Physical Sciences and Mathematics Commons^™

Paul Faulstich’S Reflective Review Of Susan A. Phillips’ Essay, Paul Faulstich

Pitzer Faculty Publications and Research

Paul Faulstich's review of Susan A. Phillips' essay titled, "Huerta del Valle: A New Nonprofit in a Neglected Landscape".

Pitzer College Outback Preserve Restoration Project, Paul Faulstich

Pitzer Faculty Publications and Research

A question we keep asking ourselves in environmental analysis at Pitzer College is whether it’s possible to create modern socionatural systems that are truly sustaining; that is, that avoid the features of contemporary systems in which the human factor dominates to the detriment of the environment. Any genuinely sustainable society must honor diversity— cultural and biological—and, at Pitzer, we’re committed to forging innovative directions for a healthy future. Toward this end, students, along with faculty and staff, have initiated a program of ecological restoration in the Pitzer College Outback Preserve.

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

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

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 …

Teaching For Change: The Leadership In Environmental Education Partnership, Paul Faulstich

Pitzer Faculty Publications and Research

Humans are transforming earth's landscape from a natural matrix with pockets of civilization to just the opposite. Most of us realize that this pattern is not sustainable. I live and work in Claremont, California, a charming college town in the midst of suburban sprawl. The town has a central village of terminally tasteful, overpriced bungalows nestled in the shade of tall, largely exotic trees. Indeed, most of the landscape of this "city of trees and Ph.D.s" has been imported; only a remnant parcel of coastal sage scrub that the Claremont Colleges have reluctantly preserved remains.

The True Truth About Kgi And The Field Station, Paul Faulstich

Pitzer Faculty Publications and Research

There are multiple truths. One is the true truth. This truth remains the same no matter what anyone thinks or says about it. For example, it is true truth that we need oxygen. and that trees provide it. No matter what we think or say about it, this is the way it is. And, the Bernard Biological Field Station is habitat to threatened and endangered plants and animals. This, too, we know to be true.

Field Station Under Threat, Paul Faulstich

Pitzer Faculty Publications and Research

As reported in the last issue of The Other Side, The Bernard Biological Field Station of the Colleges is slated to be the site of the Keck Graduate Institute, the newest (but yet unbuilt) addition to the Claremont Consortium. With Pitzer casting the sole dissenting vote, the Claremont Colleges approved construction of the Keck Institute on eleven acres of the 85 acre Field Station.

Land Development And Biotechnology At The Claremont Colleges, Paul Faulstich

Pitzer Faculty Publications and Research

Founded on the Oxford model of a cluster of institutions, the Claremont Colleges has periodically established a new school. In the Spring of 1997, the Board of Fellows of the Claremont University Center charged with policy-making for the consortium-voted to establish a seventh college; the Keck Graduate Institute of applied life sciences. or bioengineering. Despite other landholdings, including a golf course and a non-operational gravel quarry, the Board of Fellows voted to site the New Venture on a portion-approximately eleven acres--of the Bernard Biological Field Station. (Pitzer's vote was cast against building on the Field Station.)

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 …

A Mathematician Among The Molasses Barrels: Maclaurin's Unpublished Memoir On Volumes, Judith V. Grabiner

Pitzer Faculty Publications and Research

Suppose we are given a solid of revolution generated by a conic section. Slice out a frustum of the solid [14, diagrams pp. 77, 80]. Then, construct a cylinder, with the same height as the frustum, whose diameter coincides with the diameter of the frustum at the midpoint of its height. What is the difference between the volume of the frustum and the volume of this cylinder? Does this difference depend on where in the solid the frustum is taken?

The beautiful theorems which answer these questions first appear in a 1735 manuscript by Colin Maclaurin (1698–1746). This …

Descartes And Problem-Solving, Judith V. Grabiner

Pitzer Faculty Publications and Research

What can Descartes' Geometry teach us about problem solving?

Predicting The Past, Recounting The Future: Human Ecology And A Prehistory Of Consciousness, Paul Faulstich

Pitzer Faculty Publications and Research

This paper is concerned with the organic derivation and primary meaning of Pleistocene finger flutings; I propose that in order to gain insight into the significance of the flutings, we must attempt an understanding of the physical and mental contexts in which they emerged. I suggest that finger flutings provided a cultural record in the Pleistocene which documented thought and action, and made it ready for reflection. Through the process of finger fluting, the human 'self' was objected and reality was modified in the experience of self-consciuosness. I argue that finger flutings, like language, were employed to discover and convey …

Malaysian Deforestation Proceeds Apace, Paul Faulstich

Pitzer Faculty Publications and Research

A hunger fast, dubbed Fast Action, was staged in front of the Japanese Consulate General in Honolulu on July 20 to protest the destruction of the most ancient and biologically diverse ecosystem on Earth. Organized by Hawai'i Earth First! and the O'ahu Rainforest Action Group, Fast Action was designed to alert people to the destruction of tropical rainforests in Sarawak, Malaysia. Protesters demanded on immediate moratorium on the cutting of rainforests in,which the Penan and other-native peoples live.

Hawaii's Hottest Issue: Update On Geothermal Development, Paul Faulstich

Pitzer Faculty Publications and Research

Walking through Hawai'i's Wao Kele O Puna rainforest, you can hear the coarse volcanic soil crunch underfoot. A surrealistic calm lingers in the thick air while songbirds call out from the understory. Yet this is a forest under siege.

Geothermal developers want to tap the volcanic heat beneath the Wao Kele O Puna forest and use it to make electricity and profits.

Hawaiians Fight For The Rainforest, Paul Faulstich

Pitzer Faculty Publications and Research

On March 25, 141 were arrested as part of the largest demonstration yet against the drilling of geothermal wells in the Wao Kele O Puna Rainforest on the Big Island of Hawaii. The geothermal project, undertaken by True Geothermal Company and endorsed by Hawaii's governor and other high-powered, short-sighted people, has already invaded the largest intact tropical lowland rainforest in the United States. The demonstration drew over 1500 protesters,

Hawaii's Rainforest Crunch: Land, People, And Geothermal Development, Paul Faulstich

Pitzer Faculty Publications and Research

One hundred and forty-one people, led by Native Hawaiians, were arrested on 25 March 1990 as part of the largest demonstration yet against geothermal development in Hawaii. The gathering was intended to focus attention on Native Hawaiian rights and the ecological consequences of drilling geothermal wells in the near-pristine Wao Kele O Puna rain forest. The energy project, undertaken by True Geothermal Company and endorsed by Hawaii's governor and other imposing figures, has already invaded the largest intact tropical lowland rain forest in the United States.

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

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 Taman Negara Batek: A People In Transition, Paul Faulstich

Pitzer Faculty Publications and Research

Batek Negritos from the vicinity of Taman Negara National Park in West Malaysia are a hunting and gathering people presently experiencing rapid encroachment by the modern world. Under the authority of the Malaysian government, they are being encouraged to settle and to emulate Malay subsistence farming communities. Unfortunately, this strategy has had a number of adverse effects on the Batek.

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

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

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

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

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

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

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 …