Imagine all humans ever, ordered by date of their birth.
All humans of the timeline I actually find myself a part of, or all humans that could have occurred, or almost occurred, within that timeline? Unless you refuse to grant the sense of counterfactual reasoning in general, there’s no reason within a reductionist frame to dismiss counterfactual [but physically plausible and very nearly actual] values of “all humans ever”.
Even if you consider the value of “in which 10B interval will I be born?” to be some kind of particularly fixed absolute about my existence, behind the veil of Rawls, before I am born, I don’t actually know it. I can imagine the prior I would have about “in which 10B interval will I be born?” behind the veil of Rawls, and notice whether my observed experience seems strange in the face of that prior.
The Doomsday argument is not about some alternative history which we can imagine, where the past was different. It’s about our history and its projection to the future. Facts of the history are given and not up to debate.
Consider an experiment where a coin is put Tails. Not tossed—simply always put Tails.
We say that the size sample space of such an experiment consists of one outcome: Tails. Even though we can imagine a different experiment with alternative rules where the coin is tossed or always put Heads.
It seems like maybe you think I think the Doomsday Argument is about drawing inferences about the past, or something? The Doomsday Argument isn’t [necessarily] about drawing inferences about what happened in the past. It’s about using factors that aren’t particularly in the past, present, or future, to constrain our expectations of what will happen in the future, and our model of reality outside time.
It is [...] meaningless to ask about the quantity of information conveyed by the sequence 0 1 1 0 about the sequence 1 1 0 0.
But if we take a perfectly specific table of random numbers of the sort commonly used in statistical practice, and for each of its digits we write the unit’s digit of the units of its square according to the scheme
0 1 2 3 4 5 6 7 8 9
0 1 4 9 6 5 6 9 4 1
the new table will contain approximately
( log_2 10 - (8/10) ) * n
bits of information about the initial sequence (where n is the number of digits in the tables).†
I can see a single coin that was placed Tails, and I won’t be able to infer anything beyond “that coin was placed Tails”.
But if I see a hundred coins placed Tails, lined up in a row, I can validly start asking questions about “why?”.
--
†Kolmogorov’s illustration doesn’t exactly map on to mine. I would note a couple things to clarify the exact analogy by which I’m using this illustration of Kolmogorov’s to corroborate my point.
First, I think Kolmogorov would have agreed that, while it may be meaningless to talk about the quantity of information conveyed by the sequence1 0 1 0about the sequence1 1 0 0, it is not obviously meaningless to talk about the quantity of information conveyed by the sequence1 1 1 0 1 0 1 0 1 0 1 0 1about the sequence0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1, since both obviously have internal structure, and there’s a simple decompression algorithm that you can use to get from the former to the latter. Something similar seems true of a sequence of 100 coins facing Tails-up, and the simple decompression algorithm “for each of 100 coins, flip each to face Tails-up”—that is, they can communicate information about each other. Contrast with the single coin facing Tails-up, which is more like the sequence1 1 0 0in the [potential] presence of the sequence1 0 1 0, in that it seems uninterestingly random.
Secondly, I think Kolmogorov’s information theory is a strict improvement on Shannon’s but weak in points. One of these weak points is that Kolmogorov doesn’t provide any really practical mechanism for narrowing down the space of counterfactual minimal decompression algorithms [“programs”] which generated an observed sequence, even though he [I think rightly] uses the principle that the simplest algorithm can be discovered, as the basis for his measure of information. I think if you can say how much information a sequence communicates about another sequence after knowing the [clear-winner shortest] decompression scheme, you should be able to determine the decompression scheme and the seed data just from seeing the output sequence and assuming minimal information. This is what anthropics arguments [in part] aim to do, and this is what I’m trying to get at with the “100 coins all facing Tails-up” thought experiment.
It seems like maybe you think I think the Doomsday Argument is about drawing inferences about the past, or something? The Doomsday Argument isn’t [necessarily] about drawing inferences about what happened in the past. It’s about using factors that aren’t particularly in the past, present, or future, to constrain our expectations of what will happen in the future, and our model of reality outside time.
My response to that is that this would be the case if we didn’t have more information, but we do, and thus we can update away from the doomsday argument, because we have way more evidence than the doomsday argument assumes.
It’s an underconstrained model because of that, and a lot of anthropic reasoning’s weird results fundamentally come from intentionally ignoring evidence that could be true in a different world, but is not the world we live in, and we have more information on constraints that changes the probabilities of the doomsday argument drastically.
To be clear, I think the main flaw of a lot of anthropics in practice is ignoring other sources of evidence, and I suspect a lot of the problem really does boil down to conservation of expected evidence violations plus ignoring other, much larger sources of evidence.
This is why the most general versions of the simulation hypothesis/Mathematical Universe Hypothesis/computational functionalism hypothesis for consciousness are not properly speaking valid Bayesian hypotheses, because every outcome could count as confirmation of the theory, so it is utterly useless for prediction.
It’s a great universal ontology, but it’s predictive power is precisely 0.
More positively speaking, the hypotheses are just the assumed things they have for Bayesians, similarly to how logical omniscience is just assumed for Bayesians, and thus it’s great to have a universal tool-kit, but that does come with the downside of having 0 ability to predict anything (because it contains everything).
All humans of the timeline I actually find myself a part of, or all humans that could have occurred, or almost occurred, within that timeline?
All humans that actually were and all humans that actually will. This is the framework of the Doomsday argument—it attempts to make a prediction about the actual number of humans in our actual reality not in some counterfactual world.
Unless you refuse to grant the sense of counterfactual reasoning in general, there’s no reason
Again, it’s not my choice. It’s how the argument was initially framed. I simply encorage that we stayed on topic instead of wandering sideways and talking about something else instead.
I don’t see how it’s relevant. Ordered sequence can have some mutual information with a random one. It doesn’t mean that the same mathematical model describes generation of both.
We can hardly establish the sense of anthropic reasoning if we can’t establish the sense of counterfactual reasoning.
A root confusion may be whether different pasts could have caused the same present, and hence whether I can have multiple simultaneous possible parents, in an “indexical-uncertainty” sense, in the same way that I can have multiple simultaneous possible future children.
The same standard physics theories that say it’s impossible to be certain about the future, also say it’s impossible to be certain about the past.
Indexical uncertainty about the past may not be true, but you can’t reject it without rejecting standard physics.
And if there is no indexical uncertainty and all counterfactuals are logical counterfactuals and/or in some sense illusory—well, we’re still left uncomfortably aware of our subjective inability to say exactly what the future and past are and why exactly they must be that way.
As soon as we’ve established the notion of probability experiment that approximates our knowledge about the physical process that we are talking about—we are done. This works exactly the same way whether you are not sure about the outcome of a coin toss, oddness or evenness of an unknown to you digit of pi, or whether you live on a tallest or the coldest mountain.
And if you find yourself unable to formally express some reasoning like that—this is a feature not a bug. It shows when your reasoning becomes incoherent.
A root confusion may be whether different pasts could have caused the same present, and hence whether I can have multiple simultaneous possible parents, in an “indexical-uncertainty” sense, in the same way that I can have multiple simultaneous possible future children.
I think our disagreement is that you believe that one always has multiple possible parents as some metaphysical fact about the universe, while I believe that the notion of possible parent is only appropriate for a person who is in a state of uncertainty about who their parents are. Does that sound right to you?
The same standard physics theories that say it’s impossible to be certain about the future, also say it’s impossible to be certain about the past.
Consider, a coin is about to be tossed. You are indifferent between two outcomes. Then the coin is tossed and shown to you and you reflect on it a second later. Technically you can’t be absolutely sure that you didn’t misremember the outcome. But you are much more confident than beforehand, to the point where we usually just approximate away whatever uncertainty is left for the sake of simplicity.
we’re still left uncomfortably aware of our subjective inability to say exactly what the future and past are and why exactly they must be that way
Until we learn what and why they are with a high level of confidence. Then we are much less uncomfortable about it.
And yes there is still a chance that all that we know is wrong, souls are real and are allocated to humans throughout history by a random process and therefore the assumptions of Doomsday Argument just so happened to be true. Conditionally on that Doomsday Inference is true. But to the best of our knowledge this is extremely unlikely, so we shouldn’t worry about it too much and should frame Doomsday Argument appropriately.
If you can’t generate your parents’ genomes and everything from memory, then yes, you are in a state of uncertainty about who they are, in the same qualitative way you are in a state of uncertainty about who your young children will grow up to be.
Ditto for the isomorphism between your epistemic state w.r.t. never-met grandparents vs your epistemic state w.r.t. not-yet-born children.
It may be helpful to distinguish the subjective future, which contains the outcomes of all not-yet-performed experiments [i.e. all evidence/info not yet known] from the physical future, which is simply a direction in physical time.
If you can’t generate your parents’ genomes and everything from memory, then yes, you are in a state of uncertainty about who they are, in the same qualitative way you are in a state of uncertainty about who your young children will grow up to be.
Here you seem to confuse “which person has quality X” with “what are all the other qualities that a person, who has quality X has”.
I’m quite confident about which people are my parents. I’m less confident about all the qualities that my parents have. The former is relevant to Doomsday argument, the latter is not.
And even if I had no idea about who my parents are I’d still be pretty confident that they were born in the last century not in 6th BC.
It may be helpful to distinguish the subjective future, which contains the outcomes of all not-yet-performed experiments [i.e. all evidence/info not yet known] from the physical future, which is simply a direction in physical time
All humans of the timeline I actually find myself a part of, or all humans that could have occurred, or almost occurred, within that timeline? Unless you refuse to grant the sense of counterfactual reasoning in general, there’s no reason within a reductionist frame to dismiss counterfactual [but physically plausible and very nearly actual] values of “all humans ever”.
Even if you consider the value of “in which 10B interval will I be born?” to be some kind of particularly fixed absolute about my existence, behind the veil of Rawls, before I am born, I don’t actually know it. I can imagine the prior I would have about “in which 10B interval will I be born?” behind the veil of Rawls, and notice whether my observed experience seems strange in the face of that prior.
It seems like maybe you think I think the Doomsday Argument is about drawing inferences about the past, or something? The Doomsday Argument isn’t [necessarily] about drawing inferences about what happened in the past. It’s about using factors that aren’t particularly in the past, present, or future, to constrain our expectations of what will happen in the future, and our model of reality outside time.
Like Kolmogorov said,
I can see a single coin that was placed Tails, and I won’t be able to infer anything beyond “that coin was placed Tails”.
But if I see a hundred coins placed Tails, lined up in a row, I can validly start asking questions about “why?”.
--
†Kolmogorov’s illustration doesn’t exactly map on to mine. I would note a couple things to clarify the exact analogy by which I’m using this illustration of Kolmogorov’s to corroborate my point.
First, I think Kolmogorov would have agreed that, while it may be meaningless to talk about the quantity of information conveyed by the sequence
1 0 1 0about the sequence1 1 0 0, it is not obviously meaningless to talk about the quantity of information conveyed by the sequence1 1 1 0 1 0 1 0 1 0 1 0 1about the sequence0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1, since both obviously have internal structure, and there’s a simple decompression algorithm that you can use to get from the former to the latter. Something similar seems true of a sequence of 100 coins facing Tails-up, and the simple decompression algorithm “for each of 100 coins, flip each to face Tails-up”—that is, they can communicate information about each other. Contrast with the single coin facing Tails-up, which is more like the sequence1 1 0 0in the [potential] presence of the sequence1 0 1 0, in that it seems uninterestingly random.Secondly, I think Kolmogorov’s information theory is a strict improvement on Shannon’s but weak in points. One of these weak points is that Kolmogorov doesn’t provide any really practical mechanism for narrowing down the space of counterfactual minimal decompression algorithms [“programs”] which generated an observed sequence, even though he [I think rightly] uses the principle that the simplest algorithm can be discovered, as the basis for his measure of information. I think if you can say how much information a sequence communicates about another sequence after knowing the [clear-winner shortest] decompression scheme, you should be able to determine the decompression scheme and the seed data just from seeing the output sequence and assuming minimal information. This is what anthropics arguments [in part] aim to do, and this is what I’m trying to get at with the “100 coins all facing Tails-up” thought experiment.
My response to that is that this would be the case if we didn’t have more information, but we do, and thus we can update away from the doomsday argument, because we have way more evidence than the doomsday argument assumes.
It’s an underconstrained model because of that, and a lot of anthropic reasoning’s weird results fundamentally come from intentionally ignoring evidence that could be true in a different world, but is not the world we live in, and we have more information on constraints that changes the probabilities of the doomsday argument drastically.
I agree with this!
“Update away from” does not imply “discard”.
To be clear, I think the main flaw of a lot of anthropics in practice is ignoring other sources of evidence, and I suspect a lot of the problem really does boil down to conservation of expected evidence violations plus ignoring other, much larger sources of evidence.
On this:
This is why the most general versions of the simulation hypothesis/Mathematical Universe Hypothesis/computational functionalism hypothesis for consciousness are not properly speaking valid Bayesian hypotheses, because every outcome could count as confirmation of the theory, so it is utterly useless for prediction.
It’s a great universal ontology, but it’s predictive power is precisely 0.
More positively speaking, the hypotheses are just the assumed things they have for Bayesians, similarly to how logical omniscience is just assumed for Bayesians, and thus it’s great to have a universal tool-kit, but that does come with the downside of having 0 ability to predict anything (because it contains everything).
All humans that actually were and all humans that actually will. This is the framework of the Doomsday argument—it attempts to make a prediction about the actual number of humans in our actual reality not in some counterfactual world.
Again, it’s not my choice. It’s how the argument was initially framed. I simply encorage that we stayed on topic instead of wandering sideways and talking about something else instead.
I don’t see how it’s relevant. Ordered sequence can have some mutual information with a random one. It doesn’t mean that the same mathematical model describes generation of both.
We can hardly establish the sense of anthropic reasoning if we can’t establish the sense of counterfactual reasoning.
A root confusion may be whether different pasts could have caused the same present, and hence whether I can have multiple simultaneous possible parents, in an “indexical-uncertainty” sense, in the same way that I can have multiple simultaneous possible future children.
The same standard physics theories that say it’s impossible to be certain about the future, also say it’s impossible to be certain about the past.
Indexical uncertainty about the past may not be true, but you can’t reject it without rejecting standard physics.
And if there is no indexical uncertainty and all counterfactuals are logical counterfactuals and/or in some sense illusory—well, we’re still left uncomfortably aware of our subjective inability to say exactly what the future and past are and why exactly they must be that way.
As soon as we’ve established the notion of probability experiment that approximates our knowledge about the physical process that we are talking about—we are done. This works exactly the same way whether you are not sure about the outcome of a coin toss, oddness or evenness of an unknown to you digit of pi, or whether you live on a tallest or the coldest mountain.
And if you find yourself unable to formally express some reasoning like that—this is a feature not a bug. It shows when your reasoning becomes incoherent.
I think our disagreement is that you believe that one always has multiple possible parents as some metaphysical fact about the universe, while I believe that the notion of possible parent is only appropriate for a person who is in a state of uncertainty about who their parents are. Does that sound right to you?
This is really beside the point.
Consider, a coin is about to be tossed. You are indifferent between two outcomes. Then the coin is tossed and shown to you and you reflect on it a second later. Technically you can’t be absolutely sure that you didn’t misremember the outcome. But you are much more confident than beforehand, to the point where we usually just approximate away whatever uncertainty is left for the sake of simplicity.
Until we learn what and why they are with a high level of confidence. Then we are much less uncomfortable about it.
And yes there is still a chance that all that we know is wrong, souls are real and are allocated to humans throughout history by a random process and therefore the assumptions of Doomsday Argument just so happened to be true. Conditionally on that Doomsday Inference is true. But to the best of our knowledge this is extremely unlikely, so we shouldn’t worry about it too much and should frame Doomsday Argument appropriately.
If you can’t generate your parents’ genomes and everything from memory, then yes, you are in a state of uncertainty about who they are, in the same qualitative way you are in a state of uncertainty about who your young children will grow up to be.
Ditto for the isomorphism between your epistemic state w.r.t. never-met grandparents vs your epistemic state w.r.t. not-yet-born children.
It may be helpful to distinguish the subjective future, which contains the outcomes of all not-yet-performed experiments [i.e. all evidence/info not yet known] from the physical future, which is simply a direction in physical time.
Here you seem to confuse “which person has quality X” with “what are all the other qualities that a person, who has quality X has”.
I’m quite confident about which people are my parents. I’m less confident about all the qualities that my parents have. The former is relevant to Doomsday argument, the latter is not.
And even if I had no idea about who my parents are I’d still be pretty confident that they were born in the last century not in 6th BC.
Sure. But I don’t see how it’s relevant here.