Today, some reflections on form and purpose. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

Some years ago NOVA did a wonderful episode called The Shape of Things. It showed why the chambered nautilus is shaped in a spiral of Archimedes. It told why rivers carve their peculiar meandering courses. We were given a hundred ways that nature puts spheres, hexagons, and helixes to use.

I especially liked the part about tree branches. A tree has to keep its leaves -- its solar collector -- evenly spaced. This can be done in many ways: a small plant might array each leaf on its own short branch, all radiating from a central hub. But a tree has far too many leaves for that. It has to hold them all out to the sun without collapsing under its own weight. A tree minimizes its weight by subdividing its stem -- by splitting in two, over and over again -- until each leaf rides at the end of a mere twig.

Nature has all kinds of tricks up her sleeves. The shapes of snowflakes, feathers, and wind ridges on sand all achieve her ends with remarkable grace and economy.

The NOVA episode ended with a natural vista opening into a view of a city. Just when we'd been hypnotized by splash patterns and bird skeletons -- by waves and spider webs -- we suddenly saw the harsh lines of the human hand laid across nature's order.

The city, of course, is also a part of nature, and we were natures's agents in building it. Yet it does seem to intrude on the simpler rhythms of form outside it. We suddenly look at that city as though we were some disembodied intelligence from another galaxy -- never having seen earth, never having seen a human. Divining the purpose of a house, a highway, or a cathedral from that vantage point would be far more difficult than understanding the shape of a tree. We are a complex species, and the organic forms of our cities evolve in very complex ways.

But within the framework of its purpose, a city is also a beautiful thing. It fulfills our own complex, diverse, and badly understood purposes in strange and unfathomable ways.

That's why I like Houston so much. It changes form and shape on every street. Some unopened oyster -- some undiscovered pearl -- lurks in every byway. Bayous and vacant lots, the Astrodome and the Opera House, McDonald's and Maxim's, software shops and antiques stores -- they don't all serve your individual needs. But together they serve us all by serving our collective, and often abstract, needs. Few forms in nature have to fulfill such complex purposes. It's easy enough to see beauty in a sea shell. But you have to know a big sprawling city before its beauty, its functions, and its stunning range of purposes start to come clear.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

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NOVA: The Shape of Things. Vestron Video, 1985.

This episode has been greatly revised as Episode 2460.