Fractals and the Passing of Benoit Mandelbrot
I am grateful to the Triple Crisis Blog for making me aware of the passing this month of the great mathematician, Benoit Mandelbrot, who coined the term "fractal".
Mandelbrot defined a fractal as "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole." Fractals occur in nature all the time, such as the shape of a fern. Careful followers of Capital Institute will know that the background for our web pages are mathematical fractals, signifying the importance of fractals in understanding the behavior of financial markets and a connection of financial systems to natural systems. Mandelbrot's financial market analysis is contained in The (Mis)Behavior of Markets, a Fractal View of Financial Turbulence, listed in our Resource section. I referenced Mandelbrot's warning about the complexity of turbulence in my post called "From Risk to Uncertainty".
I cannot improve upon Alejandro Nadal’s post, Understanding Instability: Mandelbrot, Fractals, and Financial Crises, so simply provide a link. Mandelbrot's NY Times Obituary can be read here.
I hope and predict that Mandelbrot’s contribution to a new understanding of financial markets will grow after his death. I am awed by the connection fractals allow us to make between our financial system and nature. This cannot be a coincidence. We must learn not only how to use Mandelbrot's genius to better understand the behavior of markets (no more efficient market hypothesis and no more modern portfolio theory), we must also learn to understand the connection between finance, the real economy, and the natural system we call the biosphere of which it is a part. As the Buddhists say, it's all one.