Some seemingly-rare events show up more often than one might expect. Remember all those "once-in-a-century" floods we've had recently? How about the countless personal "coincidences" that strain probability? And don't forget political crises and stock market movements (down as well as up).
There's a little-known probability curve that's worth studying. It's called "1/f" or "inverse-frequency", and is sometimes referred to as "pink noise" to contrast it with white noise. The 1/f distribution describes a system with extreme fluctuations --- changes that sporadically leap far outside any bounds suggested by historical experience. Strictly speaking, there aren't any pure 1/f probabilities in Nature, since the 1/f function has an infinite area under its graph. But for practical purposes, 1/f applies in host of cases. What's the distribution of word usage in a text? The Nth most common term occurs about 1/N of the time (Zipf's Law). The same rule holds for city populations. It also describes the long-term drift of atomic clocks and low-frequency noise in electronic systems.
Do 1/f considerations also apply to human reckoning of goals and goods? Might the Nth most important value be roughly 1/N as critical as the first in rank? Could one then balance the achievement of many lower priorities against success in a few top-of-the-list endeavors, and vice versa?
Monday, February 14, 2000 at 05:53:04 (EST) = Datetag20000214