Search

The article presents information on several books. Some of the books are "Problems of Historical Psychology," by Zevedie Barbu and "Developments in Mathematical Psychology. The book consists of studies of three mathematical formulations that have proved of interest to psychologists during the past fifteen jean: Information theory, in which an attempt is made to characterize certain summary properties of time invariant choices; Mathematical learning theories, in which the goal is to describe the systematic changes of choices that result from environmental responses to them; Quasi-linear theories of tracking, in which a person who is trying to follow closely a continuously moving target is treated as a slightly noisy linear system. The author delineate the problem areas being treated and Introduce the basic mathematical ideas used, cite some of the major mathematical results, and survey and criticize the more important papers in which the theories are confronted with experimental data. Another book is "Industrial Productivity and Motivation."

In many cases Bayes' theorem is an appropriate algorithm for the aggregation of probabilistic evidence. As with other statistical procedures, there are restrictions that must be taken into account. In the present paper we shall comment on several approaches that have been devoted to one of these restrictions; the incorporation of uncertainty about the true state of a datum. A datum is a variable which can be partitioned into equivalence classes. These classes represent the possible data states which will be also called events. In Bayes' theorem an event is an item of information which will be used for revising the opinion about the relative likelihood of hypotheses. In any specific situation only one of the possible events will be the true event. An event may come from a source whose reporting or observational accuracy is not perfect. An example may illustrate the issue. A medical doctor wants to come to a diagnosis. To achieve this he considers several data. One datum might be the result of a medical test, which has three possible states: positive, negative, inconclusive. If the doctor reports the state of the datum to be positive, he may be wrong by whatever reasons. That is, the report of an event must not necessarily coincide with the actual or true event of the datum under consideration. This kind of uncertainty about the true event in any specific situation is a characteristic of the source. In most cases it will reduce the diagnostic impact of an event. Whenever the report of an event and the true event coincide imperfectly, measures of source inaccuracy must be incorporated into Bayes' theorem. The task can be considered as two stage probabilistic induction. The first step is induction from the reported to the actual event, the second is induction from the actual event to the creditation of hypotheses. This is the reason why Gettys and Willke (1969) speak about "cascaded inference." [ABSTRACT FROM AUTHOR]

The literature of current sociological research shows conspicuously few studies that make careful use of any accepted theory of sampling. This situation seems to be due partly to difficulties in imposing the severe requirements of a mathematical sampling theory upon the complex and uncontrolled problems which sociologists usually choose to study, partly to the prevalence of an imperfect understanding of the existing theory and its demands, and finally to the failure of the theory itself to provide many needed sampling errors for stratified samples. The present paper is an attempt to interpret, in as non-mathematical and as practical a way as possible, the meaning of the basic sampling theory as applied to social research, in the hope of directing more attention to the problem and some of its difficulties. In this case, the chance, p, of throwing a head or a six, or of a person dying, is a function of the number of sides and balance of a penny or die, or of the age, sex, and living conditions of a person.

The author states that since the publication in 1944 of the first edition of the book "Theory of Games and Economic Behavior," by John von Neumann and Oscar Morgenstern, there has been a minor flood of contributions to various aspects of the theory of games and its applications. The theory of games thus has an undisputed fascination for and a stimulating effect on, workers in many fields, ranging from pure mathematics to applied social sciences. There is a natural curiosity as to directions in which the theory of games and its application have been developing. One wishes to know which developments have found widespread agreement as against those, which still are controversial. The limited scope and non-technical nature of the present exposition can do little more than give a very sketchy indication of the nature of these developments. The author emphasizes that problems of the theory of games are characterized by the presence of two types of issues, the nature of individual behavior in situations involving uncertainty and interactions in the behavior of individuals when everyone's action may affect the well-being of others.

This paper is directed at the following question: given an incomplete set of price data relating to goods or services in some category of output for each of a number of different countries, what arithmetic should be performed on the prices to get a meaningful representation of the relative category price-levels of the countries? in the course of developing an answer to the question, some broader matters are considered and illuminated. A comparison of category price-levels for different countries is analogous to a commonly-encountered problem in many areas, that of ranking ordinally or cardinally in one dimension a group of "entities"--persons, households, firms, industries, etc.--on the basis of sets of measurements associated with the individual entities. It is this point of view which dominates the following presentation. [ABSTRACT FROM AUTHOR]

This article focuses on the use of mathematical techniques and constructions in social sciences. Some mathematical techniques and constructions require, before they can be put to use, the provision by the social sciences of the statistical data, or, alternatively, of the postulational elements, with which they are to deal. These data and postulational elements in their turn require, before they can be assembled, or before they can be given precision, an analysis of the general situation to be investigated, and the determination of a scheme of classification. The physical and mathematical spaces are forms of knowledge but knowledge itself is manifestly a social development, a process or a product according as one take it and therefore the entire development of physics and mathematics falls within the scope of the most general sociological study. On the other side, any sociology that may be established will manifestly be conditioned by physics and mathematics, because it itself is a part of knowledge and the physics and mathematics are more richly and securely established parts of that knowledge than it is. Sociological development will be conditioned by the physical spaces insofar as these latter become firmly established as forms of basic physical fact.

This article discusses some mathematical elements in social sciences. The mathematical and statistical literature which can be classified as being of interest to social scientists is continually increasing - and increasing progressively. Business economics had a comprehensive literature about conflicting interests between firms, and sociology had an equally comprehensive literature about conflicts between groups and between persons in a group, finally psychology had a treatment of the individual decision-maker's conflict state in a situation in which a decision is to be made in choosing among several uncertain alternatives. The numerical solution is a combination of available information and rules of calculation resulting in a concrete alternative. In mathematics, tradition has formerly left the latter solution in the cold, but in recent years it has returned to favor in connection with the development of the simulation method, which may enable social science to make experiments to a much higher degree and in so doing get a better approximation to the optimal situation wanted.

Points of interest. A courageous facing of the question: "Social science for what? Social science seen in relation to the total aims of college education. What about indoctrination? Social sciences may "train the mind as well as the classics and mathematics and in addition provide useful knowledge. What are the obstacles? [ABSTRACT FROM AUTHOR]

The article focuses on the author's attempt of an appraisal of relationship between economic theory and mathematics. I realize that this is a session on methodology, hence, must face some basic questions as to the nature of mathematics and of its application. Mathematics is neither a necessary nor a sufficient condition for a fruitful career in economic theory. It can be a help. It can certainly be a hindrance, since it is only too easy to convert a good literary economist into a mediocre mathematical economist. It happens to be empirically true that if one examines the training and background of all the past great economic theorists, a surprisingly high percentage had, or acquired, at least an intermediate mathematical training. Though mathematical economics is flying high these days but the author does not praise economics instead attempts to debunk its use in economics. In economics, the cornerstone of the simplest and most fundamental theory of production and distribution is based on theorem on homogeneous functions. In Clark's theory, there is the implicit assumption that scale does not count and that what does count is proportions in which factors combine and that it does not matter which of these factors of production is the hiring factor and which the hired.

SUMMARY The historian assumes the obligation to make a synthesis of all of man's activities and has therefore a larger responsability than the social scientists in their various fields of knowledge. It is difficult to identify a social science approach to history or a distinctive social science method or procedure. At least the report of the Committee on Historiography which contains a lengthy discussion of the proper method in the social sciences does not successfully differentiate it from the method of the so-called exact sciences. One of the serious problems confronting the historian is how to acquire the best current knowledge available in the social sciences. Indeed to do so necessitates learning the technical languages which have been developed in these complex and rapidly expanding fields of knowledge, especially since one of the languages now regularly employed is mathematics on a higher level than is normally reached by historians. There also remains the more fundamental problem of whether or not the findings and procedures in one highly developed branch of knowledge can be fruitfully or justifiably applied in another field. Disastrous examples to the contrary are easy to locate. Two types of historical problem on which the historian needs and would welcome assistance from the social scientist are (I) what has been the effect in history of the change in psychological experience that occurred when so large a proportion of the population grew up in a one or two child family instead of a five or six child family? (2) What are the changes in political and social history resulting from the fact that so large a proportion of the population are now employees instead of being independent economic units? The danger of social science history is that if abused or distorted it may dehumanize history. There is poetry in life. And the history, or science, that omits the poetry from life is both untrue and dangerous. [ABSTRACT FROM AUTHOR]

The article presents information about international conferences on social sciences to be held between years 1970 and 1972, published in the May 1, 1970 issue of the journal "International Social Science Journal." Some of the conferences that are scheduled during the period are "Unesco: Sixth international seminar on the use of mathematics in the social sciences," to be held between July 5 and 31, 1970 in Israel. "International Association of Workers for Maladjusted Children: Seventh Congress (Theme: The social role of the specialized 'educateur' for maladjusted children)," to be held between July 6 and 10, 1970 at Versailles, France. "International Political Science Association: Eighth World Congress," to be held between August 31 and September 5, 1970 in Munich, Germany.

Utilizing an interdisciplinary team of operations analysts, working with mathematical techniques, including mathematical modelling, mathematical programming, game theory, Markov process theory, queueing theory, etc., may help to improve the operations of various crime control activities. Some illustrations from these techniques applied to criminological problems are provided. Police operations and the risk-reward system of commuting crime and being subjected to the probabilities of social sanctions are briefly examined as fruitful areas of analysis. [ABSTRACT FROM AUTHOR]

The article discusses the basic mathematical concepts that are relevant to anthropology measurements in the U.S. Some of the basic mathematical concepts which are relevant to measurement such as the concept of a distance metric. A good introduction to the theory of scaling distinguishes nominal, ordinal, interval and ratio scales. A nominal scale is simply a categorization, an ordinal scale is a ranking-ordering, an interval scale has a real number measures of distance and a ratio scale is an interval scale with a zero point. The distance metric must satisfy three conditions positivity, symmetry and the triangle inequality.

In the past twenty-five years or so, there have been four major "approaches" or lines of inquiry in communication research, plus a number of minor ones. The major approaches are so clearly identified with and characterized by their leading proponents that they can be given names, the political approach of Lasswell, the sample survey approach of Lazarsfeld, the small groups approach of Lewin; and the experimental approach of Hoviand. The minor approaches are the reformist, the historical, the journalistic, the mathematical, the psycholinguistic and the psychiatric.