I feel like my first reaction was like you, that I do not care about simplicity THAT much, but reflicting on it has made me think that maybe I really do care about simplicity that much.
FIrst, let’s remodel the problem. There is a collection of universes, each one an infinite string of bits, which encodes a turing machine. Lets say the actual states of the TM are encoded on some finite subset of the infinite string, and the rest of the string is random bits that The TM can read if it chooses to.
The first obstacle to out intuition is that caring based on K-complexity is the same as caring about all of these different TMs equally, so what seems unfair in one model seems very fair in another model. This might be enough to convince you to care THAT much, but I imagine you have the following rebuttal:
Many of these simple TMs never even read the infinite string of random bits at the end. They are all exactly the same. I have this vague feeling of diminishing returns. A million of the same good thing and a million different bad things does not feel as good as a million of the same bad thing and a million different good things.
I feel this intuition myself, but maybe this is just a fallacy of projecting intuitions about diminishing returns from within one universe to questions about multiple universes that do not communicate with each other.
I don’t feel like considering these different ways to approach K-complexity addresses the point I was trying to make. The rebuttal seems to be arguing that we should weigh the TMs that don’t read the end of the tape equally, rather than weighing TMs more that read less of the tape. But my point isn’t that I don’t want to weigh complex TMs as much as simple TMs; it is (1) that I seem to be willing to consider TMs with one obviously disorderly event “pretty simple”, even though I think they have high K-complexity; and (2) given this, the utility I lose by only disregarding the possibility of magical reality fluid in worlds where I’ve seen a single obviously disorderly event doesn’t seem to lose me all that much utility if measureless Tegmark IV is true, compared to the utility I may lose if there actually is magical reality fluid or something like that and I ignore this possibility and, because of this, act in a way that is very bad.
(If there aren’t any important ways in which I’d act differently if measureless Tegmark IV is false, then this argument has no pull, but I think there may be; for example, if the ultrafinitist hypothesis from the end of my post were correct, that might make a difference to FAI theory.)
I feel like my first reaction was like you, that I do not care about simplicity THAT much, but reflicting on it has made me think that maybe I really do care about simplicity that much.
FIrst, let’s remodel the problem. There is a collection of universes, each one an infinite string of bits, which encodes a turing machine. Lets say the actual states of the TM are encoded on some finite subset of the infinite string, and the rest of the string is random bits that The TM can read if it chooses to.
The first obstacle to out intuition is that caring based on K-complexity is the same as caring about all of these different TMs equally, so what seems unfair in one model seems very fair in another model. This might be enough to convince you to care THAT much, but I imagine you have the following rebuttal:
Many of these simple TMs never even read the infinite string of random bits at the end. They are all exactly the same. I have this vague feeling of diminishing returns. A million of the same good thing and a million different bad things does not feel as good as a million of the same bad thing and a million different good things.
I feel this intuition myself, but maybe this is just a fallacy of projecting intuitions about diminishing returns from within one universe to questions about multiple universes that do not communicate with each other.
I don’t feel like considering these different ways to approach K-complexity addresses the point I was trying to make. The rebuttal seems to be arguing that we should weigh the TMs that don’t read the end of the tape equally, rather than weighing TMs more that read less of the tape. But my point isn’t that I don’t want to weigh complex TMs as much as simple TMs; it is (1) that I seem to be willing to consider TMs with one obviously disorderly event “pretty simple”, even though I think they have high K-complexity; and (2) given this, the utility I lose by only disregarding the possibility of magical reality fluid in worlds where I’ve seen a single obviously disorderly event doesn’t seem to lose me all that much utility if measureless Tegmark IV is true, compared to the utility I may lose if there actually is magical reality fluid or something like that and I ignore this possibility and, because of this, act in a way that is very bad.
(If there aren’t any important ways in which I’d act differently if measureless Tegmark IV is false, then this argument has no pull, but I think there may be; for example, if the ultrafinitist hypothesis from the end of my post were correct, that might make a difference to FAI theory.)