Ugh, you just HAD to make this a whole bunch of lesswrongers first impression of the show, didn't you? I've been tiptoing around mentioning it for ages planing to make a certain post abaut (still planing to, so I wont spoil it here), figures someone was going to do somehting like that.

Will you at least put up an disclaimer at the top of the post explaining how the show is great and actually one of the most rationality-inspiring shows out there with a brilliant fun-theory-compliant eutopia as the setting etc. etc.?

More on topic:

The question about the rationality of the believing in pinkie sense is actually even more interesting than it seems as first, here's somehting I wrote on another forum about it: "we here have an enormous amount of extremely strong and general evidence that excludes huge areas of hypothesis space. This is the STRONGLY DOMINANT reason you shouldn't believe certain kinds of things even if someone you trust sincerely tells you to. Things like "physical laws don't have exceptions, no exceptions", "there are no irreducibly mental (=supernatural) phenomena", "Due to huge flaws in the way human brains work, billions of people CAN be wrong, and frequently are. You can't even trust your own brain.". We have no reason to believe Equestria and ponykind have similar overriding principles. "

Or, in other words; most of the rationalist art that lesswrong is about does not necessarily translate to the ponyverse. It is specific to humans operating in a mathematical universe. If someone in OUR universe , their claim is extremely extraordinary for a bazilion reasons that evryone here knows all to well. However, in Equestria where magic is a very real phenomena used every day and somehting science is understanding a little better every day it's just a black swan. The apropriate reference class is not the same as someone here claiming to have a power that lets them predict the future by supernarural means, it's more akin to someone claiming to have a cognitive power that lets them predict what genre of music is on an LP by looking at it.

As for your actual question:

That somehting is happening does seem pretty clear. So is the fact that it's happening in her brain even if it's in a place not accessible to conciousness directly, that's how many kinds of intuition works for most humans at least, read up on embodied cognition if you're interested in this stuff. I'd focus on distinguishing between these two hypothesis: 1) information about PPs future cognition are sent back in time. In this scenario seeing a door slam up CAUSES her tail to twitch in the past. 2) She constantly have some ambiant magical sense that can see things outside the range of her normal senses. In this scenario she senses someone walking up to the door/their intention to open the door and subconsciously infers that the door is probably going to open, and her body reacts to this subconscious expectation.