Today, we close a circle. 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.
Weave a circle round him thrice,
And close your eyes with holy dread.
... says Coleridge in his poem Kubla Khan. He's talking about the need to hold our creative daemon at bay within us. The idea of circling something so that we might possess it is ancient.
When I visited the Kremlin back in the Cold War days, I felt compelled to walk all the way around its outer wall. Once I did that, the Kremlin would be mine. Crater Lake in Oregon is like that. The thirty-six mile trail around it is a hard day's walk. I haven't done that exercise, but friends have. The Lake seems to say, "You do not know me until you have circled me."
Circling is odd business. Imagine canoeing near a large whirlpool. Stop and let the canoe drift. It stays pointed in the same direction as it circles the center. You're back where you began without having turned at all. It's as though nothing happened. But that gentle lap required intense whirling within the pool.
Toward the end of their historic globe-girdling voyage, Magellan's crew reached West Africa. There, Portuguese settlers told them it was Wednesday. But they'd kept track of time and were sure it was Thursday. No one board had thought about date lines. They had yet to see how closing the circle around Earth brought mischief with it.
Engineers deal with these issues all the time. They will, for example, trace processes within a hot air engine. As the piston moves up and down the air is first compressed, then heated, then further expanded, then cooled. Finally, it's right back where it started. One might think that nothing had happened.
But in the larger world, outside the cylinder, heat has been supplied, work has been done,
and low grade heat has been rejected. The external world has been radically changed.
At lunchtime, last week, a friend observed that many people, sensitized by the events of September 11th, have taken to using the expression ground zero when they mean to say square one. Square one evokes a Monopoly board where, each time you close the loop, you leave Vermont Street and the Boardwalk changed. Perhaps that verbal slip reflects our aching awareness that ground zero in Manhattan may finally be put right, but the world surrounding it can never be the same.
When we close the circle, we alter human history. That's true as we close a path within an electrical, magnetic, thermal, or fluid field. Close the circle upon any skein of human events and then look around you. T.S. Eliot wrote,
We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.
And we read the disturbing undercurrent of those lines. For, even if our starting place looks the same, we close the journey upon a world permanently, and irredeemably, changed.
I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.
I have hinted at a number of ideas from mathematical potential theory here. Any advanced calculus text deals with these issues. I would also recommend most undergraduate engineering fluid mechanics texts or any book with the words theoretical hydrodynamics in the title. See also Episode 1306 for the story of one of the best of these texts.