The Fractal Geometry of Nature Quotes

“Why is geometry often described as ""cold" and ""dry?" One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”
― Benoît B. Mandelbrot, The Fractal Geometry of Nature

“(Since algebra derives from the Arabic jabara = to bind together, fractal and algebra are etymological opposites!)”
― Benoît B. Mandelbrot, The Fractal Geometry of Nature

“Weierstrass, Cantor, or Peano! In physics, an analogous development threatened since about 1800, since Laplace’s Celestial Mechanics avoided all illustration. And it is exemplified by the statement by P. A. M. Dirac (in the preface of his 1930 Quantum Mechanics) that nature’s “fundamental laws do not govern the world as it appears in our mental picture in any very direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies.” The wide and uncritical acceptance of this view has become destructive. In particular, in the theory of fractals “to see is to believe.”
― Benoît B. Mandelbrot, The Fractal Geometry of Nature