Somewhat ironically, out of all the hundreds of theories I've put forth in the past decade and a half, none has proved more durable than my theory of player vision. Actually, the core theory is "relative perception", of which both player vision and the vector math theory I've shown are offshoots... but that doesn't have a real great ring to it.
The reason this theory's success is sigh-worthy is because it is not one of my main theories. It's a tangental theory I came up with a very long time ago, mostly ignored except when I needed something graphics-related.
But every time I pulled it up, it succeeded. Not a little, not "in theory": it succeeded as in, "wow, everything they just said can be turned into a very simple relative perception formula". Not just game design, but office design, casino design, web page design, even fashion design.
This has made it grow steadily more popular with my neurons. Now, I've come to view it as one of my primary theories, even though it doesn't apply to any of the paths of interest I normally follow. It conflates (word of the day) very well with PAC, which makes me think they spring from the same source. Some kind of fundamental pattern recognition algorithm that I haven't figured out.
The uses of relative perception are surprising. When used for "real-world" persuits, notably architecture and landscaping, it tends to support the instincts of good architects to an uncanny level. The "relative perception" part fades out, because every application is "relative" to exactly the same set of axioms: reality. However, it is still necessary to quantify what the expectations of the people entering the space are (and, if you want to inject some PAC, how to alter those expectations with your structures).
For example, limiting player vision is critical. You never want to hit a player with "too much" unless you're trying to rush him or her through. It's pretty well acknowledged, for example, that the "big open room" casino layout isn't really a very good layout. When asked why, designers will tell you dozens of different reasons, each as if it were true. My addition to that list is based in the math of relative vision: the players see nothing that stands out from the mass of people gambling. In the case of casinos, "catching their attention" is really your goal.
If your casino is a bit more "cozy", you'll actually do better. Exactly how cozy you want to be depends on what kind of customer base you're working with and how effectively you can use your space - getting "I'm lost" and "it's so far away" is a very negative thing. But you need to partition your space such that individual elements of the whole catch their eye.
This doesn't mean a maze of twisty passages, all different. It could be in one large room, so long as there are "things" to block player vision and guide player paths. An island of large ferns is popular. Or a bar. Or a partial wall encrusted with statues or pictures.
The key here is that all the gambling stuff - the blackjack tables, the kino machines, all that stuff - it all counts as the same kind of "pattern element". Exposed to too much of any particular kind of element, the player will count it as "noise", assuming he's not looking specifically for a given kind of machine. However, the partitions both count as another kind of element and keep the player from seeing too many "gambling elements" at any given time.
These "pattern breaks" are a key element in the overall theory of relative perception, and the part which links most heavily to PAC. Moreover, the actual placement of pattern breaks can theoretically be calculated using math.
In practice, the audience varies too much. You have players who know what they want and players who are wandering. Experienced players and new players. Players who have been in your casino for a few days and players who just got here. Players who tend to look far from their location and players that tend to look near. Heck, players even cycle goals mostly at random, hence the need for food, great views, and quiet verandas.
A game is actually simpler to run mathematical calculations on. You know precisely what the player's goals are and how much they can "see": all you have to do is figure out how skilled they are at pattern recognition (and how bored they're getting, but that's a job for PAC).
Still, every time I see a mention of art, architecture, marketing... I can't help but say, "hey, that's a fairly obvious mathematical principal of relative perception!"