TDT-God can only intervene mathematically, not physically.
The power of TDT-God is to fix the answer to the mathematical question “If you were Parfit’s hitchhiker, and you prayed to the TDT-God, would you pay?” That answer must remain the same at all times, and it determines both whether you’re picked up and whether you pay. (Assuming you’re the kind of person who makes decisions by praying to the TDT-God.)
The part about praying makes it sound like the TDT-God is supposed to answer the question after getting the prayer. I guess you mean more like you pray to get his already-determined answer.
I wanted to bring out the fact that TDT is about “logical uncertainty”.
To choose according to TDT is to “choose as though controlling the logical output of the abstract computation you implement”. What is the abstract computation you implement? Whatever it is, it’s not something you can change (unless “you” are really Sam Beckett, in which case you override whatever was there previously) and the output follows by mathematical necessity from the input.
Therefore, you are choosing as though you are controlling the truth values of mathematical statements of the form “Given that this is my initial state, I ultimately do that”. (Therefore, TDT gives the correct decisions for an imaginary being (“TDT-God” if you will) who can determine which mathematical statements are true.)
No. When you are acting as a human in the physical universe, you are not “making correct decisions for an imaginary being who can determine what will happen according to the laws of physics”. Obeying the laws of physics is not a normative consideration, you are not optimizing your actions with a goal of not breaking out of Nature. According to the laws of physics, you always act according to the laws of physics, however you actually decide (according to the laws of physics).
The last paragraph feels off, although you are not saying anything explicitly/obviously wrong, so your intended meaning could be correct. Do you see what I was trying to say in my comment?
Obeying the laws of physics is not a normative consideration, you are not optimizing your actions with a goal of not breaking out of Nature. According to the laws of physics, you always act according to the laws of physics, however you actually decide (according to the laws of physics).
Yes, that all sounds right. That’s why I was puzzled—I can’t see where the tension is between that and what I’m saying.
To clarify: When I refer to “Given that this is my initial state, I ultimately do that” as a mathematical statement, the statement I’m referring to is really: “Given that this is my initial state, and given that these are the laws of physics, I will ultimately do that.” I never had in mind any idea of “trying not to break out of Nature”.
The idea of TDT-God arose as the answer to the question “for whom is it trivially true that TDT makes the correct decisions”. (Just as it’s absolutely, utterly trivial from the definitions that CDT is correct for Sam Beckett and EDT is correct for the spectator.)
(Just as it’s absolutely, utterly trivial from the definitions that CDT is correct for Sam Beckett and EDT is correct for the spectator.)
CDT is not correct in game-theoretic situations where other agents can know things about you, with the effect of its incorrectness gradual. See Ch. 7 of TDT paper:
Modeling agents as influenced to some greater or lesser degree by “the sort of decision you make, being the person that you are”, realistically describes present-day human existence.
The error could be tiny, but it could even be present where no other agents are around. On a bet with finely tuned probabilities and utilities, you’ll rule wrong if you use CDT.
It’s not at all clear in what sense one can be correct about “hoping for a particular outcome”. The problem statement to which EDT is supposed to be an answer seems to be nonsense.
Let me explain about Sam Beckett (which admittedly I should have done at the outset): In each episode of Quantum Leap, Sam’s consciousness teleports (“leaps”) into the brain of some random person, and Sam then has to Do Something Important (e.g. Stop Something Bad From Happening). No-one else expects or notices the leap.
CDT is not correct in game-theoretic situations where other agents can know things about you, with the effect of its incorrectness gradual.
Assuming for argument’s sake that Sam’s “leap” was not foreseen by “Omega-like” beings, or anyone else, other agents can only be influenced by the kind of person who was there prior to the leap, not the kind of person Sam is.
(Note: I’m also assuming for argument’s sake that after making that one decision, Sam “leaps out” leaving the original decision-maker in his place.)
I’m not sure whether I’ve got this exactly right yet, but whatever the defects of the wording, surely there’s some problem statement for which CDT is trivially correct.
It’s not at all clear in what sense one can be correct about “hoping for a particular outcome”.
It’s simply a question of: which of these possibilities, if you observed them, would maximize your expected final utility. There is a ‘fact of the matter’ about this, regardless of whether the spectator’s judgements make any difference.
The problem statement to which EDT is supposed to be an answer seems to be nonsense.
The trouble is that they’re all different kinds of nonsense. Sam doesn’t and couldn’t exist. Spectators don’t exist and make no difference if they do, and TDT-God doesn’t and couldn’t exist. (I don’t mean to denigrate TDT—I think it gives better answers than CDT or EDT. In some weird sense, TDT-God is a better approximation to “the decision-maker themselves” than Sam Beckett.)
It’s not at all clear in what sense one can be correct about “hoping for a particular outcome”.
It’s simply a question of: which of these possibilities, if you observed them, would maximize your expected final utility. There is a ‘fact of the matter’ about this, regardless of whether the spectator’s judgements make any difference.
If you take an updateless look at the situation, observations never influence utility. You can consider relevant “observational events” that contain the worlds that you expect being able to influence in the future given what you’ve observed, and then different observational events would have different utility. But possible reasons to actually compare these numbers are nonobvious (e.g. you might be able to control your observations, but then it’s not necessarily a good way to parse the consequences of that control decision), so you could just as well treat them as unrelated. Also, these are heuristic rules for simplifying the updateless calculation (by moving a constant term outside maximization operator), and given that you are stipulated to be unable to influence anything, I wonder if these should just all be empty, giving you trivially zero utility, both for all observations and a priori.
Yeah, but that presupposes that God is just another being ‘within time’ who answers prayers by ‘changing things that already exist’. This is theologically unsophisticated. God already knew what questions you were going to ask, or might have asked in each of the possible branches of the game. :-)
(Disclaimer: I am not a theist. Metadisclaimer: But I do like TDT, though!)
TDT-God can only intervene mathematically, not physically.
The power of TDT-God is to fix the answer to the mathematical question “If you were Parfit’s hitchhiker, and you prayed to the TDT-God, would you pay?” That answer must remain the same at all times, and it determines both whether you’re picked up and whether you pay. (Assuming you’re the kind of person who makes decisions by praying to the TDT-God.)
The part about praying makes it sound like the TDT-God is supposed to answer the question after getting the prayer. I guess you mean more like you pray to get his already-determined answer.
I wanted to bring out the fact that TDT is about “logical uncertainty”.
To choose according to TDT is to “choose as though controlling the logical output of the abstract computation you implement”. What is the abstract computation you implement? Whatever it is, it’s not something you can change (unless “you” are really Sam Beckett, in which case you override whatever was there previously) and the output follows by mathematical necessity from the input.
Therefore, you are choosing as though you are controlling the truth values of mathematical statements of the form “Given that this is my initial state, I ultimately do that”. (Therefore, TDT gives the correct decisions for an imaginary being (“TDT-God” if you will) who can determine which mathematical statements are true.)
No. When you are acting as a human in the physical universe, you are not “making correct decisions for an imaginary being who can determine what will happen according to the laws of physics”. Obeying the laws of physics is not a normative consideration, you are not optimizing your actions with a goal of not breaking out of Nature. According to the laws of physics, you always act according to the laws of physics, however you actually decide (according to the laws of physics).
Where do you think my previous comment begins to ‘go wrong’?
The last paragraph feels off, although you are not saying anything explicitly/obviously wrong, so your intended meaning could be correct. Do you see what I was trying to say in my comment?
Yes, that all sounds right. That’s why I was puzzled—I can’t see where the tension is between that and what I’m saying.
To clarify: When I refer to “Given that this is my initial state, I ultimately do that” as a mathematical statement, the statement I’m referring to is really: “Given that this is my initial state, and given that these are the laws of physics, I will ultimately do that.” I never had in mind any idea of “trying not to break out of Nature”.
The idea of TDT-God arose as the answer to the question “for whom is it trivially true that TDT makes the correct decisions”. (Just as it’s absolutely, utterly trivial from the definitions that CDT is correct for Sam Beckett and EDT is correct for the spectator.)
CDT is not correct in game-theoretic situations where other agents can know things about you, with the effect of its incorrectness gradual. See Ch. 7 of TDT paper:
The error could be tiny, but it could even be present where no other agents are around. On a bet with finely tuned probabilities and utilities, you’ll rule wrong if you use CDT.
It’s not at all clear in what sense one can be correct about “hoping for a particular outcome”. The problem statement to which EDT is supposed to be an answer seems to be nonsense.
Let me explain about Sam Beckett (which admittedly I should have done at the outset): In each episode of Quantum Leap, Sam’s consciousness teleports (“leaps”) into the brain of some random person, and Sam then has to Do Something Important (e.g. Stop Something Bad From Happening). No-one else expects or notices the leap.
Assuming for argument’s sake that Sam’s “leap” was not foreseen by “Omega-like” beings, or anyone else, other agents can only be influenced by the kind of person who was there prior to the leap, not the kind of person Sam is.
(Note: I’m also assuming for argument’s sake that after making that one decision, Sam “leaps out” leaving the original decision-maker in his place.)
I’m not sure whether I’ve got this exactly right yet, but whatever the defects of the wording, surely there’s some problem statement for which CDT is trivially correct.
It’s simply a question of: which of these possibilities, if you observed them, would maximize your expected final utility. There is a ‘fact of the matter’ about this, regardless of whether the spectator’s judgements make any difference.
The trouble is that they’re all different kinds of nonsense. Sam doesn’t and couldn’t exist. Spectators don’t exist and make no difference if they do, and TDT-God doesn’t and couldn’t exist. (I don’t mean to denigrate TDT—I think it gives better answers than CDT or EDT. In some weird sense, TDT-God is a better approximation to “the decision-maker themselves” than Sam Beckett.)
If you take an updateless look at the situation, observations never influence utility. You can consider relevant “observational events” that contain the worlds that you expect being able to influence in the future given what you’ve observed, and then different observational events would have different utility. But possible reasons to actually compare these numbers are nonobvious (e.g. you might be able to control your observations, but then it’s not necessarily a good way to parse the consequences of that control decision), so you could just as well treat them as unrelated. Also, these are heuristic rules for simplifying the updateless calculation (by moving a constant term outside maximization operator), and given that you are stipulated to be unable to influence anything, I wonder if these should just all be empty, giving you trivially zero utility, both for all observations and a priori.
Yeah, but that presupposes that God is just another being ‘within time’ who answers prayers by ‘changing things that already exist’. This is theologically unsophisticated. God already knew what questions you were going to ask, or might have asked in each of the possible branches of the game. :-)
(Disclaimer: I am not a theist. Metadisclaimer: But I do like TDT, though!)
There’s a reason for it being called Timeless Decision Theory. Thinking about it in timeful terms is going to get confusing.