It’s not all doom and gloom

mi2g.com

by Ian Pollock

[Epistemic status: this my first attempt to get a grip on this problem. The objections I raise are probably not unique, and may have been answered already.]

How long into the future will the human species continue to exist? If your answer to that question is “I don’t know,” then I give you full points for humility, but a penalty for not considering your background knowledge. Unless you know something I don’t, chances are very, very good that most of us will still be here tomorrow, and the next day, and the next day…

When we look at longer timespans, the issue becomes more complex. Our answer begins to depend on how technologically and politically optimistic we are. Will the new technologies of 100 or 1,000 or 10,000 years from now be put to good or bad use, or (more likely) both? If the latter, will the overall tendency be toward preserving human life (say, via new medical interventions) or toward black-swan risks (say, a gray-goo nanotechnology nightmare)?

Thinking about these things requires a lot of social and scientific theorizing, much of it wildly speculative. (Readers will note that we were supposed to have flying cars by now.)

However, according to some thinkers, we can find evidence of the likely lifespan of Homo sapiens in a single number – how many individuals of our species have existed so far.

As far as I can see, there are two major ingredients in this claim: one is a relatively uncontroversial probabilistic argument; the other is a counterintuitive and highly controversial application of this argument, which uses anthropic reasoning. Since anthropic reasoning is often very difficult to think about, it’s best to understand the general outline of the probabilistic argument first, if only in qualitative terms. That way we can be certain that any objections are coming from the important claims of the argument, rather than mere misunderstandings of probability.

Suppose that, after a devastating explosion at a large fireworks factory, you are called in to investigate. Forensic professionals are able to discern that the cause of the blast was an unstable batch of explosives being used for the company’s latest product, the “Blam-O 3000” – already on the market, which you now know to be essentially a bunch of ticking timebombs. Unfortunately, the only records of how many Blam-O’s had been sold happened to burn up in the explosion.

However, at a convenience store in a city on the other side of the country, your agents find one Blam-O with serial number 112. What does this tell you about the total number N of Blam-O’s on the market?

Trivially, it gives you a lower bound on the total number of Blam-O’s – namely, 112. But we can do a little bit better than that. Assuming that the unit found at the convenience store was selected randomly from the population N of all Blam-O’s, it seems very unlikely that N = 10 million, and much more likely that N = 1,000.

This is because if there were 10 million units, the chances of finding a serial number in the hundreds are only 999/10e6 = 0.1% – whereas if there were only 1,000 units, it becomes an effective certainty.

This somewhat frivolous problem had a more serious application during World War II, when the Allies desired to estimate the number of German tanks in existence based on observed serial numbers. The Wikipedia article on this episode is excellent and highly recommended for the quantitative details. But the qualitative importance of both my problem above and the German tank problem is that it is sometimes possible to form rational guesses about an unknown quantity of generic units N based on observation of the “rank” (serial number) of a few individual units – even a single unit.

So much for the probabilistic framework of the argument – I hope you will agree that it is valid, at least in the above application. Now we turn to the difficult part of the problem – anthropic reasoning.

The Doomsday Argument (DA) seeks to show that knowing how long it’s been since the dawn of human life tells you something about the number of humans who will have ever existed. The argument was first put forth by Brandon Carter, but has been popularized by John Leslie and Nick Bostrom, whose primer on the subject is well worth reading. I will follow the terminology and numbers in Bostrom’s primer, for the sake of inter-comparability.

Putting it into the context of the above “Blam-O” problem, we are trying to estimate N, the number of humans who will have ever lived (analogous to the number of Blam-O’s on the market), based on knowing our birth rank R (analogous to a serial number). Our birth rank is just the number of humans from the beginning of the species to our birth; for example, if Genesis were true, Eve would have a birth rank R=2. Based on what we know of hominid evolution, according to Bostrom, the birth rank of any human living today is roughly R = 60 billion.

Now, following the presentation in Bostrom’s primer, we consider two hypotheses about the life expectancy of the human species: DoomSoon and DoomLate. For simplicity, we will treat them as the only two possibilities on offer; although that isn’t true, it doesn’t affect the broad direction of the underlying logic, and it makes the math easier.

DoomSoon is the hypothesis that we are already around halfway through our existence as humans, and that we will be wiped out by some catastrophe just as the number of humans N who ever existed reaches 200 billion. DoomLate is the hypothesis that the human species will live much longer – the number of humans who will have ever existed under this hypothesis is 200 trillion.

The prior odds you assign to these hypotheses depend on your evaluation of existential risks, discussed briefly above; let us say that you think O(DoomSoon) = 50:1 against, which implies (since we stipulate that DoomSoon and DoomLate are mutually exclusive and exhaustive hypotheses) that O(DoomLate) = 1:50 against = 50:1 in favor.

What evidence does our birth rank of R = 60 billion give us about which of these worlds we are in? Well, given that DoomSoon is true, the probability of finding yourself living at birth rank 60 billion or less is P(R<60b|DoomSoon) = 60e9/200e9 = 30%.

Meanwhile, the probability of finding yourself at rank 60 billion or less, given that DoomLate is true, is P(R<60b|DoomLate) = 60e9/200e12 = 0.03%.

The evidence thus favors DoomSoon over its competitor DoomLate by a margin of 30/0.03 = 1,000. This gives posterior odds on DoomSoon of O(DoomSoon|R<60b) = (1:50)*1000 = 20:1 in favor. As we step back from our dubious simplifying assumptions, it should still be clear that the DA strongly favours hypotheses which put the end of humanity earlier over those which put it later. This is our qualitative conclusion.

As Bostrom notes, many people think they know what’s wrong with this portentous argument, but they all disagree with each other about exactly what is wrong with it. Let us move on to consider some objections.

Critique 1: There is no fact of the matter about N (yet). This objection asks whether it makes sense to say that there is some fact of the matter about what N is, given that N cannot be known without traveling to the future, and given that N depends on our actions in the here and now. Speaking loosely, it criticizes the seeming determinism of the DA.

Yet a moment’s thought will show that we can reason about the likely values of numbers that involve the future without too much difficulty. Suppose, for example, that we have one bacillus in a petri dish. Given knowledge of its doubling time and the amount of food in the dish, the number N of bacilli that will ever inhabit the dish is predictable to within reasonable margins. We can remain agnostic about whether there is a fact of the matter about N before the bacteria divide (determinism) – probability allows us to reason about N anyway, whether or not it is determined.

Critique 2: We somehow know a priori that we are among the earliest humans. E.g., we expect most humans to be cyborgs, but we are not cyborgs, therefore, we are known to be early. “All else is not equal; we have good reasons for thinking we are not randomly selected humans from all who will ever live.” (Robin Hanson)

If we had such a reason, this critique would come off. And in fact, if we assume that humans will never inhabit other planets, then you could make an argument that earth’s declining birthrates (currently 2.5 and declining; replacement is 2.1) imply a smaller future population. I’m not sure if I find this convincing, and I am still interested in the validity of the DA assuming that this objection fails.

Critique 3: Self-indicating assumption. The possibility of your existing at all depends on how many humans will ever exist (N). If this is a high number, then the possibility of your existing is higher than if only a few humans will ever exist. Since you do indeed exist, this is evidence that the number of humans that will ever exist is high.

The self-indicating assumption (SIA) completely nullifies the DA, and seems plausible. It is the most popular escape route from the problem. However, it gives results in a related problem, the sleeping beauty problem, that seem to be absurd.

Critique 4: Richard’s objection. An RS commenter named Richard got me thinking about the DA. His objection has to do with the proper assignment of priors in the DA, not directly with the validity of the Bayesian update. According to him, although there may be a 1000-to-1 likelihood ratio for DoomSoon over DoomLate, this effect is exactly counteracted by one’s priors on DoomSoon and DoomLate. DoomLate, on this view, should have a greater prior (200e12/200e9 = 1,000 times bigger, to be precise), essentially because you are likelier to find yourself in a larger group of people than a smaller one (thus, I think Richard’s objection ends up being equivalent to the self-indicating assumption).

As Richard says, Bostrum’s reply here is that if there are both larger and smaller populations, we should expect to find ourselves in a large population with a large birth rank; the fact that we do not shows that the above priors should already have been adjusted. I tentatively agree with Richard that it looks like there might be something circular going on here: we are using the DA to determine our priors, to which we then apply the DA?

Critique 5: The problem of reference classes. We are discussing the probability of “finding yourself” at rank such-and-such, but exactly what kinds of entities fall into the class that is being ranked? If we include prehistoric humans in our reference class, then our birth rank looks a little bit better and we get a different answer; if we include only people born on Mondays, the answer changes yet again; if we include all humans back to our last common ancestor, it changes yet again. And what if there are extraterrestrial observers? Couldn’t you just as easily have “found yourself” inside the body of Zaphod Beeblebrox? If so, how on earth can any conclusions be drawn about human population limits?

This objection strikes me as one of the most interesting. As far as I can tell, Bostrom agrees that the reference class you choose does determine your answer, and that in fact if there is intelligent extraterrestrial life, then the DA essentially falls apart.

Critique 6: Metaphysics of “random sampling” from the set of all observers. One difficulty I have, which is rather hard to put into words, lies in the concept of “finding oneself” at a particular birth rank. This choice of language puts me in mind of nothing so much as a deck of immaterial souls being dealt by some cosmic Dealer to various previously lifeless bodies.

Does it make any metaphysical sense to say that “I” or “my consciousness” could have “found itself” anywhere else but (supervening on) my particular body? I am having trouble formalizing this intuition, but it makes me reluctant to take the DA too seriously.

I have only dipped my toes in the literature on the DA, and on anthropic reasoning in general. I fully expect to be corrected on many misapprehensions in the above.

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For some further reading, see:

Bostrom’s Doomsday Argument FAQ

Bostrom’s literature review

Katja Grace on anthropics