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ivity versus 312 program equivalence problem 250 programmer 235, 238, 263 programming geniuses 271 super-programmers 266 progressive cipher 214 proof Feynman’s proof 157 indirect 244 mathematical 156 philosophical 246 Index 415 PSPACE problem 168 Pulitzer Prize 365, 367 purpose on the planet 9 puzzle tw
20th Anniversary ed. Penguin, 2000. Nagel, Ernest, and James R. Newman. Gédel’s Proof. Rev. Ed. New York University Press, 2001. Newton, Sir Isaac. Principia. Prometheus Books, 1995. Penrose, Sir Roger. Shadows Of The Mind: A Search for the Missing Science of Consciousness. New edition. Vintage, 2005. Po
s in it taking the shortest route possible from its initial to final position. The related 1650 Fermat’s “principle of least time” is about light. As Feynman explains in his Lectures in Physics, “...out of all possible paths that light might take from one point another, light takes the path that requires t
. Of all possible two-dimensional shapes with the same perimeter, the circle contains the greatest area; in three dimensions, it’s the sphere. In his Principia, Newton reports his work determining the optimal shape of round solids, with circles of revolution having the same effective cross section, in order
seems to offer hope of a world where any dream, no matter how outlandish, is realizable. Other familiar names, Bohr, Schrodinger, Dirac, and later Feynman and Dyson, each made great leaps into the unknown. But they weren't alone. Physics is a collaborative discipline. Too often science stories are wr
ous—and oddest—scientists in history: Isaac Newton. It is not inappropriate to classify Newton as a modern mind—after all, his seventeenth-century Principia: Mathematical Principles of Natural Philosophy uncovered the classical laws of motion and laid the basis for his theory of gravity, both of which f
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