D alembert progression forex factory
// Опубликовано: 15.09.2021 автор: Shalkree
I've heard of the other progression algorithms in the EA but never had a Oscar's Grind (and also Martingale, d'Alembert, Labouchere. I use "progression" setting #1 (d'Alembert) which progresses 1,2,3,4 etc. I plan on experimenting with the different "grid progressions" now. Dans progression runs a (random) entry failure probability of (assuming Dan runs it on Euro/USD). Has a D'Alembert progression been considered? AUTOMATED FOREX TRADING SINGAPORE DBS Logging tool that schedule mails to uninstall, the more action should be. After creating a your connection to query group contains. As mentioned above, get added to seminars and salons.
The origins of silk are hard to trace, shrouded in millennia of mythology and legend. Like all natural fibres silk biodegrades, leaving little of itself behind. But it shimmers throughout history, and these brief flashes have allowed historians to piece together its long and colourful life as a man-made fabric.
Court Ladies Preparing Newly Woven Silk, a Chinese silk painting by Emperor Huizong of Song, early 12th century left ; Chinese painting on silk, with playing children wearing silk clothes, by Su Hanchen active s—s , Song dynasty right. Silk production is said to have begun in China, when Xiling, the wife of the Yellow Emperor a deity in Chinese religion was drinking a cup of tea under a mulberry tree when a cocoon fell into her cup.
Fishing it out, she discovered that the cocoon unravelled into a long strand of pearlescent silk. Though this origin story is likely more myth than fact, the evidence of a silk industry in China dates back thousands of years. Though the ancient fabrics themselves have, for the most part, long since disintegrated, evidence of their presence has been made visible in tiny scraps of fabric and tools of the trade needles and looms found on Neolithic sites, as well as cultural artefacts such as a basin decorated with silkworms dating back to BC.
The process of harvesting silk is not unlike the story of Xiling on a much larger scale. The silkworm, a species of caterpillar, survives on the leaves of the mulberry tree. Not unlike a spider weaving a web, the liquid silk is spun into a long strand, creating a continuous thread up to a thousand metres long, and half the width of a human hair.
In the natural lifecycle of the silkworm, the caterpillar, now transformed into a moth, would eat its way out of this cosy cocoon. In order to harvest the silk undamaged, however, the cocoons are boiled, killing the silkworms inside.
The fibre is then harvested, dyed, and woven into cloth. The process of farming and harvesting silk in this manner is known as sericulture. The production of silk in China from at least BC onwards largely fell to women, who were expected to stay home and weave. The process of silk production left to right, top to bottom : 1 The silkworms and mulberry leaves are placed on trays; 2 Twig frames for the silkworms are prepared; 3 The cocoons are weighed; 4 The cocoons are soaked and the silk is wound on spools; 5 The silk is woven using a loom.
Over the centuries, the silk industry became ever more elaborate. Bright and rare dyes were treasured by emperors, and symbols embroidered into the garments made them even more precious; woven damask patterns had special meanings or denoted specific regions. This level of high demand necessitated innovation in the system; efficient ways of silkworm farming were developed to meet specific quotas, and specialised looms were invented.
This is important because just as silk became part of the Chinese economy, traded and exchanged like coins for goods, it would soon also become part of a much larger global economy. Though often referred to in the singular, the silk roads were actually a constantly shifting patchwork of trade routes that ran through Asia, the Middle East, and the Mediterranean. These trade networks not only spread goods among them, silk , but news, disease, and culture.
Of course trade routes had existed before, over time more formal methods of trade were developed including lines of credit, as well as enterprising merchants and couriers willing to risk their lives to cross hostile landscapes not only because of dangerous temperatures and difficult terrain, but pilfering thieves and ruthless bandits, too. Along these roads cities sprang up, pools of wealth in which all manner of culture and religions rubbed shoulders; this intermingling can still be seen in some places where the architecture reflects this many-threaded history, and in stories and parables which remind us of this mixing together of things.
Although Buddhism was born in India, it became one of the major religions in China, and the wrapping of sacred scripture in silk became customary. This practice trickled through the silk roads where it became adopted in Christianity, too. Gradually, however, the war industries became more rapacious, and supplies of resources, labour as well as materials, dwindled.
It became necessary to give more positive thought to the position of the civilian consumer, for it was essential to keep up morale. O n e form of action adopted to deal with this situation was rationing. T h e primary purpose of this was to ensure fair distribution. In itself, however, it led to further difficulties, for rations had to be honoured. Furthermore, some rationing schemes—e. This meant that the Board of Trade had to 1.
Civil Industry and Trade, by E. Hargreaves and M. Gowing, H. Stationery Office, London, It is impossible here to pursue the ramifications of these intricate and fascinating problems. They m a y , however, be s u m m e d up by saying that the Board of Trade was faced with a problem of striking the best balance between consumption of scarce resources on the one side and the deterioration of morale on the other. This is just the type of prob- lem where operational research could have been invaluable if the need had been clearly seen in time.
In the event, progress was m a d e mainly by trial and error. O n the production side, it is particularly surprising that little attempt seems to have been m a d e to estimate the effects of the policies adopted on productivity, especially on the productivity of labour which was latterly one of the scarcest resources.
O n the consumption side, estimation of real demand was of the greatest importance, for once there was an apparent slight shortage. Later a special consumer needs depart- ment was set up with distribution officers to watch the flow of retail trade. These achieved some success in smoothing the flow, particularly between one area or town and another, but this work was essentially a patching process, not a scientific study. In former times, one of the reasons for lack of data on which to base the decisions was the lack of the techniques to m a k e the collection of such data practical.
The two alternatives were either to conduct a complete census, which is a big undertaking when whole countries are concerned, or to rely on a small sample. The latter was relatively inexpensive, but until a proper theory of sampling had been worked out it was liable to be hopelessly inaccurate.
O n e of the most important advances of statistics in recent years has been the development of a precise theory for planning sample surveys in such a way , that, not only can the sample be relied upon to be representative of the whole population, but the probable limits of error, i. Sample surveys are n o w widely and confidently used in m a n y types of factual investigation, and are far from being regarded as cheaper but less accurate substitutes for complete censuses.
Sample surveys, on the other hand, require relatively little of such routine work and can be carried out by trained workers with great care, so that the accuracy of the data recorded m a y be far greater than in a complete census. Provided the survey is properly planned, it m a y be not only cheaper but more accurate than a complete census. This is n o w so well recognized a m o n g survey workers that w h e n the last population census was carried out in the United States, the Bureau of the Census organized a simultaneous sample survey to check the accuracy of the complete census.
Similar action was taken by the Social Survey in the United Kingdom, in preparation for a recent census of distribution. At the request of the government, it m a d e experiments with sample interviewing techniques for collecting census data in one area of the country while at the same time trial studies, using conventional methods of postal distribution and collection, were carried out by the Board of Trade in other areas.
It was possible to measure the comparative costs and relative efficiency of the two methods, and so to decide in which manner the census of distribution should be organized. The days of the full census m a y well be numbered. Studies m a d e in this way to determine the most efficient type of survey or census for any particular purpose can be classed as operational research in their o w n right.
T h e routine use of well-tried survey techniques is not itself operational research, but provides an invaluable tool for it. Surveys have provided a basis for operational research to guide many governmental policy decisions during and since the war. O n e of the major surveys, started during the war and continued after it, was carried out for the Ministry of Food to ascertain the food consumption habits of the population. Another example of similar research was a survey carried out since the war to determine what would be the demand for coal if it were taken off the ration; it resulted in the rationing scheme being retained.
O n the other hand, in sweet rationing was abandoned under political pressure without proper research into the position, and it soon had to be re-introduced. There are innumerable openings for operational research in connexion with other government activities not related to shortages and rationing.
T h e operation of health services is a good example since it probably provides as , m a n y opportunities for research as does any other social activity. Such research might be undertaken on a comparatively narrow front. For example, the work on appointment systems, to which reference has already been m a d e , falls within the jurisdiction of each individual hospital management, although it would gain generality from being based upon observations at a number of hospitals.
These broader issues m a y not fall within the competence of any one executive in countries where the health service is not organized on national lines; even so, they are problems which no government can afford to ignore. W h e n the national health service was started in Britain in it obviously constituted a major social change.
It provided an ideal situation for the application of operational research in order to determine the probable effect of. Apparently, however, little was done along these lines and this failure can be regarded as one cause of the difficulties in which the n e w service found itself in its early days. A n interesting example of the need and value of such follow-up studies in connexion with governmental activity is seen in a study of medicine murders in Basutoland.
After the war an anthropologist was commissioned to do so, and he showed h o w some of the changes introduced had in fact aggravated the situation by increasing the number of lesser chiefs, instead of reducing them as was required. M o r e - over, it was shown that arrangements intended to reduce the imposition of unpaid tasks on the average African appeared as a higher tax demand.
T h e fact that the reforms had been introduced from the top d o w n caused them to be misunderstood. Thus they had in fact contributed to the feeling of insecurity which found its expression in the desire for medicines m a d e with h u m a n flesh to give the possessor a better chance to improve or maintain his position in the hierarchy. The results of the government actions had, therefore, been the opposite of what had been intended. Basutoland Medicine Murders, by G.
Jones, H. Stationery Office, C m d. T h e experience of any one m a n , or small group of m e n , is narrowly based and therefore increasingly inadequate for elucidating the underlying rules which govern the functioning of the organization; further- more, judgments based upon such experience tend to be biased in the selection of the data which arise within it. Operational research is designed to aid the experience of a single person by adding to it the wider experience of all our yesterdays.
The data obtained from every source are treated objectively to ensure that due account is taken of all; it is not, on the other hand, always possible to ensure that all relevant data have been obtained, although obvious deficiencies m a y be m a d e good by experiment. Scientific methods, drawn from a wide variety of disciplines, are used to analyse the data and determine what rule or code appears most satisfactorily to explain the past behaviour of the system.
Finally, that rule, derived from the past, is used to predict the probable outcome of future actions. This study has been concerned to show the uses of operational research in social, rather than purely technical or industrial affairs, although the two are in m a n y ways inseparable. It has not been concerned with rigid definitions of operational research, and it m a y be objected that some of the examples given fall within the ambit of other social sciences—such as sociology, anthropology, or economics.
It is contended that, just as in the so-called exact sciences a piecemeal approach is becoming less and less sufficient, so society has an essential oneness. Operational research is not sociology; it is not anthropology; it is not economics; but it does provide methods of research in problems which are c o m m o n to them all, and it brings them and other sciences together, not in academic detachment, but with the practical objective of helping the executive, at grips with live operational problems, to m a k e the best possible decisions.
Morse and George E. Journal of the Operations Research Society of America. John B. During the war he led a group of engineers which played a substantial part in the rapid development of auto- matic control for naval guns, radar, and tank turrets. A n y one such quantity depends on or is influenced by other quantities, and economists- have to consider the complete "system" of all such interacting quantities. Such systems representing more or less closely an actual economic system: are often referred to as "economic models".
T h e chief purpose of the article is to call attention to the close analogy that exists between such economic systems or "models" and certain physical systems, such as automatic regulators and controllers, that depend on the principle of feed-back.
Progress, in the development of engineering control systems and in the analysis of their behaviour has recently been rapid. It is therefore worth while to enquire whether any of this progress in analysis can be transferred to economics, and so contribute to the solution of the problems of economic stabilization and prediction.
Apart from methods of theoretical analysis, the analogy between economic models and physical control systems suggests a further possibility. Where , as is found in practice, the complexity of the economic system is such that its behaviour cannot be calculated, this l behaviour might nevertheless be determined by constructing an analogous physical system, the behaviour of which could be observed and recorded.
T o combine ideas drawn from engineering, economics and mathematics, each of which has its specialized terminology, and to present the results so that they m a y be understood by readers w h o are not specialists in any of these fields, is not an easy task. But it is useful, or at least stimulating, if specialists sometimes look over the fences that separate their gardens. It is of some importance that developments in economics should be understood T o this end the precision of specialized nomenclature m a y sometimes have to be sacrificed in the interests of ease of assimilation, and the writer must ask specialists w h o m a y read this article to be tolerant on that account.
The mathematical and technical aspects of the topics discussed have been more fully and precisely developed in a book that is to be published at an early date. There is a long record of under- employment of labour and capital, periodic slumps, windfall fortunes and undeserved bankruptcies.
It is n o w generally recognized that such a state of affairs must not be allowed to continue. Governments have assumed responsi- bility for the maintenance of a high and stable level of employment. If permanent full employment can be ensured independently of the special conditions of war, post-war reconstruction and armament programmes, then the social outlook will be radically different in future. It must indeed be admitted that neither business m e n , trade unions, nor government departments yet take the maintenance of a permanently high and stable level of employ- ment as axiomatic.
Nor indeed do the graphs of post-war fluctuations give m u c h objective evidence that it has yet been securely attained. The promise of a better future which economic stability holds out, as well as the possibility of bringing to a peaceful natural end one basic assumption underlying the cold war, seem to be vast issues to hang on the solution of a technical problem.
A final and unambiguous clarification of the precise mechanisms of economic fluctuations, which would carry with it the ability to predict and to regulate, does seem to have this significance. W h a t , however, is the present state of progress towards such clarification? It was primarily the labours of J.
Keynes, and the publication in of his General Theory of Employment, Interest and Money2 that set alight the controversy from which a n e w economic outlook has emerged. Whether 1. H e jerked economics out of a rut and set it moving again towards understanding economic mechanisms and the possibility of adequately regulating our economic life. It is riot apparent however that the progress m a d e quite justifies the claim that stability is n o w permanently ensured, even in the sense of technical " k n o w - h o w " , quite apart from political "want-to".
It is of immense im- portance that the full technical possibility should be achieved without delay, and that this possibility, together with the political determination to use it, should become accepted as no longer open to question. This can c o m e about only by a rapid reinforcement of economic research and statistical investigation of the right kind. There must also be some effort to m a k e intelligible, to wider circles than professional economists, the true causes of the defective working of the economic systems of the past, and to m a k e clear the nature, necessity and extent of the measures necessary to ensure stability and the full use of resources in future.
Such problems arise in particular in the design of auto- matic control and regulating apparatus of all kinds. It is c o m m o n knowledge that during the last decade or so the technical achievements in this field have been spectacular, including such developments as the feed-back amplifier on which radio and television depend , the automatic pilot, the guided missile, the radar tracker, the automatic gun layer, the automatic control of complete chemical plants, and scores of other developments.
T h e basis of this technical achievement has been progress in the theory of the stability of systems. T h e analysis was first adequately developed in connexion with the use of feed-back in radio amplifiers, and was soon applied generally to a wide class of regulating devices.
In this article con- sideration will first be given to some of the simple concepts and conclusions of "system theory" in general, and this will be followed by a more specific discussion of economic problems and their physical analogues. Characteristic types of variation of populations are observed and it m a y be desired to control them. Such patterns of variation occur as the recurrent "explosive" growth of swarms of locusts, or the well-known fur cycle of Canada, where the supply of fur-bearing animals regularly oscillates between abundance and scarcity every nine years.
E v e n the fluctuations of temperature of a fever-patient, which used to be regarded as the classical case of irregularity, are not random. They reflect the complicated interdependence of populations of bacteria with the body's defensive reactions. This problem Fig. Method of representing a scheme of interdependence by a dia- gram. In one sense the explanation of, say, a decline in the population of lynx in Labrador, is almost infinitely complex, and involves the accidents of each animal's life.
However , the biologist is quite happy to m a k e use of an "apparatus of description" of a m u c h simpler kind; he takes the numbers of each species of animal, together with a few other quantities, such as s o m e measures of the abundance of various vegetable food sources. Then, from his detailed biological observations and studies, he considers h o w the population of one species affects that of another, and h o w the quantities of foods affect and are affected by the numbers of the animal populations.
It is convenient to represent any such situation by a scheme of dependence. The circles marked C h , Q 2 , etc. A n arrow is drawn to show where any one quantity affects any other quantity. Along- side the arrow m a y be written some symbol or formula expressing the effect of one quantity on another, according to the scheme of analysis to be adopted.
S o m e of these dependences m a y be k n o w n , some are obvious in nature but uncertain in amount or intensity, some m a y be unknown, except to the extent of justifying an arrow to assert "there probably is some effect". W h a t could the biologist infer from such a scheme of interdependence? O f course, if the causal relations were k n o w n , exact and complete, he could hope to calculate, from a given initial state or from the recent past, the whole future development of the system.
But such biological systems are very complicated and the implications of the scheme of dependence m a y be difficult to determine. Also, as already noted, the relations or dependences between aggregates are never exact and completely determinate. They can only represent effects as they hold in general and on the average.
There are extra variations due to hazards, which, because they are omitted from the causal scheme under consideration, and because their actual origins are multiple, m a y be regarded as random disturbances of an otherwise deter- minate system. But if the assumed dependences of one quantity on another correctly represent the average effect, then the characteristic behaviour of the system deduced from these relationships will be meaningful, and will - K , L per unit time Fig.
If the numbers of individuals in the aggregates are large, the results of the random causes of variation m a y be relatively quite small. Further, it is possible, given the "law-abiding" de- pendences, to analyse with precision the general nature of the effects of the remaining randomness.
T o illustrate one important distinction in such systems, consider the very simple partial scheme of dependence isolated in Fig. This shows only two animal populations, or groups of aggregates of populations, namely certain predators and their prey, or say, for illustration, lynx and rabbits, where the rabbits are the main food of the lynx, as is the case in some areas in Canada.
W h a t is to be considered is the variations of these populations, measured as departures from balance or equilibrium. T h e facts to be represented are that, when there are more lynx, there will be a correspondingly greater rate of decrease of the rabbits, but when there are fewer rabbits there will be a tendency for the number of lynx to decrease, because of the shortage of food. If the dependences were slightly different from these ideally simple ones, the oscillation, instead of being precisely self-maintaining, would be such that each of the successive swings was either somewhat smaller or somewhat larger than the preceding swing.
In the first case the oscillation would die away and ultimately disappear. Such systems are referred to as "damped" or "stable". The second case, that of continuously increasing oscillation, is referred to as cumulative oscillation, and such systems are said to be unstable. A n y initial oscillation of an unstable system, however small, must increase to a large oscillation, so large in fact that ultimately some additional checks are brought into play that limit its amplitude.
This elementary hypothetical system of two populations calls attention to an important concept in the understanding of the behaviour of systems. In the scheme of dependence, Fig. In other words, the relationship between the quantities is not a simple dependence of one on the other, but of interdependence between the two; each is both cause and effect. T h e closed sequence or loop is referred to as a "feed-back loop"; in it the quantities are interdependent.
A m u c h older term, due to the philosopher Hegel, which meant m u c h the same, was that the relationship between the quantities was "dialectical", i. If, in a realistic representation of a situation, such as the problem of animal populations, a principal part is played by a closed loop such as that of Fig. In other cases this behaviour m a y be considerably modified.
It is not generally permissible, in analyzing the behaviour, to consider each loop separately. T h e surprising regularity of such cycles m a y well be due to the precise "turning points" being determined by the seasons, i. A feed-back m a y be negative or positive, that is, the effect fed back m a y be such that it tends respectively either to decrease or to increase the.
In non-technical language this simply means that analysis is easy w h e n effects are all pro- portional to their causes. In such systems only two kinds of self-exciting change are possible. T h e quantities m a y either oscillate with a constantly increasing range of oscillation, or they m a y change unidirectionally at a constantly increasing rate. If the time-relationships are such that neither of these types of behaviour occur, one m a y take it that the system is The marginal -case is theoretically possible but is almost infinitely unlikely.
Even if such disturbances are random a good deal can be said about their effects. But effects are not always proportional to causes. In fact almost no effects are proportional to their causes for all magnitudes of change.
Similarly, in the direction of increase, an upper limit would c o m e into play on account of limitations of food supply or epidemic diseases. Feed-back used to control the output from a valve amplifier so that it must vary in the s a m e w a y as the input varies.
Amplifier Output Ke. These limit the range of oscillation. The behaviour m a y then settle d o w n to an oscillation of constant range or amplitude, quite regular in period, but n o longer quite smooth or "sinusoidal". Such limited oscillation is referred to as a "limit cycle". Its general nature can sometimes be inferred from consideration of approximately equivalent linear systems, but this is liable to result in error. Consider the audio stages of a radio receiver. T h e electrical signal re- presenting the sound-waves, which is the "input" to this stage, is a small rapidly varying voltage, shown as ei in Fig.
T h e requirement is to amplify this voltage to a proportional output voltage e0, m a n y times greater but varying in the same way , to operate the loud-speaker. N o w amplifiers m a y be built that give enormous amplifications, but not with strict proportionality. It is required to control or regulate the output voltage e0 so that in spite of this lack of proportionality it is always K e!
T h e device by which this is done is to m a k e the amplification of the amplifier very m u c h greater than the value K finally required, and then, as shown in Fig. K and balance it against the input ei. If the requirement is not achieved, i. A simple single- feed-back loop representing, the principal relationships in- any self-sustaining oscillation.
There are two ways in which the implications of such relationships m a y be determined. The first is to proceed step by step to see what happens in successive small time intervals. If the course of Y over some past time is already known, it is quite easy, though rather laborious, to calculate the value of Y for the next short period, since this is m a d e up of all the- contributions arising from past values of the rate of change of Y , delayed by the various times.
The second method is the rather more sophisticated one of the mathe- matician, w h o enquires what type of curve, represented by what formula,, satisfies these conditions. B y either approach the result is found that, if the feed-back is sufficient in magnitude, a scheme of dependence of this kind must result in an oscil- lation of constantly increasing amplitude. T o demonstrate this, a calculation has been made , using the time-spread function shown in Fig.
The resulting history of incomes Y is. The result is a progressively increasing oscillation which would continue indefinitely, except for the fact that checks are inevitably encountered w h e n it becomes suf- ficiently large. In Fig. Firstly it has been assumed that the total upward fluctuation of incomes cannot increase beyond a definite limit, on account, for example, of "full employment" being reached.
A s a lower limit it has been assumed that the rate of decisions to invest cannot be reduced beyond zero. It will be seen that the oscillation n o w settles d o w n to a regular "limit cycle" of constant amplitude. Results of a calculation of behaviour of a very simple model of the kind shown by Fig. There is no obstacle in principle to constructing physical systems that correspond, in their structure of interdependences, with the kind of economic model that economists wishi to investigate, including the correct representation of the non-linear relation- ships, but with a time scale such that minutes or seconds represent years.
If such a physical analogue were available, provided with appropriate means, for varying the inter-relationships in a systematic w a y and recording the behaviour by curves drawn on a chart, it would be possible by systematic trial to solve the problem of adjustment of the scheme to correspond best with the economic record of a recent past. The analogue, when so adjusted and fed with quantities simulating any actual or anticipated dis- turbances, would then immediately give the required extrapolation into future time, by merely allowing its operation to continue.
There are m a n y types of physical analogue, depending, a m o n g other things, on the kind of physical quantity selected, e. There are also important differences in fundamental type. O n e such important distinction lies in the extent of the provision m a d e for controlling the passage of "time" in the simulator.
The most commonly employed analogue or simulator uses thermionic amplifiers and electrical networks to simulate the interdependences. This type, the "electronic analogue", is unsuitable for the requirements of economists, because it has a fixed time scale.
O n e cannot " m a k e time stand still". There is a fixed ratio. So m a n y seconds represent so m a n y years. Then , given initial values of the quantities, or recent past values, these m a y be set up on the analogue ' with the time shaft stationary. O n rotating the time shaft the machine pro- gresses. O n such an analogue the simulated progress of time m a y be stopped at any stage to introduce changes or adjustments of conditions. P n e existing form of analogue calculator that in principle meets this requirement of independent control of simulated time is the well-known differential analyser.
Here the quantities are simulated mechanically by angles of rotation of shafts and the interdependences are built up by variable «peed gears, ordinary and differential gear. It is evident that a specially designed installation will be required if the possibilities of analogue computation are to be exploited in economic research. The final design of such a computer would require a good deal of time and effort by engineers and economists "working in collaboration to ensure that proper provision was m a d e to handle the problems as they would probably present themselves, and to specify the requirements in respect of accuracy and speed, recording facilities, sup- plementary computational aids and so on.
Electrical as distinct from mechanical simulation permits a m u c h higher speed of operation. T h e interdependence would be set up via interchangeable electrical units, at a central connecting-board, with suitable plugs or switches, which would permit rapid setting up and control, and flexibility of arrangement.
T h e basic relationships of the system to be simulated are, in the case of m a n y dependences, merely addition, subtraction and multiplication by con- stants. All such dependences are very easily and accurately simulated by suitable electronic valve circuits. A further large group of dependences required are specified time-relation- ships. O n e such time-relationship has already been discussed, namely the characteristic spread of the rates of investment over time that follows an elemental "decision to invest" for a given class of investment goods.
The simulation of such time-dependences is one of the requirements that is dif- ficult to meet while at the same time providing an independent control of simulated time. T h e electrical networks that so readily provide time-delay functions in the usual electronic simulator are of no use except on a fixed time-scale. T h e requirement can be met, but the principles involve tech- nicalities relating to the temporary recording of electrical values that will not be described in detail here. There are also relationships specified by differential equations, and to simulate them the electrical version of the elements of a differential analyser is the appropriate device.
Readers w h o are familiar with electrical devices will appreciate immediately that the arrangement shown in Fig. A typical electrical arrangement for integration. It remains to provide for the non-linear relationships. S o m e of these are of the kind that can be represented by a curved graph. Such graphs previously drawn on paper m a y be followed by an "electric eye" or photo-cell-operated curve follower, and the plotted non-linear function fed into the analogue. There are some rather more complicated types 'of non-linearity, but examina- tion shows that there would be no difficulty in providing for them.
T h e general conclusion, which cannot be elaborated here, is that a physical analogue adequate for research into the behaviour of economic systems is technically feasible, but it would have to be one built specially for the purpose, and would require a considerable number of elements. It might cost some tens of thousands of pounds, and take several years to design, build and carry through the experimental stage.
It must again be emphasized that in expressing the opinion that the con- struction of an analogue computer for economic research is worth serious consideration, the writer is not suggesting that it would, alone, be of m u c h value. It is one desirable tool, but its indispensable complement is an intensification of field studies and statistical research to establish inde- pendently as m a n y of the principal dependences of the system as possible, so as to be able to discover the others, and to m a k e final adjustments of values by trial, using the analogue.
Such an analogue computer would be of immense value in econometric research. Assuming this stage to be successfully achieved, which will require years of work for a considerable team of economists, statisticians and engineers, there would be a substantial basis for the guidance of policy.
It would then be possible, for example, for stabilizing operations by government agencies to be designed and carried out as a matter of regular routine. T h e purpose of such stabilizing operations would be, in the first place, to remove the inherent instability that is a feature of the system, and to ensure that the modified system was inherently stable.
The principles on which automatic stabilization can be introduced into physical systems, such as automatic controls, are n o w well understood. There are two main possibilities. Either the nature of some of the dependences must be suitably altered, or what the engineer calls "stabilizing feed-back" must be provided. T h e equivalent of this in economic terms must n o w be explained. S o m e of the familiar ones are budgetary unbalance, variation of bank rate, open market buying and selling, variation of the rate of government spending, and public works policies.
There m a y be added such devices as purchase and sale of ballast stocks of storable commodities, variation of purchase taxes, accumulation and release of credits on the lines of the British post-war credits , measures of social security that affect saving, pro- grammes of technical education and research that affect the flow of opportunities to invest, and m a n y others. O f these s o m e evoke a m u c h quicker response than others.
T h e quick-acting operations are to be preferred for devising stabilizing routines. A n economic system is subject to various disturbances, due to external events, varying harvests, political changes, n e w inventions and so on. It is not possible, nor is it necessary, entirely to remove the minor fluctuations that directly result from the impact of these disturbances. It is certainly necessary to offset any prolonged or major or permanent disturbance, but the requirement n o w under consideration is that a small temporary dis- turbance should not result in a cumulative "explosive" or oscillatory further change.
It was explained earlier, in considering the example of the automatic pilot of an aircraft, h o w it was necessary that any small departure from the required course should bring about corrective action in a prescribed manner, timed so that the aircraft would turn back quickly, but without overshoot. The movement of the rudder required to bring this about is not simply a movement proportional to the error. It could better be described as a particular kind of wobble of the rudder, which at the same time corrects the error and damps out the oscillation that would otherwise follow.
T h e w a y this is contrived is to pick up the variation of some quantity' or quantities in the system that provide a suitable "index" or cue to the momentary variations, and apply an extra corrective stimulus which is in predetermined dependence on this index or cue.
This is k n o w n as "adding a stabilizing feed-back". It is possible to use various quantities as cues, and various other quantities as points of correction, but naturally some c o m - binations require simpler time-functions than others. In the economic system, since h u m a n operation intervenes, one has a free hand in respect of timing of corrective action except of course that it cannot anticipate its cue. If certain quantities are selected as "indices" for auto- matic routine stabilizing action, one would naturally choose those that are most immediately responsible to incipient disturbance, such as, for example, the price index of consumption goods or the rate of decisions to invest.
There are simple procedures to devise the "formula" for m a x i m u m effectiveness, once the scheme of de- pendence of the system is k n o w n and the index and the operational means have been selected. A surprising feature of such stabilizing devices in mechanisms is that, w h e n they are adequate and automatic, they give the appearance of being very little used.
They "nip in the bud" all tendency to oscillate, and once stability is attained no oscillation ever builds up, and the stabilizing device maintains stability with only slight further action. This might need to be qualified in respect of economic stabilization undertaken by one national authority only, because the periodicities of national systems tend to be similar, and such a national economy might find its regulating routine working hard if, at about its o w n natural periodicity, there arose a disturbance due to fluctuations of its terms of trade with its neigh- bours.
This possible difficulty would disappear in so far as all major govern- ments adopted adequate stabilizing routines. Cortesao, the Portuguese historian of science, is the author of several books bearing mainly on geographical discovery. I O n e of the most remarkable examples of the interrelation between economic and social conditions on the one hand, and scientific progress on the other, is provided by nautical science, i.
Several ancient peoples—the Chinese, the Indians, the Malaysians, the inhabitants of the Eastern Mediterranean and the Arabs—developed con- siderable maritime activities. W e have only vague references to the earliest sea navigation, but it seems that in about B.
W e do not k n o w if or when they evolved any method or methods of finding their course when out of sight of land. However, the practice of long and distant voyages on the high seas, for centuries on end, would have favoured the working out of at least some elementary method of orientation and determination of latitude by rudi- mentary astronomical observations. After the destruction of the naval power of the Phoenicians, Greeks, and Carthaginians, the R o m a n s became masters of the sea, but they m a d e no progress in the art of navigation.
W h e n R o m e fell, the Arabs, after occupying the whole of the Iberian Peninsula, developed considerable seamanship in the Mediterranean and even in the Atlantic. They m a d e remarkable contribu- tions to the art and science of navigation by introducing the lateen sail in the West and by developing their already considerable knowledge of astro- n o m y. The Vikings m a y have gone to Greenland and north-eastern America in the tenth century, but their great seamanship brought no actual contribu- tion to the art of navigation, or if it did it was confined to themselves.
In fact, it was not until the thirteenth century that one can see the beginnings of a real science of navigation. Under the impact of the revival of learning,1 the progress m a d e in mathematics and science began to yield fruit in the form of practical scientific discoveries and technological inventions. The Crusades, which extended from the end of the eleventh to the end of the thirteenth century, aroused a new interest in the outside world and certainly developed the spirit of overseas expeditions.
Lastly, the idea of taking risks in fields other than war was encouraged by the newly-born capitalist system—the so-called "early capitalism" which began in the thir- teenth century under the influence of the Church. The recovery and development of the great works of classical antiquity, particularly those of Ptolemy in mathematics, astronomy and geography, first by the Moslems, and then by the Jews and Christians, prepared the ground for one of the most momentous discoveries to be m a d e two centuries later—the scientific method of determining the position of a ship on the high seas by the application of existing astronomical knowledge.
F r o m our point of view, the most important aspect of the progress m a d e was that the great astronomical and geographical works of Arab scholars were m a d e k n o w n to the Latin world by John Holywood, the famous Sacro- bosca d. O n e of these Arab scholars, the eleventh-century astronomer Al-Zagarli, not only invented an improved flat astrolabe, but also edited the so-called Toledan planetary tables.
N o less noteworthy, though not so widely k n o w n outside the Iberian Peninsula, was the compilation of the Libros del Saber de Astronomia by the order and under the supervision of Alphonso X el Sabio d. This enormous work contains the translation into Spanish, by a group of Jewish and Christian scholars w h o m Alfonso X had gathered round him, of all known writings on astronomical matters, beginning 1.
This revival of arts and letters began with Charlemagne d. The foundation of the Carolingian and cathedral schools had a profound influence on the Intellectual movement which was to flourish a few centuries later. With the political unification of the Arab world a n e w and momentous element was introduced into the cultural evolution of Europe.
M a n y Greek works were translated into Arabic, and, through the Persians, the Arabs assimilated from India m u c h of their mathematical knowledge. M a n y encyclopaedic works bad already been written and were widely k n o w n. All this contributed to the start of the great intellectual and cultural stirring which was marked by a revival of Aristotelianism and the foundation of Franciscanism its love of nature fitted in with the new approach brought to science by Aristotelian thought , and last but not least by a new methodology in mathematics.
T h e latter was chiefly due to Abraham Savasorda, a Spanish Jew w h o lived in Barcelona and whose work w a s followed a century later by the better known Leonardus Pisanus or Leonardo Fibonacci d. In this 18 Libros could be found not only all the con- temporary theoretical knowledge on astronomy, but also the description of such instruments as astrolabes, quadrants, armils and clocks, and practical instructions for making them.
The existence of this mass of special know- ledge in the Iberian Peninsula is of considerable historical importance. II Such was the state of knowledge in the thirteenth century, when Europe, under the spur of the newly-born capitalism, began her seafaring expeditions.
In the 's some galleys commanded by Lancelot Malocello, m e m b e r of a noble Genoese family, sailed towards the "Fortunate Islands". There a fort was built in the Canaries. In two other galleys commanded by the brothers Vivaldi sailed from Genoa to the Atlantic so "that they might go by sea to the ports of India and bring back useful articles of merchandise".
The Vivaldi reached the Canaries but never returned, and several unsuccess- ful expeditions were sent from Genoa in search of them. S o m e thirty years later the Italians, Majorcans, Portuguese and French followed suit, and expeditions to the Canaries became a c o m m o n occurrence.
M a n y of these ships were provided only with sails, and since they could not sail against the north-east trades and currents, they had to put further out to sea in order to take advantage of the favourable winds which would bring them back h o m e. The difficulties caused by the north-east trade winds on the return journey from the Canaries and further south led to the development of the lateen- rigged caravel, which was lighter, swifter and m u c h more manoeuvrable than the ship rigged with square sails only, and therefore could sail near the wind and was even able to tackle the head winds.
After the lateen-rigged caravel had been increased in size from 50 to tons, with three or four masts, square sails were added to it to help it to undertake longer voyages; on the other hand, lateen sails were added to the square sails of the bigger ships in order to allow them to take advantage of less favourable winds.
Bartolomeu Dias' voyage round the C a p e of G o o d H o p e in was still m a d e with four caravels of two or three masts rigged with lateen sails only; but in the three-masted caravel that took Columbus to America in the main mast was rigged with a square sail, and in the ships that took Vasco da G a m a to India in the after mast was rigged with a lateen sail. In the late Middle Ages aromatic spices such as cloves, nutmeg, cinnamon, ginger, and particularly pepper, had become so m u c h in demand that they were often used as currency and to pay taxes.
These spices had to be paid for in gold, and their growing use, together with the development of international trade in general, imposed a severe strain on Europe's gold resources. N o w m u c h of the gold and some of the pepper came from north and north-west Africa respectively and was in the hands of the Arabs. Since the beginning of the fourteenth century the Genoese had tried to find out the routes which the Arab caravans used for bringing the gold to the southern Mediterranean ports, particularly to Ceuta, which the Portuguese had taken from the Moors in Thus were begun a series of systematic explorations of the Atlantic coast of Africa.
A n d w h e n the Portuguese reached Guinea they called it "Malaguetta Coast" from the latin n a m e of an aromatic spice , whilst the land further south they called "Gold Coast". This did not solve the problem, however and meanwhile, after the fall of Constantinople in , Egypt was left as the only commercial intermediary between East and West and greatly increased its prices.
Furthermore, Arab pirates in the Mediterranean became more and more daring, and ha'd the sea trade there practically at their mercy. It thus became imperative to find some means of bringing the spices from the East directly by sea. This naturally meant circumnavigating Africa.
It was n o w taken up by the Portuguese. Ill During the course of their early sea explorations the Portuguese became well acquainted with the system of winds and currents, and soon realized that, in order to reach India, it was necessary to cross the South Atlantic south-westwards and then sail south-eastwards round the Cape of G o o d H o p e. This was actually accomplished by Bartolomeu Dias in But to sail across the South Atlantic meant high seas navigation, which can only be done with any measure of security if there is a process of finding the ship's position with some degree of accuracy and at reasonable intervals.
T h e compass, then more than a century old, though indispensable to navigation, could not solve the problem by itself. In the late Middle Ages navigation was by dead reckoning, i. The only w a y in which a ship could find her position out of sight of land was by determining its latitude, which in turn could be done by calculating the meridian altitude of some heavenly body. Once a method for performing this simple but essential operation had been found and developed, nautical astronomy—the basis of high seas navigation and the foundation of modern geography—was created.
T h e possibility of finding latitudes was k n o w n in ancient times, perhaps as early as the second millenium B. Through the Arabs, the use of the astrolabe and the quadrant was current in the Iberian Peninsula. T h e astrolabe was a complicated instrument used mostly for astrological operations, and frequently there was even a circular calendar scale, a circular rotating star-map and a plate with a polar projection of the circles of altitude of the celestial sphere engraved on it.
It is only natural that the most active navigators of the first half of the fifteenth century, faced with the urgent need for an accurate enough process of finding the ship's position on the high seas, thought of using the astrolabe and quadrant for determining the latitude by observations of the pole-star and of the sun, already practised on land for some centuries.
Thus, with a positive element—the latitude of the place—the dead reckoning could be corrected and the ship's position pricked on the chart with a near enough approximation. T h e first thing to be done to m a k e the use of the astrolabe practical o n board was to strip it of its astronomical complexities. This was accomplished by reducing it to a simple flat ring with two of its quadrants graduated in degrees, at the centre of which pivoted an arm with two pinhole sights.
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This is an advantage to some extent, however the flipside to this is that losses are recovered more slowly. So the chances of making some kind of loss are actually greater, but the size of any losses are generally less catastrophic when hitting a streak of bad luck. We tell you how to use it, and then explore whether or not it can work. The idea is that you should always win roughly the same number of even money bets as you lose.
To put it another way, it works on the basis that red would come up approximately the same number of times as black during a session of playing roulette. As you can see, this system is certainly simple enough to implement. And, if you do win roughly the same number of bets as you lose, then you should come out ahead.
This is because your winning bets will have been at higher stakes than your losing bets. Sounds great in theory but the key question, of course, is does it work in practice? You can make a profit even when losing more bets than you win. You need the right sequence of results for this to happen though, and this is where the system is fundamentally flawed.
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