International Law

Why Our Brains Cannot Grasp Probabilities

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Michael Shermer, writing at Scientific American, has an interesting observation about chance and the measurement of risk.

"Have you ever gone to the phone to call a friend only to have your friend ring you first?

What are the odds of that? Not high, to be sure, but the sum of all probabilities equals one.

Given enough opportunities, outlier anomalies--even seeming miracles--will occasionally happen.

Let us define a miracle as an event with million-to-one odds of occurring (intuitively, that seems rare enough to earn the moniker). Let us also assign a number of one bit per second to the data that flow into our senses as we go about our day and assume that we are awake for 12 hours a day. We get 43,200 bits of data a day, or 1.296 million a month.

Even assuming that 99.999 percent of these bits are totally meaningless (and so we filter them out or forget them entirely), that still leaves 1.3 "miracles" a month, or 15.5 miracles a year.

Thanks to our confirmation bias, in which we look for and find confirmatory evidence for what we already believe and ignore or discount contradictory evidence, we will remember only those few astonishing coincidences and forget the vast sea of meaningless data."

His explanation of why this continues is not satisfactory - viz. "the reason that our folk intuitions so often get it wrong is that we evolved in what evolutionary biologist Richard Dawkins calls "Middle World"--a land midway between short and long, small and large, slow and fast, young and old.

Out of personal preference, I call it "Middle Land." In the Middle Land of space, our senses evolved for perceiving objects of middling size--between, say, grains of sand and mountain ranges. We are not equipped to perceive atoms and germs, on one end of the scale, or galaxies and expanding universes, on the other end."

It is true that our modern understanding of probabilistic counting only starts only 350 hundred years ago.  

Ian Hacking who wrote a great book on the history and emergence of probability argues that our modern notion or scientific ideas arose when we got clearer about the distinctions between frequencies and degrees of belief.

My own, more plebian thought, is that until about 350 years ago stories could serve as perfectly good scientific justifications - we had little prediction or control over the big natural disasters.

In such an environment, controlling the thoughts and reactions of other people were more important - stories convince, data does not.

We grow up learning these tricks of persuasion, some are even taught to revel their inability to count and reason abstractly.

We would do better to focus on counting and less on using the tricks of social persuasion if we hope to grow up.

Full post as published by Misleading Advertising Law on September 04, 2008 (boomark / email).