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moridinamael comments on Problem of Optimal False Information - Less Wrong
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The Bohr model of atomic structure is a falsehood which would have been of tremendous utility to a natural philosopher living a few hundred years ago.
That said, I feel like I'm fighting the hypothetical with that answer - the real question is, should we be willing to self-modify to make our map less accurate in exchange for utility? I don't think there's actually a clean decision-theoretic answer for this, that's what makes it compelling.
That is the real question, yes. That kind of self-modification is already cropping up, in certain fringe cases as mentioned; it will get more prevalent over time. You need a lot of information and resources in order to be able to generally self-modify like that, but once you can... should you? It's similar to the idea of wireheading, but deeper... instead of generalized pleasure, it can be 'whatever you want'... provided that there's anything you want more than truth.
If you're going that far, you might as well go as far as all modern physical theories, since we know they're incomplete - with it being wrong in that it's left out the bits that demonstrate that they're incomplete.