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Patra Neutrino

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*Note to moderators: I’m not sure if this topic is mainstream enough for the forum. If you decide to remove it, I’ll understand. Not convinced I've put it in the right section either!*

I’m sure you’re all familiar with, or will easily understand, survivor bias, which is a form of selection bias. Imagine you got 3,600 people and put them into individual

__isolated__cells. Now, imagine that you sent a guard into each cell, each with two revolvers loaded with five bullets each, and you asked each guard to spin each barrel and fire both revolvers, point blank, at each prisoner’s head. Approximately (1/6)*(1/6) of the prisoners would survive, i.e. 100.

If you asked each surviving prisoner to estimate the number of bullets per chamber, they would never say five. They would underestimate the number of bullets each gun had been loaded with by virtue of having survived the event.* (Imagine it from your point of view: a guard has just come in and fired two guns at you. You heard two clicks.)

I got to thinking about apocalypses, and the probability of, say, a nuclear war. We know that it looked pretty hairy in the 1960s and 1980s, but it didn’t happen. Therefore, it is often inferred, there probably won’t be a nuclear war anytime soon, because before lots of people thought there was going to be one before, and there wasn’t.

If we make the

__initial__assumption that nuclear wars always kill 100% of the global population and further assume the multiverse** model of realty, an analogy can easily be made with the guard/prisoner example above. If human life in most other universes was wiped out in the last century, we’d never know about it, and from the anthropic principle, we would just be in one of the few universes in which there was no nuclear war.

But nuclear wars don’t always kill 100% of the population, so the calculation gets a lot messier. I have a couple of ideas myself***, but that’s enough for now. I posit, however, that we are underestimating the probability of future apocalypses due to survivor bias. Does anyone have any thoughts on the matter?

(I intend this to be a very open thread. I’m not totally convinced of my conclusion, but somewhere in all of this I’m sure there’s an interesting line of discussion regarding probability, the anthropic principle, multiverses, or something like that).

Cheers.

*Any surviving mathematicians could use Bayes’ Theorem to estimate the probability of there having been n bullets in each gun as follows: p(0)=39.6%, p(1)=27.5%, p(2)=17.6%, p(3)= 9.9%, p(4)=4.4%, p(5)=1.1%, p(6)=0%. Working available on request.

**I’m not sure it is actually necessary to assume this, but it makes things easier at first. I don't think the multiverse approach should ultimately have any bearing upon standard probability, however.

***I think that the probabilty of existing in any given universe in the multiverse is proportional to the probability of your having been born in that universe, which in this case is, I suspect, proportional to the surviving population of an apocalyptic event.