Mathematics and the Unexpected

Author: Ivar Ekeland
Publisher: University of Chicago Press
ISBN: 9780226199900
Category: Mathematics
Page: 146
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"Not the least unexpected thing about Mathematics and the Unexpected is that a real mathematician should write not just a literate work, but a literary one."—Ian Stewart, New Scientist "In this brief, elegant treatise, assessable to anyone who likes to think, Ivar Ekelund explains some philosophical implications of recent mathematics. He examines randomness, the geometry involved in making predictions, and why general trends are easy to project (it will snow in January) but particulars are practically impossible (it will snow from 2 p.m. to 5 p.m. on the 21st)."—Village Voice

The Best of All Possible Worlds

Mathematics and Destiny
Author: Ivar Ekeland
Publisher: University of Chicago Press
ISBN: 0226199959
Category: Mathematics
Page: 207
View: 4278

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Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what is the best of all possible worlds? How do we define it? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer. This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of optimization, or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today. Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of erudition—one that will be essential reading for popular-science buffs and historians of science alike.

The Broken Dice, and Other Mathematical Tales of Chance

Author: Ivar Ekeland
Publisher: University of Chicago Press
ISBN: 9780226199924
Category: Mathematics
Page: 190
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Ivar Ekeland extends his consideration of the catastrophe theory of the universe begun in his widely acclaimed Mathematics and the Unexpected, by drawing on rich literary sources, particularly the Norse saga of Saint Olaf, and such current topics as chaos theory, information theory, and particle physics. "Ivar Ekeland gained a large and enthusiastic following with Mathematics and the Unexpected, a brilliant and charming exposition of fundamental new discoveries in the theory of dynamical systems. The Broken Dice continues the same theme, and in the same elegant, seemingly effortless style, but focuses more closely on the implications of those discoveries for the rest of human culture. What are chance and probability? How has our thinking about them been changed by the discovery of chaos? What are all of these concepts good for? . . . Ah, but, I mustn't give the game away, any more than I should if I were reviewing a detective novel. And this is just as gripping a tale. . . . Beg, borrow, or preferably buy a copy. . . . I guarantee you won't be disappointed."—Ian Stewart, Science

Mathematics and the Aesthetic

New Approaches to an Ancient Affinity
Author: Nathalie Sinclair,William Higginson
Publisher: Springer Science & Business Media
ISBN: 9780387381459
Category: Mathematics
Page: 288
View: 330

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This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.

Mathematics the Truth

‘Moving mathematics teaching into the age of quantum mechanics and relativity.’
Author: Malcolm Cameron
Publisher: Malcolm Cameron
ISBN: 1925635783
Category: Mathematics
Page: 168
View: 4812

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Malcolm McDonald, FEDFA Union, State President, 1992-96

Mathematics and the Body

Material Entanglements in the Classroom
Author: Elizabeth de Freitas,Nathalie Sinclair
Publisher: Cambridge University Press
ISBN: 1107039487
Category: Education
Page: 312
View: 3780

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This book expands the landscape of research in mathematics education by analyzing how the body influences mathematical thinking.


Author: Timothy Gowers
Publisher: Sterling Publishing Company, Inc.
ISBN: 9781402768972
Category: Mathematics
Page: 180
View: 326

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Mathematics is a subject we are all exposed to in our daily lives, but one that many of us fear. Timothy Gowers’s entertaining overview of the topic explains the differences between what we learn at school and advanced mathematics, and helps the math phobic emerge with a clearer understanding of such paradoxical-sounding concepts as “infinity,” “curved space,” and “imaginary numbers.” From basic ideas to philosophical queries to common sociological questions about the mathematical community, this book unravels the mysteries of space and numbers.

Digital Youth, Innovation, and the Unexpected

Author: Tara McPherson
Publisher: MIT Press
ISBN: 0262134950
Category: Education
Page: 259
View: 7533

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How emergent practices and developments in young people's digital media can result intechnological innovation or lead to unintended learning experiences and unanticipated socialencounters.

Energy and the Unexpected

Author: Keith James Laidler
Publisher: Oxford University Press, USA
ISBN: 9780198525165
Category: Language Arts & Disciplines
Page: 146
View: 731

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Only in the early 19th century did scientists recognize that energy is a distinct physical quantity. Since then, however, it has played a pivotal role in the advancement and the understanding of science and in technology. From the steam engine to the equation e=mc2 and beyond, the concept of energy offers an essential key to our understanding of the Universe. In this entertaining and highly readable book, Professor Laidler explains the concept of energy and its characteristics as theywere discovered over the past two centuries. He describes how energy transformations, as interpreted by the second law of thermodynamics, are not absolute but can only be understood in terms of chance and probability. After looking at energy on a small scale and then at the scale of the Universe itself, he shows how these topics are linked with chaos theory according to which the unexpected is inevitable. Written for the general reader with an interest in science, the development and interrelationship of the concepts of energy, chance and chaos are set in their historical context, and illuminated by accounts of the key scientists involved and of some of their investigations.

The Unexpected Hanging, and Other Mathematical Diversions

With a New Afterword and Expanded Bibliography
Author: Martin Gardner
Publisher: N.A
ISBN: 9780226282565
Category: Mathematics
Page: 263
View: 5244

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Gathers paradoxes, logic puzzles, number problems, geometric problems, gambling puzzles, optical illusions, string, word, and chess problems featured in Scientific American

The Post-human Condition

Author: Robert Pepperell
Publisher: Intellect Books
ISBN: 9781871516456
Category: Technology & Engineering
Page: 206
View: 3573

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This work challenges many of the humanist assumptions of Western philosophy, science and art. It proposes a view of the human condition building on the findings of quantum theory, chaos theory, catastrophe theory, cybernetics, cyberpunk and New Ageism, taking into account current scientific and technological developments.

Unexpected Links between Egyptian and Babylonian Mathematics

Author: Jöran Friberg
Publisher: World Scientific
ISBN: 9814480401
Category: Science
Page: 308
View: 6488

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Mesopotamian mathematics is known from a great number of cuneiform texts, most of them Old Babylonian, some Late Babylonian or pre-Old-Babylonian, and has been intensively studied during the last couple of decades. In contrast to this Egyptian mathematics is known from only a small number of papyrus texts, and the few books and papers that have been written about Egyptian mathematical papyri have mostly reiterated the same old presentations and interpretations of the texts. In this book, it is shown that the methods developed by the author for the close study of mathematical cuneiform texts can also be successfully applied to all kinds of Egyptian mathematical texts, hieratic, demotic, or Greek-Egyptian. At the same time, comparisons of a large number of individual Egyptian mathematical exercises with Babylonian parallels yield many new insights into the nature of Egyptian mathematics and show that Egyptian and Babylonian mathematics display greater similarities than expected. Contents:Two Curious Mathematical Cuneiform Texts from Old Babylonian MariHieratic Mathematical Papyri and Cuneiform Mathematical TextsDemotic Mathematical Papyri and Cuneiform Mathematical TextsGreek-Egyptian Mathematical Documents and Cuneiform Mathematical Texts Readership: Mathematicians, historians of science, egyptologists and assyriologists. Keywords:Babylonian Mathematics;Egyptian Mathematics;Greek Mathematics;Mathematical Cuneiform Texts;Mathematical Papyri;Ancient Mathematics;Early Mathematics;History of Mathematics;Demotic Texts;Hieratic TextsKey Features:Extensive surveys of known Egyptian mathematical textsNew interpretations of particularly difficult Egyptian or Babylonian mathematical exercisesMany detailed diagrams and figures, using computer-aided methods of presentationsInteresting observations of experiments with new ways of representing fractions in demotic and Greek-Egyptian mathematical texts


The Math and Myth of Coincidence
Author: Joseph Mazur
Publisher: Hachette UK
ISBN: 0465040004
Category: Mathematics
Page: 288
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A mathematical guide to understanding why life can seem to be one big coincidence-and why the odds of just about everything are better than we would think. What are the chances? This is the question we ask ourselves when we encounter the strangest and most seemingly impossible coincidences, like the woman who won the lottery four times or the fact that Lincoln's dreams foreshadowed his own assassination. But, when we look at coincidences mathematically, the odds are a lot better than any of us would have thought. In Fluke, mathematician Joseph Mazur takes a second look at the seemingly improbable, sharing with us an entertaining guide to the most surprising moments in our lives. He takes us on a tour of the mathematical concepts of probability, such as the law of large numbers and the birthday paradox, and combines these concepts with lively anecdotes of flukes from around the world. How do you explain finding your college copy of Moby Dick in a used bookstore on the Seine on your first visit to Paris? How can a jury be convinced beyond a reasonable doubt that DNA found at the scene of a heinous crime did not get there by some fluke? Should we be surprised if strangers named Maria and Francisco, seeking each other in a hotel lobby, accidentally meet the wrong Francisco and the wrong Maria, another pair of strangers also looking for each other? As Mazur reveals, if there is any likelihood that something could happen, no matter how small, it is bound to happen to someone at some time. In Fluke, Mazur offers us proof of the inevitability of the sublime and the unexpected. He has written a book that will appeal to anyone who has ever wondered how all of the tiny decisions that happen in our lives add up to improbable wholes. A must-read for math enthusiasts and storytellers alike, Fluke helps us to understand the true nature of chance.

Complex Economic Dynamics: An introduction to macroeconomic dynamics

Author: Richard Hollis Day
Publisher: MIT Press
ISBN: 9780262041720
Category: Business & Economics
Page: 400
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Richard H. Day was one of the first economists to recognize the importance of complex dynamics, or chaos theory, to economics. He can justly be described as one of the originators of the now extensive economic literature on chaos.The two volumes of Complex Economic Dynamics show that, far from being a passing trend in economic research, complex dynamics belongs at the heart of the subject. Although they can be read independently, the volumes follow a logical sequence. Volume 1 contained nontechnical introductions to the basics of economic change and to the mathematical and theoretical tools used to describe them. Volume 2, which is concerned with macroeconomic dynamics, looks at the economy as a whole. Topics include business cycles, economic growth, economic development, and dynamical economic science and policy. The book concludes with the author's reflections on the implications of complex dynamics for economic theory, quantitative research, and government policy.

Acting under Uncertainty

Multidisciplinary Conceptions
Author: George M. von Furstenberg
Publisher: Springer Science & Business Media
ISBN: 9401578737
Category: Business & Economics
Page: 486
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Uncertainty could be associated with wisdom, enterprise, and discovery. In ordinary speech, however, it has mostly negative connotations. There is "fear of the unknown" and "ignorance is bliss;" there are maxims to the effect that "what you don't know doesn't hurt you" (or: "bother you") in several languages. This volume suggests that we need be bothered by the excessive confidence with which scientists, particularly social scientists, present some of their conclusions and overstate their range of application. Otherwise many of the questions that should be raised about all the major uncertainties attending a particular issue routinely may continue to be thwarted or suppressed. Down playing uncertainty does not lead to more responsible or surer action, it sidetracks research agendas, and leaves the decision makers exposed to nasty surprise. This volume demonstrates that recognizing the many forms of uncertainty that enter into the development of any particular subject matter is a precondition for more responsible choice and deeper knowledge. Our purpose is to contribute to a broader appreciation of uncertainty than regularly accorded in any of the numerous disciplines represented here. The seventeenth-century French philosopher Descartes, quoted in this volume, wrote that "whoever is searching after truth must, once in his life, doubt all things; insofar as this is possible. " White areas left on maps of the world in past centuries were a much more productive challenge than marking the end of the known world with the pillars of Hercules.

Unexpected Expectations

The Curiosities of a Mathematical Crystal Ball
Author: Leonard M. Wapner
Publisher: CRC Press
ISBN: 1568817215
Category: Mathematics
Page: 220
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Unexpected Expectations: The Curiosities of a Mathematical Crystal Ball explores how paradoxical challenges involving mathematical expectation often necessitate a reexamination of basic premises. The author takes you through mathematical paradoxes associated with seemingly straightforward applications of mathematical expectation and shows how these unexpected contradictions may push you to reconsider the legitimacy of the applications. The book requires only an understanding of basic algebraic operations and includes supplemental mathematical background in chapter appendices. After a history of probability theory, it introduces the basic laws of probability as well as the definition and applications of mathematical expectation/expected value (E). The remainder of the text covers unexpected results related to mathematical expectation, including: The roles of aversion and risk in rational decision making A class of expected value paradoxes referred to as envelope problems Parrondo’s paradox—how negative (losing) expectations can be combined to give a winning result Problems associated with imperfect recall Non-zero-sum games, such as the game of chicken and the prisoner’s dilemma Newcomb’s paradox—a great philosophical paradox of free will Benford’s law and its use in computer design and fraud detection While useful in areas as diverse as game theory, quantum mechanics, and forensic science, mathematical expectation generates paradoxes that frequently leave questions unanswered yet reveal interesting surprises. Encouraging you to embrace the mysteries of mathematics, this book helps you appreciate the applications of mathematical expectation, "a statistical crystal ball." Listen to an interview with the author on

The Self in European and North American Culture

Development and Processes
Author: J.H. Oosterwegel,R.A. Wicklund
Publisher: Springer Science & Business Media
ISBN: 9401103313
Category: Psychology
Page: 395
View: 8250

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How diverse or potentially overlapping are the numerous self-models, self-theories, and directions of self-research? It has become clear that the processes associated with the self are complex and diverse, and that many of the approaches associated with the self have been pursued in isolation. Moreover, the fact of there being different traditions within developmental and social psychology, as well as different traditions in Europe and North America, has also led to a certain cacophony when we examine the self-field as a whole. The chapters here confront these differences, trying to come to terms with phenomena that are overarching, that extend through the dimensions of developmental psychology, social psychology, motivation psychology, and parts of clinical psychology. The book as whole gives a clear presentation of the issues, questions and phenomena that surface in research fields known as self psychology.