Thursday, March 23, 2017

Fantastic improbability

From Doug Axe:

There's this general confusion over what probabilities mean, and that if...something has a probability and it's not zero, then that means it's not impossible.

Some people want to say, if the probability is not zero, then that means it can happen. What it really means is that if there are enough opportunities for a very small probability to become a large probability, then it can happen.

So, if something is one in a million, but you have a million shots at it, then it becomes probable. If something is one in a trillion, you're going to need a trillion shots at it for it to become probable. A million won't be enough; it's still vastly improbable.

If you push that number far enough, you reach an improbability that is so extreme that there is no way for this physical universe to give you the number of opportunities that would raise that extraordinary small probability to something that can happen, that's like, 50-50 or better.

It turns out that in these sorts of problems where you have to arrange lots of thing and get lots of things right, the improbability of each step multiples and you can get just extraordinary improbability.

So, I use the term "fantastic improbability" to refer to this sort of boundary where it's now beyond the point where this physical universe could possible overcome the improbability. That, I call "physical impossibility," distinguishing it from mathematical impossibility...One in a google [sic] is the dividing line where I say, once it's that improbable, there is no way for any real process in this physical universe to overcome that kind of improbability. That's why I call it "physically impossible."

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