The Fractal Geometry of Nature by Benoît B. Mandelbrot
My rating: 4 of 5 stars
This beautiful book is about Mandelbrot’s love of science, mathematics and all forms of knowing. He is humorous at times, dense, and waxing on about fractals and changes that are self similar. It is through the figure of a difference that something is known. Fractals are unique in that they are that difference regardless of scale, that is, as Mandelbrot said of Leibniz, that Leibniz first recognized a straight line as being a curve whose arbitrary measure was universally applicable by itself by any other arbitrary measure.
Fractals are thus, a balance of form and measure and thus perfectly applicable to describing self similiarities that occur throughout various scales. By necessity these fractals are thus found in areas of maximal distribution where it be biological, informational, materially, socially or otherwise. Each bit of aggregate from each context can be traced through out some of the other contexts so that a distribution of their differences can be expressed mathematically as a formalization of unithood — difference — itself. Fractals can thus be understood as the limit of scaleless models of difference. Mandelbrot goes over a variety of contexts in which we can understand their expressedly different dimensions, differing topographies, as structured rules through time, or a static interface that modifies itself as scale is adjusted.
At times, Mandelbrot can become overwhelming as he notices as particular “cut” in an equation, be it a variable or an expressed tendency, and in vocalizing it, circulates around that textual point to arrange chapters, whorls on whorls, in which sections and sections of sections let us know when one thing was described and another thing began.
And so, as this is a book about the fractal geometry of nature, Mandelbrot shows us his love by talking admiringly of other mathematicians, many not celebrated, or fully acknowledged in their time. These technicians and their stories become the backdrop of those who developed this metric enough to let us see, and explore these subtle differences and their odd refinements. Indeed, it is really to those quiet, anonymous men, who established the halls of science that Mandelbrot writes this book to, for he would have liked for them to experience the joy he feels at being able to explore these monsters, while many of them did not, due to the contemporaneous level of mathematical understanding not yet understanding how to recognize (and thus, explore) the fractal nature of geometry in all its glories.
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