Consider a computer which is 2 atoms thick running a simulation of you. Suppose this computer can be divided down the middle into two 1 atom thick computers which would both run the same simulation independently. We are faced with an unfortunate dichotomy: either the 2 atom thick simulation has the same weight as two 1 atom thick simulations put together, or it doesn’t.

UDASSA implies that simulations on the 2 atom thick computer count for twice as much as simulations on the 1 atom thick computer, because they are easier to specify.

I think the answer is that the 2-atom thick computer does not automatically have twice as much measure as a 1-atom thick computer. I think you’re assuming that in the (U, x) pair, x is just a plain coordinate that locates a system (implementing an observer moment) in 4D spacetime plus Everett branch path. Another possibility is that x is a program for finding a system inside of a 4D spacetime and Everett tree.

Imagine a 2-atom thick computer (containing a mind) which will lose a layer of material and become 1-atom thick if a coin lands on heads. If x were just a plain coordinate, then the mind should expect the coin to land on tails with 2:1 odds, because its volume is cut in half in the heads outcome, and only half as many possible x bit-strings now point to it, so its measure is cut in half. However, if x is a program, then the program can begin with a plain coordinate for finding an early version of the 2-atom thick computer, and then contain instructions for tracking the system in space as time progresses. (The only “plain coordinates” the program would need from there would be a record of the Everett branches to follow the system through.) The locator x would barely need to change to track a future version of the mind after the computer shrinks in thickness compared to if the computer didn’t shrink, so the mind’s measure would not be affected much.

If the 2-atom thick computer split into two 1-atom thick computers, then you can imagine (U, x) where x is a locator for the 2-atom thick computer before the split, and (U, x1) and (U, x2) where x1 and x2 are locators for the different copies of the computer after the split. x1 and x2 differ from x by pointing to a future time (and record of some more Everett branches but I’m going to ignore that for this) and to differing indexes of which side of the split of the system to track at the time of the split. The measure of the computer is split into the different future copies, but this isn’t just because each copy is half of the volume of the original, and does not imply that a 2-atom thick computer shrinking into 1-atom of thickness halves the measure. In the shrinking case, the program x does not need to contain an index about which side of the computer to track: the program contains code to track the computational system, and doesn’t need much nudging to keep tracking the computational system when the edge of the material starts transforming into something else not recognized as the computational system. It’s only in the case where both halves resemble the computational system enough to continue to be tracked that measure is split.

I think the answer is that the 2-atom thick computer does not automatically have twice as much measure as a 1-atom thick computer. I think you’re assuming that in the (U, x) pair, x is just a plain coordinate that locates a system (implementing an observer moment) in 4D spacetime plus Everett branch path. Another possibility is that x is a program for finding a system inside of a 4D spacetime and Everett tree.

Imagine a 2-atom thick computer (containing a mind) which will lose a layer of material and become 1-atom thick if a coin lands on heads. If x were just a plain coordinate, then the mind should expect the coin to land on tails with 2:1 odds, because its volume is cut in half in the heads outcome, and only half as many possible x bit-strings now point to it, so its measure is cut in half. However, if x is a program, then the program can begin with a plain coordinate for finding an early version of the 2-atom thick computer, and then contain instructions for tracking the system in space as time progresses. (The only “plain coordinates” the program would need from there would be a record of the Everett branches to follow the system through.) The locator x would barely need to change to track a future version of the mind after the computer shrinks in thickness compared to if the computer didn’t shrink, so the mind’s measure would not be affected much.

If the 2-atom thick computer split into two 1-atom thick computers, then you can imagine (U, x) where x is a locator for the 2-atom thick computer before the split, and (U, x1) and (U, x2) where x1 and x2 are locators for the different copies of the computer after the split. x1 and x2 differ from x by pointing to a future time (and record of some more Everett branches but I’m going to ignore that for this) and to differing indexes of which side of the split of the system to track at the time of the split. The measure of the computer is split into the different future copies, but this isn’t just because each copy is half of the volume of the original, and does not imply that a 2-atom thick computer shrinking into 1-atom of thickness halves the measure. In the shrinking case, the program x does not need to contain an index about which side of the computer to track: the program contains code to track the computational system, and doesn’t need much nudging to keep tracking the computational system when the edge of the material starts transforming into something else not recognized as the computational system. It’s only in the case where both halves resemble the computational system enough to continue to be tracked that measure is split.