Thursday, October 23, 2008

Undamped oscillation

Someone I know was heading west on the interstate just past downtown when ahead they saw a pickup pulling a trailer, veering a bit left then right then left as it traveled down the road. It was clear that the driver was aware of the problem, and figured that his job was to keep returning the truck to its own lane. This logic, as simple and impeccable in intent as it was, was alas dead wrong because the driver's response-time fit beautifully with the resonant-frequency of the weave. Like someone kicking one's legs at exactly the right time to pump up the motion of a playground swing, the driver's logic loop repeatedly pumped energy into the weave, which got wilder and wilder until all of a sudden the truck and trailer spun out into a parked position across five lanes of traffic.

So what?

Think about the stock market. The news media reports where it's at every day if not every minute. Like the truck driver above, however, attention is not being focused on dynamics, like the system's resonant frequencies. A kid on a playground swing knows that you can make the oscillation bigger by kicking at the right point with the right frequency. The truck driver above found this can happen inadvertantly if you pay attention only to displacement.

If you don't want the oscillation to get bigger, you can either (i) not act, or (ii) act at a different frequency. Even better computer programs that paid attention to frequency amplitude and phase as well as displacement, or even more sophisticated dynamical models, might be programmed to actively damp oscillations. So could the newsmedia.

What might be some useful first steps to this end, so we don't spin out the truck just 'cause we and our computer programs are paying attention to the wrong thing?

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