„Le mot « catastrophe » n’a donc pas ici cette connotation négative qu’il a en revanche dans la langue de tous les jours… tout simplement, en chaque point v de l’ensemble catastrophique K, les choses changent…“ (p. 6) #Thom #catastrophe
„Such a repetition of an arbitrary operation is known as ‚iteration,‘ and in the present case suffices to transform seeming dullness into boundless excitement. The motivation for iteration and many of its most important properties come straight from physics. In iteration, physicists see a simplified view of the ’state‘ of a dynamical system and its evolution in time. By definition, a dynamical system is a transform that obtains its state today from its state yesterday, and its state tomorrow from its state today. Therefore, to obtain the state tomorrow from the state yesterday, one may apply the basic transform twice in succession. But one may also apply the iterated transform once.“ (p. 260) #Mandelbrot #iteration
„A physics of mathematical communication challenges philosophy to welcome the concept of ‚mass‘ as a third in the fundamental order of physics, next to those of space and time.“ (p. 5) #Bühlmann #communication #mass #space #time
„A contribution to mathematics and/or science does not consist of a picture, but rather of a picture combined with a description. Without words and formulas, a picture can, at best, be praised for artistic quality. Without an interest in pictures and other aspects of ‚reality,‘ pictures can play no role whatsoever.“ (p. 26) #Mandelbrot #mathematics #picture
„Toute la Géométrie de Descartes est destinée à résoudre par une méthode nouvelle, analytique et non plus synthétique“. (p. 99) #Vuillemin #Descartes #méthode