A Primer on the Doomsday Argument

> The reason why this is so subtle is that it's not a given that you're in a cubicle.

The way the problem is presented, it is a given that you're in a cubicle. If you wanted to be more explicit about it, you could say that God, before creating humanity, flipped a coin, and then created either 10 or 100 humans and placed them into cubicles. You wake up and have to estimate the probability of that coin flip.

>>No. That you are in a cubicle is a given fact, so the probability that you find yourself in a cubicle is unconditionally 1.

But it's not 1 that you would be in a cubicle at all. The paradox disappears if the problem was formulated like this: "God shuffles DNA and there is 0.0000000000001 chances tha it shuffles up you and he does that for every cuebicle". Or: "God create you first, then flips a coin and put you at random in one of the created cubicles".

Formulation of the problem should mention which one is it. If it doesn't we are back to guessing what God does (similarly to 2 envelope problem which comes down to guessing what the sponsor's preferences for amounts are). As there are infinitely many ways God could decide to create humans in cubicles you can't answer that without giving some guess (priori) for probability distribution over those choices.

> Then what about the parallel universes hypotheses: what if the universe is constantly fragmenting into multiple futures.

Actually, that's the many-worlds hypothesis of quantum theory. Parallel universes refers to something else.

> This proliferation of multiple futures from any moment would tend to provide a way for doomsdays to be circumvented.

Not exactly circumvented. In the many-worlds picture, all outcomes occur, including the one predicted by the Doomsday argument.

> If you are cloned into N futures in this moment, and you're killed in N-1 of them, then you don't know it ...

True but not compelling, because quantum theories don't require each of the many worlds to be occupied by a conscious observer. Were this not so, the universe couldn't have evolved to the point where consciousness was first possible.

That's an Aristotelian viewpoint, operating logic on the basis of True and False, in which case the argument presented is indeed a fallacy. However, when you operate on probabilities, Bayes' Rule does indeed allow you to drive the logic in a way that seems "backwards" from the Aristotelian point of view.

This, by the way, has nothing to do with "Bayesian" vs. "Frequentism"... this is just the straight application of a simple and non-controversial thing call Bayes' Rule. Assuming you know the probabilities with the requisite precision you are perfectly justified in reasoning that way.

It's also worth reading the end of the article carefully too... for instance, "doom" may be a bit leading, since "doom" could include a full Singularity after which we are no longer "humans" but nobody is upset about that, or other such scenarios that are still in some sense "doom" for The Human Race (imagine those glorious calligraphy letters for that) but aren't necessarily doom in a bad way.

There's also just the casual observation that if society goes on for billions of years there are still simply some people who are born early. Sometimes people win the lottery, and we would not generally be too impressed if they reasoned backwards from there to the conclusion that winning the lottery was more likely than they would have initially thought. (That is not exactly a parallel, since a lottery is part of a much bigger net of information than the deliberately simplified version presented in the argument.) One of my objections would be that it is not clear that we can take a non-temporal line of logic as given in the beginning of the argument and directly apply it to a situation with time. And when I mean "not clear", I mean precisely that it is not clear to me, not that I'm saying it's impossible.

In general I've observed that I'm not impressed with our attempts to apply our local probability rules at cosmological scales. Is Occam's Razor really applicable at cosmological scales? It's hard to say what's "simplest" when we don't even have any reasonable priors (or translate that to whatever math framework you may like, like "have no information about"). The orders of magnitude involved even with merely the visible universe, which we have no reason to believe is even the whole of reality, IMHO can easily swamp the simple probability of error in the argument too easily. (That is to say... there's an old observation in computer science that running a "probabilistic" algorithm with a probability of failure lower than the probability of hardware failure is indistinguishable from running a deterministic algorithm. It is not clear to me that we can overcome our probability of having something wrong in our argument.)