Some things are delicately balanced, like a pencil standing on its point. It must fall; the least disturbance will cause forces that push it farther off balance, which then make still greater forces appear that push it yet harder, an accelerating catastrophe. That's an unstable equilibrium. But how does the pencil decide which way, and when, to fall if it's perfectly poised?
It doesn't "decide", of course; our model of the situation was sadly incomplete. The pencil is made of atoms, vibrating in interlocking structures; it's balanced on a table that trembles slightly; the air has subtle eddies and currents that push against it; and even if we eliminate all those disturbances, electromagnetic and gravitational influences from stars far away still tug the pencil off balance. When the slightest perturbation makes for growing error, in an amplified feedback loop, a simple symmetric picture of the situation can't work.
The pencil's precarious posture is intuitively obvious. But many other real-world systems can seem straightforward, yet hide subtle instabilities. If we try to describe them with simple models, it's critical for us to verify those models by putting in a touch of artificial "noise", tiny variations in the inputs to our calculations. If the results differ wildly, that's a sure sign that our model is broken, that we're leaving out something important — or that reality is itself at a cusp, delicately poised, teetering on a brink.
If so, then we cannot simulate with any hope of success. We already know some limits of predictability in nature, for turbulent fluid flows and for planetary orbits. We may suspect similar instabilities in biological neural networks (minds!), in political and economic systems, or in the webs of interpersonal and social relationships. Perhaps history itself is unstable. Perhaps the best we can ever do, then, is to scorn false prophets who purport to predict the unpredictable, and settle instead for estimating the limits of our uncertainty — error bars, plausible guidelines rather than rigid forecasts of the future.
Friday, August 20, 1999 at 20:04:55 (EDT) = 1999-08-20
(correlates: ManyWorlds, OnDecouplage, DarwinOnTheFaceOfNature, ...)