With respect to (1), UDT maximizes over worlds where the zillionth digit of pi is 1, 2, 3...8, 9, 0. It does this even after it knows the value of the digit in question. Most of those worlds aren’t part of the Tegmark level IV multiverse. It seems this post could benefit from distinguishing between possible and impossible possible worlds.
With respect to (1), UDT maximizes over worlds where the zillionth digit of pi is 1, 2, 3...8, 9, 10.
These are not different worlds for UDT, but a single world that can have different possible execution histories that state zillionth digit of pi to be 0,1,...,9. Mathematical intuition establishes a probability distribution over these execution histories for the fixed world program that defines the subject matter.
It seems this post could benefit from distinguishing between possible and impossible possible worlds.
That may be so, but I need to think about how to do it. I said that the possible worlds are whatever the agent’s builders thought was possible. That is, “possibility” refers to the builders’ ignorance, including their ignorance about the zillionth digit of pi.
With respect to (1), UDT maximizes over worlds where the zillionth digit of pi is 1, 2, 3...8, 9, 0. It does this even after it knows the value of the digit in question. Most of those worlds aren’t part of the Tegmark level IV multiverse. It seems this post could benefit from distinguishing between possible and impossible possible worlds.
These are not different worlds for UDT, but a single world that can have different possible execution histories that state zillionth digit of pi to be 0,1,...,9. Mathematical intuition establishes a probability distribution over these execution histories for the fixed world program that defines the subject matter.
That may be so, but I need to think about how to do it. I said that the possible worlds are whatever the agent’s builders thought was possible. That is, “possibility” refers to the builders’ ignorance, including their ignorance about the zillionth digit of pi.