Anthropically Blind: the anthropic shadow is reflectively inconsistent
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I think the application to the Hero With A Thousand Chances is partly incorrect because of a technicality. Consider the following hypothesis: there is a huge number of "parallel worlds" (not Everett branches, just thinking of different planets very far away is enough) each fighting the Dust. Every fight each of those worlds summons a randomly selected hero. Today that hero happened to be you. The world that happened to summon you has survived the encounter with the Dust 1079 times before you. The world next to it has already survived 2181, and the other one was destroyed during the 129th attempt.
This hypothesis explains the observation of the hero pretty well - you can't get summoned to a world that's destroyed or has successfully eliminated the Dust, so of course you get summoned to a world that is still fighting. As for the 1079 attempts before you, you can't consider that a lot of evidence for fighting the Dust being easy, maybe you're just 1080th entry in their database and can only be summoned for the 1080th attempt, there was no way for you to observe anything else. Under this hypothesis, you personally still have a pretty high chance of dying - there's no angel helping you, that specific world really did get very lucky, as did lots of other worlds.
So, anthropic angel/"we're in a fanfic" hypothesis explains observations just as well as this "many worlds, and you're 1079th on their database" hypothesis, so they're updated by the same amount, and at least for me the "many worlds" hypothesis has much higher prior than "I'm a fanfic character" hypothesis.
Note, this only holds from hero's perspective: from Aerhien's POV she really has observed herself survive 1079 times, which counts as a lot of evidence for the anthropic angel.
2Yeah, the hero with a thousand chances is a bit weird since you and Aerhien should technically have different priors. I didn't want to get too much into it since it's pretty complicated, but technically you can have hypotheses where bad things only start happening after the council summons you.
This has weird implications for the cold war case. Technically I can't reflect against the cold war anthropic shadow since it was before I was born. But a hypothesis where things changed when I was born seems highly unnatural and against the Copernican principle.
In your example though, the hypothesis that things are happening normally is still pretty bad to other hypotheses we can imagine. That's because there will be a much larger number of worlds that are in a more sensible stalemate with the Dust, instead of "incredibly improbable stuff happens all the time". Like even "the hero defeats the Dust normally each time" seems more likely. The less things that need to go right, the more survivors there are! So in your example, it is still a more likely hypothesis that there is some mysterious Counter-Force that just seems like it is a bunch of random coincides, and this would be a type of anthropic angel.
I think the real debate about anthropic shadows is whether anthropic angels exist.
When I think of the archetypal example of anthropic shadows, I think something like disease or war where destruction follows a positively skewed distribution, and some naive maximum likelihood fits that permit long-tailedness suggest that there's a serious likelihood of world-ending events.
Here, as I understand it, the counterargument is that there is a gap in observations around the size that would be world-ending, so we should fit a model fit smaller tails to match this gap. Such a model seems like "anthropic angels" to me.
You're probably right that Solomonoff induction recommends anthropic angels. But Solomonoff induction is weird and incapable of reasoning about its own death, so I'm not convinced it tells us anything.
I would be inclined to say that correct anthropic reasoning does normal Bayesian updates but avoids priors that postulate anthropic angels.
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To be clear, Anthropic angels aren't necessary for this argument to work. My deadly coin example didn't have one, for example.
The reason I introduce Anthropic angels is to avoid a continuity counter-argument. "If you saw a zillion LHC accidents, you'd surely have to agree with the Anthropic shadow, no matter how absurd you claim it is! Thus, a small amount of LHC accidents is a little bit for evidence for it." Anthropic angels show the answer is no, because LHC accidents are not evidence for the anthropic shadow.
I would be inclined to say that correct anthropic reasoning does normal Bayesian updates but avoids priors that postulate anthropic angels.
Like, it seems unnatural to give it literally 0% probability (see 0 And 1 Are Not Probabilities).
If there are weird acasual problems that the Anthropic angel can cause, I'm guessing you can just change your decisions without changing your beliefs. I haven't thought too hard about it though.
Here, as I understand it, the counterargument is that there is a gap in observations around the size that would be world-ending, so we should fit a model fit smaller tails to match this gap. Such a model seems like "anthropic angels" to me.
No, anthropic angels would literally be some mechanism that saves us from disasters. Like if it turned out Superman is literally real, thinks the LHC is dangerous, and started sabotaging it. Or it could be some mechanism "outside the universe" that rewinds the universe.
Keep in mind that the problems with maximum likelihood have nothing to do with death. That should be the main takeaway from my article, that we shouldn't use special reasoning to reason about our demise.
In the case of maximum likelihood, it is also bad for:
- Estimating when we will meet aliens
- Forecasting the stock market
- Being a security guard
- etc...
Which is why you should use bayesian reasoning with a good prior instead.
Suppose you have N coins. If all N coins come up 1, you die. For each coin, you have 50:50 credence about whether it always comes up 0, or if it can also come up 1.
For N=1, it reduces to your case. For N>1, you get an anthropic shadow, which means that even if you've had a bunch of flips where you've survived, you might actually have to conclude that you've got a 1-in-4 chance of dying on your next flip.
Okay, I think our crux comes from the slight ambiguity from the term "anthropic shadow".
I would not consider that anthropic shadow, because the reasoning has nothing to do with anthropics. Your analysis is correct, but so is the following:
Suppose you have N coins. If all N coins come up 1, you find a diamond in a box. For each coin, you have 50:50 credence about whether it always comes up 0, or if it can also come up 1.
For N>1, you get a diamond shadow, which means that even if you've had a bunch of flips where you didn't find a diamond, you might actually have to conclude that you've got a 1-in-4 chance of finding one on your next flip.
The "ghosts are as good as gone" principle implies that death has no special significance when it becomes to bayesian reasoning.
Going back to the LHC example, if the argument worked for vacuum collapse, it would also work for the LHC doing harmless things (like discovering the Higg's boson or permanently changing the color of the sky or getting a bunch of physics nerds stoked or granting us all immortality or what not) because of this principle (or just directly adapting the argument for vacuum collapse to other uncertain consequences of the LHC).
In the bird example, why would the baguette dropping birds be evidence of "LHC causes vacuum collapse" instead of, say, "LHC does not cause vacuum collapse"? What are the probabilities for the four possible combinations?
I think we basically agree now. I think my original comments were somewhat confused, but also the deadly coin model was somewhat confused. I think the best model is a variant of the N-coin model where one or more of the coins are obscured, and I think in this model your proof goes through to show that you should independently perform Bayesian updates on each coin, and that since you don't get information about the obscured coin, you should not update on it in a anthropic shadow style way.
1To be clear, Anthropic angels isn't necessary for this argument to work. My deadly coin example didn't have one, for example.
The reason I introduce Anthropic angels is to avoid a continuity counter-argument. "If you saw a zillion LHC accidents, you'd surely have to agree with the Anthropic shadow, no matter how absurd you claim it is! Thus, a small amount of LHC accidents is a little bit for evidence for it." Anthropic angels show the answer is no, because LHC accidents are not evidence for the anthropic shadow.
I think the thing that makes deadly coins different from LHC accidents and skew-distributed death counts is that deadly coins lack variance, so you cannot extrapolate the upper tail from the bulk of the distribution.
We could think of the LHC as having a generating process similar to a log-normal distribution. There are a number of conditions that are necessary before it can be turned on (which would be Bernoulli-distributed variables), as well as settings which affect the extent to which it is turned on (based on the probed energy levels). These all interact multiplicatively, with e.g. it only being turned on if all of the conditions are met. Of course it is not literally lognormally distributed because it is possible for it to not be turned on at all, but otherwise multiplicative interactions are the same as what happens in log-normal distributions. Multiplicatively interacting variables include:
- The vacuum must be maintained against leaks
- Machinery must be protected against outside forces
- Power must be present
- It must be configured to probe some energy level
- etc.
(Disclaimer: I know little about the LHC.)
If all of the LHC accidents go the same way, say a cleaning company keeps breaking things, then it is reasonable to infer an anthropic angel such as "the cleaning company is incompetent/malevolent and will keep breaking things until you replace them". On the other hand, if the LHC accidents are highly varied in an anticorrelated way as predicted by the anthropic shadow (e.g. birds become more likely to drop baguettes onto machinery as you increase the energy levels), then I think you can infer an anthropic shadow, because this shows that the latent generator of LHC activation is highly varied, which according to the model would lead to highly varied outputs if not for anthropic shadows.
Like, it seems unnatural to posit to give it literally 0% probability (see 0 And 1 Are Not Probabilities).
Not wrong. I haven't thought in detail about this, maybe there are some better solutions.
No, anthropic angels would literally be some mechanism that saves us from disasters. Like if it turned out Superman is literally real, thinks the LHC is dangerous, and started sabotaging it. Or it could be some mechanism "outside the universe" that rewinds the universe.
... which in turn would result in a distribution of damage with shorter tails, no?
A further thought:
For diseases or war or asteroid impacts where the means by which greater scales causes greater damage, I think an argument along these lines basically goes through.
But for things like the LHC or AI or similar, there is an additional parameter: what is the relationship between scale and damage? (E.g. what energy level does the LHC need to probe before it destroys the earth?)
Some people might want to use anthropic shadow reasoning to conclude things about this parameter. I think something along the lines of OP's argument goes through to show that you can't use anthropic shadow reasoning to infer things about this parameter beyond the obvious.
The equivalent coin example would be if you were uncertain about whether the coin will kill you.
The equivalent coin example would be if you were uncertain about whether the coin will kill you.
Or one could use my other multi-coin example, but where there is one of the coins that you can't see. So you can't update about whether it is 50:50 or 100:0.
One problem here is that quantum immortality and angel immortality eventually merges: for example, if we survive 10 LHC failures because of QI, we most likely survive only on those timelines where some alien stops LHC. So both QI and angel immortality can be true and support one another and there is no contradiction.
I have an impression is that what you call here 'anthropic shadow' is the idea of quantum immortality. One can't 'use anthropic shadow".
In that case your central thesis is reasonable for most altruistic policies. If I play a series of Russian roulette rounds and "won", it will be still a bad policy to continue playing Russian roulette.
More over, antithesis is correct: if I survive long enough, I am probably underestimating the background risks. This idea - in my view - is true anthropic shadow. And for policy it means that I should be even more cautious about risks which look benign.
Also, survival in QI/AS is "timeless". As in, rather than surviving a Russian Roulette round, you'll junt find yourself as having avoided playing to begin with. This is because your 5D measure is greater when you avoid such activities (plus survive for free) than if you don't and survive. Such activities aren't begun in a counterfactual vacuum.
One more thing, QI invokes a notion of your consciousness "shifting" to youn surviving timeline, but that's unnecessary. Since survival is timeless, you'll simply find yourself in the longer timeline from the get go already. No shifting necessary.
This model explains secularly how I find myself as being a Christian. I'm on my longest (and thickest) counterfactual timeline already from my conception (eternal life stuff). Pretty neat stuff. I shouldn't be so surprised though since secular reasoning isn't so far fallen that it concludes as it does!
Thoughts?
There is a possible bad decision theory consequence of this.
Imagine a person suffers a bad event like having a serious accident in which he damages other people. If he assumes '5D measure' or "retrospective selection of thickest timelines" to be valid, he decides to commit suicide.
As a result he-tomorrow will find himself only in timelines where the accident didn't happen.
This actually happens rather often (e.g. Epstein committed suicide after going to jail)
Check my new post which favors the longest and thickest timelines https://www.lesswrong.com/posts/hB2CTaxqJAeh5jdfF/quantum-immortality-a-perspective-if-ai-doomers-are-probably?commentId=aAzrogWBqtFDqMMpp
I'm on my longest (and thickest) counterfactual timeline already from my conception (eternal life stuff).
I mean, wouldn't that timeline be more like "my consciousness keeps somehow hanging onto a husk of a body out of increasingly unlikely coincidences as the universe approaches heat death"? Quantum Immortality strikes me as a terrible world that I really hope isn't true.
No. Husks have very little 5d measure. How? The same reason you find yourself as a man and not an ant. More precisely, as stated above previously, 5d measure is timeless. Since husks take a hit in both linear scope (4th-d) and counterfactual scope (5th-d), they occupy an infinitesimally-small to epsilon-large area of your anthropic measure landscape. This affects self-location even from the beginning. Read up on UDASSA for a similar formulation of timelessness in self-location. Though UDASSA is more environmental-affecting than this. Here, you can still find yourself as a nobody who's fully reliant on civilization to protect him against an unbounded counterfactual scope with 0 producer-participation, only consumer-participation. Also, this implies your ontological substrate is a pereto-ideal of simultaneously very full, and very simple (eg, you won't find yourself as a sim npc).
Husks have very little 5d measure.
This only holds if there is any alternative to husks which is also compatible with the laws of physics as a whole. A whole civilisation that just happens to keep drawing its energy from an ever higher entropy universe seems a lot less likely, for example, because the improbabilities compound for the whole size. Seems to me that the most likely state would always be one that requires the bare minimum.
Anyway I didn't know about UDASSA so I'll check that out, seems interesting. I'll maybe get back at this after having gone through it properly.
Yes that's what I take would happen too unless I'm misunderstanding something? Because it would seem far more probable for *just* your consciousness to somehow still exist, defying entropy, than for the same thing to happen to an entire civilization (same argument why nearly all Boltzmann brains would be just a bare "brain").
As far as I know, our current Everett branch is best explained by Born’s rule without quantum immortality (QI). There are infinitely many branches where, in the future, we start seeing evidence of it, but in each such branch Solomonoff induction (SI) will only require a finite amount of evidence to update (bounded by a constant determined by how complicated it is to implement QI in the programming language). That is what it means for SI to be universal: it works in every Everett branch, not just the typical ones.
In a sense, our observations are also well explained by Copenhagen, etc., since all interpretations make the same prediction. The supposed advantage of MWI is simplicity, but SI can't prove it without shenanigans.
Optimizing the utility of the real scenario is the same as optimizing utility in anthropic undeath, because the agent choosing "do nothing" in the anthropic undeath scenario has the same physical effect as what actually happens in the real scenario when the agent is dead. I call this the "ghosts are as good as gone" principle.
I either am not following, or disagree. You're just making this anthropic ghost a non-agent, but not unable to experience (dis)utility. If I know that a certain choice leads to death, but I expect that after death I'll still experience stuff, what I decide to do depends on what I imagine death to be like - is it going to be anthropic Heaven or anthropic Hell? Or just a Purgatory? This tangibly affects expected utility before death and thus my behaviour. It also changes the odds of there being a "me" that experiences a past with a deadly event in it - it will be a powerless me, but still a sentient one. The anthropic shadow approach requires death to be the end of sensation, not just of agency.
Anthropic undeath by definition begins when your sensory experience ends. If you end up in an afterlife, the anthropic undeath doesn't begin until the real afterlife ends. That's because anthropic undeath is a theoretical construct I defined, and that's how I defined it.
So why does this even count as not just simple death? Are you assuming this is kind of a cut off state of existence where you still have self-awareness but only that? That still leaves room for utility from internal states.
I probably should've expanded on this more in the post, so let me explain.
"Anthropic shadow", if it were to exist, seems like it should be a general principle of how agents should reason, separate from how they are "implemented".
Abstractly, all an agent is is a tree of decisions. It's basically just game theory. We might borrow the word "death" for the end of the game, but this is just an analogy. For example, a reinforcement learning agent "dies" when the training episode is over, even though its source code and parameters still exist. It is "dead" in the sense that the agent isn't planning its actions past this horizon. This is when Anthropic shadow would apply if it were abstract.
But the idea of "anthropically undead" shows that the actual point of "death" is arbitrary; we can create a game with identical utility where the agent never "dies". So if the only thing the agent cares about is utility, the agent should reason as if there was no anthropic shadow. And this further suggests that the anthropic shadow must've been flawed in the first place; good reasoning principles should hold up under reflection.
I'm still not convinced. Suppose an agent has to play a game: two rounds of Russian roulette with a revolver with one bullet and N chambers. The agent doesn't know N, and will get a reward R if they survive both rounds; if they give up after one round, they get a consolation prize C1 < R. If they give up immediately, they get one C0 < C1 < R.
The optimal strategy depends on N, and the agent's belief about it. The question is, suppose the agent already passed the first round, and survived, does this give them any information about the distribution P(N)? Anthropic shadow says "no" because, conditioned on them having any use for the information, they must also have survived the first round. So I suppose you could reframe the anthropic shadow as a sort of theorem about how much useful information you can extract out of the outcomes of a series of past rounds of a game in which loss limits your future actions (death being one extreme outcome). I need to think about formalizing this.
Anthropic shadow says "no" because, conditioned on them having any use for the information, they must also have survived the first round.
And it is wrong because the anthropic principle is true: we learned that N ≠ 1.
I need to think about formalizing this.
There is the idea of Anthropic decision theory which is related, but I'm still guessing it still has no shadow.
And it is wrong because the anthropic principle is true: we learned that N ≠ 1.
Fair, but no more. And any additional survival doesn't teach us anything else. All meaningful information only reaches us once we have no more use for it.
One such hypothesis is quantum immortality[1].
I think the same argument applies against quantum immortality, provided you care about different branches in a way that respects the Born rule (which you should).
Okay, basic sanity-check: I sit in Shrödinger box with a radioactive nucleus with half-life one minute for an hour and come out alive from it. I have two possible explanations:
- Quantum mechanics is wrong.
- Dead mes are unobservable.
And I am pretty damn sure that quantum mechanics work.
I suppose there are other possible explanations like:
3. Someone messed up the experiment so there was no radiactive nucleus in the box
4. You are mind experiment, simulating exteremely improbable scenario
1You don't observe that. You just die.
OK, technically, there is some tiny chance (i.e. small-weight branch) that you would survive, and conditional on this tiny chance (i.e. conditional on that we are considering your observations only in this small-weight branch), you would have observed it not decaying. But the weight of this branch is no larger than the weight of the branch where it didn't decay if you did the experiment without the dying part.
When physicists outside the box see you come out, they just observed something that is far greater significance than 5 sigmas. It is almost 9 sigmas, in fact. This is enough to make physicists reject QM (or at least the hypothesis "everything happened as you described and QM is true"). And you can't agree to disagree once you get outside of the box and meet them. So you'd be a physics crank in this scenario if you tell people the experiment's result was compatible with QM.
The trick is that, from my perspective, everything is going according to QM every time my death doesn't depend on it. So I can put someone else inside the box and see them die in 10 minutes.
The trick is that, from my perspective, everything is going according to QM every time my death doesn't depend on it.
Right, so this an anthropic angel hypothesis, not anthropic shadow.
I mean, there's plenty of yous that suddenly hear a hiss, see gas filling in the room, start desperately scratching at the sealed door, regretting their stupidity to be coaxed for some reason in this absurd experiment just for the sake of LW cred, grasp at their throat, and eventually slide to the floor spasming as the poison chokes the life out of them. Plenty of experience there! They just don't get to tell the story.
(it's interesting though that in a way things DO feel different if instead of poison the decaying atom triggers a nuclear bomb at point blank which obliterates you before any chances to perceive anything at all. But if that meant a real, physical difference that would imply some freaky things about consciousness and quantum mechanics)
Yes! Very good points. A clever trick with an anthropic ghost. I have a vague feeling that there may be a non-sequitur hidden there somewhere, but can't exactly point it out.
As I've mentioned here updating on "anthropic evidence" is the refusal to update on regular evidence.
Adding here the fact that core assumption of both SSA and SIA that I'm selected from a random sample are often wrong, I think it's possible to make a general case against anthropic reasoning.
Eh, don't get too cocky. There are definitely some weird bits of anthropics. See We need a theory of anthropic measure binding for example.
But I do think in cases where you exist before the anthropic weirdness goes down, you can use reflection to eliminate much of the mysteriousness of it (just pick an optimal policy and commit that your future selves will follow it). What's currently puzzling me is what to do when the anthropic thought experiments start before you even existed.
See We need a theory of anthropic measure binding for example.
I don't think I accept the premise. As with any other situation where either A or B can happen but I don't have any other relevant information I default to an equiprobable prior.
All the attempts to guess what the "universe cares more about" seem completely unsubstantiated and confused. Likewise with the equivalence of anthropic and compassion binding based on pure vibes and not any evidence that our universe has ethics encoded in its fabric in some way.
I believe my approach doesn't lead to any paradoxes or bizarre scenarios even in cases when the thought experiment started before my existence. Can you think of a counterexample?
Example1: Timmie gets cookies and I am glad he did even if I am dead and cant see him.
Example2: Timmie sucked into blackhole but I don't care as I cant see him.
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