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Scientists
Michael Arbib John S. Bell Bernard Baars Charles Bennett Ludwig Bertalanffy Margaret Boden David Bohm Neils Bohr Ludwig Boltzmann Emile Borel Max Born Leon Brillouin Stephen Brush Henry Thomas Buckle Donald Campbell Anthony Cashmore Eric Chaisson Jean-Pierre Changeux Arthur Holly Compton John Conway E. H. Culverwell Charles Darwin Abraham de Moivre Paul Dirac John Eccles Arthur Stanley Eddington Paul Ehrenfest Albert Einstein Richard Feynman Joseph Fourier Michael Gazzaniga GianCarlo Ghirardi Nicolas Gisin A.O.Gomes Joshua Greene Jacques Hadamard Patrick Haggard Sam Harris Martin Heisenberg Werner Heisenberg William Stanley Jevons Pascual Jordan Simon Kochen Stephen Kosslyn Rolf Landauer Alfred Landé Pierre-Simon Laplace David Layzer Benjamin Libet Hendrik Lorentz Josef Loschmidt Ernst Mach Henry Margenau James Clerk Maxwell Ernst Mayr Jacques Monod Roger Penrose Steven Pinker Max Planck Henri Poincaré Adolphe Quételet Jerome Rothstein David Ruelle Erwin Schrödinger Aaron Schurger Claude Shannon Herbert Simon Dean Keith Simonton B. F. Skinner Roger Sperry Henry Stapp Antoine Suarez Leo Szilard William Thomson (Kelvin) Peter Tse John von Neumann Daniel Wegner Paul A. Weiss Steven Weinberg Norbert Wiener Eugene Wigner E. O. Wilson H. Dieter Zeh Ernst Zermelo Jacques Hadamard
Jacques Hadamard was a great mathematician who studied his thought processes in solving mathematical problems. He interviewed many other leading mathematicians and scientists, including Henri Poincaré, many of whom shared Hadamard's experience that solutions to problems often came suddenly and completely, generally after long reflections on the problem.
In his 1945 book
Hadamard and the Two-Stage Model of Free Will
Hadamard described Poincaré as the source of the basic idea, but he credited Paul Valéry with the idea that there are two stages in creativity, perhaps even two entities - one to generate random alternative_possibilities, and the other to select or choose the best alternative.
These suggestions of Hadamard's were a major influence on Daniel Dennett's 1978 two-stages model of decision making which were later dubbed "Valerian." Dennett quotes the Valéry "It takes two to invent anything...," and then imagines the two stages in one mind. Hadamard quoted Mozart to show that the first stage involves ideas that just "come to us" freely. When I feel well and in a good humour, or when I am taking a drive or walking after a good meal, or in the night when I cannot sleep, thoughts crowd into my mind as easily as you could wish. Whence and how do they come? I do not know and I have nothing to do with it. Those which please me I keep in my head and hum them; at least others have told me that I do so....Then my soul is on fire with inspiration.Hadamard and Poincaré both describe ideas that "present themselves" as William James described it.
Hadamard and Irreversibility
In 1906 Hadamard wrote a review of Josiah Willard Gibbs' Elementary Principles of Statistical Mechanics. (Bulletin of the American Mathematical Society, 12, p.194-210) He called it pure mathematics, applying the calculus of probabilities (of Laplace and others) to mechanics.
He wrote: It remains to address the most important and most delicate that raises the study of the distribution phase. What happens to this distribution in the course of the movement, when part of any state: it tends, for example, to move closer to the canonical distribution or any distribution with similar properties? [Il reste à traiter la question la plus importante et la plus délicate que soulève cette étude de la distribution en phase. Que devient cette distribution au cours du mouvement, lorsqu'on part d'un état quelconque: tend-elle, par exemple, à se rapprocher de la distribution canonique ou d'une distribution présentant des propriétés analogues?We develop an answer in our treatment of micro-reversibility.
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