Submitted by Kane on
Image by Pete Linforth from Pixabay
The Doomsday Argument purports to show, probabilistically, that humanity will not endure for much longer: Likely, at least 5% of the humans who will ever live have already lived. If 60 billion have lived so far, then probably no more than 1.2 trillion humans will live, ever. (This gives us a maximum of about eight more millennia at the current birth rate of 140 million per year.) According to this argument, the odds that humanity colonizes the galaxy with many trillions of inhabitants are vanishingly small.
Why think we are doomed? The core idea, as developed by Brandon Carter (see p. 143), John Leslie, Richard Gott, and Nick Bostrom is this. It would be statistically surprising if we -- you and I and our currently living friends and relatives -- were very nearly the first human beings ever to live. Therefore, it's unlikely that we are in fact very nearly the first human beings ever to live. But if humanity continues on for many thousands of years, with many trillions of future humans, then we would in fact be very nearly the first human beings ever to live. Thus, we can infer, with high probability, that humanity is doomed before too much longer.
Consider two hypotheses: On one hypothesis, call it Endurance, humanity survives for many millions more years, and many, many trillions of people live and die. On the other, call it Doom, humanity survives for only another a few more centuries or millennia. On Endurance, we find ourselves in a surprising and unusual position in the cosmos -- very near the beginning of a very long run! This, arguably, would be as strange and un-Copernican as finding ourselves in some highly unusual spatial position, such as very near the center of the cosmos. The longer the run, the more surprisingly unusual our position. In contrast, Doom suggests that we are in a rather ordinary temporal position, roughly the middle of the pack. Thus, the reasoning goes, unless there's some independent reason to think Endurance to be much more plausible than Doom, we ought to conclude that Doom is likely.
Let me clarify by showing how Doomsday-style reasoning would work in a few more intuitive cases.
Imagine two lotteries. One has ten numbers, the other a hundred numbers. You don't know which one you've entered into, but you go ahead and draw a number. You discover that you have ticket #6. Upon finding this out, you ought to guess that you probably drew from the ten number lottery rather than the hundred number lottery, since #6 would be a surprisingly low draw in a hundred-number lottery. Not impossible, of course, just relatively unlikely. If your prior credence was split 50-50 between the two lotteries, you can use Bayesian inference to derive a posterior credence of about 91% that you are in the ten-number lottery, given that you see a number among the top ten. (Of course, if you have other evidence that makes it very likely that you were in the hundred-number lottery, then you can reasonably retain that belief even after drawing a relatively low number.)
Alternatively, imagine that you're one of a hundred people who have been blindfolded and imprisoned. You know that 90% of the prison cells are on the west side of town and 10% are on the east side. Your blindfold is removed, but you don't see anything that reveals which side of town you're on. Nonetheless, you ought to think it's likely you're on the west side of town.
Or imagine that you know that 10,000 people, including you, have been assigned in some order to view a newly discovered painting by Picasso, but you don't know in what order people actually viewed the painting. Exiting the museum, you should think it unlikely that you were either among the very first or very last.
The reasoning of the Doomsday argument is intended to be analogous: If you don't know where you're temporally located in the run of humans, you ought to assume it's unlikely that you're in the unusual position of being among the first 5% (or 1% or, amazingly, .001%).
Now various disputes and seeming paradoxes arise with respect to such probabilistic approaches to "self-location" (e.g., Sleeping Beauty), and a variety of objections have been raised to Doomsday Argument reasoning in particular (Leslie's book has a good discussion; see also here and here). But let's bracket those objections. Grant that the reasoning is sensible. Today I want to add a pair of observations that have the potential to flip the Doomsday Argument on its head, even if we accept the general style of reasoning.
Observation 1: The argument assumes that only about 60 billion humans have existed so far, rather than vastly many more. Of course this seems plausible, but as we will see there might be reason to reject it.
Observation 2: Standard physical theory appears to suggest that the universe will endure infinitely long, giving rise to infinitely many future people like us.
There isn't room here to get into depth on Observation 2. I am collaborating with a physicist on this issue now; draft hopefully available soon. But the main idea is this. There's no particular reason to think that the universe has a future temporal edge, i.e., that it will entirely cease. Instead, standard physical theory suggests that it will enter permanent "heat death", a state of thin, high-entropy chaos. However, there will from time to time be low-probability events in which people, or even much larger systems, spontaneously congeal from the chaos, by freak quantum or thermodynamical chance. There's no known cap on the size of such spontaneous fluctuations, which could even include whole galaxies full of evolving species, eventually containing all non-zero-probability life forms. (See the literature on Boltzmann brains.) Perhaps there will even be new cosmic inflations, for example, caused by black holes or spontaneous fluctuations. Vanilla cosmology thus appears to imply an infinite future containing infinitely many people like us, to any arbitrarily specified degree of similarity, perhaps in very large chance fluctuations or perhaps in newly nucleated "pocket universes".
Now if we accept this, then by reasoning similar to that of the Doomsday Argument, we ought to be very surprised to find ourselves among the first 60 billion people like us, or living in the first 14 billion years of an infinitely existing cosmos. We'd be among the first 60 billion out of infinity. A tiny chance indeed! On Doomsday-style reasoning, it would be much more reasonable, if we think the future is infinite, to think that the past must be infinite too. Something existed before the Big Bang, and that something contained observers like us. That would make us appropriately mediocre. Then, in accordance with the Copernican Principle, we'd be in an ordinary location in the cosmos, rather than the very special location of being within 14 billion years of the beginning of an infinite duration.
The situation can be expressed as follows. Doomsday reasoning implies the following conditional statement:
Conditional Doom: If only 60 billion humans, or alternatively human-like creatures, have existed so far, then it's unlikely that many trillions more will exist in the future.
If we take as a given that only 60 billion have existed so far, we can apply modus ponens (concluding Q from P and if P then Q) and conclude Doom.
But alternatively, if we take as a given that (at least) many trillions will exist in the future, we can apply modus tollens (concluding not-P from not-Q and if P then Q) and conclude that many more than 60 billion have already existed.
The modus ponens version is perhaps more plausible if we think in terms of our species, considered as a local group of genetically related animals on Earth. But if we think in terms of humanlike creatures instead specifically of our local species, and if we accept an infinite future likely containing many humanlike creatures, then the modus tollens version becomes more plausible, and we can conclude a long past as well as a long future, full of humanlike creatures extending infinitely forward and back.
Call this the Infinite Predecessors argument. From infinite successors and Doomsday-style self-location reasoning, we can conclude infinite predecessors.
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