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mantis comments on Torture vs. Dust Specks - Less Wrong
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I think that's probably more practical than trying to make it continuous, considering that our nervous systems are incapable of perceiving infinitesimal changes.
Yes, we are running on corrupted hardware at about 100 Hz, and I agree that defining broad categories to make first-cut decisions is necessary.
But if we were designing a morality program for a super-intelligent AI, we would want to be as mathematically consistent as possible. As shminux implies, we can construct pathological situations that exploit the particular choice of discontinuities to yield unwanted or inconsistent results.