I've decided to make Twilight's education a series, since so many people seemed to like the last one.
Celestia is going to teach you a valuable life-lesson one way or another, Twilight--even if she has to "call in the big guns."
After getting some feedback, it seems the comic is not very clear. This is a failure on my part, so, in case anyone cares, I will try to make up for it with some direction.
1) Celestia may or may not be omniscient--this cannot be disproved. Did she know what Twilight had seen in the flask? Did she know that by asking for a demonstration, Twilight would assent to taking the class? If Twilight had given the demonstration, would she have eo ipso learned something about friendship from Pinkie?
2) What is the liquid in the flask? Is it the liquid that conjures Pinkie's image, or is this a result of Pinkie's arcane 4th wall-breaking powers?
3) "Q.E.D." is what logicians and such write at the ends of proofs. It means "As was to be shown."
4) Twilight has looked into the abyss of friendship (a concept of which she is ignorant), and the abyss looked back.
5) The symbols along the wonky-perspective shelves in Twilight's room represent the stages of producing the philosopher's stone (viz. calcination, dissolution, separation, conjunction, putrefaction, congelation, cibation, sublimation, fermentation, exaltation, multiplication, and projection). Does this mean the essence of friendship is analogous to the philosophers stone? Is friendship likewise capable of miraculous things?
The nest comic will not be so complicated. Lesson learned.