On a somewhat-related note I've been thinking about what sort of events seem to have that magic-power quality to bystanders who don't know how they're accomplished.

My first thought was to consider the properties of explicit magic tricks, but they don't quite apply for a few reasons. Firstly, they're not real. Secondly, they're generally placed in a social context where spectators ultimately know they're not real. Thirdly, they're extremely contrived situations without a lot of practical value. It's generally the artificial sense of narrative impossibility that gives them the impact. If I could clear fallen debris with laser beams from my eyes, that would belong in a fundamentally different category to guessing a card someone thought of.

The only other skill I possess which seems to have the same sort of reaction is follow and lead in improvised partnered dance. Spectators often seem amazed that two people can coordinate their movements so well without talking to each other. The factual response is "we are talking to each other, just non-verbally".