Math & Science
An exploration of mathematical style through 99 different proofs of the same theorem
This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo--whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp--Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau's Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird's-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.
In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancé.
But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the real world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics. Pesic focuses on the contested development of algebra--which even Newton resisted--and the gradual acceptance of the usefulness and perhaps even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof.
You've probably seen it before: a human brain dramatically lit from the side, the camera circling it like a helicopter shot of Stonehenge, and a modulated baritone voice exalting the brain's elegant design in reverent tones.
To which this book says: Pure nonsense. In a work at once deeply learned and wonderfully accessible, the neuroscientist David Linden counters the widespread assumption that the brain is a paragon of design--and in its place gives us a compelling explanation of how the brain's serendipitous evolution has resulted in nothing short of our humanity. A guide to the strange and often illogical world of neural function, The Accidental Mind shows how the brain is not an optimized, general-purpose problem-solving machine, but rather a weird agglomeration of ad-hoc solutions that have been piled on through millions of years of evolutionary history. Moreover, Linden tells us how the constraints of evolved brain design have ultimately led to almost every transcendent human foible: our long childhoods, our extensive memory capacity, our search for love and long-term relationships, our need to create compelling narrative, and, ultimately, the universal cultural impulse to create both religious and scientific explanations. With forays into evolutionary biology, this analysis of mental function answers some of our most common questions about how we've come to be who we are.
To perceive, according to this enactive approach to perception, is not merely to have sensations; it is to have sensations that we understand. In Action in Perception, Noë investigates the forms this understanding can take. He begins by arguing, on both phenomenological and empirical grounds, that the content of perception is not like the content of a picture; the world is not given to consciousness all at once but is gained gradually by active inquiry and exploration. Noë then argues that perceptual experience acquires content thanks to our possession and exercise of practical bodily knowledge, and examines, among other topics, the problems posed by spatial content and the experience of color. He considers the perspectival aspect of the representational content of experience and assesses the place of thought and understanding in experience. Finally, he explores the implications of the enactive approach for our understanding of the neuroscience of perception.
After Physics presents ambitious new essays about some of the deepest questions at the foundations of physics, by the physicist and philosopher David Albert. The book's title alludes to the close connections between physics and metaphysics, much in evidence throughout these essays. It also alludes to the work of imagining what it would be like for the project of physical science--considered as an investigation into the fundamental laws of nature--to be complete.
Albert argues that the difference between the past and the future--traditionally regarded as a matter for metaphysical or conceptual or linguistic or phenomenological analysis--can be understood as a mechanical phenomenon of nature. In another essay he contends that all versions of quantum mechanics that are compatible with the special theory of relativity make it impossible, even in principle, to present the entirety of what can be said about the world as a narrative sequence of "befores" and "afters." Any sensible and realistic way of solving the quantum-mechanical measurement problem, Albert claims in yet another essay, is ultimately going to force us to think of particles and fields, and even the very space of the standard scientific conception of the world, as approximate and emergent. Novel discussions of the problem of deriving principled limits on what can be known, measured, or communicated from our fundamental physical theories, along with a sweeping critique of the main attempts at making sense of probabilities in many-worlds interpretations of quantum mechanics, round out the collection.
A century ago, discoveries in physics came together with engineering to produce an array of astonishing new technologies that radically reshaped the world: radios, televisions, aircraft, computers, and a host of still-evolving digital tools. Today, a new technological convergence--of biology and engineering--promises to create the tools necessary to tackle the threats we now face, including climate change, drought, famine, and disease
World-renowned neuroscientist and academic leader Susan Hockfield describes the most exciting new developments and the scientists and engineers who helped to create them. Virus-built batteries. Cancer-detecting nanoparticles. Computer-engineered crops. Together, they highlight the promise of the technology revolution of the twenty-first century to overcome some of the greatest humanitarian, medical, and environmental challenges of our time.
This classic work in the philosophy of physical science is an incisive and readable account of the scientific method. Pierre Duhem was one of the great figures in French science, a devoted teacher, and a distinguished scholar of the history and philosophy of science. This book represents his most mature thought on a wide range of topics.
Five long essays that trace Jung's developing interest in alchemy from 1929 onward. An introduction and supplement to his major works on the subject, illustrated with 42 patients' drawings and paintings.
In the bestselling tradition of Stuff Matters and The Disappearing Spoon: a clever and engaging look at materials, the innovations they made possible, and how these technologies changed us.
In The Alchemy of Us, scientist and science writer Ainissa Ramirez examines eight inventions--clocks, steel rails, copper communication cables, photographic film, light bulbs, hard disks, scientific labware, and silicon chips--and reveals how they shaped the human experience. Ramirez tells the stories of the woman who sold time, the inventor who inspired Edison, and the hotheaded undertaker whose invention pointed the way to the computer. She describes, among other things, how our pursuit of precision in timepieces changed how we sleep; how the railroad helped commercialize Christmas; how the necessary brevity of the telegram influenced Hemingway's writing style; and how a young chemist exposed the use of Polaroid's cameras to create passbooks to track black citizens in apartheid South Africa. These fascinating and inspiring stories offer new perspectives on our relationships with technologies.
Ramirez shows not only how materials were shaped by inventors but also how those materials shaped culture, chronicling each invention and its consequences--intended and unintended. Filling in the gaps left by other books about technology, Ramirez showcases little-known inventors--particularly people of color and women--who had a significant impact but whose accomplishments have been hidden by mythmaking, bias, and convention. Doing so, she shows us the power of telling inclusive stories about technology. She also shows that innovation is universal--whether it's splicing beats with two turntables and a microphone or splicing genes with two test tubes and CRISPR.
If you're a science and data nerd like me, you may be interested in Alice and Bob Meet the Wall of Fire and The Prime Number Conspiracy from Quanta Magazine and Thomas Lin. - Bill Gates
These stories reveal the latest efforts to untangle the mysteries of the universe. Bringing together the best and most interesting science stories appearing in Quanta Magazine over the past five years, Alice and Bob Meet the Wall of Fire reports on some of the greatest scientific minds as they test the limits of human knowledge. Quanta, under editor-in-chief Thomas Lin, is the only popular publication that offers in-depth coverage of today's challenging, speculative, cutting-edge science. It communicates science by taking it seriously, wrestling with difficult concepts and clearly explaining them in a way that speaks to our innate curiosity about our world and ourselves.
In the title story, Alice and Bob--beloved characters of various thought experiments in physics--grapple with gravitational forces, possible spaghettification, and a massive wall of fire as Alice jumps into a black hole. Another story considers whether the universe is impossible, in light of experimental results at the Large Hadron Collider. We learn about quantum reality and the mystery of quantum entanglement; explore the source of time's arrow; and witness a eureka moment when a quantum physicist exclaims: "Finally, we can understand why a cup of coffee equilibrates in a room." We reflect on humans' enormous skulls and the Brain Boom; consider the evolutionary benefits of loneliness; peel back the layers of the newest artificial-intelligence algorithms; follow the "battle for the heart and soul of physics"; and mourn the disappearance of the "diphoton bump," revealed to be a statistical fluctuation rather than a revolutionary new particle. These stories from Quanta give us a front-row seat to scientific discovery.
Contributors
Philip Ball, K. C. Cole, Robbert Dijkgraaf, Dan Falk, Courtney Humphries, Ferris Jabr, Katia Moskvitch, George Musser, Michael Nielsen, Jennifer Ouellette, John Pavlus, Emily Singer, Andreas von Bubnoff, Frank Wilczek, Natalie Wolchover, Carl Zimmer
As a young science fiction fan, physicist James Kakalios marveled at the future predicted in the pulp magazines, comics, and films of the '50s and '60s. By 2010, he was sure we'd have flying cars and jetpacks. But what we ended up with-laptop computers, MRI machines, Blu-ray players, and dozens of other real-life marvels-are even more fantastic. In The Amazing Story of Quantum Mechanics, he explains why the development of quantum mechanics enabled our amazing present day.
In his trademark style, Kakalios uses pop culture examples- everything from the graphic novel Watchmen to schlock horror movies of the '50s-to elucidate some of the most complex science there is. And he brings to life the groundbreaking scientists whose discoveries made our present life possible. Along the way, he dispels the misconception that quantum mechanics is unknowable by mere mortals. It's not magic; it's science!
For Americans entering the twenty-first century, it is the best of times and the worst of times. Material wealth is at record levels, yet disturbing social problems reflect a deep spiritual poverty. In this compelling book, well-known social psychologist David G. Myers asks how this paradox has come to be and, more important, how we can spark social renewal and dream a new American dream.
Myers explores the research on social ills from the 1960s through the 1990s and concludes that the materialism and radical individualism of this period have cost us dearly, imperiling our children, corroding general civility, and diminishing our happiness. However, in the voices of public figures and ordinary citizens he now hears a spirit of optimism. The national dialogue is shifting--away from the expansion of personal rights and toward enhancement of communal civility, away from efforts to raise self-esteem and toward attempts to arouse social responsibility, away from "whose values?" and toward "our values." Myers analyzes in detail the research on educational and other programs that deal with social problems, explaining which seem to work and why. He then offers positive and well-reasoned advice, suggesting that a renewed social ecology for America will rest on policies that balance "me thinking" with "we thinking."
An Inconvenient Truth--Gore's groundbreaking, battle cry of a follow-up to the bestselling Earth in the Balance--is being published to tie in with a documentary film of the same name. Both the book and film were inspired by a series of multimedia presentations on global warming that Gore created and delivers to groups around the world. With this book, Gore, who is one of our environmental heroes--and a leading expert--brings together leading-edge research from top scientists around the world; photographs, charts, and other illustrations; and personal anecdotes and observations to document the fast pace and wide scope of global warming. He presents, with alarming clarity and conclusiveness--and with humor, too--that the fact of global warming is not in question and that its consequences for the world we live in will be disastrous if left unchecked. This riveting new book--written in an accessible, entertaining style--will open the eyes of even the most skeptical.
Two giants of twentieth-century psychology in dialogue
C. G. Jung and Erich Neumann first met in 1933, at a seminar Jung was conducting in Berlin. Jung was fifty-seven years old and internationally acclaimed for his own brand of psychotherapy. Neumann, twenty-eight, had just finished his studies in medicine. The two men struck up a correspondence that would continue until Neumann's death in 1960. A lifelong Zionist, Neumann fled Nazi Germany with his family and settled in Palestine in 1934, where he would become the founding father of analytical psychology in the future state of Israel.
Presented here in English for the first time are letters that provide a rare look at the development of Jung's psychological theories from the 1930s onward as well as the emerging self-confidence of another towering twentieth-century intellectual who was often described as Jung's most talented student. Neumann was one of the few correspondence partners of Jung's who was able to challenge him intellectually and personally. These letters shed light on not only Jung's political attitude toward Nazi Germany, his alleged anti-Semitism, and his psychological theory of fascism, but also his understanding of Jewish psychology and mysticism. They affirm Neumann's importance as a leading psychologist of his time and paint a fascinating picture of the psychological impact of immigration on the German Jewish intellectuals who settled in Palestine and helped to create the state of Israel.
Featuring Martin Liebscher's authoritative introduction and annotations, this volume documents one of the most important intellectual relationships in the history of analytical psychology.
Frighteningly fascinating.--Booklist
Gripping stories, filled with details that are in equal part delicious and disgusting, but always fascinating.--Lisa Sanders, MD, author of Every Patient Tells a Story and the New York Times Magazine Diagnosis column
"To reproduce promiscuously and to wreak havoc wherever they can find a home," this is the sole raison d'être of viruses writes Dr. Warren Andiman, an HIV/AIDS researcher who has been on the front lines battling infectious diseases for over forty years. In Animal Viruses and Humans: A Narrow Divide, Andiman traces the history of eight zoonotic viruses --deadly microbes that have made the leap directly from animals to human populations: Middle East Respiratory Syndrome (MERS), Swine influenza, Hantavirus, Monkeypox, Severe Acute Respiratory Syndrome (SARS), Rabies, Ebola, and Henipaviruses (Nipah and Hendra). He also illustrates the labor intensive and fascinating detective work that infectious disease specialists must do to uncover the source of an outbreak.
Andiman also looks to the future, envisioning the effects on zoonoses (diseases caused by zoonotic viruses) of climate change, microenvironmental damage, population shifts, and globalization. He reveals the steps that we can, and must, take to stem the spread of animal viruses, explaining, "The zoonoses I've chosen to write about . . . are meant to describe only a small sample of what is already out there but, more menacingly, what is inevitably on its way, in forms we can only imagine."
Warren Andiman, MD is professor emeritus of pediatrics and epidemiology at the Yale Schools of Medicine and Public Health.