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In baseball, a player can gain instant fame by duplicating or exceeding one of the fabled types of batting streaks. The most well known is Joe DiMaggio's (1941) streak of hitting in 56 consecutive games. There are also other batting streaks such as Ted Williams' (1949) 84-game consecutive on-base streak, Joe Sewell's (1929) 115-game streak of not striking out in a game, and the 8-game streak of hitting at least one home run in each game, held by three players. Other streaks include most consecutive plate appearances with a hit (the record is 12 held by Walt Dropo (1952)), most consecutive plate appearances getting on-base (the record is 16 held by Ted Williams (1957)), and the most consecutive plate appearances with a walk (the record is seven held by five players).
In this paper, we present two functions to calculate the probability of a player duplicating a hitting streak. One is recursive; the other is a new piecewise function that calculates the probability directly.
We use them to compare the difficulty of duplicating different streaks, in particular, the 56-game consecutive hitting streak and the 84-game consecutive on-base streak.
Our results can be applied to streaks outside of baseball.
A recursive function to calculate the probability of a player having a 56-game hitting streak at some point in a season
Michael Freiman [1] gives a recursive function, R(n), to calculate the probability of a player having a 56-game hitting streak at some point in the season.
With all the volumes that have been written about Marx and Marxism in recent years, there has beenlittle or no attempt, in the English-speaking world at least, to relate his thinking to the general development of modern European philosophic speculation. Fundamentally this is because Marx has received short shrift as a philosopher. Both English and American commentators have been almost entirely concerned with his role as “social scientist” and polemicist, and hence have concentrated their attention upon his historical materialism and his critique of capitalist society.
For some time we have been engaged in a large scale study of various leadership strata in the United States. Our goal is to clarify similarities and differences in background, ideology and personality among members of such strata. We are also interested in the relationship between these variables and the manner in which members of different leadership groups perceive ‘reality’. This article reports preliminary findings on two groups – leading business executives and top level journalists. Our work has been partly informed by hypotheses developed by social scientists as diverse as Max Weber, Harold Lasswell, Joseph Schumpeter, S. M. Lipset, Alvin Gouldner, Jurgen Habermas, Irving Kristol, Daniel Bell and others.
In the June 1987 issue of this Review, Stanley Rothman and S. Robert Lichter offered evidence to support their argument that “the new environmental movement in the United States is partly a symbolic issue,” that elites in the news media and in public interest groups misrepresent the dangers of nuclear energy as a surrogate for more direct criticism of liberal capitalism in the United States. In this controversy, Charles J. Helm expresses skeptictem about the Rothman-Lichter line of argument; and they respond.
Changing U.S. attitudes toward new technologies are examined, as are explanations of such changes. We hypothesize that increased concern with the risks of new technologies by certain elite groups is partly a surrogate for underlying ideological criticisms of U.S. society. The question of risk is examined within the framework of the debate over nuclear energy. Studies of various leadership groups are used to demonstrate the ideological component of risk assessment. Studies of scientists' and journalists' attitudes, media coverage of nuclear energy, and public perception of scientists' views suggest both that journalists' ideologies influence their coverage of nuclear energy and that media coverage of the issue is partly responsible for public misperceptions of the views of scientists. We conclude with a discussion of the historical development of the environmental movement in the 1960s and 1970s and the relation of this movement to the public's declining support for nuclear energy.
Rather than direct himself to a serious discussion of the important substantive issues involved, Professor McGrath chose to reply to our interpretation of some of Freud's motives with a series of angry assertions. We are disappointed, but we still have a few comments on his response.
Relying heavily upon Freud's greatest work, The Interpretation of Dreams, Professors Carl Schorske and William McGrath have attempted to increase our understanding of the origins of psychoanalysis. Both authors feel that the key to Freud's discoveries lies in his reaction to the sociopolitical realities of late nineteenth-century Vienna, and while the articles differ somewhat in emphasis their arguments are sufficiently similar so that they can be treated together. To Schorske and McGrath psychoanalysis had its origins in Freud's decision to give up his initial desire to mount a direct political (even revolutionary) attack on the inequities of the existing society for a “counter-political” psychology which enabled him to adjust to the existing political situation and even achieve a measure of scientific success. As a youth Freud had radical political aspirations and was even active in radical political organizations. However, the hopelessness of the liberal position in Vienna and the rise of anti-Semitic popular movements led Freud to believe that direct political action would not be successful. By reducing political conflict to father-son conflict Freud, like other liberals, would ignore the reality of the political and learn to live (albeit imperfectly) in a world which he could not influence. A career in science could bring recognition and at least partial acceptance, and thus a minimum of satisfaction at least.
“When I use a word,” Humpty Dumpty said, in rather a scornful tone, “it means just what I choose it to mean—neither more nor less.”
“The question is,” said Alice, “whether you can make words mean so many different things.”
“The question is,” said Humpty Dumpty, “which is to be the master—that's all.”
Through the Looking Glass
It is not hard to find reasons why Barrington Moore's Social Origins of Democracy and Dictatorship has had such widespread influence. Its approach, that of comparative, historical sociology, seeks clues to the present in the past, and Moore demonstrates mastery of a wide range of historical materials. Yet I feel that the book is ultimately unsatisfactory, for it is marred by a lack of respect for its own sources of information and by contradictions and non-sequiturs at critical points in the argument.
In this critique I shall first examine the general thesis of the book and then turn to the case studies which Moore uses to support his arguments. I shall also attempt to account for the sharp contrasts in the quality of scholarship which characterize the study, and will attribute them to Moore's preconceived ideological assumptions about the nature of the good society.
Perhaps no single individual has had as much impact on the discipline of political science during the past several years as has Leo Strauss of the University of Chicago. Both he and his disciples (and they are disciples in the “classical” sense) have engaged in a full scale attack upon the premises underlying the contemporary study of politics.
Strauss argues that these premises are illfounded and self-contradictory, and, if taken seriously, lead to moral nihilism. He contends, further, that another set of premises, those of “classical natural right,” which treat man in terms of his natural end and his relation to the “mysterious whole,” are capable of providing a more adequate foundation for the study of politics.
Of the spate of articles on interest group behavior and interest group theory which have appeared since the “rediscovery” of Bentley, only a few have been mildly critical. Two American commentators have criticized the vagueness of certain terms and a British observer has noted that, somehow, empirical research on group behavior rarely makes use of the theoretical schemes which have been devised.
But surely if we are to accept the claim of the group theorists that this is indeed the key to a science of politics, it is legitimate to ask that they submit their propositions to the tests imposed by science as a method. Perhaps the gap between research and theory stems less from a lack of data than from some limitations inherent in the group approach itself? This, in fact, is the argument of the present essay. The failure of group theory to serve as an adequate guide to research is the result both of the logical inconsistencies of its propositions and of its inability to explain what it purports to explain. The two weaknesses are related, for in their empirical work group theorists are constantly forced into inconsistencies as a result of the inability of the theory to deal with certain dimensions of experience. The ability of those who use the approach to ignore these consequences stems both from a certain looseness of vocabulary and a tendency, not limited to American scholars, to universalize their own political experience.
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