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lm  ·  404 days ago  ·  link  ·    ·  parent  ·  post: Physicists find we're not living in a computer simulation

What I'm saying is that, if this problem is NP-hard, then we don't know that that exponential relationship has to be there. It's possible that there's an algorithm that takes linear time to simulate this linear relationship.

Now, between you and me, I would bet money that there is not such a thing, but I'm playing devil's advocate here!

Want to know something fun? If that exponential relationship does hold, then the size of the simulated universe that 'fits' in the 'initial' universe is proportional to the log of the host universe's size, and the size of the simulated universe that fits in that universe is proportional to the log of its host universe's size...

...which for all practical purposes means that you get at most 5 levels of simulation. Probably a lot less. Thinking about non-asymptotic functions that nonetheless grow so slowly that they might as well is fun!