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My own particular manifestation of wierdness is with dreams. Some of them contain people I don't know, or locations I don't recognise. They mean nothing and I forget about them.
'File away' would be a better description. Years down the line, the 'scene' will play out in reality, sometimes only a few seconds in length. Even the "uh oh, deja vu again" reaction to experiencing this 'action replay' is incorporated into the original dream.
Speaking as someone of the scientific persuasion, it is a completely illogical phenomonon and, frankly, embarassing to have to admit to it. It has taken me many years to gather, from similarliy guarded individuals letting slip, that this is actually quite a common experience.
Also, I have little or no control over it; I lay no claims to having a 'magical power' or any guff like that. Being uncontrollable means it seems to have no earthly purpose.
What it has given me is an unusual concept of the nature of time and think about how 'information' could pass from one point in time back to somewhere in the past (dreams) or the future (eg ghosts). I described this, in a private conversation as time being like a tangled up ball of string, which has points of contact from temporally distant locations.
Could be complete drivel but you need to come up with creative ideas sometimes so as to open up fresh lines of scientific enquiry.
The Dr Who scriptwriters came up with "Wibbly-wobbly, timey-wimey" and I was highly amused by the similarity.
So, I need to do five more impossible things before breakfast before I try a trip to Milliways...