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The Fractalist: Memoir Of A Scientific Maverick Download
the second half of the book is devoted to mandelbrot's three-decade quest to explain the fractal world. he explains the concepts of self-similarity and scaling. he discusses a variety of mathematical models of self-similarity, the most important of which is the logistic function. the logistic function is a function that has an expansion of the form x = a x (1 - x), where a is a constant. the parameter a, called the coefficient of expansion, can be tuned to give a range of shapes. it can be set so that the function diverges, has a limit (a positive or negative infinity) or oscillates. the logistic function appears in many natural and engineering systems. mandelbrot puts these ideas together and describes how he applied them to the mandelbrot set. he describes the methodology of scaling, and relates scaling to fractals. he explains the notion of self-similarity and its importance.
most of the autobiographies are written in french, including two written by french mathematicians whose english versions were not available to me. for these works, i first translated them, then performed a stylistic analysis. i also compared the autobiographies with the mathematical papers of their authors. this comparison is systematic, because mathematical authors usually present their mathematical knowledge as a whole, which is one of the characteristics of autobiographies. for example, in his work, "in memoriam benoit mandelbrot" which is part of his autobiography, m. ledoux recalls that he had a very difficult time in high school because he was not very good in mathematics. he went on to explain his difficulties in mathematics, including the difficulty to understand and solve "structured" problems, and the necessity to "acquire the habit of viewing such a problem, whether an abstract or a real problem, as a whole and not as a collection of parts" (p. 5). he then goes on to give a detailed explanation of the notion of part and whole, and of the mathematical problem of the existence and the uniqueness of a solution, as well as the notion of analyticity and of the different types of function. he also gives, through analysis of his own life and through references to classical mathematicians (lagrange, riemann, heine, poincaré, lebesgue, cantor, borel, and bourbaki), a precise description of the field of mathematics, its evolution, and its interrelations with other disciplines. in another autobiographical text, "my life as a mathematician" by j. leray, the author describes himself as "a practitioner of mathematics" (p. 5) and describes the progress of his research, starting with a study of hydrodynamics, then a study of complex dynamics, then the p-s (poisson-sobolev) equations, then a study of analytic functions, and finally, a study of singularities. he ends by asking his reader to reflect on "the passion for mathematics which has been such a part of my life" (p. 31).
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