Newsletter #003: Anthropic Reasoning
Anthropic Bias by Nick Bostrom; SIA > SSA by Joe Carlsmith; reincarnation from Michael Huemer; immortal sleeping beauty from Jens Jäger
Anthropic Bias: Observation Selection Effects in Science and Philosophy (2002) - Nick Bostrom: Recently, I’ve been interested in observation selection effects and have been reading this book by Nick Bostrom. It appears to be the go-to resource on this topic. The basic idea is that you need to incorporate the fact that you exist when you are reasoning about scientific and philosophical issues. How exactly to consider the fact that you exist is a subject of debate among philosophers. Consider the following thought experiment (Incubator, version I):
Stage (a): In an otherwise empty world, a machine called “the incubator” 3 kicks into action. It starts by tossing a fair coin. If the coin falls tails then it creates one room and a man with a black beard inside it. If the coin falls heads then it creates two rooms, one with a blackbearded man and one with a white-bearded man. As the rooms are completely dark, nobody knows his beard color. Everybody who’s been created is informed about all of the above. You find yourself in one of the rooms. Question: What should be your credence that the coin fell tails?
Stage (b): A little later, the lights are switched on, and you discover that you have a black beard. Question: What should your credence in Tails be now? (Bostrom, 2002, p. 64)
Which probability you assign at each stage reflects some philosophical assumptions about existence. Those who embrace an idea called the Self-Sampling Assumption (SSA) should believe that your credences should be 1/2 at stage (a) and 2/3 at stage (b). An additional assumption which is sometimes considered an addition to SSA is called The Self-Indication Assumption (SIA) believe that your credences should be 1/3 at stage (a) and 1/2 at stage (b). Those assumptions are:
(SSA) One should reason as if one were a random sample from the set of all observers in one’s reference class. (Bostrom, 2002, p. 66)
(SIA) Given the fact that you exist, you should (other things equal) favor hypotheses according to which many observers exist over hypotheses on which few observers exist. (Bostrom, 2002, p. 66)
While this may appear to be unimportant philosophizing, there are some important potential ethical and philosophical implications. If one accepts SSA without SIA, they may be very sympathetic to the Doomsday Argument as formulated by John A. Leslie:
One might at first expect the human race to survive, no doubt in evolutionary much modified form, for millions or even billions of years, perhaps just on Earth but, more plausibly, in huge colonies scattered through the galaxy and maybe even through many galaxies. Contemplating the entire history of the race—future as well as past history—I should in that case see myself as a very unusually early human. I might well be among the first 0.00001 per cent to live their lives. But what if the race is instead about to die out? I am then a fairly typical human. Recent population growth has been so rapid that, of all human lives lived so far, anything up to about 30 per cent . . . are lives which are being lived at this very moment. Now, whenever lacking evidence to the contrary one should prefer to think of one’s own position as fairly typical rather than highly untypical. To promote the reasonable aim of making it quite ordinary that I exist where I do in human history, let me therefore assume that the human race will rapidly die out. (Leslie 1990), pp. 65f.
There are a lot of scientific and philosophical implications that Bostrom goes over. This is likely an underresearched topic that might be very important. I plan to write more on this topic soon.
SIA > SSA (2021) by
: This is a four-part essay that Joe Carlsmith wrote defending the Self-Indication Assumption. It is rather interesting and presented in an entertaining way. It is less dry compared to Bostrom. I think that it makes clear why this area of research is fascinating. Here is the summary in the first part:I proceed as follows. The first part of the sequence (“Learning from the fact that you exist”) describes SIA and SSA. In particular, I emphasize that pace some presentations in the literature, SIA should not be seen as an additional assumption you add to SSA — one that “cancels out” SSA’s bad implications, but accepts SSA’s worldview. Rather, SIA is a different (and more attractive) picture altogether.
The second part (“Telekinesis, reference classes, and other scandals”) lays out the bulk of my case against SSA. In particular, SSA implies:
~certainty that fair coins that haven’t yet been flipped will come up heads;
a made-up and indeterminate ontology of reference classes that really seems like it shouldn’t be a thing, and which also shouldn’t be contorted willy-nilly to get whatever results you want (and also, this doesn’t work anyway);
sensitivity to differences that don’t matter (like whether a definitely-not-you observer is killed and/or given evidence you don’t get, vs. never created; or whether there are ten vs. twenty chimps in the jungle surrounding your thought experiment);
a “special snowflake” metaphysics on which, because you actually exist, you had to exist in any world still compatible with your evidence (though I think that SSA has some replies here);
The third part (“An aside on betting in anthropics”) briefly discusses betting in anthropics. In particular: why it’s so gnarly, why I’m not focusing on it, and why I don’t think it’s the only desiderata.
The fourth part (“In defense of the presumptuous philosopher”) discusses prominent objections to SIA in more detail. In particular:
I suggest that the Presumptuous Philosopher is a strong candidate for what I call a “good bullet”: that is, a counterintuitive result, acceptance of which resolves a lot of gnarly issues into a simple and pretty satisfying theory, and rejection of which invites endless complication and counterexample (fans of the repugnant conclusion, take note). This doesn’t mean we should actually bite. But we shouldn’t die on the hill of non-biting.
Pascal’s muggings and infinities are problems for SIA, but this puts SIA in pretty respectable company (expected utility theory, population ethics) — and in particular, company that still seems to make itself useful.
SIA has problems with “counting observers.” I haven’t thought that much about this one, but I have some feeling like: don’t we all?
Given some values and decision theories, SIA (like SSA) suffers from inconsistencies between “the policy you’d want to commit to, from some ‘prior’ epistemic perspective” and “how you behave ex post.” But these inconsistencies are common in many other contexts, too; and if you’re worried about them, you can use an “updateless” decision theory. But I suggest not throwing out the concept of epistemology along the way.
We can maybe do a bit to make SIA more intuitive (though not as much as I’d like).
That said, even if SSA is worse than SIA, it’s not like SIA is sitting pretty (I especially don’t like how it breaks in infinite cases, and there are presumably many other objections I’m not considering). I briefly discuss whether we should expect to find a better alternative — the “Anthropic Theory X” above. My current answer is: maybe (and maybe it’s already out there), but Anthropic Theory X should probably keep SIA’s good implications (like “thirding” in Sleeping Beauty). And the good implications seem closely tied to (some of) the bad.
I close by quickly mentioning some of SIA’s possible implications in the real world (for example, re: doomsday arguments). I think we should tread carefully, here, but stay curious.
Existence Is Evidence of Immortality (2021) by
: This was my introduction to this type of reasoning. I wrote one of my earliest articles about it—The Bayesian Case for Reincarnation. Huemer summarizes the idea in a blog post Reincarnation:Premise: There is a nonzero initial probability that persons are repeatable (can have multiple lives).
Also, the probability that you would be alive now given that persons are repeatable is nonzero.
Evidence: You are alive now.
Claim: The probability that you would be alive now, given that persons are unrepeatable, and that there is an infinite past, is zero. Rough explanation: there were infinite opportunities for you to exist in earlier centuries, which, if persons are unrepeatable, would have prevented you from existing now.
But you do exist now, so either the past is finite, or persons are repeatable. Bayesian calculation: Let H=[persons are repeatable], E=[You exist now]:
P(H|E) = P(H)*P(E|H) / [P(H)*P(E|H) + P(~H)*P(E|~H)]
= P(H)*P(E|H) / [P(H)*P(E|H) + P(~H)*0]
= P(H)*P(E|H) / P(H)*P(E|H)
= 1 (provided P(H), P(E|H) are nonzero)If persons are repeatable, then they will repeat, given sufficient time. Conclusion: if the past is infinite, then persons are reincarnated infinitely many times.
Immortal Beauty: Does Existence Confirm Reincarnation? (2021) by Jens Jäger: In this article, Jäger argues that Huemer’s argument for reincarnation does not work. He thinks that learning you exist at this exact moment is like learning the number of the winning lottery ticket; it does not give you any indication of how many winners there are. However, Jäger argues that we should believe in reincarnation if we are sympathetic to thirding in the sleeping beauty thought experiment—a position that proponents of the SIA believe:
We start by noting a parallel between the immortality case and the well-known Sleeping Beauty puzzle.
Sleeping Beauty. Beauty goes to sleep on Sunday, planning on sleeping for two full days. On Sunday night she is told that, in the night from Sunday to Monday, a team of scientists will flip a coin. If the coin comes up Heads, Beauty is woken on Monday and, shortly after, put back to sleep. If the coin comes up Tails, Beauty is woken on Monday and on Tuesday. Again, shortly after waking on Monday, she is put back to sleep; this time, while asleep, her memory of the Monday awakening is erased.
Now consider the following variation:
Immortal Beauty. God creates a universe temporally infinite toward the past and the future. God then flips a coin. If the coin comes up Heads, She incarnates Beauty in precisely one century (singular incarnation). If Tails, She incarnates Beauty in countably infinitely many centuries, with no earliest or latest century (infinite reincarnation). Prior to flipping the coin, God fixes a plan for when to incarnate Beauty, conditional on either outcome of the coin flip. Upon incarnating Beauty, God informs her of the setup, although not about the outcome of the coin flip or about what her plans say.
Thirding is a popular view about Sleeping Beauty: upon waking on Monday, Beauty should assign credence 1/3 to the hypothesis that the coin came up Heads (and thus 2/3 to Tails). Roughly, thirders think that, since there are more awakenings conditional on Tails, Beauty should become more confident of Tails upon waking—starting with a 1/2 credence in Tails on Sunday, she should update to 2/3 on Monday.
The new argument is this. If thirding is correct in Sleeping Beauty, then ‘zeroing’ is correct in Immortal Beauty. After being informed that she is in an Immortal Beauty experiment, Beauty should assign credence 0 to Heads (singular incarnation) and credence 1 to Tails (infinite reincarnation).
I am not sure whether these arguments are correct. I feel sympathetic to SIA, but perhaps I am biased. I do not want the doomsday argument to be true, and I would like to be reincarnated.
My newsletters contain links, articles, and papers that remain relevant. If you enjoyed this, consider taking a look at previous newsletters:
Newsletter #001: Cognitive Ability — Independent intelligences as a degenerating research program; against IQ threshold effects; the IQ halo effect; and IQ fadeout
Newsletter #002: Genetic Enhancement — The most important works on embryo selection for IQ (Shulman, Bostrom, Branwen); the utility of polygenic screening from Karavani et al.; genetic architecture of intelligence from Hsu
Eric Hoel recently recommended this poet turned cosmologist: https://theeggandtherock.substack.com
His argument is that there is evolution at the level of universes. The parameters for of our universe don't just happen to allow for life; they were selected for it.
Related to this post because he gets to that conclusion by taking our own existence into account, which has surprisingly powerful implications.