physicality of the initial states of a TM doesn’t make its states from sufficiently distant future any more physically computed
I’m not sure what you mean by this.
Let’s suppose the description length of our universe + bits needed to specify the location of the TM was shorter than any other way you might wish to describe such a TM. So with the lottery, you are in some sense choosing whether this TM gets a shorter or longer description.
The argument for moral worth of physically instantiated details says that details matter when they are physically instantiated. Any theories about description lengths are not part of this argument. Caring about such things is an example of caring about things other than physical world.
I’m not sure what you mean by this.
What I mean is that sufficiently distant states of the TM won’t be physically instantiated regardless of how many times its early states get to be physically instantiated. Therefore a preference that cares about things based on whether they get to be physically instantiated won’t care about distant states of the TM regardless of how many times its early states get to be physically instantiated.
A preference that cares about things other than physical instantiation can of course care about them, including conditionally on how many times early states of a TM get to be physically instantiated. Which is sufficient to implement the thought experiment, but not necessary, since one shouldn’t fight the hypothetical. If the thought experiment asks us to consider caring about unbounded TMs, that’s the appropriate thing to do, whether that happens to hold about us in reality or not.
Ah I see, the problem was ambiguity between TM-defined-by-initial-state and TM-with-full-computation-history. Since you said it was embedded in physics, I resolved ambiguity in favor of the first option, also allowing a bit of computation to take place, but not all of it. But if unbounded computation fits in physics, saying that something is physically instantiated can become meaningless if we allow the embedded unbounded computations to enumerate enough things, and some theory of measure of how much something is instantiated becomes necessary (because everything is at least a little bit instantiated), hence the relevance of your point about description length to caring-about-physics.
Right. I think that if we assign measure inverse to the exponent of the shortest description length and assume that the ϵ probability increases the description length of the physically instantiated TM by −log(ϵ) (because the probability is implemented through reality branching which means more bits are needed to specify the location of the TM, or something like that), then this actually has a numerical solution depending on what the description lengths end up being and how much we value this TM compared to the rest of our life.
Say U is the description length of our universe and L−log(ϵ) is the length of the description of the TM’s location in our universe when the lottery is accepted, K−log(1−ϵ) is the description length of the location of “the rest of our life” from that point when the lottery is accepted, T is the next shortest description of the TM that doesn’t rely on embedding in our universe, V is how much we value the TM and W is how much we value the rest of our life. Then we should accept the lottery for any ϵ>2U−TV2−LV−2−KW, if I did that right.
If we consider the TM to be “infinitely more valuable” than the rest of our life as I suggested might make sense in the post, then we would accept whenever ϵ>2U+L−T. We will never accept if U+L≥T i.e. accepting does not decrease the description length of the TM.
I’m not sure what you mean by this.
Let’s suppose the description length of our universe + bits needed to specify the location of the TM was shorter than any other way you might wish to describe such a TM. So with the lottery, you are in some sense choosing whether this TM gets a shorter or longer description.
The argument for moral worth of physically instantiated details says that details matter when they are physically instantiated. Any theories about description lengths are not part of this argument. Caring about such things is an example of caring about things other than physical world.
What I mean is that sufficiently distant states of the TM won’t be physically instantiated regardless of how many times its early states get to be physically instantiated. Therefore a preference that cares about things based on whether they get to be physically instantiated won’t care about distant states of the TM regardless of how many times its early states get to be physically instantiated.
A preference that cares about things other than physical instantiation can of course care about them, including conditionally on how many times early states of a TM get to be physically instantiated. Which is sufficient to implement the thought experiment, but not necessary, since one shouldn’t fight the hypothetical. If the thought experiment asks us to consider caring about unbounded TMs, that’s the appropriate thing to do, whether that happens to hold about us in reality or not.
I see. When I wrote
I implicitly meant that the embedded TM was unbounded, because in the thought experiment our physics turned out to support such a thing.
Ah I see, the problem was ambiguity between TM-defined-by-initial-state and TM-with-full-computation-history. Since you said it was embedded in physics, I resolved ambiguity in favor of the first option, also allowing a bit of computation to take place, but not all of it. But if unbounded computation fits in physics, saying that something is physically instantiated can become meaningless if we allow the embedded unbounded computations to enumerate enough things, and some theory of measure of how much something is instantiated becomes necessary (because everything is at least a little bit instantiated), hence the relevance of your point about description length to caring-about-physics.
Right. I think that if we assign measure inverse to the exponent of the shortest description length and assume that the ϵ probability increases the description length of the physically instantiated TM by −log(ϵ) (because the probability is implemented through reality branching which means more bits are needed to specify the location of the TM, or something like that), then this actually has a numerical solution depending on what the description lengths end up being and how much we value this TM compared to the rest of our life.
Say U is the description length of our universe and L−log(ϵ) is the length of the description of the TM’s location in our universe when the lottery is accepted, K−log(1−ϵ) is the description length of the location of “the rest of our life” from that point when the lottery is accepted, T is the next shortest description of the TM that doesn’t rely on embedding in our universe, V is how much we value the TM and W is how much we value the rest of our life. Then we should accept the lottery for any ϵ>2U−TV2−LV−2−KW, if I did that right.
If we consider the TM to be “infinitely more valuable” than the rest of our life as I suggested might make sense in the post, then we would accept whenever ϵ>2U+L−T. We will never accept if U+L≥T i.e. accepting does not decrease the description length of the TM.