Chaos - James Gleick [56]
At first blush, the idea of consistency on new scales seems to provide less information. In part, that is because a parallel trend in science has been toward reductionism. Scientists break things apart and look at them one at a time. If they want to examine the interaction of subatomic particles, they put two or three together. There is complication enough. The power of self-similarity, though, begins at much greater levels of complexity. It is a matter of looking at the whole.
Although Mandelbrot made the most comprehensive geometric use of it, the return of scaling ideas to science in the 1960s and 1970s became an intellectual current that made itself felt simultaneously in many places. Self-similarity was implicit in Edward Lorenz’s work. It was part of his intuitive understanding of the fine structure of the maps made by his system of equations, a structure he could sense but not see on the computers available in 1963. Scaling also became part of a movement in physics that led, more directly than Mandelbrot’s own work, to the discipline known as chaos. Even in distant fields, scientists were beginning to think in terms of theories that used hierarchies of scales, as in evolutionary biology, where it became clear that a full theory would have to recognize patterns of development in genes, in individual organisms, in species, and in families of species, all at once.
Paradoxically, perhaps, the appreciation of scaling phenomena must have come from the same kind of expansion of human vision that had killed the earlier naïve ideas of self-similarity. By the late twentieth century, in ways never before conceivable, images of the incomprehensibly small and the unimaginably large became part of everyone’s experience. The culture saw photographs of galaxies and of atoms. No one had to imagine, with Leibniz, what the universe might be like on microscopic or telescopic scales—microscopes and telescopes made those images part of everyday experience. Given the eagerness of the mind to find analogies in experience, new kinds of comparison between large and small were inevitable—and some of them were productive.
Often the scientists drawn to fractal geometry felt emotional parallels between their new mathematical aesthetic and changes in the arts in the second half of the century. They felt that they were drawing some inner enthusiasm from the culture at large. To Mandelbrot the epitome of the Euclidean sensibility outside mathematics was the architecture of the Bauhaus. It might just as well have been the style of painting best exemplified by the color squares of Josef Albers: spare, orderly, linear, reductionist, geometrical. Geometrical—the word means what it has meant for thousands of years. Buildings that are called geometrical are composed of simple shapes, straight lines and circles, describable with just a few numbers. The vogue for geometrical architecture and painting came and went. Architects no longer care to build blockish skyscrapers like the Seagram Building in New York, once much hailed and copied. To Mandelbrot and his followers the reason is clear. Simple shapes are inhuman. They fail to resonate with the way nature organizes itself or with the way human perception sees the world. In the words of Gert Eilenberger, a German physicist who took up nonlinear science after specializing in superconductivity: “Why is it that the silhouette of a storm-bent leafless tree against an evening sky in winter is perceived as beautiful, but the corresponding silhouette of any multi-purpose university building is not, in spite of all efforts of the architect? The answer seems to me, even if somewhat speculative, to follow from the new insights into dynamical systems. Our feeling for beauty is inspired by the harmonious arrangement of order and disorder as it occurs in natural objects—in clouds, trees, mountain ranges, or snow