Tech levels and the end of the universe

[tomBitonti]

To be clear, are you saying that you were using uniform distribution for the prior distribution, and that you think that this was in error for this problem? Because that seems to be what you're saying here, and I want to be certain I understand your position.

Right, this is Caves' rebuttal, which says that "the uniform distribution assumption is incompatible with the Copernican principle, not a consequence of it."

As that section notes, not saying where you're applying the Copernican principle is a weakness in the basic argument as presented, but this merely calls for the stated refinement of the principle, rather than its rejection. Though this admittedly flattens the model (which you do mention).

These largely solve themselves if you make the above change and presume that the uniform distribution is not a bad prior distribution.

It still doesn't call all values equally likely though, so at worst you would say that it offers a wider range of possibilities (and becomes less informative) since you're saying that the population up until now is less informative (but not completely uninformative) about the potential total population of all humans ever born. Having, as an example, 50% probability in the results generated (if you use this method) rather than 95% is a significant reduction, but not to the point of calling the exercise worthless.

I was using a uniform distribution for the prior distribution of the count of people that will ever live.

Relying on a good prior distribution seems to invalidate the technique. The problem becomes obtaining a good prior distribution.

I don't think you get anywhere close to a 50% confidence. Depending on how big the prior distribution is made, the most likely result can be made arbitrarily small (although still more likely than any other value). This is where knowing the posterior distribution matters: It may have a most likely point, and an average, but these may be useless considering the overall shape of the distribution.

Thx!

TomB

 

[Alzrius]

I was using a uniform distribution for the prior distribution of the count of people that will ever live.

Relying on a good prior distribution seems to invalidate the technique. The problem becomes obtaining a good prior distribution.

It seems to be that the uniform distribution is sufficient here; we may have to agree to disagree with respect to that.

I don't think you get anywhere close to a 50% confidence. Depending on how big the prior distribution is made, the most likely result can be made arbitrarily small (although still more likely than any other value). This is where knowing the posterior distribution matters: It may have a most likely point, and an average, but these may be useless considering the overall shape of the distribution.

I may have been unclear before, I meant that in a flat model you can get 50% confidence (e.g. you can say with 50% confidence that we're in the last 50% of the total human population).

 

[Storminator]

It seems to be that the uniform distribution is sufficient here; we may have to agree to disagree with respect to that.



I may have been unclear before, I meant that in a flat model you can get 50% confidence (e.g. you can say with 50% confidence that we're in the last 50% of the total human population).

But obviously you can't say that given the actual distribution of human population. A reasonable (tho possibly wrong!) estimate of total human population ever born is ~100 billion people. If you had continuously predicted "we're in the last 50% of the total human population" any time from 50,000+ years ago to today, you'd have been wrong 98% of the time, assuming no more humans are ever born.

I propose a bet, [MENTION=8461]Alzrius[/MENTION] - if humanity is still around in 10000 years, drinks are on you.

PS

 

[Alzrius]

But obviously you can't say that given the actual distribution of human population. A reasonable (tho possibly wrong!) estimate of total human population ever born is ~100 billion people. If you had continuously predicted "we're in the last 50% of the total human population" any time from 50,000+ years ago to today, you'd have been wrong 98% of the time, assuming no more humans are ever born.

I mentioned this upthread (emphasis mine):

Right, this is Caves' rebuttal, which says that "the uniform distribution assumption is incompatible with the Copernican principle, not a consequence of it."

As that section notes, not saying where you're applying the Copernican principle is a weakness in the basic argument as presented, but this merely calls for the stated refinement of the principle, rather than its rejection. Though this admittedly flattens the model (which you do mention).

The idea of being 50% sure that you're in the last 50% of the total population is the aforementioned "flat" model. I've been saying that the odds can be quite a bit more variant than that.

I propose a bet, [MENTION=8461]Alzrius[/MENTION] - if humanity is still around in 10000 years, drinks are on you.

Okay, but they'll be at the Restaurant at the End of the Universe.

 

[Sword of Spirit]

Instinct versus science, round two. Fight!

Instinct versus math rather.

That's not really relevant to what's there. The idea that humans would leave the Earth at some point would adjust the particulars of the DA only in that it'd increase the total capacity for how many humans would be alive at once (e.g. 20 billion people collectively supported across two planets, rather than 10 billion people supported across one). In that case, you simply adjust the calculations and modify the final results accordingly.

So every time a new planet is colonized we have to adjust the results? That's a problem right there. The formula has no way of knowing how many planets we will colonize!

It's not an inevitability by the terms of the article, just a likelihood (e.g. 95%). Given that it's plausible to state that only a finite number of humans will be born - rather than an infinite number - the premise of the article certainly seems reasonable.



I'd say that it's option B, since it's not particularly concerned with questions of how humans would theoretically come to an end. It is, as you note, a purely mathematical construct, which is sort of the point. If you presume (as noted above) that there won't be a unlimited number of humans, then it's a question of trying to make a construct to guess how many there will be, and working backwards from there.



I suspect that the hubris is in assigning humanity "infinite possibilities of the future" and in presuming that even loose models of statistical analysis don't apply to us, but that's just me.

What I'm seeing however, is just some math that seems to fail to take into account meaningful variables. Assuming the math works (and I'm not qualified to judge that with any confidence) all it can say is that if nothing significant intervenes, and if we known the maximum population, then we can estimate with a high degree of confidence how long it will take us to get there.

If we were to learn, for instance, that a bunch of asteroids were going to enter the solar system in 100 years, each of which had a certain chance of hitting earth, that would throw a wrench into the whole thing.

Now, it might actually be interesting for the purposes it was brought up for on the thread though. Determine how many habitable worlds humanity is likely to be able to reach in the universe--and therefore estimate the maximum human population of the universe, and see what that gives you with this formula. As a thought experiment in design, sure, it's fun.

 

[Alzrius]

Instinct versus math rather.

Isn't math one of the sciences? Or is science one of the maths? I can never keep them straight.

So every time a new planet is colonized we have to adjust the results? That's a problem right there. The formula has no way of knowing how many planets we will colonize!

See below for why I don't think this is actually a factor.

What I'm seeing however, is just some math that seems to fail to take into account meaningful variables. Assuming the math works (and I'm not qualified to judge that with any confidence) all it can say is that if nothing significant intervenes, and if we known the maximum population, then we can estimate with a high degree of confidence how long it will take us to get there.

If we were to learn, for instance, that a bunch of asteroids were going to enter the solar system in 100 years, each of which had a certain chance of hitting earth, that would throw a wrench into the whole thing.

Now, it might actually be interesting for the purposes it was brought up for on the thread though. Determine how many habitable worlds humanity is likely to be able to reach in the universe--and therefore estimate the maximum human population of the universe, and see what that gives you with this formula. As a thought experiment in design, sure, it's fun.

The problem here is that none of the potential variables you're throwing out are meaningful, with regards to colonizing other planets and such. It's an Occam's Razor thing: when you have competing hypotheses, the one with the fewest assumptions should be selected.

Presuming that a probabilistic model of the timeline of human extinction is flawed because it doesn't take into account an assumption of planetary colonization is backward, because it posits an event that has no particular model for suggesting, however remotely, that such a thing will happen.

You're saying that because something could theoretically happen, we can't make a prediction as to what might happen. That's the equivalent of not planning out your week because you can't be certain that the world won't suddenly combust. You make predictions with the best data you have on hand, and discount the things that don't have some suggestion of likelihood.

 

[tomBitonti]

It seems to be that the uniform distribution is sufficient here; we may have to agree to disagree with respect to that.

I may have been unclear before, I meant that in a flat model you can get 50% confidence (e.g. you can say with 50% confidence that we're in the last 50% of the total human population).

A uniform distribution would be sufficient, if we had lots of random samples. We have one.

I'm pretty sure that single sample provides much less than a 50% confidence.

Btw, the German Tank Problem is presented exactly as that:

http://en.wikipedia.org/wiki/German_tank_problem

Lots of better math there. These are notable:

k point estimate confidence interval
1 2m [m, 20m]
2 1.5m [m, 4.5m]
5 1.2m [m, 1.82m]
10 1.1m [m, 1.35m]
20 1.05m [m, 1.16m]

Immediate observations are:

For small sample sizes, the confidence interval is very wide, reflecting great uncertainty in the estimate.

The range shrinks rapidly, reflecting the exponentially decaying likelihood that all samples will be significantly below the maximum.

The confidence interval exhibits positive skew, as N can never be below the sample maximum, but can potentially be arbitrarily high above it.

Bold added by me.

There is a following section which does the math for "one tank", which is the exact problem we have. This result is provided:

One tank

Observing one tank randomly out of a population of n tanks gives the serial number m with probability 1/n for m ≤ n, and zero probability for m > n.

...

The maximum likelihood estimate for the total number of tanks is N0 = m.

The total likelihood is infinite, being a tail of the harmonic series.

Again, bold added by me.

Thx!

TomB

 

[Alzrius]

A uniform distribution would be sufficient, if we had lots of random samples. We have one.

No, we have several billion. Each person is a sample.

The German Tank Problem had the entirety of the observed tanks to act as samples of the entirety of tanks that existed; those observed tanks were not collectively regarded as one sample. Likewise, the Doomsday Argument is based on having the entirety of all people who've lived so far (though this is estimated with regards to the total number of people who've died up until now) to act as samples for the sum total of humans that will ever live.

The part about trying to take a sample size based off of one tank is accurate, but that's the equivalent of trying to figure out how many humans there will ever be based on a sample size of one person.

Also, apologies for truncating the rest of your post. I usually don't do that, but it seemed appropriate here, as the remainder of what you wrote was based off of the part that I quoted.

 

[Morrus]

Dang, this conversation really changed.

 

[Storminator]

Dang, this conversation really changed.

Coming in first place in the understatement category . . .

PS