VII. On the theory of local probability, applied to straight lines drawn at random in a plane; the methods used being also extended to the proof of certain new theorems in the integral calculus

1868 ◽  
Vol 158 ◽  
pp. 181-199 ◽  
Keyword(s):  
Integral Calculus ◽  
Past Generation ◽  
Differences Of Opinion ◽  
Local Probability ◽  
Modern Analysis ◽  
The Subject ◽  
Latent Error ◽  
Straight Lines ◽  
Distinguishing Features ◽  
Inherent Ambiguity

1. The new Theory of Local or Geometrical Probability, so far as it is known, seems to present, in a remarkable degree, the same distinguishing features which characterize those portions of the general Theory of Probability which we owe to the great philosophers of the past generation. The rigorous precision, as well as the extreme beauty of the methods and results, the extent of the demands made on our mathematical resources, even by cases apparently of the simplest kind, the subtlety and delicacy of the reasoning, which seem peculiar to that wonderful application of modern analysis— ce calcul delicat , as it has been aptly described by Laplace—reappear, under new forms, in this, its latest development. The first trace which we can discover of the Theory of Local Probability seems to be the celebrated problem of Buffon, the great naturalist— a given rod being placed at random on a space ruled with equidistant parallel lines, to find the chance of its crossing one of the lines. Although the subject was noticed so early, and though Buffon’s and one or two similar questions have been considered by Laplace, no real attention seems to have been bestowed upon it till within the last few years, when this new field of research has been entered upon by several English mathematicians, among whom the names of Sylvester and Woolhouse are particularly distinguished. It is true that in a few cases differences of opinion have arisen as to the principles, and discordant results have been arrived at, as in the now celebrated three-point problem, by Mr. Woolhouse, and the four-point problem of Professor Sylvester; but all feel that this arises, not from any inherent ambiguity in the subject matter, but from the weakness of the instrument employed; our undisciplined conceptions of a novel subject requiring to be repeatedly and patiently reviewed, tested, and corrected by the light of experience and comparison, before they are purged from all latent error. The object of the present paper is, principally, the application of the Theory of Probability to straight lines drawn at random in a plane; a branch of the subject which has not yet been investigated. It will be necessary to begin by some remarks on the general principles of Local Probability. Some portion of what follows I have already given elsewhere.

scholarly journals II. On the theory of probability, applied to random straight lines

1868 ◽  
Vol 16 ◽  
pp. 266-269
Keyword(s):  
Local Probability ◽  
The Subject ◽  
Straight Lines

This paper relates to the Theory of Local Probability—that is, the application of Probability to geometrical magnitude. This inquiry seems to have been originated by the great naturalist Buffon, in a celebrated problem proposed and solved by him. Though the subject has been more than once touched upon by Laplace, yet the remarkable depth and beauty of this new Calculus seem to have been little suspected till within the last few years, when the attention of several English mathematicians has been directed to it, and results of a most singular character have been obtained. The problems on Local Probability which have been hitherto treated relate almost exclusively to points taken at random. The object of the present paper is to show how the Theory of Probability is to be applied to straight lines whose position is unknown, or, in other words, which are taken at random.

The sufficiency of virtue for happiness: not so easily overturned?

2001 ◽  
Vol 46 ◽  
pp. 121-139 ◽  
Author(s):  
R.W. Sharples
Keyword(s):  
Nicomachean Ethics ◽  
Differences Of Opinion ◽  
The Subject

The sufficiency of virtue for happiness is a central Stoic doctrine. Indeed it can be argued that it is one of the doctrines that define the Stoic position; and it was the subject of extensive controversy in antiquity, coming under attack both from Academics and from Peripatetics. And Peripatetics had a particular interest in the topic, for Aristotle had already discussed it in Nicomachean Ethics 1.8–10, in a way which, to say the least, left room for a range of divergent interpretations.The objections that were raised against the Stoic position in antiquity differ in their degree of persuasiveness. Some indeed point to fundamental differences of opinion of the sort that are not easily, if at all, reconcilable by argument. But others simply misinterpret or misrepresent the Stoic position. It is with some of the latter that the present paper will chiefly be concerned. Its aims are therefore limited even though the issue is important.

Modern Society and the Realms of Spirit

1961 ◽  
Vol 23 (1) ◽  
pp. 20-36
Author(s):  
Glenn Tinder
Keyword(s):  
Modern Society ◽  
Physical World ◽  
Industrial Society ◽  
Exact Nature ◽  
The West ◽  
Public And Private ◽  
Differences Of Opinion ◽  
The Subject ◽  
The Individual ◽  
True Contact

There is a wide measure of agreement among contemporary observers that something is seriously wrong in modern industrial society. As to the exact nature of the disorder there are differences of opinion: some denounce above all a vulgarization of culture which they see as stemming from the supremacy of mass taste; others view modern men as victims of the illnesses of overorganization, with all spontaneity and uniqueness increasingly compressed within the patterns of public and private bureaucracies; still others believe that the crucial failure of present civilization in the West is that beneath the various forms of mass and organizational “togetherness,” the individual lies stranded, as it were, on the shores of nothingness, deprived of true contact with his fellowmen, with the physical world, or even with himself. Thus there is little agreement as to how the dehumanization of contemporary man is best to be described. That such dehumanization is a fact, however, is the subject of profound and widespread consensus.

Mathematical Background

1993 ◽  
Author(s):  
Greg M. Anderson ◽  
David A. Crerar
Keyword(s):  
Free Energy ◽  
Real World ◽  
First Principles ◽  
Mathematical Language ◽  
Integral Calculus ◽  
The Road ◽  
Mathematical Background ◽  
The Subject ◽  
The Relationship ◽  
Theoretical Side

Thermodynamics, like other sciences, has a theoretical side, expressed in mathematical language, and a practical side, in which experiments are performed to produce the physical data required and interpreted by the theoretical side. The mathematical side of thermodynamics is simple and elegant and is easily derived from first principles. This might lead to the conclusion that thermodynamics is a simple subject, one that can be easily absorbed early in one's education before going on to more challenging and interesting topics. This is true, if by learning thermodynamics one means learning to manipulate its equations and variables and showing their interrelationships. But for most students the subject is actually far from simple, and for professors it is a considerable challenge to present the necessary material intelligibly. The equations and the variables are somehow related to the real world of beakers and solutions, fuels and engines, rocks and minerals, and it is this interface that provides most of the difficulties. What do variables such as entropy and free energy really mean, and what physical processes do the equations describe? The difficulty in understanding and using thermodynamics is conceptual, not mathematical. We will attempt to explain the relationship between the mathematical and the physical sides of thermodynamics, but it is advisable first to review the mathematics involved and subsequently to define the terms used in thermodynamics. The mathematics required for thermodynamics consists for the most part of nothing more complex than differential and integral calculus. However, several aspects of the subject can be presented in various ways that are either more or less mathematically based, and the "best" way for various individuals depends on their mathematical background. The more mathematical treatments are elegant, concise, and satisfying to some people, and too abstract and divorced from reality for others. In this book we attempt to steer a middle-of-the-road course. We review in the first part of this chapter those aspects of mathematics that are absolutely essential to an understanding of thermodynamics. The chapter closes with mathematical topics that, although not essential, do help in understanding certain aspects of thermodynamics.

The Cities and their Money

2005 ◽  
Author(s):  
Weiss Peter
Keyword(s):  
Roman Empire ◽  
Central Importance ◽  
The West ◽  
Authority Control ◽  
Central Concern ◽  
Differences Of Opinion ◽  
The Subject ◽  
Provincia Asia ◽  
Narrow Space ◽  
Clear Conception

In their Kind Invitation to Contribute to this book the editors assigned me the topic of ‘Authority/control’. The authors of RPC devoted an intensive discussion to the subject, with many facets and displaying an extraordinary knowledge of the material. This is in many respects a difficult field, and it is obvious how wide and heterogeneous is the material, how different the presuppositions were in the various parts of the Roman empire, and with what a broad timespan one has to deal: some three centuries, in which there were many developments and several changes. Despite its gigantic bulk, the coinage affords far fewer unambiguous indications permitting a clear conception of how minting came about and was controlled than one would wish. Epigraphy, which in other cases provides an enormous fund of information, here by contrast leaves us almost entirely in the lurch. It follows that many differences of opinion exist, and in many matters, even on points of central importance, our vision is still clouded. The topic is too complex to permit a thorough discussion of all the questions before us in this narrow space. For that reason I have undertaken a limited evaluation. In what follows, I am concerned only with coins pertaining to the cities. Attention is therefore not paid, for example, to the cistophori in Asia, the coins of Alexandria in Egypt, or of Caesarea in Cappadocia, or to the provincial coinage of Syria. I shall first consider the question of Roman control, but only in the form of some basic observations and reflections. Much must here remain unresolved. My central concern will therefore be the following set of questions: How did the cities organize their monetary production? How were responsibilities apportioned, and who was directly involved? What range of possibilities was there? How in this context are we to interpret the numerous names and functional titles on the coins of many Roman cities, especially in the west, down to Julio-Claudian times, and above all, in continuity with Hellenistic practice, on very many coins from the Greek poleis in Provincia Asia?

Anne Pauwels, Women changing language. (Real language series). London & New York: Addison Wesley Longman, 1998. Pp. xvi, 267. Hb £40.00, pb £14.99.

2000 ◽  
Vol 29 (2) ◽  
pp. 269-273
Author(s):  
Deborah Cameron
Keyword(s):  
New York ◽  
Language Reform ◽  
The Subject ◽  
Real Language ◽  
Distinguishing Features

This is a book about feminist language reform. The subject is not exactly neglected; since the late 1970s there has been no shortage either of practical guides to nonsexist language (for English see, inter alia, Miller & Swift 1980) or of historical, descriptive, and theoretical discussions (book-length examples include Nilsen et al. 1977, Vetterling-Braggin 1981, and Baron 1986). Pauwels's text is primarily descriptive, though it also has theoretical and practical elements; there is an appendix advising on how to draft nonsexist language guidelines. Like most previous work on this subject, it is written by a self-identified feminist, and one who is clearly sympathetic to the general project of feminist language reform. But that is not to say that Pauwels breaks no new ground: in fact, Women changing language has two important distinguishing features.

An analysis of the waters of the Dead Sea and the river Jordan

1832 ◽  
Vol 1 ◽  
pp. 275-278
Keyword(s):  
Dead Sea ◽  
Modern Analysis ◽  
The Subject ◽  
The Dead

This analysis is preceded by a short abstract of the notice taken of the Dead Sea by various ancient authors, by Strabo, by Tacitus, and by Pliny, as well as by Pococke, Volney, and other modern travellers, who all concur with respect to the intense saltness of the water, which is such as to prevent either animals or vegetables from living in it,—a peculiarity from which it has derived its name. The only analysis which Dr. Marcet has been able to find recorded, is that of Macquer, Lavoisier, and Sage, in the Mém. de l' Académie for 1778. But these chemists had not attained that accuracy of which modern analysis is susceptible, and appear not to have bestowed upon the subject that attention which is requisite in minute analytical experiments.

Manifestations and Arguments

2020 ◽  
pp. 229-262
Author(s):  
Peer Zumbansen
Keyword(s):  
Social Order ◽  
Legal Theory ◽  
Competent Authority ◽  
Legal Pluralism ◽  
The State ◽  
Social Ordering ◽  
The Subject ◽  
Critical Legal Theory ◽  
Distinguishing Features ◽  
Legal Sociology

While the term “legal pluralism’ literally denotes a plurality of legal orders, it is their plurality of and the distinguishing features between them, which continues to make the subject matter a very charged and hotly debated one. Seen through the lens of legal sociology and anthropology, the plurality of coexisting, normative orders appears, above all, as a matter of description, as a fact of social ordering. Meanwhile, as some of these normative systems are being claimed as being “law,” while others are associated with nonlegal forms of social order, such as customary, traditional, or indigenous norms as well as, perhaps, sector-specific rules of professional or industry conduct, the categories used to draw the lines between legal and nonlegal norms become in themselves highly contentious. The chapter argues that to neglect the fundamental distinction between legal pluralism as “manifestation” and as “argument” perpetuates a troubling inability on the part of positivist and analytical legal theory to engage with law’s inherent instability. Especially at a time, where the actors, norms, and processes that together constitute and shape emerging transnational regulatory regimes are located and operating both within and beyond the state as the purportedly singularly competent authority of law creation and enforcement, the deconstruction of “legal pluralism” as “nonlaw” and threat to the state can serve as the foundation for a new, critical legal theory.

scholarly journals On Extraneous Values in Simultaneous Equations

1914 ◽  
Vol 16 ◽  
pp. 183-184
Author(s):  
G. D. C. Stokes
Keyword(s):  
Simultaneous Equations ◽  
Geometrical Meaning ◽  
The Subject ◽  
Straight Lines

Mr Ridley's note in the January number giving an algebraic explanation of extraneous values suggests an elementary treatment of the subject on the geometrical side. It must be assumed that the pupil is able to trace from their equations straight lines, circles, and parabolas of the type y = ax2 + bx + c. He should be made to draw the curves in cases like those given here, and to state the geometrical meaning of every distinct step in the algebra.

scholarly journals Analysis and evaluation of students' results in the subject of Mathematics for Technicians

2020 ◽  
Vol 6 (2) ◽  
pp. 80-87
Author(s):  
Vladimír Matušek ◽  
Eva Matušeková
Keyword(s):  
Definite Integral ◽  
Test Results ◽  
Integral Calculus ◽  
Main Hypothesis ◽  
Analysis And Evaluation ◽  
The Subject

Integral calculus is a branch of mathematics concerned with the determination, properties, and application of integrals. It is predominantly used in technical applications. Technical engineers, statics, physicists and others use it in their calculations on practice. There was a requirement from practice for technical universities to include integral calculus in their curricula. The subject Mathematics for Technicians is taught at the Department of Mathematics, the Slovak University of Agriculture in Nitra. The content of this subject is to teach its students to calculate indefinite and definite integral. Our research analysed students' knowledge in counting indefinite and definite integral. We used the methodology of evaluation and comparison of test results taken in the 8th week of the term and at the end of the term. The main hypothesis saying that the results of students’ tests taken at the end of the term are better that those taken in the mid- term has confirmed to be correct.

Sign in / Sign up

Export Citation Format

Share Document