Nature, Science, & Mathematics: December 2004 Archives

Let All Creation Praise Him!


We find reasons for praise and sources of wonder in the oddest places. This after it was once again in Mandelbrot's book.

from The (Mis)Behavior of Markets
Benoit Mandelbrot and Richard L. Hudson

It is an extraordinary feature of science that the most diverse, seemingly unrelated, phenomena can be described with the same mathematical tools. The same quadratic equations with thich the ancients drew right angles to build their temples can be used today by a banker to calculate the yield to maturity of a new, two-year bond. The same techniques of calculus developed by Newton and Leibniz two centuries ago to study the orbits of Mars and Mercury can be used today by a civil engineer to calculate the maximum stress on a new bridge, or the volume of water to pass beneath it. Now, none of this means that the bridge, river, and planets work in the same way; or that an archaeologist at the Acropolis should help price an Accenture bond. . . . But the variety of natural phenomna is boundless while, despite all appearances to the contrary, the number of really distinct mathematical concepts and tools at our disposal is surprisingly small. When a man goes to clear a jungle he has relatively few types of tools: To cut, perhaps a machete; to knock down, a bulldozer; to burn, fire. Science is like that. When we explore the vast realms of natural and human behavior, we find our most useful tools of measurement and calculation are based on surprisingly few basic ideas. When a man has a hammer, all he sees around him are nails to hit. So it should be no great surprise that, with our small number of effective mathematical tools, we can find analogies between a wind tunnel and a Reuters screen.

This brief passage inspired in me a diffuse chain of thought. If these things may all be described with a limited number of tools (as Mandelbrot maintains) then the infinite diversity and complexity of phenomena that we see about are are really all variations of a few key themes.

I will not contend that this speculation proves anything at all, but merely that looking upon this possible conclusion, one can see for a moment the image of the mind of the maker--infinitely varied and yet discrete and accessible. That all of these varied things should have in common some underlying language, some limited group of descriptors either means that we are not truly describing them, or their relationships are by far more important than their perceived differences.

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