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Viliam_Bur comments on No Universally Compelling Arguments in Math or Science - Less Wrong
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Paperclipper has an optimizing power. Let it enter your solar system, and soon you will see a lot of paperclips. Watch how it makes them. Then create some simple obstacles to this process. Wait for a while, and see even more paperclips after your obstacles were removed or circumvented.
Doesn't happen with a rock. I can't quite imagine what an anti-inductive mind would do... probably random actions most likely leading to a soon self-destruction (at which point it stops being a mind).
Measuring optimization power requires a prior over environments. Anti-inductive minds optimize effectively in anti-inductive worlds.
(Yes, this partially contradicts my previous comment. And yes, the idea of a world or a proper probability distribution that's anti-inductive in the long run doesn't make sense as far as I can tell; but you can still define a prior/measure that orders any finite set of hypotheses/worlds however you like.)