Well, fascinating thread. It sent me back to read some words by Blaise Pascal this weekend (in between the Grand Prix, the Indy 500, and the sports car races at Lime Rock Park).
Pascal is one of my favorites: He practically personified the "duality" that I read into this thread (in his real life).
A great scientist/mathematician, he practically (along with his friend Fermat) invented statistical mathematics, and the precise logic of that part of his work stands to this day. And yet, statistical math is, in a way, sort of "mystical" in that it deals not with absolute sums or results, but rather in "probability". Math where you add things up but do not arrive at a set provable single answer. Yet, his writing on this subject reads just as clearly as an IBM manual for the machine language instruction set of one of their computers.
Such is "quantum physics", mentioned here several times earlier.
Pascal was also considered a great mystic - and, to top it off, a "christian" mystic at that. Here is a statement - from the Pensees, part 274:
"All our reasoning reduces itself to yielding to feeling. But fancy is like, though contraty to, feeling - so that we cannot distinguish between these contraries. One person says that my feeling is fancy, another that his fancy is feeling. We should have a rule. Reason offers itself; but it is pliable in every sense; and thus there is no rule."
I think it expresses my "feeling" on mysticism very well. It very like the koans of Hofstadter, the Goedel Law, or even the mind-bending "duality" of such artists as M.C.Escher. It is very like the underlying "truth" of quantum physics - even if we could know the position and momentum of every single particle in the whole universe, we could not predict the outcome of the universe any more than the exact shape and path of the next snowflake to fall.
It means that there are certain propositions that can be expressed by human language or thought, that by basic principle cannot be proven or disproven. They are demonstrably not sillyness (like the red string, or some longing for curative special water, or such). They are well-ordered thoughts that are simply beyond the power of language, science, or thought to analyze and prove. And I believe that such thoughts represent some of mankind's highest form of intellectual achievement.
This is what "Mysticism" represents to me, and as Narkissos has pointed out - why would you beat yourself up trying to prove something to be "real" that is simply not provable?