Benoit Mandelbrot examined data drawn from rivers. He obtained data from Egyptians on the height of the Nile River for millennia. He found that the Nile had unusually great variation, as it flooded in some years, and subsidized in others. Mandelbrot classified the variations he observed using the Noah and Joseph Effects. The Noah effect meant discontinuity: when a quantity changes, it was change very fast. The Joseph Effect meant persistence: change over time was constant. These Effects explained how trends in nature are real and can vanish very quickly. Mandelbrot also studied geometry, which when applied to the real world is not perfect. It mirrors a rough universe, that doesn’t perfectly mirror the accepted geometric shapes. For example, mountains are not cones and lightning does not travel in a straight line.
Since Euclid measure
ments – lengths, depth, thickness- failed to capture irregular shapes, Mandelbrot turned to idea of dimensions, then fractional dimensions. A fractional dimension is a way of measuring quantities that do not otherwise have a clear definition. For example, measuring the degree or definition of roughness or brokenness, or irregularity in an object. Fractal dimensions, as they were soon called, found applications on a series of problems that connected to surfaces that were in contact with each other. Several examples include the contact between tire treads and concrete, the contact between joints, and contact in electricity. Then there are the equations of fluid flow, which are dimensionless, meaning they do not require a set scale. Blood vessels, from aorta to capillaries, form a continuum as they branch and divide until they have to move in a single file. With the nature of its structure, the circulatory system performs dimension magic, as they it manages to squeeze a large surface area into a small volume. Yet, the blood only takes up five percent of the body. This is one thing I found very fascinating. How did the body evolve to form such a perfectly complex system?
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