The paradox of the visibly irrelevant

The chief illustration of last month's essay -- Mandelbrot's familiar argument that the coast of Maine has no absolute length, but depends upon the scale of measurement -- also epitomizes this month's theme. When we study guppies in a pond in Trinidad, we are measuring the coastline by wrapping our string around every boulder on every headland of Acadia National Park. When we trace the increase in size of the human brain from Lucy (about 4 million years ago) to Lincoln, we are measuring the coastline as depicted on my page of Maine in Hammond's Atlas. Both scales are exactly right for their appropriate problems. You would be a fool to spend an summer measuring the details in one cove of Acadia if you just wanted to know the distance from Portland to Machiasport for your weekend auto trip.

I find a particular intellectual beauty in such fractal models, for they use hierarchies of inclusion (the single cove embedded within Acadia, embedded within Maine) to deny hierarchies of worth, importance, merit, or meaning. You may ignore Maine while studying the sand grain and be properly oblivious of the grain while perusing the single-page map of Maine.

But you can love and learn from both scales at the same time. Evolution does not lie patent in a clear pond on Trinidad any more than the universe (pace Mr. Blake) lies revealed in a grain of sand. But how poor would be our understanding -- how bland and restricted our sight -- if we could not learn to appreciate the rococo details that fill our immediate field of vision, while forming geology's irrelevant and invisible jigglings.

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