The Chilean Coast

Once, with a friend in my beach house observe the sun hiding in the distance and he told me that the perimeter of the Chilean coast is infinite. I could not believe it. But how it might be possible I answered; If we consider only the region of Chiloe and if its perimeter must be infinite, how is it possible that I have traveled the entire island from end to end, on the main road? The big island of Chiloé and the entire Juan Fernandez archipelago has an area of land measurable and finite. However, its perimeter still being infinite, said me my dear friend. How can that be possible?

When Benoit Mendelbrot used to work for IBM, he would devote, among others things, to investigate the length of the coast of Britain. He understood that the measure depends on the accuracy and precision of the ruler used. For every ruler that is used, there will be twists and turns that must be ignored and we realize that measured obtained is always an approximation of the actual length. No matter how small the ruler, the results will be always approximations. If we use an infinitesimal measure it will give as result that the length of the coast of Brittany and the Chilean coast are infinite (¥). Because of this, he had to resort to fractal geometry which measures the degree of ruggedness and discontinuity of an object presenting a constant state of irregularity at different scales.

I must admit that I felt ashamed of my giant selfishness to understand an infinity so small.