Tuesday, October 16, 2012

Strogatz on Powers of 10

In the last of his current series of articles on math, Visualizing Vastness, Steven Strogatz starts with the solar system, generalizes to powers of 10, and then offers these two paragraphs:
This style of thinking, this powers-of-10 mentality, is our best hope for making sense of the immensity of the natural world. What makes subjects like biology and climate science so hard is not just that they involve so many variables; it’s that the crucial phenomena in them occur over such a wide range of scales. Biologists need to contend with everything from nano-size DNA molecules on up to cells, organs, organisms and ecosystems. For climate scientists the relevant scales go from the molecular (the photochemistry of ozone) to the global (the fluid mechanics of the jet stream). Many of the great scientific puzzles of our time have this multiscale character.

A contentious example, especially in this election season, is inequality. The distribution of wealth in the United States spans at least 10 powers of 10, ranging from people whose net worth is measured in tens of billions of dollars, to those with barely a dollar to their names. This disparity dwarfs even the six powers of 10 in the solar system. As such, the distribution is extremely difficult to depict on a single graph, at least on the standard kinds of plots with linear axes, which is why you never see it displayed on one page.
The juxtaposition is striking.