I put the book back into its place, as I droned on with my work hours, only to realize it was one from a set of ten. A look at the book followed by a simple glance at the shelf would've given away its place. I guess that is the difference between me and Benoit Mandelbrot.
Mandelbrot expected symmetry and similarity, not formulas and equations, to provide answers. At school he would solve math questions by imagining the equations as shapes and would solve them by folding and manipulating them. Of course, as the equations grew more complicated this came up short but he never stopped believing that the small could be analyzed by visualizing the whole. Much along the lines of medieval science.
In the eighteenth century, people believed that small things were merely scaled-down versions of bigger ones. For example when sperm was discovered, science thought it was a small man swimming around. If we zoomed in or zoomed out the world would look more or less the same. Of course, now with our microscopes and telescopes we know better. The sperm is very different from a small man and perhaps more interesting. Atoms are not made of smaller atoms which are made of even smaller atoms, but protons and neutrons which are in turn made of a wide variety of quarks - each with its own unique properties. And so, to describe everything at its own specific scale we came up with equations and formulas to identify these unique objects. Much like the unique identification number on my book. But Mandelbrot never liked equations. He believed in visualising the whole, in geometry and symmetry.
A biologist may say arteries, arterioles and capillaries are entirely different things. An economist might say that the day to day fluctuations give no insight into year-long or ten-year trends. Yet Mandelbrot trained himself to see 'self-symmetry'. Self symmetry describes vaguely similar trends that we choose to ignore, saying that they are, in fact, different systems governed by different laws. And out of this symmetry arose fractal geometry: 'Mandlebrot coined the word fractal himself'.
A new math. The math of nature. A math that described the jagged shape of coastlines. That predicted the patterns of trees, leaves, lightning and erratic consumer behaviour. Fractal geometry describes most chaotic systems to a great detail. No more assuming that the cow is spherical. No more saying biological systems have far too many complexities to be governed by simple math formulae.