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.

Bestselling author and acclaimed physicist Lawrence Krauss offers a paradigm-shifting view of how everything that exists came to be in the first place."Where did the universe come from? What was there before it? What will the future bring? And finally, why is there something rather than nothing?"One of the few prominent scientists today to have crossed the chasm between science and popular culture, Krauss describes the staggeringly beautiful experimental observations and mind-bending new theories that demonstrate not only can something arise from nothing, something will always arise from nothing. With a new preface about the significance of the discovery of the Higgs particle, A Universe from Nothing uses Krauss's characteristic wry humor and wonderfully clear explanations to take us back to the beginning of the beginning, presenting the most recent evidence for how our universe evolved--and the implications for how it's going to end. Provocative, challenging, and delightfully readable, this is a game-changing look at the most basic underpinning of existence and a powerful antidote to outmoded philosophical, religious, and scientific thinking.

Throughout our history, humans have been captivated by mythic beasts and legendary creatures. Tales of Bigfoot, the Yeti, and the Loch Ness monster are part of our collective experience. Now comes a book from two dedicated investigators that explores and elucidates the fascinating world of cryptozoology.

Daniel Loxton and Donald R. Prothero have written an entertaining, educational, and definitive text on cryptids, presenting the arguments both for and against their existence and systematically challenging the pseudoscience that perpetuates their myths. After examining the nature of science and pseudoscience and their relation to cryptozoology, Loxton and Prothero take on Bigfoot; the Yeti, or Abominable Snowman, and its cross-cultural incarnations; the Loch Ness monster and its highly publicized sightings; the evolution of the Great Sea Serpent; and Mokele Mbembe, or the Congo dinosaur. They conclude with an analysis of the psychology behind the persistent belief in paranormal phenomena, identifying the major players in cryptozoology, discussing the character of its subculture, and considering the challenge it poses to clear and critical thinking in our increasingly complex world.

"Perception is not something that happens to us, or in us," writes Alva Noë. "It is something we do." In Action in Perception, Noë argues that perception and perceptual consciousness depend on capacities for action and thought--that perception is a kind of thoughtful activity. Touch, not vision, should be our model for perception. Perception is not a process in the brain, but a kind of skillful activity of the body as a whole. We enact our perceptual experience.

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.

The true story that inspired the 2020 film.

The autobiography of mathematician Stanislaw Ulam, one of the great scientific minds of the twentieth century, tells a story rich with amazingly prophetic speculations and peppered with lively anecdotes. As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects.

With his wide-ranging interests, Ulam never emphasized the importance of his contributions to the research that resulted in the hydrogen bomb. Now Daniel Hirsch and William Mathews reveal the true story of Ulam's pivotal role in the making of the "Super," in their historical introduction to this behind-the-scenes look at the minds and ideas that ushered in the nuclear age. An epilogue by Françoise Ulam and Jan Mycielski sheds new light on Ulam's character and mathematical originality.

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.

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.

Accessible, essential coverage of the latest findings in challenging, speculative, and cutting-edge science, from the Pulitzer Prize-winning leaders in scientific journalism at Quanta Magazine

"If you're a science and data nerd like me, you may be interested in Alice and Bob Meet the Wall of Fire . . . 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. Winner of the 2022 Pulitzer Prize for Explanatory Reporting, Quanta once again gives 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

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.

This volume presents recent work on Babylonian celestialdivination and on the Greek inheritors of the Babyloniantradition.In the ancient world, the collection and study of celestial phenomena and the intepretation of their prophetic significance, especially as applied to kings and nations, were closely related sciences carried out by the same scholars. Both ancient sources and modern research agree that astronomy and celestial divination arose in Babylon. Only in the late nineteenth century, however, did scholars begin to identify and decipher the original Babylonian sources, and the process of understanding those sources has been long and difficult. This volume presents recent work on Babylonian celestial divination and on the Greek inheritors of the Babylonian tradition. Both philological and mathematical work are included. The essays shed new light on all of the known textual sources, including the omen series Enuma Anu Enlil, which contains omens from as far back as the early second or even third millennium, and the earliest personal horoscopes, from about 400 B.C., as well as the Astronomical Diaries, ephemerides, and other observational and mathematical texts. One essay concerns astronomical papyri that confirm the extensive transmission of Babylonian methods into Greek; a study of Ptolemy's lunar theory suggests that Ptolemy relied more on his own observations than previously thought; and an analysis of Theon's commentary on Ptolemy's Handy Tables shows that Theon explicated their meaning both conscientiously and competently.ContributorsAsger Aaboe, Alan C. Bowen, Lis Brack-Bernsen, John P. Britton, Bernard R. Goldstein, Gerd Graßhoff, Hermann Hunger, Alexander Jones, Erica Reiner, F. Rochberg, N. M. Swerdlow, Anne Tihon, C. B. F. Walker

"Radical, before it meant a person who advocates strong political reform, meant getting to the root of things, the origin. It comes from the Latin radix, radicis, meaning radish, a root vegetable."--BK Loren

These meditative essays range in subjects from a transcendental encounter with a pack of coyotes ironically juxtaposed with her neighbor's claim that nature "has gone out of vogue," to Loren's mother's slow yet all-encompassing deterioration from Parkinson's, and the unexpected way the Loma Prieta earthquake eroded her depression by offering the author a sense of her small place in a wild and worthwhile world.

Loren has an empathetic and gentle approach to the world. In detailing the intricacies of human relationships and consciousness--fear of death and time, cooperation born of clashing viewpoints, tradition's beauty even when destructive, a love of language, a sense of loss amid the fast-paced materialistic world--she peels back the film of popular thinking in order to expose herself to the secrets so few of us ever see.