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Zero has been axial in human development, but the origin and discovery of zero has never been satisfactorily addressed by a comprehensive, systematic and above all interdisciplinary research program. In this volume, over 40 international scholars explore zero under four broad themes: history; religion, philosophy & linguistics; arts; and mathematics & the sciences. Some propose that the invention/discovery of zero may have been facilitated by the prior evolution of a sophisticated concept of Nothingness or Emptiness (as it is understood in non-European traditions); and conversely, inhibited by the absence of, or aversion to, such a concept of Nothingness in the West. But not all scholars agree. Join the debate.
In the tradition of "Longitude, " a small and engagingly written book on the history and meaning of zero--a "tour de force" of science history that takes us through the hollow circle that leads to infinity. 32 illustrations.
The invention of numerals is perhaps the greatest abstraction the human mind has ever created. Virtually everything in our lives is digital, numerical, or quantified. The story of how and where we got these numerals, which we so depend on, has for thousands of years been shrouded in mystery. Finding Zero is an adventure filled saga of Amir Aczel's lifelong obsession: to find the original sources of our numerals. Aczel has doggedly crisscrossed the ancient world, scouring dusty, moldy texts, cross examining so-called scholars who offered wildly differing sets of facts, and ultimately penetrating deep into a Cambodian jungle to find a definitive proof. Here, he takes the reader along for the ride. The history begins with the early Babylonian cuneiform numbers, followed by the later Greek and Roman letter numerals. Then Aczel asks the key question: where do the numbers we use today, the so-called Hindu-Arabic numerals, come from? It is this search that leads him to explore uncharted territory, to go on a grand quest into India, Thailand, Laos, Vietnam, and ultimately into the wilds of Cambodia. There he is blown away to find the earliest zero—the keystone of our entire system of numbers—on a crumbling, vine-covered wall of a seventh-century temple adorned with eaten-away erotic sculptures. While on this odyssey, Aczel meets a host of fascinating characters: academics in search of truth, jungle trekkers looking for adventure, surprisingly honest politicians, shameless smugglers, and treacherous archaeological thieves—who finally reveal where our numbers come from.
A NEW YORK TIMES NOTABLE BOOK The Babylonians invented it, the Greeks banned it, the Hindus worshipped it, and the Christian Church used it to fend off heretics. Today it's a timebomb ticking in the heart of astrophysics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything. Within the concept of zero lies a philosophical and scientific history of humanity. Charles Seife's elegant and witty account takes us from Aristotle to superstring theory by way of Egyptian geometry, Kabbalism, Einstein, the Chandrasekhar limit and Stephen Hawking. Covering centuries of thought, it is a concise tour of a world of ideas, bound up in the simple notion of nothing.
A symbol for what is not there, an emptiness that increases any number it's added to, an inexhaustible and indispensable paradox. As we enter the year 2000, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematics as we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean? Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, and then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our ancestors were in trying to figure large sums without the aid of the zero. (Try multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they were, didn't have a zero--or did they? We follow the trail to the East where, a millennium or two ago, Indian mathematicians took another crucial step. By treating zero for the first time like any other number, instead of a unique symbol, they allowed huge new leaps forward in computation, and also in our understanding of how mathematics itself works. In the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders. At first it was called "dangerous Saracen magic" and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools like double-entry bookkeeping. Zero quickly became an essential part of increasingly sophisticated equations, and with the invention of calculus, one could say it was a linchpin of the scientific revolution. And now even deeper layers of this thing that is nothing are coming to light: our computers speak only in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything. Robert Kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for looking not only into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. The beauty of mathematics is that even though we invent it, we seem to be discovering something that already exists. The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. A tour de force of science history, The Nothing That Is takes us through the hollow circle that leads to infinity.
Hollis Henry never intended to work for global marketing magnate Hubertus Bigend again. But now she’s broke, and Bigend has just the thing to get her back in the game... Milgrim can disappear in almost any setting, and his Russian is perfectly idiomatic—so much so that he spoke it with his therapist in the secret Swiss clinic where Bigend paid for him to be cured of his addiction... Garreth doesn't owe Bigend a thing. But he does have friends from whom he can call in the kinds of favors powerful people need when things go sideways... They all have something Bigend wants as he finds himself outmaneuvered and adrift, after a Department of Defense contract for combat-wear turns out to be the gateway drug for arms dealers so shadowy they can out-Bigend Bigend himself. “Zero History is [Gibson’s] best yet, a triumph of science fiction as social criticism and adventure.”—BoingBoing.net
#1 NEW YORK TIMES BESTSELLER • “This book delivers completely new and refreshing ideas on how to create value in the world.”—Mark Zuckerberg, CEO of Meta “Peter Thiel has built multiple breakthrough companies, and Zero to One shows how.”—Elon Musk, CEO of SpaceX and Tesla The great secret of our time is that there are still uncharted frontiers to explore and new inventions to create. In Zero to One, legendary entrepreneur and investor Peter Thiel shows how we can find singular ways to create those new things. Thiel begins with the contrarian premise that we live in an age of technological stagnation, even if we’re too distracted by shiny mobile devices to notice. Information technology has improved rapidly, but there is no reason why progress should be limited to computers or Silicon Valley. Progress can be achieved in any industry or area of business. It comes from the most important skill that every leader must master: learning to think for yourself. Doing what someone else already knows how to do takes the world from 1 to n, adding more of something familiar. But when you do something new, you go from 0 to 1. The next Bill Gates will not build an operating system. The next Larry Page or Sergey Brin won’t make a search engine. Tomorrow’s champions will not win by competing ruthlessly in today’s marketplace. They will escape competition altogether, because their businesses will be unique. Zero to One presents at once an optimistic view of the future of progress in America and a new way of thinking about innovation: it starts by learning to ask the questions that lead you to find value in unexpected places.
Division by Zero Calculus—History and Development by Saburou Saitoh Pdf
This is based on the record of how I have been discovering and pioneering a new world by breaking the first of the Ten Commandments of Mathematics, which has been 2300 years since Aristotle and must not be divided by zero. I am involved in the basic issues of humankind involved in mathematical physics, philosophy, and worldview. What is eternity and what is infinity? What is the significance of human existence?
Discover the New 52 origin of the Dark Knight in BATMAN: ZERO YEAR! Witness the twists and turns as Bruce Wayne takes the final steps toward his destiny and confronts the dangers of Gotham City at this point in time. New York Times bestselling author Scott Snyder and artist Greg Capullo delve into Bruce Wayne's past and reveal his journey to becoming Batman. BATMAN: ZERO YEAR features secret moments from Bruce's training abroad, run-ins with aspiring district attorney Harvey Dent, and how Bruce learned to work with his new ally, Lieutenant Jim Gordon. This collection spins into total darkness as the Riddler stirs up chaos in Gotham City in the "Secret City," "Dark City," and "Savage City" events. What corners of Batman's past will be revealed? And how will they impact his very near future? Unravel the mysteries set forth by the Riddler and join the madness as Batman gets closer to the endgame. Collects Batman #21-27 and Batman #29-33.
An Introduction to Measure Theory by Terence Tao Pdf
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Greek Mathematical Thought and the Origin of Algebra by Jacob Klein Pdf
Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th-16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. 1968 edition. Bibliography.
A History of Mathematics by Carl B. Boyer,Uta C. Merzbach Pdf
The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments. Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.
Reclaiming the first century as common ground rather than the origin of deeply entrenched differences: liberating the past to speak to us in another way. Conventional readings of antiquity cast Athens against Jerusalem, with Athens standing in for "reason" and Jerusalem for "faith." And yet, Susan Buck-Morss reminds us, recent scholarship has overturned this separation. Naming the first century as a zero point--"year one"--that divides time into before and after is equally arbirtrary, nothing more than a convenience that is empirically meaningless. In YEAR 1, Buck-Morss liberates the first century so it can speak to us in another way, reclaiming it as common ground rather than the origin of deeply entrenched differences. Buck-Morss aims to topple various conceptual givens that have shaped modernity as an episteme and led us into some unhelpful postmodern impasses. She approaches the first century through the writings of three thinkers often marginalized in current discourse: Flavius Josephus, historian of the Judaean war; the neo-Platonic philosopher Philo of Alexandria; and John of Patmos, author of Revelation, the last book of the Christian Bible. Also making appearances are Antigone and John Coltrane, Plato and Bulwer-Lytton, al-Farabi and Jean Anouilh, Nicholas of Cusa and Zora Neale Hurston--not to mention Descartes, Kant, Hegel, Kristeva, and Derrida. Buck-Morss shows that we need no longer partition history as if it were a homeless child in need of the protective wisdom of Solomon. Those inhabiting the first century belong together in time, and therefore not to us.
This graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial equations in n variables over an algebraically closed field. The text collects and synthesizes a number of works on Bernstein’s theorem of counting solutions of generic systems, ultimately presenting the theorem, commentary, and extensions in a comprehensive and coherent manner. It begins with Bernstein’s original theorem expressing solutions of generic systems in terms of the mixed volume of their Newton polytopes, including complete proofs of its recent extension to affine space and some applications to open problems. The text also applies the developed techniques to derive and generalize Kushnirenko's results on Milnor numbers of hypersurface singularities, which has served as a precursor to the development of toric geometry. Ultimately, the book aims to present material in an elementary format, developing all necessary algebraic geometry to provide a truly accessible overview suitable to second-year graduate students.