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August 27, 2008

Miracles are just the law of large numbers

If enough things happen, some will be "miraculous." That's a given, if a miracle is taken to mean something way out of the ordinary.

Every time somebody wins a gigantic lottery prize, that's a miracle. What are the odds!? Hundreds of millions or more against those numbers being picked.

Yet, some set of numbers necessarily had to be chosen. So the winner feels it was utterly unlikely he or she got the prize, while it was completely predictable that eventually the money would be won by somebody.

In "Folk Numeracy and Middle Land" Michael Shermer discusses our inability to comprehend the laws of large numbers, mistaking them for other-worldly miracles.

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.

So it's possible it will rain on Obama's parade tomorrow. But if that happens, it won't be prayer that made it happen. Just a meteorological anomaly.

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