Forthcoming in the Journal of Social and Personality Psychology--essentially the most prestigious journal in social psychology--is an article by Daryl Bem--one of the most respected social psychologists not just here at Cornell but generally, an article entitled "feeling the future" that tried to show that "psi" or psychic powers exist. He basically replicates that experiment Bill Murray conducted in Ghost Busters (having people predict what's behind cards) but computerized.
I'm actually personally very sympathic to the possibility of magic and psychic powers. But I'm still skeptical here, in part because there have been quite a few literatures esp in psychology that have been shown to be false recently due to poor experimental or statistical procedure (like cognitive dissonance).
But Bem's article is very well written, addressing all of the confounds I can think of on p-values, effect sizes, randomization, etc. I don't think there's anything else he could have written to convince me more.
Still you worry about mistakes in execution. When we say something is 95% significant, it means if you do this 20 times, you will mistakingly find an effect one of those times. It is plausible that Bem and others tried this experiment 20 times and only the one success gets reported. Bem of course discusses this possibility and dismisses in the paper, but still I remain to be convinced.
But yeah, maybe Dan Brown's pseudo-science, not so pseudo after all?