OK, the grand picture has been framed, the analogies have been made...it's time to focus.
Let's look at the first specific aspect of Vector Theory; the Perfect Mirror.
A perfect mirror reflects a ray of light effortlessly, the ray doesn't even notice the presence of the mirror. It simply diverts the path in a new direction.
A good GM is like a perfect mirror. The flow of the story continues in a straight line, the good GM introduces something that initially seems subtle, it might even be ignored. But that little introduction shifts the course of the story forever.
Under the influence of a good GM, the players might think that their story hasn't even diverted, and that things were always heading in the final direction. The player's don't feel that their actions have been "railroaded", they feel as though they have followed their own destiny.
A good mechanism within the rules is like a perfect mirror. The mechanism flows seamlessly as a part of the experience, it doesn't get in the way of the story flow, it doesn't cause a jarring disconnect with the established reality, and it integrates so well with the other mechanisms of the game that it feels instinctive.
If the mechanisms influencing a story purely consist of perfect mirrors, we consider the shifting narrative to be a carefully crafted piece of literature (or maybe just a rollicking good piece of pulp). A writer using perfect mirrors to alter the course of their story deliberately uses the tropes of their literary format, people expect certain twists to occur and it thus becomes inevitable that those twists appear. As a specific case in point, I went to see "Percy Jackson and the Lightning Thief" with Leah a couple of weeks ago. I knew the twists and turns that were coming, but even though I can be harsh in my criticism of some movies I couldn't be upset with the obvious twists in the narrative of Percy Jackson because I went to the movies to see a modern day retelling of the Hero's Journey. All the steps were followed, A call to adventure, a denial of the call, a meeting with a mentor, an escalation of events, allies and enemies met along the way, a journey to the underworld, great loss...pretty much everything you would expect, if you know the tropes of the journey. The only thing I found upsetting with the movie is that it probably could have gone a lot darker, but it was family entertainment, so it ticked those boxes as well.
If the mechanisms influencing a game purely consisted of perfect mirrors, there wouldn't be any point playing the game; the final destination of the experience is predetermined. The players aren't making choices, they are simply following the narrative path, bounced around by the whim of the GM. They might not realise it, because they don't even see the diversions thrust apon them, but even the most oblivious player will start to develop a nagging feeling that they have no control over the story's destiny. Andrew Smith made a great commentary on Monopoly a while back, and when you consider the overall context of the game there are a few subtle aspects behind the rules that push the game down the same negative spiral every time it is played. These mechanisms are perfect mirrors in the background, no-one really acknowledges that the game will always end up in a downward spiral with a majority of the players being losers, ironic given that this is directly in the title of the game. Instead people hope against the odds that they will be the one winner.
The ascending levels of responsibility in Gregor Hutton's 3:16 might be described in this way. Each one doesn't seem to make a lot of influence on game play, they are just little ideas that most people keep in the backs of their minds. But, one-by-one they work their way insidiously into the way the game is played, until it stops being a heroic game about humanity against the dreadful unknown, and it suddenly becomes very dark.
The entire game "Stoke-Birmingham 0-0" (p44, Norwegian Style) is easily filled with perfect mirrors. These mirrors are introduced by the players rather than the rules or a centralised GM, everyone simply introduces their elements into the scene through natural conversation. Once in play, an idea shifts the outcome of the scene. Anything said, is said in character. Anything done is done in character, there are no meta-rules to worry about, it's pure roleplaying. The narrative of the scene might simply flow in a straight line if no-one introduces anything, or it could end up incredibly twisted and complicated if everyone tries to introduce their own mirrors to further the narrative toward a specific end point. (I should styop now before my commentary on the game ends up more detailed than the game itself).
If someone isn't looking for the perfect mirror, they'll completely miss the influence it plays on a game or story. If someone does know where the perfect mirror should be, or if they know what it's intended effects should be, they can appreciate the perfect mirror for what it is.
The biggest problem with perfect mirrors is that they are incredibly hard to create. This applies in a literal as well as a figurative sense; a perfect mirror is a sign of an incredibly well crafted game, game-master or story.
More often than not, mirrors will be imperfect. Occasionally diverting the flow subtly, and sometimes blatantly.