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A Primer on the Doomsday Argument

anthropic-principle.com

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Re: A Primer on the Doomsday Argument

#31

Post by bluecalm »

baddox wrote: post #23
spacehome wrote: post #22

Earlier quoted context omitted.

The reason why this is so subtle is that it's not a given that you're in a cubicle. It's more likely for you to be put in a cubicle the more people who are put into cubicles.

> 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 probability isn't 50% because there is underlying probability that you would be in cubicle at all (1 vs 0.5 after first flip). There is the same problem with doomsday argument just better masked.

Re: A Primer on the Doomsday Argument

#32

Post by spacehome »

bluecalm wrote: post #25
lisper wrote: post #13

Earlier quoted context omitted.

> the probability that you find yourself in a cubicle at all is ten times higher in that case No. That you are in a cubicle is a given fact, so the probability that you find yourself in a cubicle is unconditionally 1.

>>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…

There are only finitely many ways to arrange matter in a finite volume under a finite temperature. If it's safe to assume that anything we could classify as "human" will fit inside a sphere of radius 1 light-year and has a temperature under 10^20 K, there are finitely many humans.

Re: A Primer on the Doomsday Argument

#33

Post by bluecalm »

spacehome wrote: post #32
bluecalm wrote: post #25

Earlier quoted context omitted.

>>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…

There are only finitely many ways to arrange matter in a finite volume under a finite temperature. If it's safe to assume that anything we could classify as "human" will fit inside a sphere of radius 1 light-year and has a temperature under 10^20 K, there are finitely many humans.

Yeah but it's not given that God chooses at random who is going to cubicle. He might have for example created you first and then put you in a cubicle regardless if it's 100 of them or 10. I agree with your resolution of that paradox though. It's reasonable to assume - having no information about the process - that God creates humans randomly and it's 10x more likely that you are created in a world with 100 cubicles than in a world in 10 cubicles. In my mind there is no paradox at all there.

Re: A Primer on the Doomsday Argument

#34

Post by livingparadox »

lmkg wrote: post #30
livingparadox wrote: post #24

Perhaps I'm ignorant of some deeper concept... but it seems that this argument is deeply flawed on the basis that they are presuming that finding yourself in cubicles 1-10 somehow indicates that cubicles 11+ are probably vacant. In both doom soon and doom late, cubicles 1-10 are occupied. There's no aspect of doom late that would be made less likely as a result of cubicles 1-10 being occupied. The reverse works well,…

The reasoning in the article is correct. Cubicles 1-10 are occupied in both scenarios, but the observation of (self conditional probability of Doom Soon is much higher. They key point is that, if Doom Late occurred, then the probability of ending up in cubicle 1-10 is only 10%. So if the only observation that you have is that your cubicle is numbered 1-10, which is more likely: Doom Soon (50% absolute probability), o…

The premises in the argument can abstracted into the following:

if doom_soon, then the probability of myself being in cubicles 1-10 is 100%; if doom_soon, then the probability of myself being in cubicles 11-100 is 0%;

if doom_late, then the probability of myself being in cubicles 1-10 is 10%; if doom_late, then the probability of myself being in cubicles 11-100 is 90%;

???

Therefore if I am the cubicles 1-10, the probability of doom soon is 81%;

In any logic class, this argument would quickly be pointed out as a fallacy. The statement of "if p, then q" says nothing about the truth of p, given q. Which is exactly what this argument seems to do, reason backwards from the conclusion when none of the premises are able to be logically inferred from the conclusion.

Re: A Primer on the Doomsday Argument

#35

Post by rm445 »

livingparadox wrote: post #24

Perhaps I'm ignorant of some deeper concept... but it seems that this argument is deeply flawed on the basis that they are presuming that finding yourself in cubicles 1-10 somehow indicates that cubicles 11+ are probably vacant. In both doom soon and doom late, cubicles 1-10 are occupied. There's no aspect of doom late that would be made less likely as a result of cubicles 1-10 being occupied. The reverse works well,…

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 is 90.9% - we could go round in circles trying to choose words that everyone understands, but the numbers speak for themselves.

Re: A Primer on the Doomsday Argument

#36

Post by livingparadox »

lmkg wrote: post #30
livingparadox wrote: post #24

Perhaps I'm ignorant of some deeper concept... but it seems that this argument is deeply flawed on the basis that they are presuming that finding yourself in cubicles 1-10 somehow indicates that cubicles 11+ are probably vacant. In both doom soon and doom late, cubicles 1-10 are occupied. There's no aspect of doom late that would be made less likely as a result of cubicles 1-10 being occupied. The reverse works well,…

The reasoning in the article is correct. Cubicles 1-10 are occupied in both scenarios, but the observation of (self conditional probability of Doom Soon is much higher. They key point is that, if Doom Late occurred, then the probability of ending up in cubicle 1-10 is only 10%. So if the only observation that you have is that your cubicle is numbered 1-10, which is more likely: Doom Soon (50% absolute probability), o…

I thought of a better way of explaining the invalidity of the argument.

What would happen if, instead of inferring from our own presence in the cubicle, we take an external role. Furthermore, instead of taking the probability that a randomly selected person exists in of the two sets, we look at the probability that /someone/ exists in one of the two sets.

If doom soon occurred, then the probability of cubicles 1-10 being occupied is 100%; If doom soon occurred, then the probability of cubicles 11-100 being occupied is 0%;

If doom late occurred, then the probability of cubicles 1-10 being occupied is 100%; If doom late occurred, then the probability of cubicles 11-100 being occupied is 100%;

So given those two probabilities, we have a 100% chance of cubicles 1-10 being occupied and a 50% chance of cubicles 11-100 being occupied.

In either scenario, the occupancy status of cubicles 1-10 is assured. So checking in cubicles 1-10 gives us no meaningful information about which of the two scenarios occurred. Checking in cubicles 11-100 on the other hand /would/ affect our results. The occupancy of cubicles 11-100 on the other hand would tell us exactly which scenario occured.

Re: A Primer on the Doomsday Argument

#37

Post by titanomachy »

typomatic wrote: post #18

Let's go back to step II: Imagine that the coin that we're flipping isn't fair, and comes up heads with prior probability p. Further, suppose that the ratio between the small population and the large population is R (in the article this is R = 10 / 100 = .1). In this situation, upon discovering that you're inside the small population, the posterior probability of heads ends up as p / (R - p * (1 - R)) So what if the…

I played around with the model a bit and based on a couple assumptions it can be scaled to

    P(Doom Soon) = x/(1+x) where
    x = B/b * d
where B is the number of humans born in the Doom Late scenario, b is the number of humans born so far, and d is the prior probability of Doom Soon.

Assumptions: a) the number of humans born between now and Doom Soon is negligible and b) the Doom Late scenario has many more humans than Doom Soon (B + b ~= B).

Notice I made no assumptions about the prior, d. Of course d does matter, but the point is that as long as the number of humans in Doom Long is assumed to be large enough, the probability will go close to one even for very small d.

For example, if we use a Doom Late population of 200 trillion like in the post, then we have 95% probability of Doom Soon even if d ~= 0.0001.

That being said, I am still fairly unconvinced by this argument. It would have every intelligent species continually concluding that they are about to go extinct, right up until the moment that they either do go extinct or they achieve immortality and stop reproducing.

Re: A Primer on the Doomsday Argument

#38

Post by otakucode »

bluecalm wrote: post #25
lisper wrote: post #13

Earlier quoted context omitted.

> the probability that you find yourself in a cubicle at all is ten times higher in that case No. That you are in a cubicle is a given fact, so the probability that you find yourself in a cubicle is unconditionally 1.

>>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…

And I don't understand why we ignore that human beings created the cubicles and there is no random god involved in any of it. Whether there is a human in the cubicle or not is entirely a result of physical processes. Any statement about probability is nothing but an explanation of our ignorance. Yeah, we might not be capable of knowing the totality of physical history of all the people who build the cubicles and where they are now and such... so what? That says nothing about the history of their species.

Re: A Primer on the Doomsday Argument

#39

Post by livingparadox »

rm445 wrote: post #35
livingparadox wrote: post #24

Perhaps I'm ignorant of some deeper concept... but it seems that this argument is deeply flawed on the basis that they are presuming that finding yourself in cubicles 1-10 somehow indicates that cubicles 11+ are probably vacant. In both doom soon and doom late, cubicles 1-10 are occupied. There's no aspect of doom late that would be made less likely as a result of cubicles 1-10 being occupied. The reverse works well,…

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…

Okay, here's a simplified probability tree.

Scenario 1: Doom soon

10 people have a room number less than or equal to 10.

Scenario 2: Doom late

10 people have a room number less than or equal to 10.

---

Given that each scenario has an equal probability in isolation, there are 20 possible positions for the the Of those 20 possibilities, 10 of those are in the doom soon scenario. The remaining 10 are in the doom late scenario.

10 doom soon to 10 doom late is a 50/50 probability.

Edit: writing up a script as well, right now. Will add to link to it in my original comment when complete.

Re: A Primer on the Doomsday Argument

#40

Post by otakucode »

bicknergseng wrote: post #3

"If the Doomsday argument is correct, what precisely does it show?" That philosophers are not statisticians?

"That we have a level of ignorance and inability to predict the future... and a poor understanding of where that ignorance and inability comes from."
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