If I think to myself 4*5 = 20 does this fail to "repeat the calculation" because I have it cached in my brain instead of having to calculate 5+5+5+5=10+5+5=15+5=20?
Does this mean that if a computer has some values cached instead of physically needing to bang together particles every single time in order to measure the results, this will likewise fail to repeat the "computation"?
Yes, it fails to repeat the computation, simply because there is no machine doing active computation.
Although whether or not using cached values to make a person in a sim think they were tortured is a moral quandary to me. Highly relevant is this lw post linked to elsewhere in this thread here.
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?