Thursday, September 03, 2020

Benford's Law

On a Netflix series called CONNECTED, I recently watched an episode about Benford's Law, a theory new to me. Here's the Wikipedia article on this theory. It's dense with equations and mathematical terms, but you can get a general idea of the concept from the explanatory sections:

Benford's Law

In brief, it states that in any large set of numbers, about 30% begin with the digit 1, about 17% with 2, about 12% with 3, and so on, decreasing predictably with each digit. The larger the sample, the more reliably this pattern shows up. "As a rule of thumb, the more orders of magnitude that the data evenly covers, the more accurately Benford's law applies." It doesn't matter what kind of statistics we're examining. Population figures of cities, a list of the sixty tallest structures in the world, death rates, house prices—all follow the pattern. Furthermore, it doesn't matter what units of measurement are used. The data are so predictable that this principle has been used in fraud detection and granted legal status in court cases.

This phenomenon seems downright spooky, especially since nobody knows for sure why numbers work that way. The Wikipedia article explains various hypotheses in detail, with mathematical terminology and symbols that I skipped over because they made my head spin. The host of the Netflix program raised an existential question: What does Benford's Law mean for human free will? If the statistical outcome of such a wide variety of human activities is so predictable, are our individual choices freely made?

I believe the two levels of phenomena don't negate each other. Patterns of large numbers of events in the aggregate follow the "law." Nevertheless, the decisions of any particular person in a given situation can't be reliably predicted. For instance, at the Naval Postgraduate School in Monterey, a half-serious rule was discovered that every couple stationed there eventually got a pet, a baby, or a divorce. My husband and I had our third baby while he attended the school. But that decision wasn't compelled by the "rule." Somehow, by acting freely in their own lives, human beings collectively fulfill demographic "laws." Yet each action is still chosen, not compelled.

Maybe it's as C. S. Lewis proposes in his allegorical novel THE GREAT DIVORCE: From the perspective of eternity, predestination and free will are not incompatible. Likewise, there's no contradiction between predictable statistical probabilities and individuals' conscious choices.

Margaret L. Carter

Carter's Crypt

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