The Seven Follies Of Science A Popular Account Of The Most Famous Scientific Impossibilities And The Attempts Which Have Been Made To Solve Them

Tales of Impossibility

A comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs—which demonstrated the impossibility of solving them using only a compass and straightedge—depended on and resulted in the growth of mathematics. Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems. Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.

Mysteries and Secrets Revealed

Mysteries and Secrets Revealed uncovers the reality behind mysteries of nature and secrets of frauds that eluded common understanding. The journey begins in the ancient Greek city of Delphi, where priests claimed the gift of a priceless gold lion was an acknowledgement of their clairvoyant powers. But their concocted story concealed an embarrassing blunder. Those sufficiently savvy to catch the lie became aware of even deeper problems. Author Loren Pankratz then guides us through the conflicts of Renaissance scholars, including Galileo who explained things in ways that enraged philosophers and infuriated priests. Galileo's methods of investigation were perpetuated by the meticulous work of the Academy of Experiment, and Bernard Fontenelle's enthralling dialogue enabled common people to accept life in the rearranged sun-centered universe. Clairvoyants in a mesmeric trance claimed they could visit distant planets and endure brutal surgical procedures. If any of this was real, how was it possible? One nineteenth century mesmeric savant, Alexis Didier, was so convincing that someone claimed no case of clairvoyance could be made for anyone if his accomplishments were not real. This unchallenged declaration is now unraveled here for the first time through information gleaned from uncommon documents and rare antiquarian pamphlets. The surprising manifestations of modern spiritualism quickly escalated into a psychic arms race that included mysterious tipping and turning of tables. Scientist Michael Faraday devised ingenious experiments to show how subtle muscle reactions outside of awareness created these manifestations. On the other hand, explanations for table levitations and mysterious writing on slates could only be solved by individuals with acute observational skills and acquainted with the methods of trickery. Each story in Mysteries and SecretsRevealed captures the tension of conflict, the thrill of discovery, and the strategies of science that unmasked frauds, fakes, false belief, and the enigmas of our natural world.

Foibles and Fallacies of Science