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Articles 1 - 13 of 13
Full-Text Articles in Physical Sciences and Mathematics
Review: Robert H. Nelson, The New Holy Wars: Economic Religion Vs. Environmental Religion In Contemporary America, Andre Wakefield
Review: Robert H. Nelson, The New Holy Wars: Economic Religion Vs. Environmental Religion In Contemporary America, Andre Wakefield
Pitzer Faculty Publications and Research
This is a book review of Robert H. Nelson's The New Holy Wars: Economic Religion vs. Environmental Religion in Contemporary America. Nelson argues that environmentalism and economics represent competing religious worldviews. Within this framework, debates over issues like global warming and acid rain become veiled theological disputes between these two “secular religions.” Nelson paints with a broad, aggressive brush. This is both the strength and weakness of his book, as he conjures a world of epic battles between the economic faithful, who worship material progress, and the environmentally pious, who bemoan the corruption visited by humans upon the natural world. …
Why Did Lagrange "Prove" The Parallel Postulate?, Judith V. Grabiner
Why Did Lagrange "Prove" The Parallel Postulate?, Judith V. Grabiner
Pitzer Faculty Publications and Research
In 1806, Joseph-Louis Lagrange read a memoir "proving" Euclid's parallel postulate to the Institut de France in Paris. The memoir still exists in manuscript, and we’ll look at what it says. We ask why he tried to prove the postulate, and why he attacked the problem in the way that he did. We also look at how the ideas in this manuscript are related to such things as Lagrange’s philosophy of mathematics, artists’ ideas about space, Newtonian mechanics, and Leibniz's Principle of Sufficient Reason. Finally, we reflect on how this episode changes our views about eighteenth-century attitudes toward geometry, space, …
Newton, Maclaurin, And The Authority Of Mathematics, Judith V. Grabiner
Newton, Maclaurin, And The Authority Of Mathematics, Judith V. Grabiner
Pitzer Faculty Publications and Research
Sir Isaac Newton revolutionized physics and astronomy in his Principia. How did he do it? Would his method work on any area of inquiry, not only in science, but also about society and religion? We look at how some Newtonians, most notably Colin Maclaurin, combined sophisticated mathematical modeling and empirical data in what has come to be called the "Newtonian Style." We argue that this style was responsible not only for Maclaurin’s scientific success but for his ability to solve problems ranging from taxation to insurance to theology. We show how Maclaurin’s work strengthened the prestige of Newtonianism and …
Was Newton's Calculus A Dead End? The Continental Influence Of Maclaurin's Treatise Of Fluxions, Judith V. Grabiner
Was Newton's Calculus A Dead End? The Continental Influence Of Maclaurin's Treatise Of Fluxions, Judith V. Grabiner
Pitzer Faculty Publications and Research
We will show that Maclaurin's Treatise of Fluxions did develop important ideas and techniques and that it did influence the mainstream of mathematics. The Newtonian tradition in calculus did not come to an end in Maclaurin's Britain. Instead, Maclaurin's Treatise served to transmit Newtonian ideas in calculus, improved and expanded, to the Continent. We will look at what these ideas were, what Maclaurin did with them, and what happened to this work afterwards. Then, we will ask what by then should be an interesting question: why has Maclaurin's role been so consistently underrated? Thse questions will involve general matters of …
The Centrality Of Mathematics In The History Of Western Thought, Judith V. Grabiner
The Centrality Of Mathematics In The History Of Western Thought, Judith V. Grabiner
Pitzer Faculty Publications and Research
This article explores the interplay of mathematics and philosophy in Western thought as well as applications to other fields.
Computers And The Nature Of Man: A Historian's Perspective On Controversies About Artificial Intelligence, Judith V. Grabiner
Computers And The Nature Of Man: A Historian's Perspective On Controversies About Artificial Intelligence, Judith V. Grabiner
Pitzer Faculty Publications and Research
The purpose of the present paper is to provide a historical perspective on recent controversies, from Turing's time on, about artificial intelligence, and to make clear that these are in fact controversies about the nature of man. First, I shall briefly review three recent controversies about artificial intelligence, controversies over whether computers can think and over whether people are no more than information-processing machines. These three controversies were each initiated by philosophers who, irrespective of what the programs of their time actually did, viewed with alarm the argument that if a machine can think, a thinking being is just a …
The Changing Concept Of Change: The Derivative From Fermat To Weierstrass, Judith V. Grabiner
The Changing Concept Of Change: The Derivative From Fermat To Weierstrass, Judith V. Grabiner
Pitzer Faculty Publications and Research
Historically speaking, there were four steps in the development of today's concept of the derivative, which I list here in chronological order. The derivative was first used; it was then discovered; it was then explored and developed; and it was finally defined. That is, examples of what we now recognize as derivatives first were used on an ad hoc basis in solving particular problems; then the general concept lying behind them these uses was identified (as part of the invention of calculus); then many properties of the derivative were explained and developed in applications both to …
Who Gave You The Epsilon? The Origins Of Cauchy's Rigorous Calculus, Judith V. Grabiner
Who Gave You The Epsilon? The Origins Of Cauchy's Rigorous Calculus, Judith V. Grabiner
Pitzer Faculty Publications and Research
This paper recounts the history of how calculus came to get a rigorous basis in terms of the algebra of inequalities. The result is a brief history of the 150 years from Newton and Leibniz to Cauchy that produced the foundations of analysis.
Course Syllabus: Perspectives On Computers And Society, Judith V. Grabiner
Course Syllabus: Perspectives On Computers And Society, Judith V. Grabiner
Pitzer Faculty Publications and Research
Weizenbaum's statement is a compelling exhortation to his fellow professionals; nevertheless, I cannot wholly agree. It should be possible for nonprofessionals to understand, as a result of their own reading and experience, how computers interact with the rest of human life. The problems are not just technical, and their nature is not entirely unprecedented.
Závisí Matematická Pravda Od Času?, Judith V. Grabiner
Závisí Matematická Pravda Od Času?, Judith V. Grabiner
Pitzer Faculty Publications and Research
This is a Slovak translation of Judith Grabiner's "Is Mathematical Truth Time-Dependent?," published in Volume 81 of American Mathematical Monthly (April 1974).
Mathematics In America: The First Hundred Years, Judith V. Grabiner
Mathematics In America: The First Hundred Years, Judith V. Grabiner
Pitzer Faculty Publications and Research
There are two main questions I shall discuss in this paper. First, why was American mathematics so weak from 1776 to 1876? Second, and much more important, how did what happened from 1776-1876 produce an American mathematics respectable by international standards by the end of the nineteenth century? We will see that the "weakness" -at least as measured by the paucity of great names- co-existed with the active building both of mathematics education and of a mathematical community which reached maturity in the 1890's.
The Mathematician, The Historian, And The History Of Mathematics, Judith V. Grabiner
The Mathematician, The Historian, And The History Of Mathematics, Judith V. Grabiner
Pitzer Faculty Publications and Research
The historian's basic questions, whether he is a historian of mathematics or of political institutions, are: what was the past like? and how did the present come to be? The second question --how did the present come to be?-- is the central one in the history of mathematics, whether done by historian or mathematician. But the historian's view of both past and present is quite different from that of the mathematician. The historian is interested in the past in its full richness, and sees any present fact as conditioned by a complex chain of causes in an almost unlimited past. …
Is Mathematical Truth Time-Dependent?, Judith V. Grabiner
Is Mathematical Truth Time-Dependent?, Judith V. Grabiner
Pitzer Faculty Publications and Research
Another such mathematical revolution occurred between the eighteenth and nineteenth centuries, and was focused primarily on the calculus. This change was a rejection of the mathematics of powerful techniques and novel results in favor of the mathematics of clear definitions and rigorous proofs. Because this change, however important it may have been for mathematicians themselves, is not often discussed by historians and philosophers, its revolutionary character is not widely understood. In this paper, I shall first try to show that this major change did occur. Then, I shall investigate what brought it about. Once we have done this, we can …