He presents a bunch of arguments that SSA leads to insane conclusions there that I don't see you engaging with. (I can be more specific if that would be helpful.)
Having read about half of the Joe Carlsmith article so far, I have to say it feels like his approach seems to be going in a direction I don’t fully agree with. I'll continue reading it, but would certainly appreciate if you could point me to the specific objections you'd like me to address.
I believe the correct way to model the SB problem, and anthropics in general, is that we exist according to a process:
1. A universe is created
2. Observers are "placed" in this universe, as a result of the universe's inherent processes
3. You are "assigned" to one of these observers at random
Under this paradigm, the result is mathematically well defined and none of the issues that I've seen him list so far seem to exist. If you insist on declaring some kind of reference class, then it would be the class of observers - people who are capable of asking questions about anthropic reasoning. But it's not like you wouldn't also need to define this exact same class of observers in the SIA, so there's no special disadvantage to using it with the SSA.
I'll read in more detail and give another comment later, but this is what I saw in the short amount of time I had to look at it right now.
So, suppose you don't know how many observers will come to exist, but you seem to be early and have control over how many observers come to exist. (A classic example is "you are Adam or Eve, and can unilaterally decide not to have kids, meaning only two people will ever exist, or to reproduce, in which case there will at least be hundreds of billions".) Do you agree that SSA says you should be much more surprised to be "early" if lots of people come to exist? If so, do you think you can cause a coin to come up heads by committing to keep the population low iff it does? (This is described as "telekinesis" by Carlsmith.)
I'm really appreciating the Carlsmith series - thanks for the link. It's helping me see several cases I hadn't considered, though I haven't been convinced all of them are relevant. I have too many thoughts on the example you gave to fit into one comment, so I'll do my best to cover the important bits.
Upfront, I think the right way to model things is not necessarily SIA or SSA - it's to figure out the model that actually matches the process you care about, and then model that, approximating where necessary. In the absence of testable predictions, this is our only hope. This is not a universally applicable approach, and when it isn't applicable I don't necessarily take that to mean we should take a different inapplicable approach just because we can.
In the case you gave, the issue is that if you are Adam or Eve your decision is by construction nonrandom. As such, it is impossible to model it as a random variable, and any function of that variable cannot be truly random.
Of course, if we were anyone besides Adam then we could model Adam/Eve's decision as a random variable and the math would be fine. But if you *are* Adam then that's not a reasonable approach, and once the universe you're in and/or the number of people within it stop being random, probability stops being meaningful.
I also reject the idea that this failure somehow makes the SIA more reasonable. Applying the SIA still requires you to assume the existence of people who don't exist, and that simply doesn't match the process we're trying to model.
This may just be a case where our tools are too limited to give us the answers we want. Other such cases exist - consider the measure problem in cosmology. Either way, definitely something I will continue to think about, thanks again for the recomendation.
>>"Upfront, I think the right way to model things is not necessarily SIA or SSA"
Carlsmith gestures at this at the end, with his discussion of UDASSA, which I think is a step in the right direction despite the paradoxes. Personally, I think something like this--but with more of the deflationary attitude you took in your Tegmark post, when it comes to thinking about the output of Turing machines as "real"--feels promising to me.
On Sleeping Beauty, I have both halferish and thirderish instincts: I think halferism is right that we're trying to predict *the world* not the *observer moment*; possible worlds with lots of observers that never actually exist shouldn't count towards our expectation.
On the other hand, Radford Neal's Fully Non-Indexical Conditioning, and a calculation inspired by it done by ksvanhorn, convinced me that you can still get 1/3 as a reasonable answer even without the metaphysically dubious stuff that SIA seems to carry with it.
An interesting takeaway from ksvanhorn's calculation is that you can model it so that SB should predict any number from 1/2 to 1/3 as an asymptote, as a function of how much information SB has observed and how the probability distributions governing the info she can observe differs between the two awakenings.
Finally, on the weird metaphysics, I also don't like that SSA has some bad consequences too: aside from the determinism stuff mentioned in the comments above, there's also Carlsmith's observation that SSA has a bit of a vibe of, "since this is a world where I exist, and we're doing our expectation only over people in actual worlds, I *must* exist"---which strikes me as equally bad as the "all possible people exist" of SIA.
I think one of the things that appeals to me about UDASSA or something like it is that it is borrows a bit of both: you're picking over worlds first, via Turing machines, but then also picking over observers within worlds. The complexity penalty on observers means that we're still primarily picking based on worlds: adding more observers to a world doesn't help much if they don't emerge "naturally" from a simpler representation of the world; but we can still consider alternate worlds with different observers.
Sorry to add to an already long digression, but one more thought occurs to me:
One reason I think people's intuitions on SIA vs SSA for anthropic reasoning get pulled in different directions is that: if SSA is thinking about uncertainty over what world you're in, and SIA over what observer you are, then depending on the framing of the problem we may feel inclined to think that our uncertainty is more a matter of world vs observer: I think this is why "expect like a thirder, believe like a halfer" feels right for SB: predicting a coin feels like a "world-like" question.
But when it comes to questions about why the world is the why it is and fine tuning etc, it's much harder to even know how to factor our uncertainty into these components.
Thanks for the thoughtful engagement! I'm glad you've backed off the "this is simple; SSA is straightforwardly right" angle.
If you're still interested in talking about it, I'd enjoy getting to hear a bit more about your model of the telekinesis problem. In particular, I'm confused about "it doesn't make sense to model your own actions as a random variable." Notably, the telekinesis result still works if you hook up a machine that sterilizes you iff the coin comes up heads. After you've hooked up the machine, but before you flip the coin, does it seem right to say that whether you'll be sterile after the flip is random? Put another way, I don't think you need to make any random decisions to get telekinesis; you only need to tie the existence/non-existence of future people to a random outcome.
ETA: Also, am I right that if you're Adam, and *Eve* is like "check this out; I can make the coin come up heads by telekinetically committing to only have kids if it doesn't" you would say it makes sense to predict heads with ~100% probability?
Well, I still think SSA is straightforwardly right in the uncomplicated Sleeping Beauty problem, but I see how I overstated my case. It's also clear though that, for all I thought I read, I clearly had not covered all my bases. Those are the hazards of writing outside my core expertise, I suppose.
Anyway, to your point, I think the best I can do at this point is think aloud. Since you've stated that Eve's actions are actually independent of her choice let's simplify for a moment and remove her from the equation entirely. Let's say you have a universe that has at least N people. After the Nth person, a coin is flipped and then if it heads, no more people are created. If it's tails, then we create another 10000N people.
Conditioned on the knowledge you are one of the first N people, should you assign very low credence that the coin came up heads? I think that, to the extent it makes sense to assign probability to observers at all, the answer would have to be yes.
And if the answer is "No," which it could be, then I think the solution is that the problem is undefined, or at least incorrectly defined by either SSA or SIA.
One thing that keeps hovering in the back of my mind for all of this, however, is that the concept of probability itself is not always this super well-defined, deterministic thing. We're using probabilities here to represent ratios of outcomes of certain processes, and the issue we're running into is how to fit a situation (you are randomly selected among observers) into a process where we can then compute ratios. It's entirely possible that there is no meaningful way to do that.
Which I guess makes some of what I wrote in my essay wrong, or at least only right conditional on the reasonableness of selecting observers randomly.
Seems like we're converging. I don't think it makes sense to allocate probability to observers, and I think both SSA and SIA are confused in thinking that "indexical probability" is a thing. My position (which I attempt to argue in my blog post, linked in my root comment) is that there's no truth about which instance you are across the multiverse, and what we actually allocate is something more like caring than like probability mass.
gah wrote a long comment but substack deleted it when i accidentally swiped off.
I'm a thirder who believes in SIA, but I acknowledge that I have no idea what to do when infinity gets involved. I used to be a double halfer like you seem to be, but I was convinced over. Obviously I disagree that P(A)=P(A | H)=1, because A should be "this very awakening occurs", which will lead to the standard P(H | this awakening) Bayes equation that I'm sure you've seen thirders use before in their papers.
The interesting thing with Sleeping Beauty problem is that indeed anthropic reasoning is very odd and strange, and it has wide implications. I'll give one of the standard thirder vibes-based interpretation instead of getting too bogged down in the Bayes:
If heads, woken up once. If tails, woken up a million times in a row, mind erased each time, of course.
I can vividly imagine waking up, unsure of the day, and being asked whether I think the coin came up heads, and thinking of the potential thousands, tens of thousands, hundreds of thousands of people with my same conscious experience that came before or will come after me that were asked the same question. I consider what they felt -- were they unsure? Groggy? tired? did one of them see a butterfly? did a hundred of them see the same bug in the corner of the room that I see? And I think thinking of them each as individual perspectives with individual, unique experiences is best. If I’m just one “observer-moment” plucked out of that huge sea of near-duplicates, the mere fact that I find myself awake at all is way better explained by the scenario that provided a million of these unique experiences than a scenario which provides a single one.
If you wake up regardless of what happens, then P(A) (the probability you wake up) will be 1 and the probability of waking up in a specific world, such as P(A|H) is also 1. The math just means "there's no world where you don't wake up."
(To be clear, I'm not defending that statement. For example, one could argue that it's equivocating between waking up the first time vs waking up the second time. But I think the math is fine, if you agree with the premise that "waking up" is an event that happens in both timelines.)
Well, not really. 1 / (# of time points) would, by definition, be your probability of waking up at a given time.
To Realifin’s comment, the probability of waking up the first time would not be the probability of waking up, it would be, tautologically, the probability of waking up the first time. Your probability of waking at all would be the sum of all the probabilities of waking.
The idea here is that in all scenarios, there is a number of times you wake up, and though you may not know which one you are, you know you must be one of those. If you select over possible observers, then by mathematical necessity (as explained in the warehouse section) you will have probability of being in a time you *don’t* wake up. This doesn’t really make sense, because there’s no physical analog to the statement “the existence of your non-existence.”
I would love to see an implementation of this in python to really FEEL the difference between thirders and halfers. I find the Monty Hall problem much more intuitive when presented in the necessarily constructive manner of code.
I had considered adding something like that. Here's an attempt I haven't actually run, so apologies for any typos. You can see that in some sense the process is switched. In SIA, the observers exist first, in SSA the coin flip happens first:
(It seems the formatting is a little mangled, actually. I may see if I can post elsewhere and link)
I see! Perhaps it’s not that the observers necessarily exist first, but the question boils down to whether to apply the principle of indifference to the possible *worlds* or the possible *awakenings*, yes?
Thanks for writing this! Some of it resembles my stance on the topic, particularly around "expect like a thirder, believe like a halfer." (https://utopiandreams.substack.com/p/anthropic-reasoning)
I'm curious if you encountered/read Joe Carlsmith's essays arguing for SIA > SSA.
https://joecarlsmith.com/2021/09/30/sia-ssa-part-1-learning-from-the-fact-that-you-exist
He presents a bunch of arguments that SSA leads to insane conclusions there that I don't see you engaging with. (I can be more specific if that would be helpful.)
Having read about half of the Joe Carlsmith article so far, I have to say it feels like his approach seems to be going in a direction I don’t fully agree with. I'll continue reading it, but would certainly appreciate if you could point me to the specific objections you'd like me to address.
I believe the correct way to model the SB problem, and anthropics in general, is that we exist according to a process:
1. A universe is created
2. Observers are "placed" in this universe, as a result of the universe's inherent processes
3. You are "assigned" to one of these observers at random
Under this paradigm, the result is mathematically well defined and none of the issues that I've seen him list so far seem to exist. If you insist on declaring some kind of reference class, then it would be the class of observers - people who are capable of asking questions about anthropic reasoning. But it's not like you wouldn't also need to define this exact same class of observers in the SIA, so there's no special disadvantage to using it with the SSA.
I'll read in more detail and give another comment later, but this is what I saw in the short amount of time I had to look at it right now.
So, suppose you don't know how many observers will come to exist, but you seem to be early and have control over how many observers come to exist. (A classic example is "you are Adam or Eve, and can unilaterally decide not to have kids, meaning only two people will ever exist, or to reproduce, in which case there will at least be hundreds of billions".) Do you agree that SSA says you should be much more surprised to be "early" if lots of people come to exist? If so, do you think you can cause a coin to come up heads by committing to keep the population low iff it does? (This is described as "telekinesis" by Carlsmith.)
I'm really appreciating the Carlsmith series - thanks for the link. It's helping me see several cases I hadn't considered, though I haven't been convinced all of them are relevant. I have too many thoughts on the example you gave to fit into one comment, so I'll do my best to cover the important bits.
Upfront, I think the right way to model things is not necessarily SIA or SSA - it's to figure out the model that actually matches the process you care about, and then model that, approximating where necessary. In the absence of testable predictions, this is our only hope. This is not a universally applicable approach, and when it isn't applicable I don't necessarily take that to mean we should take a different inapplicable approach just because we can.
In the case you gave, the issue is that if you are Adam or Eve your decision is by construction nonrandom. As such, it is impossible to model it as a random variable, and any function of that variable cannot be truly random.
Of course, if we were anyone besides Adam then we could model Adam/Eve's decision as a random variable and the math would be fine. But if you *are* Adam then that's not a reasonable approach, and once the universe you're in and/or the number of people within it stop being random, probability stops being meaningful.
I also reject the idea that this failure somehow makes the SIA more reasonable. Applying the SIA still requires you to assume the existence of people who don't exist, and that simply doesn't match the process we're trying to model.
This may just be a case where our tools are too limited to give us the answers we want. Other such cases exist - consider the measure problem in cosmology. Either way, definitely something I will continue to think about, thanks again for the recomendation.
>>"Upfront, I think the right way to model things is not necessarily SIA or SSA"
Carlsmith gestures at this at the end, with his discussion of UDASSA, which I think is a step in the right direction despite the paradoxes. Personally, I think something like this--but with more of the deflationary attitude you took in your Tegmark post, when it comes to thinking about the output of Turing machines as "real"--feels promising to me.
On Sleeping Beauty, I have both halferish and thirderish instincts: I think halferism is right that we're trying to predict *the world* not the *observer moment*; possible worlds with lots of observers that never actually exist shouldn't count towards our expectation.
On the other hand, Radford Neal's Fully Non-Indexical Conditioning, and a calculation inspired by it done by ksvanhorn, convinced me that you can still get 1/3 as a reasonable answer even without the metaphysically dubious stuff that SIA seems to carry with it.
An interesting takeaway from ksvanhorn's calculation is that you can model it so that SB should predict any number from 1/2 to 1/3 as an asymptote, as a function of how much information SB has observed and how the probability distributions governing the info she can observe differs between the two awakenings.
Finally, on the weird metaphysics, I also don't like that SSA has some bad consequences too: aside from the determinism stuff mentioned in the comments above, there's also Carlsmith's observation that SSA has a bit of a vibe of, "since this is a world where I exist, and we're doing our expectation only over people in actual worlds, I *must* exist"---which strikes me as equally bad as the "all possible people exist" of SIA.
I think one of the things that appeals to me about UDASSA or something like it is that it is borrows a bit of both: you're picking over worlds first, via Turing machines, but then also picking over observers within worlds. The complexity penalty on observers means that we're still primarily picking based on worlds: adding more observers to a world doesn't help much if they don't emerge "naturally" from a simpler representation of the world; but we can still consider alternate worlds with different observers.
Sorry to add to an already long digression, but one more thought occurs to me:
One reason I think people's intuitions on SIA vs SSA for anthropic reasoning get pulled in different directions is that: if SSA is thinking about uncertainty over what world you're in, and SIA over what observer you are, then depending on the framing of the problem we may feel inclined to think that our uncertainty is more a matter of world vs observer: I think this is why "expect like a thirder, believe like a halfer" feels right for SB: predicting a coin feels like a "world-like" question.
But when it comes to questions about why the world is the why it is and fine tuning etc, it's much harder to even know how to factor our uncertainty into these components.
Thanks for the thoughtful engagement! I'm glad you've backed off the "this is simple; SSA is straightforwardly right" angle.
If you're still interested in talking about it, I'd enjoy getting to hear a bit more about your model of the telekinesis problem. In particular, I'm confused about "it doesn't make sense to model your own actions as a random variable." Notably, the telekinesis result still works if you hook up a machine that sterilizes you iff the coin comes up heads. After you've hooked up the machine, but before you flip the coin, does it seem right to say that whether you'll be sterile after the flip is random? Put another way, I don't think you need to make any random decisions to get telekinesis; you only need to tie the existence/non-existence of future people to a random outcome.
ETA: Also, am I right that if you're Adam, and *Eve* is like "check this out; I can make the coin come up heads by telekinetically committing to only have kids if it doesn't" you would say it makes sense to predict heads with ~100% probability?
Well, I still think SSA is straightforwardly right in the uncomplicated Sleeping Beauty problem, but I see how I overstated my case. It's also clear though that, for all I thought I read, I clearly had not covered all my bases. Those are the hazards of writing outside my core expertise, I suppose.
Anyway, to your point, I think the best I can do at this point is think aloud. Since you've stated that Eve's actions are actually independent of her choice let's simplify for a moment and remove her from the equation entirely. Let's say you have a universe that has at least N people. After the Nth person, a coin is flipped and then if it heads, no more people are created. If it's tails, then we create another 10000N people.
Conditioned on the knowledge you are one of the first N people, should you assign very low credence that the coin came up heads? I think that, to the extent it makes sense to assign probability to observers at all, the answer would have to be yes.
And if the answer is "No," which it could be, then I think the solution is that the problem is undefined, or at least incorrectly defined by either SSA or SIA.
One thing that keeps hovering in the back of my mind for all of this, however, is that the concept of probability itself is not always this super well-defined, deterministic thing. We're using probabilities here to represent ratios of outcomes of certain processes, and the issue we're running into is how to fit a situation (you are randomly selected among observers) into a process where we can then compute ratios. It's entirely possible that there is no meaningful way to do that.
Which I guess makes some of what I wrote in my essay wrong, or at least only right conditional on the reasonableness of selecting observers randomly.
Seems like we're converging. I don't think it makes sense to allocate probability to observers, and I think both SSA and SIA are confused in thinking that "indexical probability" is a thing. My position (which I attempt to argue in my blog post, linked in my root comment) is that there's no truth about which instance you are across the multiverse, and what we actually allocate is something more like caring than like probability mass.
gah wrote a long comment but substack deleted it when i accidentally swiped off.
I'm a thirder who believes in SIA, but I acknowledge that I have no idea what to do when infinity gets involved. I used to be a double halfer like you seem to be, but I was convinced over. Obviously I disagree that P(A)=P(A | H)=1, because A should be "this very awakening occurs", which will lead to the standard P(H | this awakening) Bayes equation that I'm sure you've seen thirders use before in their papers.
The interesting thing with Sleeping Beauty problem is that indeed anthropic reasoning is very odd and strange, and it has wide implications. I'll give one of the standard thirder vibes-based interpretation instead of getting too bogged down in the Bayes:
If heads, woken up once. If tails, woken up a million times in a row, mind erased each time, of course.
I can vividly imagine waking up, unsure of the day, and being asked whether I think the coin came up heads, and thinking of the potential thousands, tens of thousands, hundreds of thousands of people with my same conscious experience that came before or will come after me that were asked the same question. I consider what they felt -- were they unsure? Groggy? tired? did one of them see a butterfly? did a hundred of them see the same bug in the corner of the room that I see? And I think thinking of them each as individual perspectives with individual, unique experiences is best. If I’m just one “observer-moment” plucked out of that huge sea of near-duplicates, the mere fact that I find myself awake at all is way better explained by the scenario that provided a million of these unique experiences than a scenario which provides a single one.
Are you familiar with Wei Dai's paradox? (https://www.lesswrong.com/posts/QmWNbCRMgRBcMK6RK/the-absolute-self-selection-assumption?commentId=QyYS5mWQrTLQMp4w4)
(Also discussed here: https://utopiandreams.substack.com/p/anthropic-reasoning)
I'm curious if you have a sense of how SIA deals with it.
"using Bayes Rule and the fact that you wake up at least once in each scenario, meaning P(A) = P(A|H) = 1"
You've lost me here - why does the fact you wake up at least once in each scenario mean P(A) = P(A|H) ?
If you wake up regardless of what happens, then P(A) (the probability you wake up) will be 1 and the probability of waking up in a specific world, such as P(A|H) is also 1. The math just means "there's no world where you don't wake up."
(To be clear, I'm not defending that statement. For example, one could argue that it's equivocating between waking up the first time vs waking up the second time. But I think the math is fine, if you agree with the premise that "waking up" is an event that happens in both timelines.)
Thanks. That's helped me work out what I disagree with.
The probability that you wake up isn't 1. It's 1 / (how many time points you're measuring).
Well, not really. 1 / (# of time points) would, by definition, be your probability of waking up at a given time.
To Realifin’s comment, the probability of waking up the first time would not be the probability of waking up, it would be, tautologically, the probability of waking up the first time. Your probability of waking at all would be the sum of all the probabilities of waking.
The idea here is that in all scenarios, there is a number of times you wake up, and though you may not know which one you are, you know you must be one of those. If you select over possible observers, then by mathematical necessity (as explained in the warehouse section) you will have probability of being in a time you *don’t* wake up. This doesn’t really make sense, because there’s no physical analog to the statement “the existence of your non-existence.”
I would love to see an implementation of this in python to really FEEL the difference between thirders and halfers. I find the Monty Hall problem much more intuitive when presented in the necessarily constructive manner of code.
I had considered adding something like that. Here's an attempt I haven't actually run, so apologies for any typos. You can see that in some sense the process is switched. In SIA, the observers exist first, in SSA the coin flip happens first:
(It seems the formatting is a little mangled, actually. I may see if I can post elsewhere and link)
```
# Halfer (`all` will be 50% H, 25% T1 or T2):
all = Counter()
for _ in range(10000):
if random.choice(['H', 'T']) == 'H':
observers = ['H']
else:
observers = ['T1', 'T2']
self = random.choice(observers)
all[self] += 1
```
--------------------
--------------------
--------------------
```
#Thirder (`all` will be 1/3 H, T1, T2)
all = Counter()
for _ in range(10000):
possible_observers = ['1', '2']
if random.choice(['H', 'T']) == 'H':
if random.choice(possible_observers) == '1':
self = 'H1'
else:
# observer 2 never wakes up
continue
else:
# Coin was tails - you can be either observer
self = 'T' + random.choice(possible_observers)
all[self] += 1
```
I see! Perhaps it’s not that the observers necessarily exist first, but the question boils down to whether to apply the principle of indifference to the possible *worlds* or the possible *awakenings*, yes?
Yes, with a “but.” Indifference to possible awakenings mathematically requires you to assign probability mass to not waking. This means:
1. You need to explain the physical analog to “an observer who exists mathematically but not in reality.”
2. I can make up worlds with arbitrarily low probability but arbitrarily more people, and those are automatically more likely.
> add another narcoleptic princess - let’s call her “Snow White.”
Wait, Snow White is not narcoleptic!