the doomsday argument: or, inductive logic run amok

[sophiaserpentia]

So, i'm reading Stephen Baxter's Manifold Time, and it's okay, not great, not horrible. Towards the outset of this book the protagonist is introduced to, and convinced by, the Doomsday Argument, which holds that we consistently underestimate the likelihood of human extinction in the near future and that we have 150-220 years to live. The reasoning goes as follows (adapted from anthropic-principle.com):

Imagine there are a hundred cubicles numbered from 1 to 100. A fair coin is tossed (by God perhaps). If the coin falls heads, one person is created in each cubicle. If the coin falls tails, then persons are only created in cubicles 1 through 10.

You find yourself in one of the cubicles and are asked to guess whether there are ten or one hundred people. Before you look at the number on your cubicle, you know that the chance that there are 10 people is 50%, and the chance that there are 100 people is 50%, since this is determined by a coin toss.

But then you open the door to the cubicle and discover that you are in cubicle number 7. Again you are asked, how did the coin fall? But now the probability is greater than 50% that it fell tails. The precise new probability of tails can be calculated using Bayes’ theorem, at approximately 91%. So after finding that you are in cubicle number 7, you should think that with 91% probability there are only ten people.

Now, to transpose these results to our actual situation here on Earth. Let’s formulate the following two rival hypotheses.

• Doom Soon: humankind goes extinct in the next century and the total number of humans that will have existed is, say, 200 billion.
• Doom Late: humankind survives the next century and goes on to colonize the galaxy; the total number of humans is, say, 200 trillion.

Doom Soon corresponds to there only being ten people in the first thought experiment, while Doom Late corresponds to there being one hundred people. Corresponding the numbers on the cubicles, we now have the "birth ranks" – your birth rank being a number corresponding to how many people are born after you, and how many are born before you.

Suppose, based on ordinary empirical estimates of potential threats to human survival, such as nuclear or biological warfare, a meteorite destroying the plant, runaway greenhouse effect, self-replicating nanomachines running amok, a breakdown of a metastable vacuum state due to high-energy particle experiments and so on (and presumably there are dangers that we haven’t yet thought of), that you think that there is a 5% probability of Doom Soon. The exact number doesn’t matter for the structure of the argument.

You find that your birth rank is about 60 billion (that’s approximately how many humans have lived before you). Just as finding you are in cubicle 7 increased the probability of the coin having fallen tails, so finding that you are human number 60 billion gives you reason to think that Doom Soon is more probable than you previously thought. Exactly how much more probable will depend on the precise numbers you use. In the present example, the posterior probability of Doom Soon will be very close to one. You can with near certainty rule out Doom Late.

Or, to summarize it even more succinctly (again adapting from anthropic-principle.com), based on the principles of statistics you should not expect to be one of the very first or very last human beings who ever lived. Other things equal, you should expect to find yourself to be among the middle 95%. At present, the human population of Earth comprises 15% of all the humans who have ever lived. Assuming that the population will continue to double every 20-25 years, as time passes you and i each slide out further from the statistical norm on the bell curve of historical human population. If humanity thrives for another million years, then you and i will have "self-sampled" to find ourselves in a statistically unlikely place on the bell curve.

IOW, based on a bundle of statistical laws and categorizations some philosophers claim they can predict with near certainty that humanity will go extinct in the next 200 years, even without stipulating a mechanism by which this may occur.

As Nick Bostrom, who compiled anthropic-principle.com admits, most people when exposed to this argument have an intuitive sense that it is wrong. He's complied a long list of arguments demonstrating why he thinks the Doomsday Argument (which he does not seem to personally believe, BTW) is not so easy to refute or dismiss.

But i think it doesn't hold water, and here's why. It is a case of inductive reasoning run amok, and all of the arguments for it and against it all play by the rules, by implicit agreement to accept certain frames and limitations on our conceptualizations. IOW they contain a hidden agenda. Western philosophers spend a lot of time dealing with "paradoxes" like this because they cannot rid themselves of troublesome arguments like this one, or the Simulation Argument which bears many similarities, or the Goedel Incompleteness Theorems, or the Hard Problem of Consciousness, and so on, without questioning the couch-cushion fort of conceptualizations and abstractions they've built up around themselves and upon which their livelihoods depend.

First (not stepping entirely outside the philosophical box but stretching it a little) i contest this idea of "all the humans who will ever live" as an easily-delineated set. Each one of us as individuals exists as a special case, born with unique DNA bearing variations on themes of the DNA of previous organisms. Each one of us has mutations in our DNA and so we are part of a continuum of evolution. It is not "humanity" that will live for millions of years, because the descendants of this generation will continue to evolve and will at some point, which may or may not be easily discernable, constitute one or more new species. If our descendants take to the stars and eventually inhabit the entire galaxy, it is likely that they will branch out into hundreds or thousands of new species. Some branches of this evolution may even be consciously guided by genetic engineering. Will such people still be "humanity," for the purposes of this thought experiment, as we now know it?

[I suspect this may be the direction Baxter is actually going in his book, but if you know don't tell me, i'm only 100 pages in.]

Secondly (and this is where my objection really begins) this notion that we can self-sample to find our location on an indexical continuum of "all the humans who will ever live" is based on an unspoken but assumed body-soul duality. It assumes that there is something special about humanity, that at some very clear point we stopped being "mere beasts" and became "humans with souls" qualitatively distinguishable from the beasts around us.

Suppose that instead of seeing myself as "one of a finite number of beings with souls" i see myself as a little bit of the universe folded on itself in a particular way, a unique unfolding of the holomovement renewed in every instant. What i see as "me" is a persistent pattern of unfoldings associated with a subjective consciousness. I exist in the now, and any human being who perceives and contemplates the mystery of their existence will be, similarly, a little bit of the universe folded on itself.

Taken this way, there is no logical imperative for me to see myself as a member of any given indexical continuum. If i were to self-sample and place myself on an indexical continuum of "all the humans who will ever live," why not "all the organisms who will ever live" or "all the conscious unfoldings that will ever perceive themselves to exist"? Why must i necessarily interpret my understanding of myself qua humanhood? The only answer is that the argument presumes there to be something special about the experience of "what it is like to be human" that indicates a meaningful and unique divergence from all other kinds of system... IOW a presumption analogous to saying that humans have souls and other beings do not (or do not at least have souls like ours).

Comments

[akycha.livejournal.com]

I strongly agree with you that trying to quantify a "beginning" to a "line" of humans is arbitrary (and from a biological standpoint, slightly insane in the classic "chicken and egg" way). In fact, speciation is arbitrary, often disagreed about by classification biologists, and for all purposes meaningless in a thought-experiment like this. Given this, there is no finite number of human beings, because we do not know where "humanity" starts. (I rather like this idea, and I like the idea that I am connected, albeit in the distant past, to beings who were quite different from me.)

Also, I am inclined (with my limited-but-not-entirely-trivial understanding of statistics) to doubt the "cubicle number" influence in the first part of the thought-experiment. Why would knowing your own cubicle number affect the probability of which 50% chance had happened? Certainly, if your number was higher than ten, you have your answer. What I do not understand is how if the number is lower than ten it affects the 50% probability at all. I have examined this several times and don't see that it does. Do you (or anyone else) have an understanding of the math involved here? I really don't.

[sophiaserpentia.livejournal.com]

Why would knowing your own cubicle number affect the probability of which 50% chance had happened?

Bayes' Theorem covers the re-calculation of probabilities in light of new information.

As you said, if your number was higher than ten the probability of tails is no longer 50% but 0%.

So, take the case of your number being 7. In the case of heads, the likelihood of being in one of the cubes 1-10 is 10%. In the case of tails, the likelihood of being in one of the cubes 1-10 is 100%. Heads or tails each independently remain 50%. To combine these bits of information we use the Bayes formula to combine all these probabilities to get the relevant figure.

[akycha.livejournal.com]

Thank you for the link. I just spent an enjoyable forty minutes absorbing the information. Fascinating, and very non-intuitive for me.

[moralxdilemma.livejournal.com]

I have a (non-scientific, so possibly false) belief that anything with a beginning will inevitably have an end. So I can understand that the choice here is doom now or doom later. But why is it split 50%/50%? In my opinion, "doom" via pollution is more certain than by an extintion level asteroid impact. An asteroid impact is more certain (within the timeframe of 200 years) than "doom" via space-travel induced evolution of the species.

I also wonder what the response to this argument should be on a philosophical level. Does the author say at all? Everybody dies at the appointed time, with no exceptions. Are we supposed to be worried? What would that accomplish?

[sophiaserpentia.livejournal.com]

But why is it split 50%/50%?

The split is only 50%/50% in the first part of the thought experiment. In the second part, the split is more presumed to start at 5%/95%.


Does the author say at all?

The author seems to think the argument is irrefutable, but that there is no such thing as "destiny" or "fate," and that the universe would repair itself if someone could reach into the past and change it.

[nebris.livejournal.com]

We're like cockroaches. It will take A LOT to kill all of us off.

~M~