Omega (who experience has shown is always truthful) presents the usual two boxes A and B and announces the following. “Before you entered the room, I ran a simulation of this problem as presented to an agent running TDT.
There seems to be a contradiction here. If Omega siad this to me I would either have to believe omega just presented evidence of being untruthful some of the time.
If Omega simulated the problem at hand then in said simulation Omega must have siad: “Before you entered the room, I ran a simulation of this problem as presented to an agent running TDT.” In the first simulation the statement is a lie.
Problem 2 has a similar problem.
It is not obvious that the problem can be reformulated to keep Omega constantly truthfully and still have CDT or EDT come out ahead of TDT.
Your difficulty seems to be with the parenthesis “(who experience has shown is always truthful)”. The relevant experience here is going to be derived from real-world subjects who have been in Omega problems, exactly as is assumed for the standard Newcomb problem. It’s not obvious that Omega always tells the truth to its simulations; no-one in the outside world has experience of that.
However you can construe the problem so that Omega doesn’t have to lie, even to sims. Omega could always prefix its description of the problem with a little disclaimer “You may be one of my simulations. But if not, then...”.
Or Omega could simulate a TDT agent making decisions as if it had just been given the problem description verbally by Omega, without Omega actually doing so. (Whether that’s possible or not depends a bit on the simulation).
I do not know if Omega can say that truthfully because I do not know weather the self referential equation representing the problem has a solution.
The problems set out by the OP assumes there is a solution and a particular answer but with out writing out the equation and plugging in his solution to show the solution actually works.
It may or may not be proven that TDT settles on answers to questions involving TDT. If TDT doesn’t get an answer, then TDT can’t get an answer.
Presumably it is true that TDT settles but if it isn’t proven, it may not be true; or it could be that the proof (i.e. a formalization of TDT) will provide insight that is currently lacking (such as cutting off after a certain level of resource use; can Omega emulate how many resources the current TDT agent will use? Can the TDT agent commit to using a random number of resources? Do true random-number generators exist? These problems might all be inextricable. Or they might not. I, for one, don’t know.)
Having several formalizations is 90% of a proof, not 100% of a proof. Turn the formalization into a computer program AND either prove that it halts or run this simulation on it in finite time.
I believe that it’s true that TDT will get an answer and hence Omega will get an answer, but WHY this is true relies on facts about TDT that I don’t know (specifically facts about its implementation; maybe facts about differential topology that game-theoretic equilibrium results rely on.)
The linked posts have proofs that the programs halt and return the correct answer. Do you understand the proofs, or could you point out the areas that need more work? Many commenters seemed to understand them...
I do not understand the proofs, primarily because I have not put time in to trying to understand them.
I may have become somewhat defensive in these posts (or withdrawn I guess?) but looking back my original point was really to point out that, naively, asking whether the problem is well-defined is a reasonable question.
The questions in the OP set off alarm bells for me of “this type of question might be a badly-defined type of question” so asking whether these decisions are in the “halting domain” (is there an actual term for that?) of TDT seems like a reasonable question to ask before putting too much thought into other issues.
I believe the answer to be that yes these questions are in the “halting domain” of TDT, but I also believe that understanding what that is and why these questions are legitimate and the proofs that TDT halts will be central to any resolution of these problems.
What I’m really trying to say here is that it makes sense to ask these questions, but I don’t understand why, so I think Davorak’s question was reasonable, and your answer didn’t feel complete to me. Looking back, I don’t think I’ve contributed much to this conversation. Sorry!
There seems to be a contradiction here. If Omega siad this to me I would either have to believe omega just presented evidence of being untruthful some of the time.
If Omega simulated the problem at hand then in said simulation Omega must have siad: “Before you entered the room, I ran a simulation of this problem as presented to an agent running TDT.” In the first simulation the statement is a lie.
Problem 2 has a similar problem.
It is not obvious that the problem can be reformulated to keep Omega constantly truthfully and still have CDT or EDT come out ahead of TDT.
Your difficulty seems to be with the parenthesis “(who experience has shown is always truthful)”. The relevant experience here is going to be derived from real-world subjects who have been in Omega problems, exactly as is assumed for the standard Newcomb problem. It’s not obvious that Omega always tells the truth to its simulations; no-one in the outside world has experience of that.
However you can construe the problem so that Omega doesn’t have to lie, even to sims. Omega could always prefix its description of the problem with a little disclaimer “You may be one of my simulations. But if not, then...”.
Or Omega could simulate a TDT agent making decisions as if it had just been given the problem description verbally by Omega, without Omega actually doing so. (Whether that’s possible or not depends a bit on the simulation).
Omega could truthfully say “the contents of the boxes are exactly as if I’d presented this problem to an agent running TDT”.
I do not know if Omega can say that truthfully because I do not know weather the self referential equation representing the problem has a solution.
The problems set out by the OP assumes there is a solution and a particular answer but with out writing out the equation and plugging in his solution to show the solution actually works.
There is a solution because Omega can get an answer by simulating TDT, or am I missing something?
It may or may not be proven that TDT settles on answers to questions involving TDT. If TDT doesn’t get an answer, then TDT can’t get an answer.
Presumably it is true that TDT settles but if it isn’t proven, it may not be true; or it could be that the proof (i.e. a formalization of TDT) will provide insight that is currently lacking (such as cutting off after a certain level of resource use; can Omega emulate how many resources the current TDT agent will use? Can the TDT agent commit to using a random number of resources? Do true random-number generators exist? These problems might all be inextricable. Or they might not. I, for one, don’t know.)
We have several formalizations of UDT that would solve this problem correctly.
Having several formalizations is 90% of a proof, not 100% of a proof. Turn the formalization into a computer program AND either prove that it halts or run this simulation on it in finite time.
I believe that it’s true that TDT will get an answer and hence Omega will get an answer, but WHY this is true relies on facts about TDT that I don’t know (specifically facts about its implementation; maybe facts about differential topology that game-theoretic equilibrium results rely on.)
The linked posts have proofs that the programs halt and return the correct answer. Do you understand the proofs, or could you point out the areas that need more work? Many commenters seemed to understand them...
I do not understand the proofs, primarily because I have not put time in to trying to understand them.
I may have become somewhat defensive in these posts (or withdrawn I guess?) but looking back my original point was really to point out that, naively, asking whether the problem is well-defined is a reasonable question.
The questions in the OP set off alarm bells for me of “this type of question might be a badly-defined type of question” so asking whether these decisions are in the “halting domain” (is there an actual term for that?) of TDT seems like a reasonable question to ask before putting too much thought into other issues.
I believe the answer to be that yes these questions are in the “halting domain” of TDT, but I also believe that understanding what that is and why these questions are legitimate and the proofs that TDT halts will be central to any resolution of these problems.
What I’m really trying to say here is that it makes sense to ask these questions, but I don’t understand why, so I think Davorak’s question was reasonable, and your answer didn’t feel complete to me. Looking back, I don’t think I’ve contributed much to this conversation. Sorry!