The way I think about it is (ignoring the meta-anthropic thing) is that if for some reason every human who has ever lived or will live said aloud “I am in the final 95% of humans to be born”, then trivially 95% of them would be correct. You are a human, if you say this aloud, there is a 95% chance you are correct, therefore doom.
I understand objections with regard to whether this is the correct reference class, but my understanding is that you think the above logic does not make sense. What am I missing?
Sorry about the double reply, and it’s been a while since I thought seriously about these topics, so I may well be making a silly mistake here, but --
There’s a shop that uses a sequential ticketing system for queueing: each customer takes a numbered ticket when they enter, starting with ticket #1 for the first customer of the day. When I enter the shop, I know that it has been open for a couple of hours, but I have absolutely no idea when it closes (or even whether its ‘day’ is a mere 24 hours). I take my ticket and see that it’s #20. I have also noticed that the customer flow seems to be increasing more than linearly, such that if the shop is open for another hour there will probably be another 20 customers, and if it’s open for a few more hours there will be hundreds. Should I update towards the shop closing soon, on the grounds that otherwise my ticket number is atypically low? If so, wtf, and if not, what are the key differences between this and the doomsday argument?
I like the analogy. Here’s a simplified version where the ticket number is good evidence that the shop will close sooner rather than later.
There are two types of shop in Glimmer. Half of them are 24⁄7 shops that stay open until they go out of business. Half of them are 9-5 shops that open at 9am and close at 5pm.
All shops in Glimmer use a numbered ticket system that starts at #1 for the first customer after they open, and resets when the shop closes.
I walk into a shop in Glimmer at random and get a ticket.
If the ticket number is #20 then I update towards the shop being a 9-5 shop, on the grounds that otherwise my ticket number is atypically low. If the ticket number is #43,242 then I update towards the shop being a 24⁄7 shop.
The argument also works with customer flow evidence:
Like Glimmer, there are two types of shop in Silktown. Half of them are 24⁄7 shops that stay open until they go out of business. Half of them are 9-5 shops that open at 9am and close at 5pm.
All shops in Silktown experience increasing customer flow over time, starting with a few customers an hour, rising over time, and capping at hundreds of customers an hour after about ten hours of opening.
I walk into a shop in Silktown and observe the customer flow.
If the customer flow is low then I update towards the shop being a 9-5 shop, on the grounds that otherwise there will most likely be hundreds of customers an hour. If the customer flow is high then I update towards it being a 24⁄7 shop.
Reading through your hypothetical, I notice that it has both customer flow evidence and ticket number evidence. It’s important here not to double-update. If I already know that customer flow is surprisingly low then I can’t update again based on my ticket number being surprisingly low. Also your hypothetical doesn’t have strong prior knowledge like Silktown and Glimmer, which makes the update more complicated and weaker.
In this case, all those customers were already alive when the shop opened (I assume), so the observation does suggest that, if this process is in fact going to continue for several more hours with the store getting more and more crowded, then there might well be be some mechanism that applies to most customers that causes them to choose to arrive late, but somehow doesn’t apply to you. For example, maybe they do know when the store closes, and that the store’s chili gets stronger the longer it’s cooked, and they all like very strong chili.
The causality here is different, because you can reasonably assume that the other customers got up in the morning, thought about “When should I go to Fred’s Chili Shop?” and it seems a lot of them picked “not long before it closes”. But you are implicitly assuming that you already know this process is in fact going to continue. So it’s rather as if you asked Fred, and he told you yeah, there’s always a big rush at the end of the day, few people get here as early as you. At that point the causal paradox has just gone away: you actually do have solid grounds for making a prediction about what’s going to happen later in the day — Fred told you, and he should know.
But if you know for a fact that all the customers are only 10 minutes old (including you) so decided to come here less than 10 minutes ago, then the only reasonable assumption is that there’s a very fast population explosion going on, and you have absolutely no idea how much longer this is going to last, or how soon Fred will run out of chili and close the shop. In that situation, your predictability into the future is just short, and you just don’t know what’s going to happen after that — and clearly neither does Fred, so you can’t just ask him.
But you are implicitly assuming that you already know this process is in fact going to continue. So it’s rather as if you asked Fred, and he told you yeah, there’s always a big rush at the end of the day, few people get here as early as you.
I didn’t mean to imply certainty, just uncertain expectation based on observation. Maybe I asked Fred, or the other customers, but I didn’t receive any information about ‘the end of the day’—only confirmation of the trend so far.
(I’m not trying to be difficult for the sake of it, by the way! I just want to think these things through carefully and genuinely understand what you’re saying, which requires pedantry sometimes.)
edit in response to your edit:
But if you know for a fact that all the customers are only 10 minutes old (including you) so decided to come here less than 10 minutes ago, then the only reasonable assumption is that there’s a very fast population explosion going on, and you have absolutely no idea how much longer this is going to last, or how soon Fred will run out of chili and close the shop. In that situation, your predictability into the future is just short, and you just don’t know what’s going to happen after that — and clearly neither does Fred, so you can’t just ask him.
I think I’m not quite understanding the distinction here. Why is there an important difference between “this trend is based on mechanisms of which I’m ignorant, such as the other customers’ work hours or their expectations about chili quality over time” and “this trend is based on different mechanisms of which I’m also ignorant, i.e. birth rates and chili inventory”?
I think it’s because of our priors. In the normal city case, we already know a lot about human behavior, we have built up very strong priors that constrain the hypothesis space pretty hard. The hotter-chili hypothesis I came up with seems plausible, there are others, but the space of them is rather tightly constrained. So we can do forward modelling fairly well. Whereas in the Doomsday Argument case, or my artificial analogy to it involving 10 minute lifespans and something very weird happening, our current sample size for “How many sapient species survive their technological adolescence?” or “What happens later in the day in cities of sapient mayflies?” is zero. In dynamical systems terms, the rest of the day is a lot more Lyapunov times away in this case. From our point of view, a technological adolescence looks like a dangerous process, but making predictions is hard, especially about the future of a very complex very non-linear system with 8.3 billion humans and an exponentially rising amount of AI in it. The computational load of doing accurate modelling is simply impractical, so our future even 5–10 years out looks like a Singularity to our current computational abilities. So the constraints on our hypothesis distribution are weak, and we end up relying mostly on our arbitrary choice of initial priors. We’re still at the “I really just don’t know” point in the Bayesian process on this one. That’s why people’s P(DOOM)s vary so much — nobody actually knows, they just have different initial default priors, basically depending on temperament. Our future is still a Rorschach inkblot. Which is not a comfortable time to be living in.
Fair point, and I do find anthropic problems puzzling. What I find nonsensical are framings of those problems that treat indexical information as evidence—e.g. in a scenario where person X (i.e. me) exists on both hypothesis A and hypothesis B, but hypothesis A implies that many more other people exist, I’m supposed to favour hypothesis B because I happen to be person X and that would be very unlikely given hypothesis A.
The Doomsday Argument, translated into the Bayesian framework, is actually:
Suppose everyone who has lived since the invention of Science Fiction said “I don’t know if we’re all going to die soon, so I’m one of the later humans ever (let’s call that probability X%) or if we’re going to spread to the stars and I’m one of the very first humans ever by some extremely large factor Y (with a 100-X% chance).
100-X% divided by an extremely large factor Y is obviously an extremely small number, approximately zero, therefore X is almost certainly equal to 100.
Notice that step 2 here is completely specious, and no one thinking in a Bayesian framework would entertain it for a moment. It’s confused thinking that sounds plausible if you think like a Frequentist and get careless with causality.
I don’t think you need completely specious reasoning to get to a kind of puzzling position, though. For us to be in the first <relatively small n>% of people, we don’t need humanity to spread to the stars—just to survive for a while longer without a population crash. And I think we do need some principled reason to be able to say “yes, ‘I am in the first <relatively small n>% of people’ is going to be false for the majority of people, but that’s irrelevant to whether it’s true or false for me”.
Humans have a very understandable tendency, when they see what appears to be a low-probability event occurring, to get suspicious and wonder if some opponent has maneuvered things somehow to finagle a high probability of an apparently-low-probability event. We pay attention to what look like flukes, and are dubious about them. But if you can safely dismiss the possibility that before you were incarnated your soul was carried back to this time by an evil time-traveling mastermind, then the only remaining possibility is just “viewed from an achronous perspective, a low probability event has occurred — just like they always do right at the start of anything”. Sometimes they do. Especially if there were a vast number of other equally low probability events that could have occurred. Rolling a 1 on a million-sided die is kind of neat, though not actually any more improbable than rolling 314,159, and it’s not actually suspicious unless it advantages someone else who had their hands on the die. But if you watch a clock for long enough, sooner-or-later it will read 00:00:00.
“viewed from an achronous perspective, a low probability event has occurred — just like they always do right at the start of anything”
What’s the ‘low probability event’? I think this is the kind of framing I was disagreeing with in my original reply; there seems to be an implicit dualism here. So your reply isn’t, from my perspective, addressing my reasons for finding anthropic reasoning difficult to completely dismiss.
“viewed from an achronous perspective, a low probability event has occurred” means: an event such that, if I were in a position to do a random sampling over all humans who ever live – something which can only be done once we’re extinct – would then have a low probability of occurring in that random sample: such as (temporarily assuming that humans do get to go to the stars before becoming extinct) randomly selecting, out of all humans ever, one of the tiny 1-in-10∼10 minority of humans who lived before humans went to the stars.
So, if an alien archeologist from after humans go extinct wanted to write “a day in the life of a typical human” and selected a ‘typical’ human randomly, and then got one from before humans got to go to the stars, like you or me, that would be very atypical (and they might reconsider their definition of typical, or at least reroll).
So yes, there really is a dualism element here, as you put it: we’re positing some sort of extraneous random selection process, specifically one that inherently can only occur in the (hopefully far) future, and then assuming that has some relationship to our viewpoint. It simply doesn’t — it having such a relationship would necessarily break causality. The concept of “a typical human randomly selected out of all humans who have ever or will ever live” currently just isn’t well defined, no matter how intuitive it might sound to a Frequentist. Later, the concept of “a typical human out of all humans that did ever live” will become well defined once we’re extinct, but assuming that you currently know anything about it now or that it could have any causal relationship to your viewpoint is false, because that would require precognition. If we get to go to the stars, you previously having existed will then be exactly as surprising as the existence of the point 0.1 nanometer to the right of the 0 on a meter ruler. Yes, it’s in some sense an atypical point. They exist. Currently we don’t know if we’re going to get to go to the stars, and your existence isn’t surprising now either.[1]
However, we are not participating in a “roll a lucky winner” competition held at the end of time (that we know of). Where you happen to find yourself standing has nothing to do with events in the far future. Happening to find yourself standing at a time before humans may, or may not, go to the stars tells you absolutely nothing about the future, including not about whether they will or not. Causality doesn’t work that way. Bayesianism is about the process of acquiring knowledge over time, so it is carefully set up to account for causality: we have observations about the past, we can only attempt to make predictions about the future. Frequentism isn’t, and stuff that actually makes no causal sense often seems quite intuitive if you use Frequentism.
But that’s not how I’m thinking of it in the first place—I’m not positing any random selection process. I just don’t see an immediately obvious flaw here:
by definition, “I am in the first 10% of people” is false for most people
so I should expect it to be false for me, absent sufficient evidence against
And I still don’t quite understand your response to this formulation of the argument. I think you’re saying ‘people who have ever lived and will ever live’ is obviously the wrong reference class, but your arguments mostly target beliefs that I don’t hold (and that I don’t think I am implicitly assuming).
I don’t think I really get what the objection is?
The way I think about it is (ignoring the meta-anthropic thing) is that if for some reason every human who has ever lived or will live said aloud “I am in the final 95% of humans to be born”, then trivially 95% of them would be correct. You are a human, if you say this aloud, there is a 95% chance you are correct, therefore doom.
I understand objections with regard to whether this is the correct reference class, but my understanding is that you think the above logic does not make sense. What am I missing?
Sorry about the double reply, and it’s been a while since I thought seriously about these topics, so I may well be making a silly mistake here, but --
There’s a shop that uses a sequential ticketing system for queueing: each customer takes a numbered ticket when they enter, starting with ticket #1 for the first customer of the day. When I enter the shop, I know that it has been open for a couple of hours, but I have absolutely no idea when it closes (or even whether its ‘day’ is a mere 24 hours). I take my ticket and see that it’s #20. I have also noticed that the customer flow seems to be increasing more than linearly, such that if the shop is open for another hour there will probably be another 20 customers, and if it’s open for a few more hours there will be hundreds. Should I update towards the shop closing soon, on the grounds that otherwise my ticket number is atypically low? If so, wtf, and if not, what are the key differences between this and the doomsday argument?
I like the analogy. Here’s a simplified version where the ticket number is good evidence that the shop will close sooner rather than later.
There are two types of shop in Glimmer. Half of them are 24⁄7 shops that stay open until they go out of business. Half of them are 9-5 shops that open at 9am and close at 5pm.
All shops in Glimmer use a numbered ticket system that starts at #1 for the first customer after they open, and resets when the shop closes.
I walk into a shop in Glimmer at random and get a ticket.
If the ticket number is #20 then I update towards the shop being a 9-5 shop, on the grounds that otherwise my ticket number is atypically low. If the ticket number is #43,242 then I update towards the shop being a 24⁄7 shop.
The argument also works with customer flow evidence:
Like Glimmer, there are two types of shop in Silktown. Half of them are 24⁄7 shops that stay open until they go out of business. Half of them are 9-5 shops that open at 9am and close at 5pm.
All shops in Silktown experience increasing customer flow over time, starting with a few customers an hour, rising over time, and capping at hundreds of customers an hour after about ten hours of opening.
I walk into a shop in Silktown and observe the customer flow.
If the customer flow is low then I update towards the shop being a 9-5 shop, on the grounds that otherwise there will most likely be hundreds of customers an hour. If the customer flow is high then I update towards it being a 24⁄7 shop.
Reading through your hypothetical, I notice that it has both customer flow evidence and ticket number evidence. It’s important here not to double-update. If I already know that customer flow is surprisingly low then I can’t update again based on my ticket number being surprisingly low. Also your hypothetical doesn’t have strong prior knowledge like Silktown and Glimmer, which makes the update more complicated and weaker.
In this case, all those customers were already alive when the shop opened (I assume), so the observation does suggest that, if this process is in fact going to continue for several more hours with the store getting more and more crowded, then there might well be be some mechanism that applies to most customers that causes them to choose to arrive late, but somehow doesn’t apply to you. For example, maybe they do know when the store closes, and that the store’s chili gets stronger the longer it’s cooked, and they all like very strong chili.
The causality here is different, because you can reasonably assume that the other customers got up in the morning, thought about “When should I go to Fred’s Chili Shop?” and it seems a lot of them picked “not long before it closes”. But you are implicitly assuming that you already know this process is in fact going to continue. So it’s rather as if you asked Fred, and he told you yeah, there’s always a big rush at the end of the day, few people get here as early as you. At that point the causal paradox has just gone away: you actually do have solid grounds for making a prediction about what’s going to happen later in the day — Fred told you, and he should know.
But if you know for a fact that all the customers are only 10 minutes old (including you) so decided to come here less than 10 minutes ago, then the only reasonable assumption is that there’s a very fast population explosion going on, and you have absolutely no idea how much longer this is going to last, or how soon Fred will run out of chili and close the shop. In that situation, your predictability into the future is just short, and you just don’t know what’s going to happen after that — and clearly neither does Fred, so you can’t just ask him.
I didn’t mean to imply certainty, just uncertain expectation based on observation. Maybe I asked Fred, or the other customers, but I didn’t receive any information about ‘the end of the day’—only confirmation of the trend so far.
(I’m not trying to be difficult for the sake of it, by the way! I just want to think these things through carefully and genuinely understand what you’re saying, which requires pedantry sometimes.)
edit in response to your edit:
I think I’m not quite understanding the distinction here. Why is there an important difference between “this trend is based on mechanisms of which I’m ignorant, such as the other customers’ work hours or their expectations about chili quality over time” and “this trend is based on different mechanisms of which I’m also ignorant, i.e. birth rates and chili inventory”?
Hmmm… Good question. Let’s do the Bayesian thing.
I think it’s because of our priors. In the normal city case, we already know a lot about human behavior, we have built up very strong priors that constrain the hypothesis space pretty hard. The hotter-chili hypothesis I came up with seems plausible, there are others, but the space of them is rather tightly constrained. So we can do forward modelling fairly well. Whereas in the Doomsday Argument case, or my artificial analogy to it involving 10 minute lifespans and something very weird happening, our current sample size for “How many sapient species survive their technological adolescence?” or “What happens later in the day in cities of sapient mayflies?” is zero. In dynamical systems terms, the rest of the day is a lot more Lyapunov times away in this case. From our point of view, a technological adolescence looks like a dangerous process, but making predictions is hard, especially about the future of a very complex very non-linear system with 8.3 billion humans and an exponentially rising amount of AI in it. The computational load of doing accurate modelling is simply impractical, so our future even 5–10 years out looks like a Singularity to our current computational abilities. So the constraints on our hypothesis distribution are weak, and we end up relying mostly on our arbitrary choice of initial priors. We’re still at the “I really just don’t know” point in the Bayesian process on this one. That’s why people’s P(DOOM)s vary so much — nobody actually knows, they just have different initial default priors, basically depending on temperament. Our future is still a Rorschach inkblot. Which is not a comfortable time to be living in.
Fair point, and I do find anthropic problems puzzling. What I find nonsensical are framings of those problems that treat indexical information as evidence—e.g. in a scenario where person X (i.e. me) exists on both hypothesis A and hypothesis B, but hypothesis A implies that many more other people exist, I’m supposed to favour hypothesis B because I happen to be person X and that would be very unlikely given hypothesis A.
The Doomsday Argument, translated into the Bayesian framework, is actually:
Suppose everyone who has lived since the invention of Science Fiction said “I don’t know if we’re all going to die soon, so I’m one of the later humans ever (let’s call that probability X%) or if we’re going to spread to the stars and I’m one of the very first humans ever by some extremely large factor Y (with a 100-X% chance).
100-X% divided by an extremely large factor Y is obviously an extremely small number, approximately zero, therefore X is almost certainly equal to 100.
Notice that step 2 here is completely specious, and no one thinking in a Bayesian framework would entertain it for a moment. It’s confused thinking that sounds plausible if you think like a Frequentist and get careless with causality.
I don’t think you need completely specious reasoning to get to a kind of puzzling position, though. For us to be in the first <relatively small n>% of people, we don’t need humanity to spread to the stars—just to survive for a while longer without a population crash. And I think we do need some principled reason to be able to say “yes, ‘I am in the first <relatively small n>% of people’ is going to be false for the majority of people, but that’s irrelevant to whether it’s true or false for me”.
Humans have a very understandable tendency, when they see what appears to be a low-probability event occurring, to get suspicious and wonder if some opponent has maneuvered things somehow to finagle a high probability of an apparently-low-probability event. We pay attention to what look like flukes, and are dubious about them. But if you can safely dismiss the possibility that before you were incarnated your soul was carried back to this time by an evil time-traveling mastermind, then the only remaining possibility is just “viewed from an achronous perspective, a low probability event has occurred — just like they always do right at the start of anything”. Sometimes they do. Especially if there were a vast number of other equally low probability events that could have occurred. Rolling a 1 on a million-sided die is kind of neat, though not actually any more improbable than rolling 314,159, and it’s not actually suspicious unless it advantages someone else who had their hands on the die. But if you watch a clock for long enough, sooner-or-later it will read 00:00:00.
What’s the ‘low probability event’? I think this is the kind of framing I was disagreeing with in my original reply; there seems to be an implicit dualism here. So your reply isn’t, from my perspective, addressing my reasons for finding anthropic reasoning difficult to completely dismiss.
“viewed from an achronous perspective, a low probability event has occurred” means: an event such that, if I were in a position to do a random sampling over all humans who ever live – something which can only be done once we’re extinct – would then have a low probability of occurring in that random sample: such as (temporarily assuming that humans do get to go to the stars before becoming extinct) randomly selecting, out of all humans ever, one of the tiny 1-in-10∼10 minority of humans who lived before humans went to the stars.
So, if an alien archeologist from after humans go extinct wanted to write “a day in the life of a typical human” and selected a ‘typical’ human randomly, and then got one from before humans got to go to the stars, like you or me, that would be very atypical (and they might reconsider their definition of typical, or at least reroll).
So yes, there really is a dualism element here, as you put it: we’re positing some sort of extraneous random selection process, specifically one that inherently can only occur in the (hopefully far) future, and then assuming that has some relationship to our viewpoint. It simply doesn’t — it having such a relationship would necessarily break causality. The concept of “a typical human randomly selected out of all humans who have ever or will ever live” currently just isn’t well defined, no matter how intuitive it might sound to a Frequentist. Later, the concept of “a typical human out of all humans that did ever live” will become well defined once we’re extinct, but assuming that you currently know anything about it now or that it could have any causal relationship to your viewpoint is false, because that would require precognition. If we get to go to the stars, you previously having existed will then be exactly as surprising as the existence of the point 0.1 nanometer to the right of the 0 on a meter ruler. Yes, it’s in some sense an atypical point. They exist. Currently we don’t know if we’re going to get to go to the stars, and your existence isn’t surprising now either.[1]
However, we are not participating in a “roll a lucky winner” competition held at the end of time (that we know of). Where you happen to find yourself standing has nothing to do with events in the far future. Happening to find yourself standing at a time before humans may, or may not, go to the stars tells you absolutely nothing about the future, including not about whether they will or not. Causality doesn’t work that way. Bayesianism is about the process of acquiring knowledge over time, so it is carefully set up to account for causality: we have observations about the past, we can only attempt to make predictions about the future. Frequentism isn’t, and stuff that actually makes no causal sense often seems quite intuitive if you use Frequentism.
At least, not on the basis of what little information I’m aware of about you!
But that’s not how I’m thinking of it in the first place—I’m not positing any random selection process. I just don’t see an immediately obvious flaw here:
by definition, “I am in the first 10% of people” is false for most people
so I should expect it to be false for me, absent sufficient evidence against
And I still don’t quite understand your response to this formulation of the argument. I think you’re saying ‘people who have ever lived and will ever live’ is obviously the wrong reference class, but your arguments mostly target beliefs that I don’t hold (and that I don’t think I am implicitly assuming).