The premise of this thread seems to be "Why don't we start again and try to test for psychic phenomena nobody's even claimed might exist?".
Possibly it's a variant of that: "why don't we consider, and test for the possibility, that phenomena we think we understand scientifically are actually paranormal?"
Maybe not on the level of "smart phone screens actually work using captive conjured fire spirits instead of electronics," but the same general idea applied to more elusive and complex things like weather, health, consciousness... or coincidences.
In the esoteric community I mentioned in the OP, I once raised the question of how one might go about holding a "fair" lottery. By "fair" I meant that I wanted the outcome to depend
only on random chance, and not be affected by the players' respective karmic statuses, or how anyone's stars aligned that day, or what deities or angels they'd prayed to, or what chronic curses or long-term blessings might be attached to them, or what talismans they were carrying or magical rituals they'd performed, or what spiritual entities had designs on the course of their futures. The clear unanimous answer was that what I was describing was totally impossible, nearly unthinkable. About the same reaction as if I'd asked people here how to design a spacecraft to be unaffected by gravity.
A very atypical answer from an admittedly atypical population? I don't think so. Anyone who believes deities answer prayers, or that karma "balances," or that "everything works out for the best," or that a positive attitude will help them win a game of chance, or that certain actions bring good or bad luck, or that the winner's stars must have aligned in some special way, or that they have a destiny or a fate, must at some level of their cognition come to the same basic conclusion even if they never consciously take the reasoning that far. And the union of those sets is pretty close to everyone.
That basic conclusion is, random chance doesn't actually exist. Not for the technical reasons we sometimes discuss here (the trajectory of the dice through the air is theoretically calculable; computers only generate
pseudo- random numbers) but because ineffable forces or entities (perhaps only one; perhaps whole swarms and legions and empires of them) constantly have their fingers or their noodly appendages on the numbered ping pong balls of fortune.
Coincidences being explained as an expected consequence of random chance?
But there's no such thing. The significance of the results of ESP trials being determined by statistical tests based on the mathematical behavior of sequences of random events?
But there's no such thing. Evolution depending in part on random mutations and random recombinations?
But there's no such thing. Quantum mechanics?
Fughettaboutit.
The gap in world models between that and the rationalist view is wider and stranger than between the starship captains and any of the alien cultures in
Star Trek. Darmok and Jalad might have fought the Beast at Tanagra, but they probably agreed with Picard that random chance occurs. In the alien world we actually live in, there's no such thing as fair random lotteries, only ones that "maybe I deserve to win this time."
Is that closer to what you want to see investigated more, Warp12?