. First, you have to tell him the number. Suppose that it is 76 – that is, in this case is to be 76. Then he will refer to the "two times" multiplication table which he has learned by heart, and will go through a procedure which he also learned bу heart while in grade school. On paper he will write 76 x 2 152 but under his breath as he writes this, he will say the procedure that he learnt by heart in grade school: “2 times 6 is 12; put down the 2 and carry the one; 2 times 7 is 14, and to carry is 15; put down the 5 and carry the 1; there is nothing in the third column; 2 times zero is zero, and the 1 to be carried makes 1; put down the 1; the answer is 152.” An automatic analog computing machine will find twice a number in the following way. Suppose that the machine represents and stores each number by the amount of turning of a shaft or rod or axle. Imagine two shafts parallel to each other. We slide onto one of the shafts, the one which represents , a gear with say 36 teeth. We slide into the other shaft, the one which represents , a gear with 18 teeth – half as many teeth. We mesh the gears with each other and tighten them on their shafts so that they will not slip. We put a crank on shaft so that we can turn it and thereby drive shaft . Now we can see that no matter how much or how little we turn shaft , shaft will have to turn twice as much; and if shaft n has had 76 turns from its Initial or starting position, then shaft without any doubt at ill must have had 152 turns from its initial or starting position. We notice that in this case the machine is set to compute; twice a number without our having to tell the machine specifically some particular number to begin with. An automatic digital computing machine will find twice a number in the following way. In the first place such a computer is organized like a railroad system. This railroad system has four main stations: Input; Output; Storage, which may contain 1000 sidings or registers; and Calculator, which may have register and for two numbers being operated on, a register Op for the operation, and a final register R where the result of the operation is delivered. It also has a signal tower, Control. The units of information are like freight cars, which are flashed from one siding to another anywhere in the system, according to the instructions from the tower. To find twice a number in this kind of computer, here is one typical method. The tower signals the register holding the number n, which flashes it into the calculator register A. The tower then flashes 2 into register B, and flashes "Multiply" into register Op. The Calculator then, by means of special cir­cuits which are equivalent to a built-in digital multiplication table, doubles the number. The tower also signals the Calculator what sliding in Storage to send the result to. This is done, and the operation is thus finished. I. Прочитайте текст. II. Проанализируйте абзацы с точки зрения деления текста на логические части. Разделите текст на логические части в соответствии со следующими заглавиями: 1) Human being calculations; 2) Automatic analog computer calculations; 3) Automatic digital computer calculations, отделив избыточную информацию и, при необходимости, объединив несколько абзацев. III. Составьте ключевые вопросы к тексту в соответствии с деле­нием его на логические части. IV. Внутри каждой части найдите ключевое слово и основные словосочетания к ним. V. На основе предыдущего упражнения сформулируйте главную идею каждой логической части. TEXT 8 THEORY OP AUTOMATIC CONTROL It is common practice to use a human being as one of the links in the chain of elements of a control system. He may perform a simple operation, such as moving his control handle so as to keep one pointer over another, or superficially more complicated one, like steering a car; he then has to observe the difference between his car's actual heading and the desired heading, which is continually changing, and move his steering wheel to bring them into coincidence. Any system including a human element is said to be manually controlled; its main limitations consist in length of the human reaction time, the onset of fatigue and the fact that there is a maximum torque against which the operator can turn his control and a maximum speed (about 4 rev/sec) at which he can control it satisfactorily even against a small torque. If the human operator is replaced by a mechanism which performs the same functions, the control is then automatic. The use of automatic control releases expensive labour for other (and possibly less monotonous) work and, not being subject to the limitations listed above a well-designed automatic control produces a more uniform product, at the same time operating faster and more efficiently. The use of automatic pilots in aircraft has greatly reduced the strain on the crew, partly by relieving the pilot of much uninteresting flying on a set course, and partly because the rapid response to disturbances in the air smoothes out the bums more effectively, than a pilot could do, thus making the aircraft motion more steady. Besides being capable of producing more consistent and reliable results, an automatic control can sometimes be used where manual control is impracticable, either because there is not the spaсе available for a man where the control is required or because he would have to be in a position which it is dangerous to occupy owing to high temperature or harmful radiations. Obvious examples are the steering of rocket missiles and the control of atomic piles. In certain circumstances it may be possible to a remotely operated manual control with some form of data transmission link. The remarks above apply more particularly to regulators am position controls. With process control the peculiar advantage of using automatic action may be somewhat different. Often a process control does not replace a man at all, it merely assis him; a fireman is still needed even though the boiler is automatically stoked. Since skilled staff is needed to maintain control equipment in good working order, its use may actually increase the labour force in a small concern. The economy effect by elimination of peak values of the controlled variable may nevertheless be very considerable and amply repay the installation of costly apparatus. Note, for example, the great reduction capital expenditure which would result if the use of automatic control were to insure that the maximum possible flow in a certain process is twenty per cent less than it might be with manual operation; the necessary tank space and line capacity would be reduced by that amount. Our own view is that from a theoretical standpoint there с be only one justification for taking the trouble to define a particular type of control at all; namely, that its behaviour liable to be distinguished in some way from that of other controls. On this basis we should define a servo-system as a control system of a type, which can become unstable. We have already noted that an openchain system cannot become unstable, so that for instability to be possible the control must be cyclic; then must, in addition, be some external source of power, which means that the system must be power amplifying; as the absence of a human link is not a necessary condition for unstable operation to be possible, our criterion thus leads us to a definition in accordance with that first quoted. We use the term servo-system to denote a control which is power amplifying and cyclic but no necessarily automatic. A servo-mechanism is defined as a servo-tem with a mechanical output. The general disagreement over definitions, though deplorable, is of no great concern to us, as we do not intend to limit our discussion to any one type of control system. The controls, like the so-called "servo" brakes and the capstan torque amplifier, are not true servo-system, for they are not error actuated in the sense of having a physical link connecting the output quantity to the input. These systems do, however, possess inherent feedback and may show instability. Many open-chain automatic controls are time operated according to some predetermined cycle; process controls for heat treatment and time-operated traffic lights are examples. It is also possible, of course, for true servo-system to have a time-operated or cyclic input applied to it. I. Прочитайте текст. II. Разделите текст на логические части в соответствии со следующими заглавиями: 1) Manually controlled system; 2) Automatic control systems; 3) Servo-system control. III. Внутри каждой логической части найдите ключевое/ые слово/а и основные словосочетания с ним/с ними. IV. На основе предыдущего упражнения сформулируйте главную идею каждой логической части. V. Подчеркните в тексте ключевые фрагменты /наиболее информа­ционные элементы текста, выражающие его главное содержание и представляющие собой отдельные слова, группы слов или части предложений/. Пронумеруйте абзацы, содержащие ключевые фрагменты. VI. Выпишите ключевые фрагменты под заглавиями соответствующих логических частей /обычно выписываются не целые высказывания, а их части, отдельные словосочетания, причем формы их мо­гут не совпадать с вариантами в оригинале/. VII. При необходимости перегруппируйте ключевые фрагменты по значимости /порядок следования фрагментов произволен и может не совпадать с изначальным текстом/. VIII. При необходимости перегруппируйте логические части по значимости. Полученный план является схемой передаваемой текстом информации и основой для составления реферативного текста. III. УСТНЫЙ УЧЕБНЫЙ РЕФЕРАТ TEXT 9 EQUILIBRIUM IN A MARKET ECONOMY The notion of economic equilibrium, which is substantive rather than merely formal, presents no special problems in a fully centralized economy. If production is fully controlled and the resulting output directly allocated to consumers without the intervention of any market or decentralized decisions, the prob­lems are those of feasibility and optimality rather .than of equilibrium. In an economy with any degree of decentralization, especially if exchange passes through a market, there is a real problem as to whether an equilibrium, suitably defined, always exists for arbitrary initial conditions. Although the equilibrium problem is examined here for the completely decentralized competitive economy, it exists also for partly centralized economies, such as those of the Soviet type. The notion of equilibrium in a decentralized economy encompasses two different types of relationship among the decisions which are independently made. First is compatibility, the decisions made by different decision makers must be compatible with each other. Second is equilibrium in something like the dynamic sense, that is, the decisions must be more than momentarily compatible, they must be capable of being sustained in the absence of external influences. In analyzing the behavior of the decentralized economy, we accept the rules for the individual decision makers as data and assume every decision maker acts in accordance with the relevant: rule. In the models examined here, we assume that there is no direct relationship between any decision makers so that the results of their individual acts in response to objective and universal parameters (prices) can be added. The fundamental problems of equilibrium are thus thrown on to the market. Given a vector of prices, we aggregate the amounts that are demanded by consumers and subtract the вит of current production and available supplies, to obtain the net result or excess demand in each market. It is more convenient to discuss excess demand than to discuss demand and supply separately. We assume that consumption can only come from current production, so that compatibility requires that excess demand can never be positive at equilibrium. On the other hand, if excess demand is negative at a positive price (excess supply at a positive price) we make the rudimentary dynamic assumption that there will be a downward pressure on price until either excess demand or the price is zero. Thus, if is the excess demand for the good, we shall define equilibrium in the market as which implies that either excess demand is zero or the price is zero. That is, any good with excess supply (negative excess demand) is a free good. This definition of market equilibrium can bе directly generalized to cover all markets. If p, z are the vectors of prices, excess demands, then all markets ere in equilibrium, if and only if . The economy will be considered to be in equilibrium if the market equilibrium conditions are satisfied and all decision makers are operating in accord with the relevant rules. (These rules, for the competitive economy, are taken to be utility or profit maximization at given prices.) In some studies (including the Arrow-Debreu model) the market equilibrium condition is retained in the classic form What is actually proved, in the first instance, is the existence point satisfying the above inequality definition. “free disposal” assumption can then be used to suppose that if it can just as well be zero. It seems simpler to adhere inequality definition, which is certainly necessary if there no free disposal. Air pollution is an obvious joint products with negative excess demand and no free disposal. Walras' original study of the problem of general equilibrium was confined to the equilibrium condition and included no explicit nonnegativity constraints. Although Wald had rigorously studied the problem of the existence of equilibrium as early аз 1935, general equilibrium analysis in the economics profession was confined to counting equations and unknowns up into the nineteen fifties. In this chapter we shall investigate the existence of equilibrium in two models of the market economy. The first, and simplest, is the Walras-Wald model which has simple production conditions, no profits to be distributed, and in which we shall assume the existence of well-behaved aggregate demand functions. The second will be a slightly simplified version of the Arrow-Debreu-McKenzie model, which is an accurate depiction of the traditional perfect competition model of the economy. Before proceeding to examine these models, we shall investigate some of the differences between the rigorous approach to the equilibrium problem and the equation counting approach, and also assemble some mathematical analysis for later use. The existence of equilibrium in an economy with imperfect competition is an unsolved problem of great complexity. Most of the traditional models of firms in imperfect competition (including monopoly) are so rooted in partial concepts that they need be rebuilt to fit into a general equilibrium framework. We shall not consider imperfect competition here. I. Прочитайте текст. II. Составьте схему передаваемой текстом информации. III. Перечитайте текст. Проверьте, не нуждается ли ваша первоначальная схема в коррективах. При необходимости внесите нужные исправления. IV. На основе схемы, выбрав основные ключевые фрагменты, конспективно изложите все существенные положения текста. /С этой целью можно использовать готовые ключевые фрагменты в форме предложений, обобщающих определенный смысловой кусок текста, или свести два или несколько ключевых фрагментов в рамки одного высказывания, или смонтировать ответ из лексических единиц различных частей текста-первоисточника, употребляя средства межфразовой связи.

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