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The Doomsday Argument

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Last week in Overalls Nation we considered a logical proof of God’s existence.  Most people seem to sense that there is something wrong with the argument, but they can’t pinpoint the flaw.  This is the kind of problem that the gourmet mind finds most delicious. You think it’s wrong but you don’t know why. While your humble  blogger’s mind does not rise to the gourmet level, he begs leave to explore one more formidable argument with a conclusion that is intuitively perverse yet hard to refute.  For the sake of the Overalls Nation theme we’ll use overalls to develop the argument, and maybe make a political point as well.

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Did you ever lie on the ground in your sleeping bag while the fire burned low, as stars whirled overhead and rare existential questions began to arise in your thoughts?   Perhaps you wondered why you happen to be alive at this point in history and not among the neolithic cavemen of the past or among the starship trekkers  of the far future.  Why now?  If your thoughts were rigidly logical enough, you may have caught glimpse of a startling conclusion:  Humanity is doomed to extinction –  and soon.

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The Doomsday Argument is a statistical formulation, but we don’t have to delve much into the mathematics  to understand it (you can find the formulae in the book*).  A simple thought experiment will be enough to get the point.

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Imagine you are the manager of a department store, and you’ve ordered a shipment of overalls.  The truck drops two boxes on your receiving dock.  In one box are ten pairs of overalls, and each pair has a label attached numbering it sequentially (1,2,3, . . . 10).  In the other box are a thousand pairs of overalls each numbered in the same way (1,2,3, . . . 1000).  The employee who received the shipment opens one of the boxes (you don’t know which,) removes one pair of overalls at random and brings it to your office.  You notice that it is labelled #7.

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Reasoning only from statistical probabilities, which box did this pair of overalls most likely come from?  The answer is, of course, the box of ten.  The odds of randomly pulling #7 from a box of 1000 are 1:1000.  But the odds of pulling #7 from a box of 10 are significantly better at 1:10.  So you reason that it is a hundred times more likely that this pair of overalls came from the box of ten than from the box of a thousand.   By extending this same logic to the potential number of  people who will ever live, you can make an informed guess about whether it’s “doom soon” or “doom later” for the human species.

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Imagine that instead of overalls the two boxes contain two different futures for the human species.  One box is the Doom Soon box.  In it, each individual who ever lived or who will ever live is numbered sequentially, 1 to 100 billion.   At the present time,  about 60 billion people have been born over the course of human history. At the current rate of population growth it won’t take long, say, a century or two, to reach the 100 billion limit proposed by the Doom Soon scenario.

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The other box is the Doom Later box.   In this scenario, humanity survives into the far future, perhaps sending great ships to the stars and spreading human civilization (and overalls, we hope)  through the galaxy.  All the people who will have ever lived are numbered in the Doom Later box, 1 through 100 trillion.

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In the order of human birth, you are number 60 billion. Since the rise of mankind 59,999,999,999 people were born before you, and so 60 billion is your unique number.  This is just like the number attached to the pair of overalls in the previous scenario.  The question is, in which box – in which hypothetical scenario – do you most likely find yourself?  You don’t know which box you’re in, but given your knowledge that you are human number 60 billion, which box do the odds favor, the box containing 100 billion or the box containing 100 trillion?  Probability overwhelmingly skews toward the possible future represented by the Doom Soon box.  For the same statistical reason as in the overalls scenario, Doom Soon is a thousand times more likely than Doom Later, and the better bet is for extinction of the human race, whether by ecological disaster or by the mushroom cloud, as opposed to any bright, star-trekking future.

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This is one of those arguments that must be wrong, but darned if we can see why.  It seems airtight.  And if we end up taking it seriously, how can it inform our life choices or our politics?  If the odds of human beings surviving to see the shining, glorious future we seek is as vanishing small as the Doomsday Argument suggests, then don’t we want to do whatever we can to skew the odds in our favor?  And if we have a political choice between a platform that responds to the science of global warming with ridicule and one that responds with action, which should we prefer?  Will we favor an ever more bloated military-industrial complex, or one that is reigned in? Will we continue to deregulate industry at the expense of conservation, or apply rational controls to manage our dwindling resources?

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* Lestlie, John.  The End of the World:  The Science and Ethics of Human Extinction. Routledge: 1996

3 comments on “

  1. Anonymous says:

    okay this is stuped how can you tell from you number how many people get bron i guess you have to be some college jenius

  2. gbear says:

    You should be considering the odds of which box was picked. Not the odds of what is in the box. So the odds would be 50% for either box.

  3. Cabel says:

    I know I’m like an eon late here, but the reason the argument is invalid is that with the boxes of overalls you’re talking about two distinct sets. One with 10, one with 1000. In the population argument you’re talking about the same set. YOU are in BOTH sets, which invalidates comparing the two sets, as they are really one set.

    Imagine a box with 1000 pairs of overalls. You’re only going to be able to sell 10 of those overalls. Your employee plucks out pair #7. Is that the #7 from the group of overalls you’re going to sell, or the #7 from the group that you’re only going to partially be able to sell?

    The answer is YES, it’s part of both sets, just like you are part of both sets of extinction groups.

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