The Motion Paradox: The 2,500-Year Old Puzzle Behind All the Mysteries of Time and Space
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The epic tale of an ancient, unsolved puzzle and how it relates to all scientific attempts to explain the basic structure of the universe
At the dawn of science the ancient Greek philosopher Zeno formulated his paradox of motion, and amazingly, it is still on the cutting edge of all investigations into the fabric of reality.
Zeno used logic to argue that motion is impossible, and at the heart of his maddening puzzle is the nature of space and time. Is space-time continuous or broken up like a string of beads? Over the past two millennia, many of our greatest minds—including Aristotle, Galileo, Newton, Einstein, Stephen Hawking, and other current theoreticians—have been gripped by the mystery this puzzle represents.
Joseph Mazur, acclaimed author of Euclid in the Rainforest, shows how historic breakthroughs in our understanding of motion shed light on Zeno’s paradox. The orbits of the planets were explained, the laws of motion were revealed, the theory of relativity was discovered—but the basic structure of time and space remained elusive.
In the tradition of Fermat’s Enigma and Zero, The Motion Paradox is a lively history of this apparently simple puzzle whose solution—if indeed it can be solved—will reveal nothing less than the fundamental nature of reality.
Paris, Toulouse, Padua, and Naples. All degrees and teachers had to be approved by one of the popes, a control inherited from the time when the university was a guild of teachers and students of the cathedral schools. By then Aristotle’s works were permitted and fashionable. Aquinas’s commentaries and interpretations had made them acceptable to the church. The Physics was the wisest thing available and—though it had no references or glories to a Christian God—it did not seem to interfere with
quarters—early morning and forenoon, afternoon and evening. By the first century CE, Romans were getting more sophisticated. Daylight hours were treated differently than nighttime hours. At the height of winter, when the sun shone for a bit less than nine hours (by our meaning of hour), the Romans would still break the daylight hours into twelve forty-five-minute segments (by our meaning of minute). In the summer, this would be reversed. Their water clocks should have been reset each day, but
pneumatics, ship construction, thermodynamics, magnetism, materials science, and navigation—and this list is not exhaustive. Together they constitute one of the greatest revolutions in the history of mathematics. But still, the paradox of motion was not fully answered. When Newton gave figurative credit to those giants on whose shoulders he stood, he must have been referring to René Descartes, for paving the way with coordinate geometry; and Evangelista Torricelli, Bonaventura Cavalieri, Gilles
account, simplifying the form of the law of universal gravitation by concentrating the mass at a single point. Calculus first sees each bulky mass (the earth, for example) as an ordered collection of small masses, each mutually affected by the inverse-square law. It then uses its powerful limit arguments to converge on the collective effect. Even though a mass may be bizarrely irregular and vast in size, the force it contributes acts as though it is coming from a single, mathematical point at its
wavelike in nature. But wave motion needs a medium in which to propagate, and so it was declared that there must be some invisible material medium filling the entire universe. Some called it “luminiferous ether,” suggesting that it permeates all matter, visible and invisible—vacuum, gases, glass, and any other material that light could penetrate. On the one hand, the ether seemed absurd; after all, such a rigid solid defied all experience. On the other, it was useful to justify not only the