What you've said makes sense to me, that the flipbooks do not constitute a calculation. However, it feels like there is a fuzzy boundary somewhere nearby, similar to the fuzzy boundary of what constitutes life. Maybe there is a information theory explanation which relates the two.
If the flipbooks contain enough information to continue the calculation then they are the same as a backup. Ok, so a flipbook is a series of closely spaced backups. What constitutes a calculation? I've read about these things, but I've never tried to work it out for myself before.
A backup is a static result of a calculation. Static results are static. They don't count as alive, they don't count as a calculation.
What counts as a calculation? I'm getting stuck. Let's say we do the calculation as a state machine. You have static states that are updated according certain rules. State 1 determines/causes state 2. The calculation is implemented somewhere. So there are patterns of matter/energy that represent the states and represent the arithmetic needed to change states. I guess the calculation is here?
However, it feels like there is a fuzzy boundary somewhere nearby, similar to the fuzzy boundary of what constitutes life. Maybe there is a information theory explanation which relates the two.
You might find it useful thinking about computations in terms of turing machines and the tape they use: http://lesswrong.com/r/discussion/lw/5vx/torture_simulated_with_flipbooks/4b7p
What if the brain of the person you most care about were scanned and the entirety of that person's mind and utility function at this moment were printed out on paper, and then several more "clock ticks" of their mind as its states changed exactly as they would if the person were being horribly tortured were printed out as well, into a gigantic book? And then the book were flipped through, over and over again. Fl-l-l-l-liiiiip! Fl-l-l-l-liiiiip!
Would this count as simulated torture? If so, would you care about stopping it, or is it different from computer-simulated torture?