Foldback story - yeah whatever

Today I've learned a new term.
Foldback story.
I've done without it for years in the industry, and yet I'm supposed to have missed something fundamental.
I wanted to learn more about it and after a few strokes on my keyboard, grand master Google sent me here.

Inn the chapter on “Storytelling and Narrative” in Fundamentals of Game Design (pages 194-204), Adams & Rollings categorise stories as linear, or non-linear. Non-linear stories further subdivided as branching or foldback stories.

So, there it comes from. Adams' & Rollings' FoGD (too bad they added design, otherwise the acronym would have been most accurate).
If you don't understand it, don't be afraid, it's normal. The name of a principle, or even ideology, is supposed to give an idea of what it is about; what the heck are you supposed to guess by "foldback" pray tell?
You know, when you fold back, you generally get a feeling that it's going to involve something moving backwards, which is quite problematic from the perspective of general storytelling in video games, wherein stories not only often times prove to be linear, but also going forward.
Why not try something like, err... the Squeeze Theory?

The foldback story structure is build around a series of key, inevitable events through which a story must progress. In many games, user interactivity allows the player a certain amount of freedom in how they make their way between inevitable events, before folding back to the inevitable events. Foldback stories support a degree of “replayability”: that is, they are capable of keeping the player engaged if they play the game more than once, by allowing them to find a different way through it, even if they know the ending. Where a potentially unknown outcome is essential for maintaining player engagement, the final inevitable event may provide a staging point for several different endings.

Ah, so they used the verb that describes what the story essentially does at a point in time as the name of the principle, as an illustration of the distance put between the player's decisions and the main story, which goes through a series of inevitable stages. The "back" part is completely unnecessary and actually spoils the pure meaning of "fold" when used alone. Not only that's a silly mistake which could have been easily avoided by a mere glance at some random dictionary, but I guess "funnel story" was just too obvious eh? Or "grow-shrink story" you know, as it expands and contracts; and just for that, there's like a good many analogies to pick. I mean, there's like a gazillion far more intuitive terms than foldback.

We can (must?) be even more vicious. Consider for a moment the amount of time allotted to the mental brewing that precedes the revolutionary idea behind the identification of the narrative pattern. We all know that it must sound very clever, and so let's outdo the clever.
See, the idea of folding back presupposes going one way and then the opposite way. However, it all depends on your reality, your world of reference. Let's assume you're some entity living in a two-dimensional environment. Then, some omniscient being decided to wrap the fabric of your reality and made that plane you lived on return to its original point, like if you were to bend back the corner of some table cloth. You'd still move forward, but from a higher dimensional perspective, you'd also be returning closer to the story's spine, its "center", or core.

Sure thing, we could use an example with you living on a line (in one dimension) and some omniscient being having that line split into two lines (something which only can only happen in two dimensions), without you noticing that you suddenly branched "away" (onto another line). Only for that auxiliary line to fuse with the main line later on (and so everything returns to normal, although you, one-dimensional creature, didn't see a difference). In two dimensions, you'd have moved away from the main line, then approached the same line later on to merge with it.

This is the only way to actually project, geometrically wise, the concept of a story that keeps going forward while the story itself folds. If this sounds too complicated, it's probably because it has no intuitive value at all, where the lay man will merely see anything folding back as a contrived return to the point of departure, which is certainly not the idea that the term is supposed to convey, which is refocusing on the main story while never having stopped moving on!

The foldback concept could only make a glimpse of sense if the main story was paused and nothing could go on until you'd actually return to the very moment that main story was paused, so as to resume it. Then, of course, the whole concept of the story folding back would be meaningless and still erroneous. The story would not fold back because it would have precisely been immobile the whole time.
In other words... PAUSED!
*gasp!*
The kind of stuff that happens so many times in free roaming games, like the GTAs. Very few games actually allow the player to follow two distinctively different paths, both story-wise and space-wise, while having the possibility or the obligation to return to the same must-pass-through storyline-check later on.

And this brings me to the next part. The reality of games forcing you through very specific (key)holes at a given point in time is one of checkpoints; and how lovely would that be to use such a widely known term among gaming circles!
The idea with checkpoints is that you can't just move forward until you precisely go through checkpoints.
Some games may guide you towards such checkpoints while you keep playing no matter what, when other ones would let you do whatever you want, like wandering around some and even allowing you to complete side quests, but ultimately leaving you unable to go any further through the main story without willingly conceding your recently obtained -yet relative- liberty, waiting that you return to the checkpoint and step through it, even if it means returning to a specific point in space from where the next step in the main narrative can finally occur.

Besides, if you want to make this fancier, you can always try to boost your sex appeal at some nerdy party and impress the ladies with the lovely notion of mirrored-time-synchronous waves, where one signal regularly crosses the path of its inverted-polarity sibling, to form a figure which should basically look like that:

Please notice the obvious bonus effect of implanting suggestive imagery into the subconscious of your next female conquest (so you think).
Let's also understand that it looks sciency and abstract enough to fit inside some random game theorist's consecratory (read potentially superfluous) book.

Oh, did I talk about the stomach analogy? You know, the one that really fits the whole concept of story lines actually merging at some point, like if they were shoved through one single obligatory hole?
Or what about that one: