Math & Science
David Abram's first book, The Spell of the Sensuous has become a classic of environmental literature. Now he returns with a startling exploration of our human entanglement with the rest of nature.
As the climate veers toward catastrophe, the innumerable losses cascading through the biosphere make vividly evident the need for a metamorphosis in our relation to the living land. For too long we've ignored the wild intelligence of our bodies, taking our primary truths from technologies that hold the living world at a distance. Abram's writing subverts this distance, drawing readers ever closer to their animal senses in order to explore, from within, the elemental kinship between the human body and the breathing Earth. The shape-shifting of ravens, the erotic nature of gravity, the eloquence of thunder, the pleasures of being edible: all have their place in this book.
How scientists through the ages have conducted thought experiments using imaginary entities--demons--to test the laws of nature and push the frontiers of what is possible
Science may be known for banishing the demons of superstition from the modern world. Yet just as the demon-haunted world was being exorcized by the enlightening power of reason, a new kind of demon mischievously materialized in the scientific imagination itself. Scientists began to employ hypothetical beings to perform certain roles in thought experiments--experiments that can only be done in the imagination--and these impish assistants helped scientists achieve major breakthroughs that pushed forward the frontiers of science and technology. Spanning four centuries of discovery--from René Descartes, whose demon could hijack sensorial reality, to James Clerk Maxwell, whose molecular-sized demon deftly broke the second law of thermodynamics, to Darwin, Einstein, Feynman, and beyond--Jimena Canales tells a shadow history of science and the demons that bedevil it. She reveals how the greatest scientific thinkers used demons to explore problems, test the limits of what is possible, and better understand nature. Their imaginary familiars helped unlock the secrets of entropy, heredity, relativity, quantum mechanics, and other scientific wonders--and continue to inspire breakthroughs in the realms of computer science, artificial intelligence, and economics today. The world may no longer be haunted as it once was, but the demons of the scientific imagination are alive and well, continuing to play a vital role in scientists' efforts to explore the unknown and make the impossible real.
Benjamin Franklin is well known to most of us, yet his fundamental and wide-ranging contributions to science are still not adequately understood. Until now he has usually been incorrectly regarded as a practical inventor and tinkerer rather than a scientific thinker. He was elected to membership in the elite Royal Society because his experiments and original theory of electricity had made a science of that new subject. His popular fame came from his two lightning experiments--the sentry-box experiment and the later and more famous experiment of the kite--which confirmed his theoretical speculations about the identity of electricity and provided a basis for the practical invention of the lightning rod. Franklin advanced the eighteenth-century understanding of all phenomena of electricity and provided a model for experimental science in general.
I. Bernard Cohen, an eminent historian of science and the principal elucidator of Franklin's scientific work, examines his activities in fields ranging from heat to astronomy. He provides masterful accounts of the theoretical background of Franklin's science (especially his study of Newton), the experiments he performed, and their influence throughout Europe as well as the United States. Cohen emphasizes that Franklin's political and diplomatic career cannot be understood apart from his scientific activities, which established his reputation and brought him into contact with leaders of British and European society. A supplement by Samuel J. Edgerton considers Franklin's attempts to improve the design of heating stoves, another practical application that arose from theoretical interests. This volume will be valuable to all readers wanting to learn more about Franklin and to gain a deeper appreciation of the development of science in America.
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 year's finest writing on mathematics from around the world, with a foreword by Nobel Prize-winning physicist Roger Penrose
This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2013 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Philip Davis offers a panoramic view of mathematics in contemporary society; Terence Tao discusses aspects of universal mathematical laws in complex systems; Ian Stewart explains how in mathematics everything arises out of nothing; Erin Maloney and Sian Beilock consider the mathematical anxiety experienced by many students and suggest effective remedies; Elie Ayache argues that exchange prices reached in open market transactions transcend the common notion of probability; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematical physicist Roger Penrose and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.
The year's finest writing on mathematics from around the world
This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2014 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here John Conway presents examples of arithmetical statements that are almost certainly true but likely unprovable; Carlo Séquin explores, compares, and illustrates distinct types of one-sided surfaces known as Klein bottles; Keith Devlin asks what makes a video game good for learning mathematics and shows why many games fall short of that goal; Jordan Ellenberg reports on a recent breakthrough in the study of prime numbers; Stephen Pollard argues that mathematical practice, thinking, and experience transcend the utilitarian value of mathematics; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes an introduction by editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.
The year's finest writing on mathematics from around the world
This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2015 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates.
Here David Hand explains why we should actually expect unlikely coincidences to happen; Arthur Benjamin and Ethan Brown unveil techniques for improvising custom-made magic number squares; Dana Mackenzie describes how mathematicians are making essential contributions to the development of synthetic biology; Steven Strogatz tells us why it's worth writing about math for people who are alienated from it; Lisa Rougetet traces the earliest written descriptions of Nim, a popular game of mathematical strategy; Scott Aaronson looks at the unexpected implications of testing numbers for randomness; and much, much more.
In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.
-- "Publishers Weekly"
The year's finest mathematics writing from around the world
This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2016 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates.
Here Burkard Polster shows how to invent your own variants of the Spot It! card game, Steven Strogatz presents young Albert Einstein's proof of the Pythagorean Theorem, Joseph Dauben and Marjorie Senechal find a treasure trove of math in New York's Metropolitan Museum of Art, and Andrew Gelman explains why much scientific research based on statistical testing is spurious. In other essays, Brian Greene discusses the evolving assumptions of the physicists who developed the mathematical underpinnings of string theory, Jorge Almeida examines the misperceptions of people who attempt to predict lottery results, and Ian Stewart offers advice to authors who aspire to write successful math books for general readers. And there's much, much more.
In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.
-- "Math Tango"
The year's finest mathematics writing from around the world
This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2017 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates.
Here Evelyn Lamb describes the excitement of searching for incomprehensibly large prime numbers, Jeremy Gray speculates about who would have won math's highest prize--the Fields Medal--in the nineteenth century, and Philip Davis looks at mathematical results and artifacts from a business and marketing viewpoint. In other essays, Noson Yanofsky explores the inherent limits of knowledge in mathematical thinking, Jo Boaler and Lang Chen reveal why finger-counting enhances children's receptivity to mathematical ideas, and Carlo Séquin and Raymond Shiau attempt to discover how the Renaissance painter Fra Luca Pacioli managed to convincingly depict his famous rhombicuboctahedron, a twenty-six-sided Archimedean solid. And there's much, much more.
In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.
The year's finest mathematical writing from around the world
This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2018 makes available to a wide audience many pieces not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice--and taking readers behind the scenes of today's hottest mathematical debates.
James Grime shows how to build subtly mischievous dice for playing slightly unfair games and Michael Barany traces how our appreciation of the societal importance of mathematics has developed since World War II. In other essays, Francis Su extolls the inherent values of learning, doing, and sharing mathematics, and Margaret Wertheim takes us on a mathematical exploration of the mind and the world--with glimpses at science, philosophy, music, art, and even crocheting. And there's much, much more.
In addition to presenting the year's most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable pieces on mathematics.
This is a must-read for anyone interested in where math has taken us--and where it is headed.
The year's finest mathematical writing from around the world
This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2019 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice--and taking readers behind the scenes of today's hottest mathematical debates. In this volume, Moon Duchin explains how geometric-statistical methods can be used to combat gerrymandering, Jeremy Avigad illustrates the growing use of computation in making and verifying mathematical hypotheses, and Kokichi Sugihara describes how to construct geometrical objects with unusual visual properties. In other essays, Neil Sloane presents some recent additions to the vast database of integer sequences he has catalogued, and Alessandro Di Bucchianico and his colleagues highlight how mathematical methods have been successfully applied to big-data problems. And there's much, much more. In addition to presenting the year's most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable writings on mathematics. This is a must-read for anyone interested in where math has taken us--and where it is headed.
The year's finest mathematical writing from around the world
This annual anthology brings together the year's finest mathematics writing from around the world--and you don't need to be a mathematician to enjoy the pieces collected here. These essays--from leading names and fresh new voices--delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice, and taking readers behind the scenes of today's hottest mathematical debates. Here, Viktor Blåsjö gives a brief history of "lockdown mathematics"; Yelda Nasifoglu decodes the politics of a seventeenth-century play in which the characters are geometric shapes; and Andrew Lewis-Pye explains the basic algorithmic rules and computational procedures behind cryptocurrencies. In other essays, Terence Tao candidly recalls the adventures and misadventures of growing up to become a leading mathematician; Natalie Wolchover shows how old math gives new clues about whether time really flows; and David Hand discusses the problem of "dark data"--information that is missing or ignored. And there is much, much more.
Believe it or not, today we may be living in the most peaceful moment in our species' existence. In his gripping and controversial new work, New York Times bestselling author Steven Pinker shows that despite the ceaseless news about war, crime, and terrorism, violence has actually been in decline over long stretches of history. Exploding myths about humankind's inherent violence and the curse of modernity, this ambitious book continues Pinker's exploration of the essence of human nature, mixing psychology and history to provide a remarkable picture of an increasingly enlightened world.
Contents include "On the Hypotheses which Lie at the Foundations of Geometry" by Georg Friedrich Riemann; "On the Facts which Lie at the Foundations of Geometry" and "On the Origin and Significance of Geometrical Axioms" by Hermann von Helmholtz; "A Comparative Review of Recent Researches in Geometry" by Felix Klein; "On the Space Theory of Matter" by William Kingdon Clifford; "On the Foundations of Geometry" by Henri Poincaré; "Euclidean Geometry and Riemannian Geometry" by Elie Cartan; and "The Problem of Space, Ether, and the Field in Physics" by Albert Einstein.
These remarkably accessible papers will appeal to students of modern physics and mathematics, as well as anyone interested in the origins and sources of Einstein's most profound work. Peter Pesic of St. John's College in Santa Fe, New Mexico, provides an introduction, as well as notes that offer insights into each paper.
Freud approved the overall editorial plan, specific renderings of key words and phrases, and the addition of valuable notes, from bibliographical and explanatory. Many of the translations were done by Strachey himself; the rest were prepared under his supervision. The result was to place the Standard Edition in a position of unquestioned supremacy over all other existing versions.Newly designed in a uniform format, each new paperback in the Standard Edition opens with a biographical essay on Freud's life and work --along with a note on the individual volume--by Peter Gay, Sterling Professor of History at Yale.
Buddhism shares with science the task of examining the mind empirically; it has pursued, for two millennia, direct investigation of the mind through penetrating introspection. Neuroscience, on the other hand, relies on third-person knowledge in the form of scientific observation. In this book, Matthieu Ricard, a Buddhist monk trained as a molecular biologist, and Wolf Singer, a distinguished neuroscientist--close friends, continuing an ongoing dialogue--offer their perspectives on the mind, the self, consciousness, the unconscious, free will, epistemology, meditation, and neuroplasticity.
Ricard and Singer's wide-ranging conversation stages an enlightening and engaging encounter between Buddhism's wealth of experiential findings and neuroscience's abundance of experimental results. They discuss, among many other things, the difference between rumination and meditation (rumination is the scourge of meditation, but psychotherapy depends on it); the distinction between pure awareness and its contents; the Buddhist idea (or lack of one) of the unconscious and neuroscience's precise criteria for conscious and unconscious processes; and the commonalities between cognitive behavioral therapy and meditation. Their views diverge (Ricard asserts that the third-person approach will never encounter consciousness as a primary experience) and converge (Singer points out that the neuroscientific understanding of perception as reconstruction is very like the Buddhist all-discriminating wisdom) but both keep their vision trained on understanding fundamental aspects of human life.
BACK IN PRINT with a new preface and a new chapter
In this unusual book, first published by The MIT Press in 1980 and now updated with a new chapter, Steven Brams applies the mathematical theory of games to the Hebrew Bible. Brams's thesis is that God and the human biblical characters acted rationally--that is, given their preferences and their knowledge of other players' preferences, they made strategy choices that led to the best attainable outcomes. Beginning with the Creation and focusing on those stories richest in conflict and intrigue, Brams uses elementary game-theoretic tools to elucidate the rational calculations of biblical players and to show precisely the manner in which they sought to achieve their goals. He relies almost exclusively on noncooperative theory, making use of both game tree and matrix forms of games. Brams uses his strategic analyses to build a detailed assessment of God's character and motivations, including the reasons for His frequently wrathful behavior. Brams's insights have application to biblical studies, the philosophy of religion, political theory, and game theory and methodology.In the new chapter, Brams surveys the literature of the past twenty years on political-strategic interpretations of the Hebrew Bible. He also extends the game-theoretic analysis, using the theory of moves, to study a counterfactual situation--what if Abraham had refused God's command to sacrifice Isaac?--and to examine the rationality of believing in a superior being.
Why birds are smarter than we think
Birds have not been known for their high IQs, which is why a person of questionable intelligence is sometimes called a birdbrain. Yet in the past two decades, the study of avian intelligence has witnessed dramatic advances. From a time when birds were seen as simple instinct machines responding only to stimuli in their external worlds, we now know that some birds have complex internal worlds as well. This beautifully illustrated book provides an engaging exploration of the avian mind, revealing how science is exploding one of the most widespread myths about our feathered friends--and changing the way we think about intelligence in other animals as well. Bird Brain looks at the structures and functions of the avian brain, and describes the extraordinary behaviors that different types of avian intelligence give rise to. It offers insights into crows, jays, magpies, and other corvids--the "masterminds" of the avian world--as well as parrots and some less-studied species from around the world. This lively and accessible book shows how birds have sophisticated brains with abilities previously thought to be uniquely human, such as mental time travel, self-recognition, empathy, problem solving, imagination, and insight. Written by a leading expert and featuring a foreword by Frans de Waal, renowned for his work on animal intelligence, Bird Brain shines critical new light on the mental lives of birds.
A captivating A-Z treasury about birds and birding
Birdpedia is an engaging illustrated compendium of bird facts and birding lore. Featuring nearly 200 entries--on topics ranging from plumage and migration to birds in art, literature, and folklore--this enticing collection is brimming with wisdom and wit about all things avian. Christopher Leahy sheds light on hawk-watching, twitching, and other rituals from the sometimes mystifying world of birding that entail a good deal more than their names imply. He explains what kind of bird's nests you can eat, why mocking birds mock, and many other curiosities that have induced otherwise sane people to peer into treetops using outrageously expensive optical equipment. Leahy shares illuminating insights about pioneering ornithologists such as John James Audubon and Florence Bailey, and describes unique bird behaviors such as anting, caching, duetting, and mobbing. He discusses avian fossils, the colloquial naming of birds, the science and history of ornithology, and more. The book's convenient size makes it the perfect traveling companion to take along on your own avian adventures. With charming illustrations by Abby McBride, Birdpedia is a marvelous mix of fact and fancy that is certain to delight seasoned birders and armchair naturalists alike.
From award-winning author and ornithologist Tim Birkhead, a sweeping history of the long and close relationship between birds and humans
Since the dawn of human history, birds have stirred our imagination, inspiring and challenging our ideas about science, faith, art, and philosophy. We have worshipped birds as gods, hunted them for sustenance, adorned ourselves with their feathers, studied their wings to engineer flight, and, more recently, attempted to protect them. In Birds and Us, award-winning writer and ornithologist Tim Birkhead takes us on a dazzling epic journey through our mutual history with birds, from the ibises mummified and deified by Ancient Egyptians to the Renaissance fascination with woodpecker anatomy--and from the Victorian obsession with egg collecting to today's fight to save endangered species and restore their habitats. Spanning continents and millennia, Birds and Us chronicles the beginnings of a written history of birds in ancient Greece and Rome, the obsession with falconry in the Middle Ages, and the development of ornithological science. Moving to the twentieth century, the book tells the story of the emergence of birdwatching and the field study of birds, and how they triggered an extraordinary flowering of knowledge and empathy for birds, eventually leading to today's massive worldwide interest in birds--and the realization of the urgent need to save them. Weaving in stories from Birkhead's life as scientist, including far-flung expeditions to wondrous Neolithic caves in Spain and the bustling guillemot colonies of the Faroe Islands, this rich and fascinating book is an unforgettable account of how birds have shaped us, and how we have shaped them.