Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    E. Lendon surveys a millennium of warfare to discover how militaries change—and don’t change—and how an army’s greatness depends on its use of the past. Noting this was an age that witnessed few technological advances, J. E. Lendon shows us that the most successful armies were those that made the most effective use of cultural tradition. Ancient combat moved forward by looking backward for inspiration—the Greeks, to Homer; the Romans, to the Greeks and to their own heroic past. The best ancient armies recruited soldiers from societies with strong competitive traditions; and the best ancient leaders, from Alexander to Julius Caesar, called upon those traditions to encourage ferocious competition at every rank.Ranging from the Battle of Champions between Sparta and Argos in 550 B.C. through Julian’s invasion of Persia in A.D. 363, Soldiers and Ghosts brings to life the most decisive military contests of ancient Greece and Rome. Lendon places these battles, and the methods by which they were fought, in a sweeping narrative of ancient military history. On every battlefield, living soldiers fought alongside the ghosts of tradition—ghosts that would inspire greatness for almost a millennium before ultimately coming to stifle it.

    Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.

    Iamblichus' biography is universally acknowledged as deriving from sources of the highest antiquity. Its classic translation by Thomas Taylor was first printed in 1818 and is once again brought to light in this edition.During Iamblichus' life, the depth and sublimity of his writing and discourse attracted a multitude of associates and disciples from all parts of the world. The Emperor Julian wrote of him, "that he was posterior indeed in time, but not in genius, to Plato," and all the Platonists who succeeded him honored him with the epithet of "divine."Iamblichus' account of the life of Pythagoras begins with the great philosopher's birth on the island of Samos, his youth, and his wide renown in Greece. It briefly covers his early travels and his studies with the philosophers Anaximander and Thales, his twenty-two years of instruction in the temples of Egypt, and his initiation into the Egyptian and Babylonian mysteries. The later life and work of Pythagoras are richly elaborated, with humorous and profound anecdotes illustrating his philosophy and providing a unique view of community life under his tutelage in Crotona.Included are excerpts from his teachings on harmonic science, dietetic medicine, friendship, temperance, politics, parenthood, the soul's former lives and many other topics. The book also contains substantial sections on the Fragments of the Ethical Writings (the work of very early Pythagoreans) and the Pythagoric Sentences.Sage of Samos, initiate of the mysteries, and transmitter of the ancient wisdom, Pythagoras was a pivotal figure in all of Western philosophy and thought. His life is as much an example for us today as it was for his students nearly twenty-five centuries ago.

    Describes how fractals were discovered, explains their unique properties, and discusses the mathematical foundation of fractals.

    For centuries, the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. Zero follows this number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe and its apotheosis as the mystery of the black hole. Today, zero lies at the heart of one of the biggest scientific controversies of all time, the quest for the theory of everything. Elegant, witty, and enlightening, Zero is a compelling look at the strangest number in the universe and one of the greatest paradoxes of human thought.

    Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.