Giles comments on Simulationist sympathetic magic - Less Wrong
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I assume that if a statistically significant number of people noticed that they were trying sympathetic magic and it was working, then the simulation would have to be restarted or tweaked since it could alter the history of the world in significant ways. So you might want to plan out that aspect of your strategy before collecting any data.
We're already living in a world where huge numbers of people believe sympathetic magic is working.
How many of them wouldn't believe it if it wasn't working?