Hey Tim,
I have in my possession data from multiple remote viewing sessions that I have personally observed. Some that I posted on this site, other more recent ones that I have not bothered to post (I view the "critical discussions" here as not so critical anymore, at least for me, lol). I am convinced, beyond any stretch of a reasonable doubt, that actual remote viewing--veridical perceptions--occurred (not lucky guesses, coincidence, law of large numbers, faulty recollection, or any of the other "usual suspects").
Years ago, I corresponded with Ed May about this (who according to Craig Weiler, who met May, is an atheist and a materialist). May is quite convinced that remote viewing occurs, and has some theory that it relates somehow to "shannon entropy" between brains. I leave it to science and advanced math to determine the exact "mechanisms" through which this phenomena manifests, but I am incapable (and admit so) of accepting that such mechanisms do not exist, or are illusory. If brains are indeed capable of producing this phenomena by themselves, without something called consciousness, then so be it. It is amazing. The fact that primordial ooze from the Big Bang arranged itself (by chance) in such a way as to develop into mechanisms to contemplate and understand the mathematical laws and physical characteristics required for their existence, is to me more amazing than the fact that remote viewing or psychic phenomena actually occur.
Cheers,
Bill