Recommendations based on "Dreams of a Final Theory"

An accessible and fascinating exploration of how Alan Turing’s mathematical theory gave rise to modern computer science and applications—from the desktops to cell phonesIn 1936, when he was just 24 years old, Alan Turing wrote a remarkable paper in which he outlined the theory of computation, laying out the ideas that underlie all modern computers. This groundbreaking and powerful theory now forms the basis of computer science. In Turing’s Vision, Chris Bernhardt explains the theory for the general reader, beginning with its foundations and systematically building to its surprising conclusions. He also views Turing’s theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turing’s later work, and the birth of the modern computer.Turing wanted to show that there were problems that were beyond any computer’s ability to solve; in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turing’s ideas, Bernhardt examines 3 well-known decision problems to explore the concept of undecidability; investigates theoretical computing machines, including Turing machines; explains universal machines; and proves that certain problems are undecidable, including Turing’s problem concerning computable numbers.

Product Description 'I'll stop doing it as soon as I understand what I'm doing.' Somewhere between a historical account and work of philosophy, Socrates' Defence details the final plea of Plato's beloved mentor. Introducing Little Black Classics: 80 books for Penguin's 80th birthday. Little Black Classics celebrate the huge range and diversity of Penguin Classics, with books from around the world and across many centuries. They take us from a balloon ride over Victorian London to a garden of blossom in Japan, from Tierra del Fuego to 16th-century California and the Russian steppe. Here are stories lyrical and savage; poems epic and intimate; essays satirical and inspirational; and ideas that have shaped the lives of millions. Plato (474 BC-347 BC). Plato's works available in Penguin Classics are Republic, The Last Days of Socrates, The Laws, Phaedrus, Protagoras and Meno, Timaeus and Critias, Theaetetus, Early Socratic Dialogues, The Symposium and Gorgias. About the Author Plato (474 BC-347 BC). Plato's works available in Penguin Classics are Republic, The Last Days of Socrates, The Laws, Phaedrus, Protagoras and Meno, Timaeus and Critias, Theaetetus, Early Socratic Dialogues, The Symposium and Gorgias.

There is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations.Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objective in order to silence critics of their political agendas, including eugenics.Clayton provides a clear account of the mathematics and logic of probability, conveying complex concepts accessibly for readers interested in the statistical methods that frame our understanding of the world. He contends that we need to take a Bayesian approach―that is, to incorporate prior knowledge when reasoning with incomplete information―in order to resolve the crisis. Ranging across math, philosophy, and culture, Bernoulli’s Fallacy explains why something has gone wrong with how we use data―and how to fix it.

The seminal work by one of the most important thinkers of the twentieth century, Physics and Philosophy is Werner Heisenberg's concise and accessible narrative of the revolution in modern physics, in which he played a towering role. The outgrowth of a celebrated lecture series, this book remains as relevant, provocative, and fascinating as when it was first published in 1958. A brilliant scientist whose ideas altered our perception of the universe, Heisenberg is considered the father of quantum physics; he is most famous for the Uncertainty Principle, which states that quantum particles do not occupy a fixed, measurable position. His contributions remain a cornerstone of contemporary physics theory and application.

Introduction : doing science in a complex world. Science by humans ; Science in a complex world ; The payoff : idealizations and many aims -- Complex causality and simplified representation. Causal patterns in the face of complexity ; Causal patterns ; Causal complexity ; Simplification by idealization ; Reasons to idealize ; Idealizations' representational role ; Rampant and unchecked idealization -- The diversity of scientific projects. Broad patterns : modeling cooperation ; A specific phenomenon : variation in human aggression ; Predictions and idealizations in the physical sciences ; Surveying the diversity -- Science isn't after the truth. The aims of science ; Understanding as science's epistemic aim ; Separate pursuit of science's aims ; Understanding, truth, and knowledge ; The nature of scientific understanding ; The role of truth and scientific knowledge -- Causal pattern explanations. Explanation, communication, and understanding ; An account of scientific explanation ; The scope of causal patterns ; The crucial role of the audience ; Adequate explanations -- Levels and fields of science. Levels in philosophy and science ; Going without levels ; Against hierarchy ; Prizing apart forms of stratification ; The fields of science and how they relate -- Scientific pluralism and its limits. The entrenchment of social values ; How science doesn't inform metaphysics ; Scientific progress.

Taking Emerson as his starting point, Cornel West’s basic task in this ambitious enterprise is to chart the emergence, development, decline, and recent resurgence of American pragmatism. John Dewey is the central figure in West’s pantheon of pragmatists, but he treats as well such varied mid-century representatives of the tradition as Sidney Hook, C. Wright Mills, W. E. B. Du Bois, Reinhold Niebuhr, and Lionel Trilling. West’s "genealogy" is, ultimately, a very personal work, for it is imbued throughout with the author’s conviction that a thorough reexamination of American pragmatism may help inspire and instruct contemporary efforts to remake and reform American society and culture."West . . . may well be the pre-eminent African American intellectual of our generation."—The Nation"The American Evasion of Philosophy is a highly intelligent and provocative book. Cornel West gives us illuminating readings of the political thought of Emerson and James; provides a penetrating critical assessment of Dewey, his central figure; and offers a brilliant interpretation—appreciative yet far from uncritical—of the contemporary philosopher and neo-pragmatist Richard Rorty. . . . What shines through, throughout the work, is West's firm commitment to a radical vision of a philosophic discourse as inextricably linked to cultural criticism and political engagement."—Paul S. Boyer, professor emeritus of history, University of Wisconsin–Madison.Wisconsin Project on American WritersFrank Lentricchia, General Editor

Kurt Gödel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computation theory, as well as for the strong individuality of his writings on the philosophy of mathematics. Less well-known is his discovery of unusual cosmological models for Einstein's equations, permitting "time-travel" into the past.This second volume of a comprehensive edition of Gödel's works collects together all his publications from 1938 to 1974. Together with Volume I (Publications 1929-1936), it makes available for the first time in a single source all of his previously published work. Continuing the format established in the earlier volume, the present text includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, a facing English translation of the one German original, and a complete bibliography. Succeeding volumes are to contain unpublished manuscripts, lectures, correspondence, and extracts from the notebooks.Collected Works is designed to be accessible and useful to as wide an audience as possible without sacrificing scientific or historical accuracy. The only complete edition available in English, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science. These volumes will also interest scientists and all others who wish to be acquainted with one of the great minds of the twentieth century.

Ever since Newton created dynamics, there has been controversy about its foundations. Are space and time absolute? Do they form a rigid but invisible framework and container of the universe? Or are space, time, and motion relative? If so, does Newton's 'framework' arise through the influence of the universe at large, as Ernst Mach suggested? Einstein's aim when creating his general theory of relativity was to demonstrate this and thereby implement 'Mach's Principle'. However, it is widely believed that he achieved only partial success. This question of whether motion is absolute or relative has been a central issues in philosophy; the nature of time has perennial interest. Current attempts to create a quantum description of the whole universe keep these issues at the cutting edge of modern research. Written by the world's leading expert on Mach's Principle, The Discovery of Dynamics is a highly original account of the development of notions about space, time, and motion. Widely praised in its hardback version, it is one of the fullest and most readable accounts of the astronomical studies that culminated in Kepler's laws of planetary motion and of the creation of dynamics by Galileo, Descartes, Huygens, and Newton. Originally published as Absolute or Relative Motion?, Vol. 1: The Discovery of Dynamics (Cambridge), The Discovery of Dynamics provides the technical background to Barbour's recently published The End of Time, in which he argues that time disappears from the description of the quantum universe.

This is a rare book on a rare topic: it is about 'action' and the Principle of Least Action. A surprisingly well-kept secret, these ideas are at the heart of physical science and engineering. Physics is well known as being concerned with grand conservatory principles (e.g. the conservation of energy) but equally important is the optimization principle (such as getting somewhere in the shortest time or with the least resistance). The book explains: why an optimization principle underlies physics, what action is, what `the Hamiltonian' is, and how new insights into energy, space, and time arise. It assumes some background in the physical sciences, at the level of undergraduate science, but it is not a textbook. The requisite derivations and worked examples are given but may be skim-read if desired. The author draws from Cornelius Lanczos's book "The Variational Principles of Mechanics" (1949 and 1970). Lanczos was a brilliant mathematician and educator, but his book was for a postgraduate audience. The present book is no mere copy with the difficult bits left out - it is original, and a popularization. It aims to explain ideas rather than achieve technical competence, and to show how Least Action leads into the whole of physics.

This comprehensive reference provides an exhaustive guide to current scholarship on the perennial problem of Free Will--perhaps the most hotly and voluminously debated of all philosophical problems. While reference is made throughout to the contributions of major thinkers of the past, the emphasis is on recent research. The essays, most of which are previously unpublished, combine the work of established scholars with younger thinkers who are beginning to make significant contributions. Taken as a whole, the Handbook provides an engaging and accessible roadmap to the state of the art thinking on this enduring topic.