TLDR AHOY
It's a theory that I find myself unable to subscribe to on the "supernatural" level, however the problem solver side of my personality understands how it can have some merit (when viewed on a more basic level as a concept.)
I do believe that our subconscious continues to analyze data without us even knowing it consciously. Certain events can happen and our mind is doing the math while we semi-focus on monotonous chores. So, in that sense, sure... we can have a certain level of what is suggested here.
Great sci-fi writers generally look at "where we are" and can generally accurately predict "where we are going". Star Trek being a great example (since it was mentioned), look at phasers/tasers set to "stun", look at food replicators and the ipads & iphones that they basically used on Deep Space 9, holograms, cloning, etc. Phillip K. Dick did a lot of this too, many would argue that his use of psychotropic drugs helped open parts of his mind to a lot of such ideas. I mean, the title here is basically the plot to Minority Report. People out there also argue that these sci-fi ideas influence culture so greatly that technology starts heading in that direction based off of the desire to live in that "future".
So art imitates life and life imitates art in a back-and-forth motion.
In precog, I would more than likely not have all of the "facts", I'd have something more along the lines of a "vibe" or a component of a bigger, more elaborate plot. When I try to steer myself away from or towards a specific event/outcome, there would be the chance of altering fate into just as much of an unknown outcome as it would've been without a "vision" or "vibe".
"Hindsight" is much different. Hindsight has more of a finality to it. If I go through a bunch of small steps to reach a goal and I never reach that goal, then I can look back at all the facts and by reviewing results I can see where I failed at key points in reaching my goal.
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