An irreverent look at how randomness influences our lives, and how our successes and failures are far more dependent on chance events than we recognize.

How Singular? How singular is the Singularity? Will it happen in an instant? Lets consider again the derivation of the word. In mathematics a singularity is a value that is beyond any limit - in essence, infinity. The Singularity as we have discussed it in this book, does not achieve infinite levels of computation, memory, as any other other measurable attribute. But it certainly achieves vast levels of all these qualities, including intelligence. With the reverse engineering of the human brain we will be able to apply the parallel, self-organizing, chaotic, algorithms of human intelligence to enormously powerful computational substrates. This intelligence will then be in a position to improve its own design, both hardware and software, in a rapidly accelerating iterative process.

Doing Physics makes concepts of physics easier to grasp by relating them to everyday knowledge. Addressing some of the models and metaphors that physicists use to explain the physical world, Martin H. Krieger describes the conceptual world of physics by means of analogies to economics, anthropology, theater, carpentry, mechanisms such as clockworks, and machine tool design. The interaction of elementary particles or chemical species, for example, can be related to the theory of kinship—who can marry whom is like what can interact with what. Likewise, the description of physical situations in terms of interdependent particles and fields is analogous to the design of a factory with its division of labor among specialists. For the new edition, Krieger has revised the text and added a chapter on the role of mathematics and formal models in physics. Doing Physics will be of special interest to economists, political theorists, anthropologists, and sociologists as well as philosophers of science.

Though financial models imitate the style of physics and employ the language of mathematics, ultimately they deal with human beings. There is a fundamental difference between the aims and potential achievements of physics and those of finance. In physics, theories aim for a description of reality; in finance, at best, models can shoot only for a simplistic and very limited approximation to it. When we make a model involving human beings, we are trying to force the ugly stepsister's foot into Cinderella's pretty glass slipper. It doesn't fit without cutting off some of the essential parts. Physicists and economists have been too enthusiastic to acknowledge the limits of their equations in the sphere of human behavior which of course is what economics is all about. Models.Behaving.Badly includes a personal account of Derman's childhood encounters with failed models, the oppressions of apartheid and the utopia of the kibbutz. He describes his experience as a physicist on Wall Street, the models quants generated, the benefits they brought and the problems, practical and ethical, they caused. Derman takes a close look at what a model is, and then highlights the differences between the successes of modeling in physics and its failures in economics. Describing the collapse of the subprime mortgage CDO market in 2007, Derman urges us to stop the naïve reliance on these models, and offers suggestions for mending them. This is a fascinating, lyrical, and very human look behind the curtain at the intersection between mathematics and human nature.

"Mazur's book treats luck in a fresh light. The philosophy and emotional aspects (along with a little mathematics) are all there. The reader who delves in will be lucky indeed." --Persi Diaconis, Stanford University "Blending math with memoir, probability with psychology, and heuristics with history, Mazur has written an essential book for anyone who wants to get a better idea of why we consistently bet against the odds. From the betting window to Wall Street, he offers insights into both the mechanics of chance and the enduring appeal that luck holds for those who wager every day, whether they call it gambling, speculation, or just hoping for the best. Engaging and illuminating, this is a guaranteed winner." --David G. Schwartz, director of the Center for Gaming Research at the University of Nevada, Las Vegas, and author of Roll the Bones: The History of Gambling "This is a fascinating book. It's a fresh, funny, philosophical look at gambling by a mathematician who knows what he's talking about, and who has quite obviously thought about gambling for a long time. Mazur isn't afraid to make provocative, opinionated statements. I have not seen a gambling book like this before. I think it will attract a lot of readers." --Paul J. Nahin, author of Digital Dice "This book is significant in that it offers a lively and diverse collection of gambling-related ideas. Mazur's robust blend of anecdotes, history, psychology, and mathematics differs from other attempts to discuss these ideas. He offers plenty of insights into the questions and issues he raises." --Edward Packel, author of The Mathematics of Games and Gambling

"From the time of Pythagoras, we have been tempted to treat numbers as the ultimate or only truth. This book tells the history of that habit of thought. But more, it argues that the logic of counting sacrifices much of what makes us human, and that we have a responsibility to match the objects of our attention to the forms of knowledge that do them justice. Humans have extended the insights and methods of number and mathematics to more and more aspects of the world, even to their gods and their religions.Today those powers are greater than ever, as computation is applied to virtually every aspect of human activity.But the rules of mathematics do not strictly apply to many things-from elementary particles to people-in the world.By subjecting such things to the laws of logic and mathematics, we gain some kinds of knowledge, but we also lose others. How do our choices about what parts of the world to subject to the logics of mathematics affect how we live and how we die?This question is rarely asked, but it is urgent, because the sciences built upon those laws now govern so much of our knowledge, from physics to psychology.Number and Knowledge sets out to ask it. In chapters proceeding chronologically from Ancient Greek philosophy and the rise of monotheistic religions to the emergence of modern physics and economics, the book traces how ideals, practices, and habits of thought formed over millennia have turned number into the foundation-stone of human claims to knowledge and certainty.But the book is also a philosophical and poetic exhortation to take responsibility for that history, for the knowledge it has produced, and for the many aspects of the world and of humanity that it ignores or endangers.To understand what can be counted and what can't is to embrace the ethics of purposeful knowing"--

Internationally honored for brilliant achievements throughout his career, author of Cybernetics, ExProdigy, and the essay God and Golem, Inc., which won the National Book Award in 1964, Norbert Wiener was no ordinary mathematician. With the ability to understand how things worked or might work at a very deep level, he linked his own mathematics to engineering and provided basic ideas for the design of all sorts of inventions, from radar to communications networks to computers to artificial limbs. Wiener had an abiding concern about the ethics guiding applications of theories he and other scientists developed. Years after he died, the manuscript for this book was discovered among his papers. The world of science has changed greatly since Wiener's day, and much of the change has been in the direction he warned against. Now published for the first time, this book can be read as a salutary corrective from the past and a chance to rethink the components of an environment that encourages inventiveness.Wiener provides an engagingly written insider's understanding of the history of discovery and invention, emphasizing the historical circumstances that foster innovations and allow their application. His message is that truly original ideas cannot be produced on an assembly line, and that their consequences are often felt only at distant times and places. The intellectual and technological environment has to be right before the idea can blossom. The best course for society is to encourage the best minds to pursue the most interesting topics, and to reward them for the insights they produce. Wiener's comments on the problem of secrecy and the importance of the "free-lance" scientist are particularly pertinent today. Steve Heims provides a brief history of Wiener's literary output and reviews his contributions to the field of invention and discovery. In addition, Heims suggests significant ways in which Wiener's ideas still apply to dilemmas facing the scientific and engineering communities of the 1990s.

Papers on the location and behavior of zeros, including some of Polya's most influential work.The papers in this volume cluster about the following topics: the location of the zeros of polynomials and other analytic functions; the approximation of analytic functions by polynomials in which the location of zero is restricted (these papers represent some of Polya's most influential work); the behavior of the zeros of successive derivatives; the zeros of functions defined by trigonometric integrals; and the signs of derivatives and their analytic character. The volume also includes a paper that is not about zeros but contains a representation theorem for positive polynomials in several variables.

The transformation of mathematics from its ancient Greek practice to its development in the medieval Arab-speaking world is approached by focusing on a single problem proposed by Archimedes and the many solutions offered. From a practice of mathematics based on the localized solution (originating in the polemical practices of early Greek science), we see a transition to a practice of mathematics based on the systematic approach (grounded in the deuteronomic practices of Late Antiquity and the Middle Ages). A radically new interpretation is accordingly offered of the historical trajectory of pre-modern mathematics.