(Commenters: talking about the 'supernatural' in terms of metaphysics is metaphysically interesting but phenomenologically speaking it just clouds the issue unnecessarily. The way most people actually use the concept is just 'weird things happening that would require human or transhuman agency, in situations where there's no good reason to suspect human agency'. Talking about reductionism &c. is missing the point---it doesn't matter whether the agency comes from an engineered superintelligence or an "ontologically fundamental" god, what matters is there's non-human agency around. Note that all reports of supernatural phenomena can be explained "naturally" by superintelligences, simulators, highly advanced aliens, &c., all of which seem not-unlikely in a big universe. The improbability stems from the necessity of their having seemingly bizarre motivations; the mechanisms themselves, however, aren't fantastically improbable.)