I didn't know why I was so taken with the meanders of the Nova show, but I started following them to obscure corners of the library -- the kinds of places you might end-up if you are, say, checking for titles by John McPhee. The more I learned about the phenomenon of the meander, the more apt it seemed as a metaphor for what happens in an essay. Throughout the writing, I was trying to call something to mind, something else that meanders, something not on the show, but important for what I am groping toward saying.

A Nova show about the forms of nature prompts me to look up "meander."

Having always used the word to refer to walking, I am surprised to learn that it comes from water. Rivers and streams meander, verb, have meanders, noun. "Meander," in fact, comes from the name of a river, one in ancient Phrygia, now part of Turkey -- the Maeander, now the Menderes. Change of name notwithstanding, the waters still flow from the Anatolian plateau to the Aegean Sea. A namesake, a Meander River, meanders in northern Alberta.

In what we do on foot, meandering implies an aimless wandering, with the pleasant connotation that the very aimlessness of the wander is something freely, even happily, chosen.

The meanders of water seem equally aimless, but are, it turns out, very regular in their irregularity -- although if you were walking along the bank of a meandering river, you might find that hard to believe. You would head in one direction, and then curve around until you are going the opposite way, and then around again, following a path which turns upon itself and makes no sense. Could a helicopter or fairy godmother, though, raise you high enough, you would see that what seems like chaos below actually forms a regular repeating pattern of serpentine flexuosity.

The shortest distance between two points may be a straight line, but a river neither knows nor cares. It seldom flows straight for a distance of more than about ten times its width. A river erodes its banks, and the way of the world is such that one side invariably erodes faster than the other. It eventually collapses and its sediment is carried along and deposited downstream. Two curves are thus begun: the erosion point becomes the outside of one; the sediment pile, the inside of the next.

The water on the outside has to flow faster to keep up, causing more erosion, more sediment movement. The outsides get deeper, the insides shallower. At any point, the shape of the river shows its history. If other forces do not prevent, the bends over time work toward becoming perfectly elliptical. "Ellipse" comes from the Greek for "to fall short," an ellipse falling as it does short of a perfect circle.

This has all been observed in nature and shown experimentally in laboratories, and is thought by many to be sufficient explanation for meanders.

Others disagree, especially now that infrared images from satellites show I that ocean currents -- which have no erodable banks -- also meander. The jet stream appears to meander as well. Mathematicians have calculated that the most probable path between two points on a surface is in fact a meander. Meanders then may be the norm, not the exception. The question may be not why some rivers meander, but why every river we see does not.

* * *

There might be particular essays whose shape is more akin to one of the other basic natural forms -- a sphere or hexagon, a spiral, say, or helix or branch -- but on the whole, I think, what essays do best is meander. They fall short of the kind of circular perfection we expect of fiction or poetry. They proceed in elliptical curves, diverging, digressing.

We can float or row or swim or speed or sail along the meandering course of an essay. We can meander on foot on the river bank with the essayist. We expect only to go somewhere in the presence of someone.

Perhaps we will end up close to where we started, perhaps far away. We will not see the shape of our journey until we are done, and can look back on it whole, as it were, from the air. But we will, and very quickly, come to know the shape of our company -- the mind, the sensibility, the person, with whom we are traveling. That much seems necessary to essay structure -- one individual human speaking to another who wants to listen.

* * *

Flattened out, the thin human cortex, the gray matter of the brain, is much too large for the skull within which it must fit. The problem has been elegantly solved by intricate pleating and folding, as if the cortex were a piece of thick fabric gathered in tightly to fit. In anatomy books, we can see pictures of cross-section slices of the gathers. The shape is unmistakable, like a close-packed river shot from above, meandering within.