Book: Anthropic Bias

In 1983, Carter expressed regret about naming it "anthropic principle", suggesting better names would be "the psychocentric principle", "the cognizability principle" or "the observer self-selection principle". <2023-Jan-12> I like "observer selection principle".

The principle has nothing to do with homo sapiens, and this name has misled some authors (according to Bostrom: Gale 1981, Gould 1985 and Worrall 1996 among others). If you talk about it under this name, emphasize that it concerns intelligent observers in general.

Why nitpick? It's paramount if we want to apply anthropic reasoning to hypotheses about other possible life forms, and it's crucial when we discuss the Doomsday Argument. Also it makes it look "as if it were part of a project to restitute Homo sapiens into the glorious role of Pivot of Creation. For example, Stephen Jay Gould's 1985 criticism is based on this misconception."

• Carter (1974): vague. "…what we can expect to observe must be restricted by the conditions necessary for our presence as observers."
• Gott: underdeveloped
• Leslie
• Barrow & Tipler: dodgy baloney

• Weak anthropic principle (WAP)
  • Superweak anthropic principle
• Strong anthropic principle (SAP)
• Participatory (PAP)
• Final (FAP)
• Completely Ridiculous (CRAP)
• Copernican

Carter's WAP: "we must be prepared to take account of the fact that our location in the universe is necessarily privileged to the extent of being compatible with our existence as observers."

Carter's SAP: "the universe (and hence the fundamental parameters on which it depends) must be such as to admit the creation of observers within it at some stage"

These formulations have been attacked for being tautologies (the WAP in particular) and speculative (the SAP in particular), and vague.

Leslie 1989 argues that AP, WAP and SAP can all be understood as tautologies and the difference is purely verbal.

Leslie's Superweak AP: "If intelligent life's emergence, NO MATTER HOW HOSPITABLE THE ENVIRONMENT, always involves very improbable happenings, then any intelligent living beings that there are evolved where such improbable happenings happened."

Michael Hart 1982 has given a figure of 1 in 10³⁰⁰⁰ as his most optimistic estimate of how likely it is that the right molecules would just happen to bump into each other to form a short DNA string capable of self-replication, although it's possible there exists some as yet unknown abiotic process bridging the gap between amino acids and full replicators. He stresses that we shouldn't assume that the evolution of life on an Earth-like planet is even remotely probable, just because it happened on our Earth-like planet.

• Let B : we are in a big world
• Let T : some theory that is compatible with B
• Let E : some proposition asserting that some specific observation is made

Then by Bayes Theorem,

Pr(T|E&B) = Pr(E|T&B) Pr(T|B) / Pr(E|B)

In order to know that observing E lets us judge T as any truer (or less true) than before we observed it, we'd need the expression Pr(T|E&B) – Pr(T|B) to evaluate to something nonzero, right? With algebra, we can see that:

Pr(T|E&B) - Pr(T|B) ≈ 0 if and only if Pr(E|T&B) ≈ Pr(E|B)

Ok, what Bostrom seems to have been saying is that there's something wrong in this methodology, and that if we take it as given, it doesn't matter which Big World theory is actually true, for our judgments of any T. New empirical findings would be pointless except to provide further support for the hypothesis that we are living in some Big World, for instance by showing that the universe is open.

Also the leaky connection between theory and observation spills over into other domains than cosmology; since nothing hinges on how we define T, we can extend the argument to prove that no observation has any bearing on any empirical scientific question(!) so long as we are living in a Big World. And I'll call that absurd – though it's startling to realize that even Newtonian mechanics and all its proof could be something I dreamed up just now, and it's a fascinating perspective on provability of theories (in addition to Occam's Razor discussions, Duhem-Quine thesis etc), and a principled way to reason about it seems called for.

(SSA) One should reason as if one were a random sample from the set of all observers in one's reference class.

(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.

Some of the more profound criticisms of specific anthropic inferences rely implicitly on SIA. In particular, adopting SIA annihilates the DA.

Bostrom rejects SIA in Chapter 7.

• The fine-tuning observation
  • 20 or so physical constants, any of which if they were different would make life impossible

• If R is your reference class, it must be between these extremes: R^ε ⊂ R ⊂ R^U.
• To be rational, must not use a reference class that's too broad
• To be rational, must not use a reference class that's too narrow (all people born since my own birth) nor a gerrymandered reference class (the class that includes myself and all observers born after 2020).

Similar to what Eliezer said in 2008 about finding the simplest generalizations (www.greaterwrong.com/posts/S8ysHqeRGuySPttrS/many-worlds-one-best-guess) AKA carving thingspace well:

Now there are gruesome questions about the proper generalization that covers all these tiny cases. Call an object “grue” if it appears green before January 1, 2020 and appears blue thereafter. If all emeralds examined so far have appeared green, is the proper generalization, “Emeralds are green” or “Emeralds are grue”?

The answer is that the proper generalization is “Emeralds are green.” I’m not going to go into the arguments at the moment. It is not the subject of this essay, and the obvious answer in this case happens to be correct. The true Way is not stupid (www.greaterwrong.com/posts/6ddcsdA2c2XpNpE5x/newcomb-s-problem-and-regret-of-rationality): however clever you may be with your logic, it should finally arrive at the right answer rather than a wrong one.

In a similar sense, the simplest generalizations that would cover observed microscopic phenomena alone take the form of “All electrons have spin 1/2” and not “All electrons have spin 1/2 before January 1, 2020” or “All electrons have spin 1/2 unless they are part of an entangled system that weighs more than 1 gram.”

Assume that as time passes, the amount of observers increases superlinearly, up to some cutoff point such as a doomsday event. This would imply that the largest share of observers are born just before that cutoff point. Therefore if you could've been born as any person in any time, it's overwhelmingly likely you're one of the people in that time slice just before the end times.

Variants:

• Gott pg. 90-94
• Carter-Leslie pg. 94-96, 105-107
• Bostrom's explication pg. 96-105

Ways to invalidate the DA:

• By accepting SIA—which you shouldn't per Bostrom
• Something about applying the Observer Equation (I didn't follow the reasoning near the end of the book)

Some paradoxes go away when you stop thinking of observers as a contiguous entity extruded over the time-axis, a whole with a single identity as if they had a label like "person #4346921040" somewhere in a grand record outside Time, and instead slice the observer up by instants of time: observer-moments.

these quantities may be different:

1. How many observers can expect to find themselves as a Boltzmann brain? (Some fraction of total observers)
2. How many observer-moments can expect to be experienced by a Boltzmann brain? (A strictly lower fraction of total observer-moments?)

The 1mm animal Trichoplax (en.wikipedia.org/wiki/Trichoplax) can regenerate a full body after having most of it chopped off, and notably, when chopped apart, the pieces will try to find each other and join back together. That invites some questions about continuity of consciousness. When you split in two, there are two observers, and if you merge with your split-buddy… is one murdered?

(The Star Trek Voyager episode "Tuvix" plays with this conundrum. In reality, I think merging of consciousness might be given a very different ethical frame than we'd expect, if done in a principled way the entrants regularly agree to, especially if the merging mechanism works differently such that from the entrants can have more reliable expectations about the succeeding observer-moment)

It seems to me (as of [2023-01-13 Fri]) that continuity of consciousness is an illusion, and accepting that dissolves many such conundrums.

I am a series of observer-moments, and you could say I die every second (or rather every Planck interval).

It resolves the moral conundrum of the Star Trek transporter. No need to worry about whether it kills me and creates a copy when I am anyways dying and creating a copy every second. You could say I am in fact wrong about expecting to experience the next moment – that just won't be me in "this consciousness" doing that.

(Hell of an argument for valuing other peoples' QALYs equal to your own)

When we think of death as a tragedy, it's because it ends a series of observer-moments, each of which expects there to be another observer-moment like itself immediately afterwards, and in fact develops long-term ambitions and desires because of the apparent reliability of this process (it would not bother to have any ambitions if it could only remember a series of random experiences none of which had ever affected the next).

With the Star Trek transporter, there is no tragedy: the series of observer-moments is not broken. Does it matter if the spacetime coordinates of the observer-moment-generator jumps sharply? Even without teleporting, the brain is different in every moment than in the preceding moment, and the spacetime coordinates on each neuron has changed slightly, and some neurons are in different states and may even have exchanged a molecule with the environment.

Can you take a fraction of infinity? If we have two quantites A and B, where A is some huge number and B must be strictly less than A, let's say 0.01A, can we still think of B as strictly smaller if we increase A to infinity? For the sake of probabilistic estimates such as "how likely is it that my universe belongs to the A category rather than the B category?". Or is it suddenly equally likely that my universe is in A vs. B?

Bostrom speaks as if B is meaningfully less than A.

Math has stuff to say about infinities, specifically figuring out whether some quantity is "aleph-0 infinite" or "aleph-1 infinite", but this seems a totally different topic.

It feels related somehow. Maybe just because tickles the same "counterfactual thinking" pathways. … "if I'm not here working as a doctor in Britain, someone else would be in my office doing my job, so what's my actual total effect on society?" feels similar to thinking about indexical evidence.

Given on page 172-173.

Variables:

• α : an observer-moment
• P_α : the observer-moment α's subjective probability function
• Ω_α : all possible observer-moments in α's reference class
• w_α : the possible world in which α is located
• e : some evidence
• h : some hypothesis
• Ω_e : class of observer-moments "about whom" e is true
• Ω_h : class of observer-moments "about whom" h is true
  • h can be indexical like "this is an observer-moment that has a black beard", or if h is non-indexical, it is true about all and only those possible observer-moments that live in possible worlds where h holds true
• Ω(w) : the class of observer-moments in the possible world $w$ .

The Observer Equation:

$$P_{\alpha}(h|e) = \frac{1}{\gamma} \sum_{\sigma \in \Omega_{h} \cap \Omega_{e}} \frac{ P_{\alpha}(w_{\sigma}) }{ |\Omega_{\sigma} \cap \Omega(w_{\sigma})| }$$

where γ is a normalization constant (note the thing being summed is the same as above):

$$\gamma = \sum_{\sigma \in \Omega_{e}} \frac{ P_{\alpha}(w_{\sigma}) }{ |\Omega_{\sigma} \cap \Omega(w_{\sigma})| }$$

I observe that this equation takes the form of the basic $\Pr(h|e) = \Pr(h \cap e) / \Pr(e)$ .

Are you facing different outcomes for which you know the quantum measure (probability of observing)? Then you can use the QOE. Note this is rare!

The QOE is just the same as the OE but includes a factor for the quantum measures, μ.

A very banal principle, but philosophers had to discuss it. The principle is that when you know some objective chance, you set your subjective credence to the same, unless you have other relevant information.

• Three sources of uncertainty
• 2023-08-20
• Reasoning
• Why care about quantum physics?
• Portal: On my mind
• Reasoning about unknown reasoners