I am currently re-reading Stephen Baxter's "Time". In this book, he uses (not necessarily endorses) the so called Carter Catastrophe. As Baxter is an author who usually has his science right (if on the speculative side), his use of this doomsday argument - even as a plot device - is heckling me.

The argument runs as follows (extract from "The Doomsday Argument" on www.anthropic-principle.com):

In Baxter's book, one character calculates based on this argument that Doomsday is 150, maximum 200 years away.

Deep in my gut I have the feeling that this argument is fundamentally flawed (read: rubbish), but I can't come up with a clean and neat rebuttal. The best I can come up with: As the human population has grown roughly exponentially in the known past, exactly the same argument has been valid for each and every generation before us - for instance also for the generation that lived, say, 300 years ago. And yet we are here, 300 years after an imminent doom.

What are your takes on this argument?

Yep, a nonsense argument. It is not because something has started only recently that it will end soon, or vice versa. You could just as well argue that the human race has an inherent life span of 1 quintillion people, and that because we are only at number 12 billion now, the impending dommsday is still far far away. This argument is equally rubbish.
A better way would be to calculate the average lifespan of a species on Earth that has survuved for at least 100,000 years (I mean from evolution till extinction, not the lifespan of individuals), and compare that to ours. It would still be only a statistic, not a certainty by far, but it might give a better idea.

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Shark number 7 must have been even more certain that the sharks were about to pass from this planet. Here the sharks are 200 million years later, wondering what the heck number 7 was thinking.

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I've also wondered about this argument, though I didn't know it had a name. I thought of it when I heard it mentioned that it is "natural" for the Sun to be about halfway through its main-sequence lifetime, since it would be unlikely to be very near the beginning or very near the end. I don't know the relative merits of the two different applications of this general idea, but I would agree that Madalone's argument completely shatters the Carter catastrophe idea. (Fram's point is also well taken, but there is already nothing left of the argument that survives the OP!). It's a little like asking someone who wins a grand prize in a lottery what they would estimate their chances of winning were. It would boggle their mind if they hadn't really thought about it before. Yet somebody had to win, and that person is in such a special position that you can't ask them to apply the same logic as a "normal" person.

That's in essence what Madalone has said, and has shown that the Carter catastrophe hypothesis has already been disproven. The only thing I would add is that this is an example of the subtleties presented by the anthropic principle-- you can't ask the people who are in a special place to use probability arguments that assume they are not in a special place. Otherwise, why could I not turn the catastrophe argument around, and conclude that humans will survive for a significant fraction of the duration of the universe, otherwise if "today" is a date chosen at random, what would have been the likelihood that humans would be here today?

Good point, I like this one.

To retranslate it into the urn/ball thougt experiment:

"Imagine that two big urns are put in front of you, each containing a million red and blue balls. You know that one of them contains red and blue balls fifty-fifty and the other a thousand red balls in just under a million blue ones, but you are ignorant as to which is which. Now you take a ball at random from the left urn, and it turns out to be red. Clearly, this is a strong indication that that urn contains red and blue balls fifty-fifty.

Now consider the balls depicting millenia, where red balls stand for the time humanity exists, it is easiy to see that humankind must exist for a seizable portion of the lifespan of the universe."

But as I am writing this, I see a catch: Arguing from Carter's perspective, it is now obvious that doom is imminent not only for mankind, but for the universe as a whole: The fewer blue balls are in the second urn (i.e. the shorter the livespan of the universe), the better is the probability to draw a red one. Hence, the probability of being alive today is maximized if the universe ends tomorrow.

I am starting to like this line of reasoning. I guess one can prove everything (and its opposite) applying probabilities "ex post" on preexisting facts...

Simply noting that people in the past would have been wrong when they used the Carter argument to predict their own imminent demise doesn't get you out of Carter's bind. It's inevitable that from any vantage point in time we'll see a group preceding us who "would have been wrong". But because of the exponential growth in population, that group is always small compared to the mass of people living today and in our future.
Carter's saying that a small number of people will be wrong to use his argument, but a large number will be right, because they'll be close to the extinction event, or the start of the exponential decline in population - they'll be in the population bulge, where the area under the population curve is high.
So if we choose a life at random from under the population curve, we have a small chance of ending up in the group who are wrong (those in the early days of population growth), and a large chance of ending up in the group who are right (those in the population bulge before the decline).
The way out of Carter's argument is to point out that exponential growth is unsustainable, and if we are to survive we are going to have to achieve population equilibrium. Once the population curve becomes a level line leading off to infinity, we're just as likely to find ourselves anywhere under that line (because there's no bulge to "concentrate lives" in one temporal region), and so we can't infer anything about survival time in the future.
Either we have exponential growth, and Carter's right, and we're likely to be living in the End of Days; or we level out our population, and Carter can't make any deductions about the future - the areal midpoint under an infinite level curve is anywhere.

Grant Hutchison

Edited for clarity, by changing "to use" to "when they used" in sentence 1

I see the Carter Doomsday argument is not receiving much credence here at this point in time; funny, because last time it was discussed it did have a few supporters.
The most debatable point about this argument is the fact that it assumes that a person living now has no special place in the sample of all humans who have ever lived and will ever live; a kind of argument of Copernican mediocrity principle with respect to our position in a population of unknown size.

But our position in that population is not chosen at random; we are alive at the exact period when statistical maths develops to the point where predictions like Carter's can be made for the first time. This coincides with the period when the population is rising out of the long slow growth of the pre-industrial age towards a much more densely populated developed civilisation; a change which is still in progress. I think it is safe to say that these two periods are more likely to coincide than not; an increase in mathematical knowledge is bound to accompany a successful indiustrial civilisation.
In other words, as Robin Hanson has said,
All else is not equal; we have good reasons for thinking we are not randomly selected humans from all who will ever live.

See this wiki page about the arguments for and against this concept;
http://en.wikipedia.org/wiki/Doomsday_argument

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I'm not sure I buy this one, at least not without seeing some elaboration. It seems that the "privileged viewpoint" card being played here is irrelevant to the particular kind of mediocrity relevant to the argument. Carter's maths apply whether or not the population is aware of it. We're interested only in the area under the curve, not which bit of that curve is self-aware.
A bunch of superintelligent aliens roaming the galaxy might stop at a mediaeval planet and say: "There's a 95% chance they'll all be dead before x more births." Then they see us, and say "There's a 95% chance they'll all be dead before y more births. Then they move on to a star-spanning civilization that has been aware of Carter's calculation for many millennia: "There's a 95% chance they'll all be dead before z more births." If Carter's maths apply, 5% of such predictions will be wrong, the other 95% will be correct.

Grant Hutchison

Edit:If anything, Hanson's suggestion serves to undermine one of the counterarguments to Carter: that external evidence indicates species survive for many more million years than we have done so far, so we are more likely to be at the start of our career as a species. But our privileged viewpoint as a self-aware, mathematical, industrial civilization means that we are not like other species, and so their data cannot be applied to us.

I don't agree. The point is, anyone who makes the Carter argument will always come to the conclusion that the end is fairly near. Exponential growth is not a crucial logical component, it just means that you infer the end is very near. But the conclusion is totally unsupportable either way, because everyone will reach a different conclusion for the likely survival time, depending on when they are alive. For example, if Cain and Abel had used the argument, regardless of whether or not the growth is exponential at the time, they would have found it totally unbelievable that humanity would survive them by thousands of years. I say that an argument that is wrong when used by them is also wrong when used by us, as there is nothing to distinguish us. The other arguments against the Carter hypothesis are sound, but unnecessary-- this idea is logically DOA (even though it may be right, sadly, but for totally different reasons).

Put differently, if exponential growth is a crucial element, then the Carter hypothesis would argue that either humanity will die, or it will cease exponential growth forever. But if we populate the stars, of course we will see the return of exponential growth. We will have to have exponential growth again at some point, or we will die out (in millions of years, let's say).

I am pretty sure that we are not likely to show the same pattern as other species, so arguments from sharks are probably irrelevant. For one thing, we are likely to consciously take control of our own evolution before too many millenia have passed; this autoevolution hasn't happened in other species as far as I am aware. Whether that would signal the end of the human race and the collapse of the Homo sapiens population I wouldn't really know; on this page (warning-sci fi) I have suggested that the population of H. sap sap might continue to increase even when the rest of our civilisation has autoevolved into something else. So the future population curve may easily change into something that is unlike that of any other species.
If such an observer were to see the Palaeolithic human population, with its slow growth, then it would calculate that our species had a long future ahead; similarly an observer meeting the star-spanning culture would note the long, slow growth of population dictated by interstellar distances and calculate a long, if not indefinite future.
It is only today, when our population is growing very fast - almost but not quite exponentiating - that the calculations show a quick die-off. But this is the exact period when our culture has discovered the Bayesian interpretation of probability, so it is the only example of such a calculation we are aware of.

If we could talk to our far future descendants they would tell us that the period of time when the Carter-Leslie argument predicts a near-future doomsday is a brief and anomalous one. If we could also talk to other long-lived alien civilisations they are likely to tell us that they passed through this stage of rapid growth too, and many of them probably discovered statistical arguments of a similar nature during this same stage. By comparing all the values from all the calculations, from palaeolithic, (hypothetical) far-future and (hypothetical) extraterrestrial sources, we would see that almost all indicate long term survival, because they all show much slower growth than our own current situation.

Only the values calculated during the period of rapid industrialisation, an anomalous phase, show a near-future doomsday; exactly the same period when such statistical tools become available. Keep making the same prediction using the same tools once the world has become technologically advanced,and the population has stabilised, then the date of doomsday-with-95%-certainty recedes into a remote future once again.

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That's right. And Carter says that some of them will be wrong, and most of them will be right, the exact ratio depending on the confidence interval chosen.
So the fact that people were wrong in the past doesn't make it any more or less likely that we are wrong now. They're independent coin tosses of a heavily weighted coin.

Grant Hutchison

Look at it from another perspective, namely your own.
You are "ball number 7". When you are pulled out of the barrel, what is the chance that you will be number 7? Why, 100% of course. What is the chance you will be taken out of the barrel? Well, that chance will be much higher when your barrel has only 7 or 8 balls then when it has 100 billion, the Carter scenario says (paraphrasing of course). So probably you are in a small barrel (i.e. extinction will occur soon).
This is where the scenario has gone wrong, in my view. We don't know and have no reason to assume that only one ball is taken out of the barrel. If all balls are taken out, ours has to be taken out as well, and the fact that ball number 7 has been taken says nothing at all about the size of the barrel.

Let's look at it again, but from a completely different angle.
I am filling a barrel with numbered balls slowly and in order. One ball drops every second. After ten seconds, you pick a ball. It's number 7. What does this say about the total number of balls that will end up in the barrel?
The Carter scenario says that 95% certain, this will be only 20 or so. I guess it is plain for everyone to see that we have no information whatsoever to make such a statement. The only thing we know is that a) there will be at least 7 balls, as I have picked ball seven, and b) there will even be at least 10 balls, as so much seconds had passed (the observer can of course see the balls dropping). Nothing more.

Relating this to the original presentation of the scenario: you have two of those slowly filling barrels. One will stop at 100, the other at 10000. After ten seconds, you pull out ball 7. Does this help in any way to know which one will stop at 100 and which at 10000? No.

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I see your point, but I don't quite agree...

First, as the urn/ball example shows, exponential grow is not a necessary prerequisite for the basic argument; it just lets The End draw closer to the present point in time.

Second, the population curve is finite at least at one end (the past), so we have an asymmetry which makes a populated future "unlikely".

I just think trying to beat the Carter argument on its own premises is missing the point; my basic gripe ist still that the argument makes a statistical statement based on a sample size of precisely one...

But, heck, why am I arguing with you anyway? Probably you dont even exist! I know that Switzerland is roughly 200km across. The fact that I'm Swiss would be very, very unlikely if the World was seizably bigger than, say, 1000km. So, in all likelyhood, anything beyond the English Channel must be a figment of my Imagination!

Madalone

We know that only one ball is extracted, in this analogy. You live only once, and therefore you represent one ball.

You have no control over the time at which the ball is selected. You simply come into existence, and check your position in the birth order. If there are a very large number of balls, then you're unlikely to find yourself in the first few.

Grant Hutchison

You're right. I was trying to explain the particular urgency in Baxter's scenario, and didn't make that properly clear.


But it's not a great argument against the Carter calculation, since you do have access to counter-information. Whereas we don't have any knowledge of "how big the world really is" with reference to the total number of humans that will ever exist. Carter's calculation is therefore probabilistic from limited information, and can't be undermined by analogy with other situations in which information is more complete.

Grant Hutchison

If you are number 7, then you are very likely to be in the first few This is a variation on the strong vs. weak anthropogenic principle. You have to make the distinction between an outsider who has the choice from all balls and picks out a low number, or a ball itself, which has a number, period. I am ball number 7, and that says nothing at all about the chances for survival of humanity in the next 100, 1000 or billion years. I can not pick any ball I want, and so the "choice" of a ball is no choice at all.

To expand my slowly filling barrel analogy to make it more resemble reality. The barrel is slowly filling and even more slowly emptying again. You are allowed one moment to pick one ball. If you get a low number, then this only proves that the barrel didn't exist very long yet. This says nothing at all about how long it will exist in the future.
It's like madalone says:

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Exactly. So it would be odd to find yourself among one of the first balls. The number you find yourself to be therefore does allow you to make a statistical inference about how many balls there are.

Grant Hutchison

I think (but I am not sure) that my argument can explain away that oddness. We are a special case, so not representative.

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No argument from me. A population with no growth at all would judge that they are likely to survive into the future as long as they have existed in the past. But they would still see the same Carter limit to the number of likely future lives. I agree the urgency has gone, but Carter's argument isn't undone.

Grant Hutchison

Yes, but it would be meaningless. It focuses on one point and ignores many others. It would be odd if I was the first human. It would be odd if I was the last human. It would be odd if I were the middlest (?) human. It would be odd if my 'birthnumber' would be exactly a prime number. Yet, someone has to be (or will be or has been) one of these. For a species to exist 100 years, a specimen has to exist after ten years. For a species to exist 100 billion years, a specimen has to exist after ten years. As long as we don't know what the average lifetime of a species (or an intelligent species, or whatever distinction you like to make) is, we can't make any useful statistics.

Using 'your' statistics, the best chance for a long future of humanity would be to kill all humans except a hundred or so, and keep humanity at that number. That would mean that if my number 9 billion is an average number (which wouldn't be that odd compared to it being an early number), we could have 90 million generations more after this one. Reduce it to a couple that has two children and so on, and you'll have 4.5 billion of those couples before homo sapiens gets extinct! I think you'll see that this shows that statistics can 'prove' anything and that the basic premisse (of the peculiarity of us living now unless we are doomed fairly soon) is flawed.

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But it would not be odd if you were in the last 90% of humans ever to live. That's all Carter's talking about, not the specific number on your ball. And the population bulge of exponential growth crowds that last 90% into the last few years of humanity's existence.

Grant Hutchison

What we are basically arguing are the "rules of the game", not probability or logic per se. My original support of Madalone's was simply that it can't be logic if it leads even a minority to the wrong conclusion. Grant's point is that who said it had to be logic, it is merely an argument that leads most to the correct conclusion (that they are close to the end times, for exponential growth). So it's probability. Fram is saying that this assumes we could have come at any time, when in fact we are what we are, number 10 billion or whatever. It's part of who we are. It's a question of what is known. One could say that either it is the end times or it isn't, so without any information, it's a 50/50 chance!

So my scenario for extending the lifetime of the human race by eliminating all but a few specimen should work?

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Grant knows that killing most of humanity wouldn't help things, because you would know that you did it and therefore mucked with the probabilities. He is saying that if you did such a heinous act, and the survivors had no knowledge of it other than where they fell in the order of humans born, they would in fact conclude that humanity's "clock" has been extended. It's a little like playing poker. If your opponent has four of a kind, he/she is pretty sure they'll win and will bet in that expectation. But if you're sitting on a full house, you say, "bring it on". It's not until they see how you are betting that they begin to get an uncomfortable sensation.... The issue is, probability is not an absolute thing, except in quantum mechanics. Everywhere else, it is a matter of information. So the question really is, what information do we possess that can give us a better estimate of our "chances" than the Carter hypothesis, which is what I meant by, in the complete lack of all information, the odds are always 50/50, but that's a pretty meaningless way to inform your decisions! This is related to Fram's initial point that there may be better ways of estimating our longevity than using the "default" thinking of the Carter hypothesis.

Well, all the people you killed would already have lived, so that wouldn't reduce the total count.
So you might more humanely achieve the same effect by simply reducing the birthrate very dramatically.
Either way, you would neatly and satisfactorily have enacted the abrupt catastrophic fall in human population that Carter's reasoning predicts. Q.E.D.

Grant Hutchison

But you are in effect agreeing that the timetable for human extinction could be extended by reducing population levels. That's not a reasonable hypothesis in and of itself, although it may get support from completely unrelated issues like the rate at which we use resources, etc. Note that any argument of the latter type is what I mean by the poker game-- doing a better job of inferring probabilities than a "default" thinking mode (in short, if Carter really thinks that way, I'd love to play some high-stakes poker with him!).

Let me clarify this point, since it is crucial. If you don't know anything about gravity, you use probabilistic arguments to reason that the Earth's atmosphere should be spread evenly over the whole solar system and beyond. Then someone explains gravity, and suddenly you have it tightly stuck to the surface of our planet. A little information goes a long way when using probability arguments, and the Carter hypothesis is only valid in the absence of any information at all other than birth order. It would be very foolish to use so little information in making a probability argument, along the lines of the 50/50 argument I presented.

No I'm not. I'm teasing Fram for creating an illustrative case to undermine Carter which in fact would do Carter's work for him. But surely Fram's point was that this imagined situation is ridiculous?
You can't manipulate a priori probability this way. If an actuary tells you and five friends that, as a group, your various life expectancies sum to 180 years, you would not prolong your own life by killing your five friends. You'd just change the rules for the calculation, and the estimate would need to be redone.
In Carter's calculation, one of the vexed points is: Which lives count towards the total? When do we start counting entities and when do we stop counting entities? Some would argue that a near-extinction bottleneck merited the start of a new count, so that the survivors of the Framocaust would perhaps see themselves as having rather short future prospects. (Though they might argue that they were undoubtedly in the first 5% of the New Count humans, and so fend off Carter's calculations for a few generations.)

Grant Hutchison