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Response to cpwm17 (Reply #13)

Sat May 10, 2014, 10:32 AM

14. I got 133 hits.

"necessary improbability"

Let's say I number 5000 pennies (on the side, using massless ink) 1 to 5000. Each has a chance of 50% being heads if I drop it.

Now I define an outcome. Penny 1 is heads, penny 2 is heads, penny 3 is tails, penny 4 is heads, penny 5 is tails, penny 6 is tails ... and I go on, stipulating what the outcome is. The probability of that, IIRC, is 1 in 2^5000. One in 1.4 x 10^1505. That's pretty darned improbable.

In fact, that's the odds of *any* combination of heads and tails for those pennies. The one I stipulated. The one where all pennies are heads. The one where all pennies are tails. The one where all even numbered pennies are heads and the odds are tails, or vice-versa.

The probability of any outcome is vanishingly small. Only a fool would bet on any outcome. In fact, you could argue that since every outcome is so highly unlikely, there'll be no outcome--but that, again, would land us in fool territory.

I throw the pennies by handfuls up in the air so they fall down Baltimore's shot tower and land.

But look! There it is, an outcome. No matter how improbable that outcome, an outcome was necessary. It was a necessarily improbable event that happened. Improbability =/= impossible. In fact, if you sum up all those impossible odds you get 100: There had to be an outcome, however unlikely any outcome might be.

In the end, after the fact, the probability of that outcome is 100% by definition. It happened.

It works the same if there are two possible outcomes, one very improbable and one probable. There will be an outcome. And sometimes it will be the improbable one. After it happens, whatever the improbability before the event (in terms of prediction), its probability was 100% after the event (because it happened). As the Doctor would say, "It's not impossible, it's just highly implausible."

I might check back to see if I abduced the right meaning for the term. Perhaps SS will comment.

The term seems to have started in quasi-secular theological circles, dealing with the utter improbability of miracles being an argument against having miracles happen. A priori calculations don't mean must a posteriori.

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