How shocking are rare past events?

This post describes variations on a thought experiment involving the anthropic principle. The variations were developed through discussion with Andreas Albrecht, Charles Bennett, Leonid Levin, and Andrew Arrasmith at a conference at the Neils Bohr Institute in Copenhagen in October of 2019. I have not yet finished reading Bostrom’s “Anthropic Bias“, so I don’t know where it fits in to his framework. I expect it is subsumed into such existing discussion, and I would appreciate pointers.

The point is to consider a few thought experiments that share many of the same important features, but for which we have very different intuitions, and to identify if there are any substantive difference that can be used to justify these intuitions.

I will use the term “shocked” (in the sense of “I was shocked to see Bob levitate off the ground”) to refer to the situation where we have made observations that are extremely unlikely to be generated by our implicit background model of the world, such that good reasoners would likely reject the model and start entertaining previously disfavored alternative models like “we’re all brains in a vat”, the Matrix, etc. In particular, to be shocked is not supposed to be merely a description of human psychology, but rather is a normative claim about how good scientific reasoners should behave.

Here are the three scenarios:

Scenario 1: Through advances in geology, paleontology, theoretical biology, and quantum computer simulation of chemistry, we get very strong theoretical evidence that intelligent life appears with high likelihood following abiogenesis events, but that abiogenesis itself is very rare: there is one expected abiogenesis event per 1022 stars per Hubble time. (There are fewer than 1012 stars in the Milky Way.) Furthermore, such an event is confidentally known to have taken place on Earth in its primordial past.In particular, we assume primordial life was not carried to Earth by an asteroid.a   However, there is thought to be roughly 1023 stars in the observable universe, and the universe might extend very far beyond the observable universe, so this was likely to have happened somewhere.

Scenario 2: Terrorists release a carefully engineered virus that wouldn’t naturally arise and has a vastly higher fatality rate than natural pathogens. In fact, it is designed to incubate for several years, infect every human on the planet, and then kill each host unless the host has a randomly chosen precise selection of genetic variants, which is expected to occur only once per 4 billion people. (There are 7 billion people on the planet at the time.) One of the following takes place:

  • 2(a): Two people, a man and a woman, are the lone survivors with the correct genetic variants. They find each after everyone else is wiped out by quickly getting on Twitter (before the power goes down) and agreeing on somewhere to meet. They fall in love, have a child, and that child is you.
  • 2(b): You are an infant when the pandemic hits, and you are the lone survivor. You are raised by the terrorists and grow up.
  • 2(c): You are an adult when the pandemic hits, and you are the lone survivor.

In all versions of this scenario, having one or two people worldwide survive is a probabilistically reasonable outcome.

Scenario 3: You live 50 years in the future when there are lots of highly agile robots; however, like today, they are very dumb with no signs of anything we might call intelligence of consciousness. One day you are abducted by evil robots to an underground lair and subjected to a cruel punishment: You are given a fair coinThis could be a quantum coin if you know what that means and you prefer.b  , which you inspect very carefully, and you are forced to flip it 33 times. If you flip 33 heads in a row (a chance of 1 in 233 = 8,589,934,592 ≈ 8.6 billion), you will be released unharmed. But if any of the flips land tails up, then on the following day you will be…

You proceed to flip 33 heads in a row, and the robots release you alive and with a comfortable scalp. You later find out that Earth was taken over by an insane dictator with robot armies who rounded up everyone and subjected them to the same cruel experiment, and that you were the lone winner.

In all cases, we are reasoning from a situation where our past contains an extremely unlikely event that was necessary (except for Scenario 3(b)) for us to exist in the present when we are doing our reasoning. Furthermore, the event, though extremely unlikely considered in isolation, was likely to occur somewhere because it was attempted a very large number of times.

In Scenario 1, it’s seems we should not be shocked. Abiogenesis may be extremely rare in any given galaxy, but we are not bothered by finding evidence for such an event in our past because it is necessary (given the laws of physics in our universe) for an intelligent observers to trace their origins to such an event, and the universe is big enough that this should have happened at least once.

In Scenario 3, it seems you should be shocked, and should conclude that the coin must have been rigged, or something. For Scenario 3(b), it’s pretty obvious that you personally have been singled out beyond all reasonable odds. And to see that Scenario 3(a) is equivalent, just consider how you should react immediately after flipping the coins, before the time you were scheduled to be executed had you not succeeded. At that point in time, the unlikely event is not necessary for you to exist.This is the modification to the quantum suicide thought experiment that in the past always convinced me there was no quantum immortality. That is, if there is a delay between the quantum measurement event and the potential mortal blow, then you should expect to exist no matter what the measurement outcome was, and the measurement out statistics should be normal, i.e., you should be shocked to see an extremely rare event.c   And if flipping all those heads in a row is shocking immediately after it happens, how could it suddenly become un-shocking later, after the execution would have taken place?

In Scenario 2, I am confused. In all of these cases, the unlikely event can be said to take place before you’re bornThat event is either (a) the initial formation of a zygote’s genome, whether you or your parents, or (b) the choice of which genetic variant the virus should allow to live, which for the sake of argument we can assume was randomly chosen by the terrorists before you were born in all three versions of the scenario. And of course, events (a) and (b) could be spacelike separated!d  , and you wouldn’t be around to do the reasoning unless the unlikely event had happened. Scenario 2(a) is especially close to Scenario 1 on the key factors. Yet, there also don’t seem to be any substantive differences between Scenarios 2(c) and Scenario 3(a).

Footnotes

(↵ returns to text)

  1. In particular, we assume primordial life was not carried to Earth by an asteroid.
  2. This could be a quantum coin if you know what that means and you prefer.
  3. This is the modification to the quantum suicide thought experiment that in the past always convinced me there was no quantum immortality. That is, if there is a delay between the quantum measurement event and the potential mortal blow, then you should expect to exist no matter what the measurement outcome was, and the measurement out statistics should be normal, i.e., you should be shocked to see an extremely rare event.
  4. That event is either (a) the initial formation of a zygote’s genome, whether you or your parents, or (b) the choice of which genetic variant the virus should allow to live, which for the sake of argument we can assume was randomly chosen by the terrorists before you were born in all three versions of the scenario. And of course, events (a) and (b) could be spacelike separated!
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3 Comments

  1. My personal philosophy on these kinds of “shocking” events is the same as my philosophy on fine-tuning and naturalness. Mathematically, the absolute likelihood of an event is completely irrelevant — literally any state of the world can be made to have an arbitrary low likelihood if it is specified precisely enough. What matters, as Bayes’ theorem tells us, is the likelihood ratio. That is, if we have two qualitatively similar theories that purport to explain that event, and one gives a much higher likelihood than the other, then that theory is better.

    “Shock” is just an imperfect heuristic for this. We are shocked to see a coin come up heads 100 times in a row, but not, say, in the sequence “HTHHTTHTTTTHHHTH…”, even though the likelihoods of both are 1/2^100, because in the former case there is a simple theory that explains the result with much higher likelihood (the coin is rigged). We are shocked to see a strong CP angle of zero (to within 10^(-10)) but would have been shocked to see a strong CP angle of 1.837492498 (to within 10^(-10)), even though both have the same likelihood under the uniform distribution, because there are simple theories that give us a near-zero strong CP angle automatically.

    The same goes for all 3 of your scenarios. The only difference between them is how difficult it is to come up with an alternative theory that explains the result with higher likelihood. In scenario 3, all you need is for a coin to be rigged. In scenario 1, it seems hard to come up with anything besides a benevolent God, a hypothesis which we generally disallow in science because it would screw everything else up. In scenario 2, whether or not there’s a good alternative explanation depends on how the terrorists designed the virus, which is why you have different intuitions for it upon different framings.

    • Thanks for your comment, Kevin. Your first two paragraphs re-state the problem in your preferred language, but they don’t seem to address the main issue. Indeed, I made it clear that “shocked” can be equated to the threshold when you start entertaining alternative theories because they are now more plausible relative to the previously leading theory. So I wasn’t relying on absolute probabilities.

      Regarding your third paragraph: We can easily adjust Scenario 3 to make it clear that the “coin is rigged” explanation is just as disfavored as supernatural explanations for abiogenesis. (I tried to make it express this by saying that you inspect the coin very carefully, but perhaps it wasn’t emphasized enough.) We could say that you were allowed to use any coin, and you chose to go dig up a coin that you secretly buried on your 10th birthday near a tree behind your house. Or, instead of 33 heads flipped, we could make the condition something like “a lightning strike hits your house during an N-second period announced a month in advance” since we’re confident that your captors can’t control the weather, but there is enough people on the planet that someone’s house is likely to get struck during an N-second window.

      Similarly, the details of how the terrorists designed the virus cannot be driving our different intuitions about Scenario 2 since the three version, (a)-(c), have no obvious relation to such viral-design details, yet give different intuitions. And in any case, for the purposes of this argument, we can just modify Scenario 2 however is necessary to make it clear that simple rigging is very unlikely, as I just did for Scenario 3

      The thing that seems to be driving the different intuition between coin-flipping case and abiogenesis is (1) the fact that abiogenesis applies to everyone while the coin applies to only me and (2) the coin flip is happening now, whereas abiogenesis happened in the very distant past.

      • Like a lot of philosophical discussions, we may just have to agree to disagree, because of differing intuitions.

        In both cases (1) and (3), I default to being “shocked”, and stop being shocked if there’s sufficiently strong evidence against alternative theories. In case (1), you listed “advances in geology, paleontology, theoretical biology, and quantum computer simulation of chemistry”, while in case (3) you just say that I get to inspect a coin carefully. That’s the sole reason my intuition differed. If you now modify case (3) to have equally strong evidence as in case (1), I’m no longer shocked! In other words, my intuition really is in line with the Bayesian reasoning I said.

        Moreover (as in a lot of very abstract thought experiments) I don’t have any “intuition about intuition”, i.e. I don’t have any idea what other people’s intuitions would be, or even the meta-intuition about how people would intuitively intuit the validity of their intuition. It just all sounds very slippery to me.

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