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A Primer on the Doomsday Argument

anthropic-principle.com

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Re: A Primer on the Doomsday Argument

#51

Post by amalcon »

So, there are a few problems here:

The argument assumes that the only possible end-state for humanity is doomsday; that is, there are a finite number of humans, and when there are no more doomsday has occurred. The article touches on this with the infinite humans / transhuman stuff at the end.

The argument assumes exponential growth in number of humans until the terminal state, but this is not a foregone conclusion. While this doesn't change the reasoning in a strict sense, it may put the "soon" cutoff millions of years in the future.

Finally, the prior probability is chosen arbitrarily. It does matter quite a bit. Take the exponential argument for evidence as to why: For any given probabilty p that doomsday will occur on a given day, it is more likely today than on any single other day! This is simply because if doomsday occurs today, it cannot occur on any future day, making it less likely on each successive day.

Except that if p=1E-10, doomsday is fantastically unlikely to occur this year. The Bayesian argument has the same problem, you just start seeing it at a different value of p.

Re: A Primer on the Doomsday Argument

#52

Post by marcosdumay »

andybak wrote: post #12
dogecoinbase wrote: post #11

Other than the fact that you can't coherently reason based on your own existence (existence is not a predicate), one should rightfully be wary of an argument that would have been valid and false at every point in the past. The Doomsday Argument is not an argument in favor of its conclusion -- it's a reductio ad absurdum that demonstrates why this type of reasoning is invalid.

Is this not a weakness in many (all?) deductive arguments? i.e. if we throw out this argument then we have to throw out much of science.

Science (the way that it's practiced nowadays) has no ambition to reach logical truths. It just collects empirical validation.

Re: A Primer on the Doomsday Argument

#53

Post by lisper »

bluecalm wrote: post #31
baddox wrote: post #23

Earlier quoted context omitted.

> 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.

It is given that you are but it's not given that that was a sure thing to happen. Imagine this: God flips a coin, creates 10 cubicles. If the coin is heads he puts you in one of them if it tails the God flips another coin and if it tails again he puts you in one of the cubicles but if it heads he doesn't. You wake up in a cubicle. It's given that you are in one! what are the chances the first coin landed heads ? The…

Ah, I see. It makes more sense if you forget about cubicles and just call the final outcomes A or B. Call the outcomes of the two coin flips H1/T1 and H2/T2. We have: H1->A, T1,H1->A, T1,T2->B. P(H1|A) is therefore 67% if the coin is fair, but in any event P(H1|A)>P(H1).

So the doomsday argument is actually correct. :-) But it's really nothing more than the (IMO vacuous) observation that (say) half of the people who ever live will have a birth order number greater than the median, and so the odds are 50-50 that fewer people will be born after you than before you. More generally, the odds that N times as many people will be born after you as before you is equal to 1/2N.

Re: A Primer on the Doomsday Argument

#54

Post by baddox »

bluecalm wrote: post #46
baddox wrote: post #28

This is a much better discussion of the Doomsday Argument, and the self-indication and self-sampling assumptions: http://www.scottaaronson.com/democritus/lec17.html The whole course is also very good, and will probably be interesting to many HN users.

Very nice read, from this lecture: >>So you're in the room. Conditioned on that fact, how worried should you be? How likely is it that you're going to die? A: 1/36. Scott: OK. That would be one guess. >>One answer is that the dice have a 1/36 chance of landing snake-eyes, so you should be only a "little bit" worried (considering). A second reflection you could make is to consider, of people who enter the room, what t…

I think it's still a "problem." Which one is the "correct probability" that you're going to die? If, instead of dying, a red light in the room might turn on after a minute, how would you place a bet about whether the red light would turn on?

Re: A Primer on the Doomsday Argument

#55

Post by lisper »

Here's a simpler way to see what is going on. Number all the humans that will ever live in order of their birth from 1 to N. The odds of your birth order number (call it B) being in the range of 1..MAnother way to look at it: half of the humans who ever live will have fewer people born after them than before them. Your a priori odds of being such a person are exactly 1/2.

Re: A Primer on the Doomsday Argument

#56

Post by rm445 »

livingparadox wrote: post #50
rm445 wrote: post #35

Earlier quoted context omitted.

It's probably not worth worrying about the fate of humanity till you've figured out the rooms example. Since you're on this site I'm sure you can trivially knock up a script to simulate what happens. Or just draw the probability tree. In any case the relevant question is,, out of those who find their room number is less than ten, what is the probability that the coin toss meant only ten rooms are occupied. The answer…

Here's a simulation to test this argument. http://jsfiddle.net/3f49ry5u/ So... unless I did the simulation wrong, it supports my conclusion. If I did do it wrong, please show me a corrected simulation which supports your position.

Sorry amigo, I gotta get to work. Here's my code I wrote last night, hope it makes sense:

http://pastebin.com/79rmjmKr

Typical result:

494644 results in rooms less than 10: 449838 had 10 rooms (90.9%), 44806 had 100 rooms 9.1%

Note that anyone who finds themselves in a high-numbered room can draw the obvious conclusion. The question is, what can you infer about the situation if you find yourself in a low-numbered room?

To hammer the point, let say the coin toss decides between 1 room and ten million. If you find yourself in room One, do you still think the chance the coin has come up heads is 50%? If you do, don't tell me, write a letter to Monty Hall.

My vague ponderings about the actual doomsday problem is that it holds up, i.e. it's a reasonable argument that it makes eventual populations of say 10^400 simulated souls using the whole universe as a computer highly unlikely. But the sheer bigness of the possible-but-unlikely population leaves plenty of room for astronomical-sized future populations and doom isn't necessarily imminent in human terms.

Re: A Primer on the Doomsday Argument

#57

Post by typomatic »

titanomachy wrote: post #48
typomatic wrote: post #42

Earlier quoted context omitted.

As B -> \infty, also t -> \infty. I'm reminded of the Fight Club quote: On a long enough timeline, the survival rate for everyone drops to zero. :)

Haha nice. Although, in this case we are looking ahead, basing our short-term survival on what a long-term survival would theoretically look like. So the more people there are in the hypothetical Doom Late, the more likely Doom Soon becomes. The more I think about this the more absurd it seems.

Yeah, all this analysis (both what we've done and in the original article) are facile--a proper Bayesian treatment would have continuous priors/posteriors that would be a little more informative than an either-or.

The problem you're seeing here is that if you make your possibilities "Humans live forever (even past the heat death of the universe)" or "All humans die in the next 10 minutes", you'll find that the chance that humans die in the next 10 minutes is really absurdly high.

Re: A Primer on the Doomsday Argument

#58

Post by scotty79 »

BoppreH wrote: post #45
scotty79 wrote: post #14

Imagine you have 100 ordered rooms. All initially are filled with gold and ponies. God tosses a coin and depending on the result of the flip God strips 10 or 100 rooms of ponies and gold. You are in one of the rooms, open your eyes and see that there is no gold and ponies around. You take a look at your room number and see 7. Then you know that best decision is to operate on assumption that there is 91% chance that o…

The Doomsday Argument works because the result (Doom Soon or Doom Late) affects the number of observers, and we can work backwards to update our beliefs on which one will be. That is why replacing the words with ponies and gold won't work unless you are a pony or sentient gold.

For my argument I just replaced "existing" with "not having gold and ponies" and drew parallel not between "specific rooms being occupied" and our civ existing at specific time but between "specific rooms not being emptied of gold and ponies" and "our civ having decent tech at specific time".

It works. Use your own substitutions.

Phisolophical reasonings often latch onto inexplicit meaning of words. If you replace them with different words that fullfill same role in language but have different meaning argument becomes much less apparently profound or even false.

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