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Nornagest comments on What are your contrarian views? - Less Wrong
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What's a Copernican explanation?
I've never heard the term before, but in context I'd guess it means something like "an explanation that implies we're less important than the previous explanation did". Heliocentrism vs. geocentrism, evolution vs. a supernatural creation narrative culminating in people, etc.
Freud's psychoanalysis has been often put in the same category of "Copernican" things as heliocentrism and evolution.
Why is MWI more Copernican than the Copenhagen interpretation?
You do realize that an "observer" doesn't have to be conscious, right? The Copenhagen interpretation doesn't treat humans specially. If anything, I'd say that the Copenhagen interpretation is more Copernican, since it explains the Born probabilities without requiring anthropics.
My comment was not intended to be an endorsement of polymathwannabe's analysis. I'm not a QM expert and am not qualified to comment on the details of either interpretation.