Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Contradiction --- Aristotle. --- Criticism and interpretation.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In Nonplussed!, popular-math writer Julian Havil delighted readers with a mind-boggling array of implausible yet true mathematical paradoxes. Now Havil is back with Impossible?, another marvelous medley of the utterly confusing, profound, and unbelievable--and all of it mathematically irrefutable. Whenever Forty-second Street in New York is temporarily closed, traffic doesn't gridlock but flows more smoothly--why is that? Or consider that cities that build new roads can experience dramatic increases in traffic congestion--how is this possible? What does the game show Let's Make A Deal reveal about the unexpected hazards of decision-making? What can the game of cricket teach us about the surprising behavior of the law of averages? These are some of the counterintuitive mathematical occurrences that readers encounter in Impossible? ? Havil ventures further than ever into territory where intuition can lead one astray. He gathers entertaining problems from probability and statistics along with an eclectic variety of conundrums and puzzlers from other areas of mathematics, including classics of abstract math like the Banach-Tarski paradox. These problems range in difficulty from easy to highly challenging, yet they can be tackled by anyone with a background in calculus. And the fascinating history and personalities associated with many of the problems are included with their mathematical proofs. Impossible? will delight anyone who wants to have their reason thoroughly confounded in the most astonishing and unpredictable ways.

Mathematics --- Paradox --- Problem solving --- Methodology --- Psychology --- Decision making --- Executive functions (Neuropsychology) --- Figures of speech --- Logic --- Contradiction --- Mathematics.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Lancé à propos de la société civile et de l'État dans le manuscrit de Kreuznach (1843) connu sous le titre de Critique du droit public hégélien, le fameux mot de Marx sur les " vrais extrêmes effectifs qui ne se réclament ni ne se complètent l'un l'autre, précisément parce qu'ils sont des extrêmes effectifs, qu'ils n'ont rien de commun, qu'ils sont des essences opposées " rend un son pour le moins revêche à l'oreille quelque peu rompue, si l'on peut dire, au délié de la dialectique. Et de fait, dans ce brouillon de critique littérale de la philosophie de l'État développée par Hegel (au chapitre de la Sittlichkeit de sa philosophie du droit), la formule, pour le moins abrupte, récuse hardiment le statut dialectique des extrêmes en direction de l'idée de destruction réciproque. Tout pousse à croire en effet qu'au-delà de la Realopposition kantienne, c'est l'esprit de la contrarietas spinozienne (Éthique III, prop 5) qui l'imprègne. Quinze ans avant les Grundrisse mais un seul avant les manuscrits parisiens, nulle trace de Capital-et-Travail et, pourtant, déjà une ligne de fuite qui, à y insister jusque dans la lecture de la critique de l'économie politique, ruine, pour le communisme, tout fantasme de culmination réconciliatoire à l'horizon de l'accumulation moderne "qui sue le sang et la boue par tous les pores ".

Hegel, Georg Wilhelm Friedrich, --- Marx, Karl, --- Criticism and interpretation --- Hegel, Georg Wilhelm Friedrich, - 1770-1831 --- Marx, Karl, - 1818-1883 - Criticism and interpretation --- Marx, Karl (1818-1883) --- Contraires (logique) --- Dialectique --- Contradiction --- Contribution à la philosophie sociale --- Marx, Karl, - 1818-1883

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In today's unpredictable and chaotic world, we look to science to provide certainty and answers--and often blame it when things go wrong. The Blind Spot reveals why our faith in scientific certainty is a dangerous illusion, and how only by embracing science's inherent ambiguities and paradoxes can we truly appreciate its beauty and harness its potential. Crackling with insights into our most perplexing contemporary dilemmas, from climate change to the global financial meltdown, this book challenges our most sacredly held beliefs about science, technology, and progress. At the same time, it shows how the secret to better science can be found where we least expect it--in the uncertain, the ambiguous, and the inevitably unpredictable. William Byers explains why the subjective element in scientific inquiry is in fact what makes it so dynamic, and deftly balances the need for certainty and rigor in science with the equally important need for creativity, freedom, and downright wonder. Drawing on an array of fascinating examples--from Wall Street's overreliance on algorithms to provide certainty in uncertain markets, to undecidable problems in mathematics and computer science, to Georg Cantor's paradoxical but true assertion about infinity--Byers demonstrates how we can and must learn from the existence of blind spots in our scientific and mathematical understanding. The Blind Spot offers an entirely new way of thinking about science, one that highlights its strengths and limitations, its unrealized promise, and, above all, its unavoidable ambiguity. It also points to a more sophisticated approach to the most intractable problems of our time.

Uncertainty (Information theory) --- Science --- Measure of uncertainty (Information theory) --- Shannon's measure of uncertainty --- System uncertainty --- Information measurement --- Probabilities --- Questions and answers --- Science and society --- Sociology of science --- Social aspects. --- Acknowledgment (creative arts and sciences). --- Algorithm. --- Ambiguity. --- Analogy. --- Approximation. --- Axiom. --- Axiomatic system. --- Basic research. --- Big O notation. --- Calculation. --- Certainty. --- Chaos theory. --- Circumference. --- Computation. --- Concept. --- Conjecture. --- Consciousness. --- Consistency. --- Contingency (philosophy). --- Continuous function. --- Continuum hypothesis. --- Contradiction. --- Counting. --- David Bohm. --- Dynamism (metaphysics). --- Emergence. --- Euclidean geometry. --- Explanation. --- Feeling. --- Fermat's Last Theorem. --- Geometry. --- Gestalt psychology. --- Gregory Chaitin. --- Gödel's incompleteness theorems. --- Human behavior. --- Human intelligence. --- Hypothesis. --- Ideology. --- Inference. --- Integer. --- Irrational number. --- Learning. --- Logic. --- Logical reasoning. --- Mathematician. --- Mathematics. --- Measurement. --- Methodology. --- Modernity. --- Molecule. --- Natural number. --- Nature. --- Paradigm shift. --- Paradox. --- Participant. --- Phenomenon. --- Philosopher. --- Philosophy of mathematics. --- Philosophy of science. --- Philosophy. --- Platonism. --- Prediction. --- Principle. --- Probability. --- Pythagoreanism. --- Qualitative property. --- Quantification (science). --- Quantity. --- Quantum mechanics. --- Randomness. --- Rational number. --- Rationality. --- Real number. --- Reality. --- Reason. --- Reductionism. --- Relationship between religion and science. --- Result. --- Science. --- Scientific method. --- Scientific progress. --- Scientific theory. --- Scientist. --- Self-reference. --- Set theory. --- Special case. --- Subatomic particle. --- Subjectivity. --- Suggestion. --- Technology. --- The Philosopher. --- Theorem. --- Theoretical physics. --- Theory of everything. --- Theory. --- Thomas Kuhn. --- Thought. --- Uncertainty. --- Universality (philosophy). --- Writing. --- Sociology of knowledge