We're in for a rip-roaring time in chapter nine, the appropriately-titled "Riding in the Wagon with Ben". In which Kvothe...rides in a wagon. With Ben.
Ben tells him about the Arcanum of the University and what it takes to become a fully-qualified Arcanist (years of study, if one is able to gain entry to the University in the first place), the idea of which immediately enchants Kvothe.
This comment from Ben is interesting, because if I remember correctly (these books are long), the idea of "knacks" like this never come up again, nor do we ever meet anyone who has one. These sorts of inherent abilities don't really fall anywhere within the books' various magic systems, and I'm curious what the in-universe explanation for them is supposed to be.
This conversation is the launching-off point for Ben to begin teaching Kvothe his arcanely ways, starting with rudimentary chemistry and first aid. Thus begins Kvothe's transformation into a magical renaissance man.
Thank you, Kvothe, for making sure to tell us how godlike you are at boning.
The next chapter is mostly taken up with Kvothe learning the basic skills of sympathy, which involves a series of altered mental states that seem like they'd be far more difficult to achieve than they're presented here. First, Kvothe has to believe something he knows to be impossible--that a rock will float--and then, when he's got that down, he has to simultaneously believe that the rock will float and that it won't. This isn't a matter of mere visualization; in order to work sympathy, an arcanist has to literally split their mind in half, such that they hold two contradictory beliefs with equal conviction (a bit later, Kvothe learns how to hide information from himself by giving it to the "other" part of his mind).
That frankly doesn't sound possible, but even the first exercise seems dubious. Getting someone to honestly change their beliefs about something is notoriously difficult, as anyone who's ever entered a political debate online can attest to; now imagine how hard it would be to convince yourself that gravity doesn't work the way you've observed it to. Yet Kvothe pulls it off after an afternoon of really intense concentration. He picks it up quicker than most--Kvothe picks up everything quicker than most--but there's nothing to indicate that these skills are exceptional or out of the reach of ordinary humans. Anyone could theoretically learn them with the proper training and instruction.
This might sound like a pointless nit-pick--why can I accept the existence of magic and supernatural beings, but not impossible mental tricks?--but it highlights the often-sharp dividing line when it comes to suspension of disbelief. Magic posits the existence of something that is fundamentally impossible, and is therefore a completely fantastical invention; Kvothe's sympathy mind-games are something that anyone can do (and are explicitly stated to not be magical--Ben is very clear in stating that sympathy "isn't magic" but more like a manipulation of natural forces), which implies, accidentally or not, that the psychology of the human mind in this universe operates differently to how it does in our world. But it's the only difference we ever see. Apart from these abilities, everyone seems to think and feel exactly the same way as they do in real life.
Toning all of this down even slightly would have solved the problem. The human mind is a powerful tool, and many people can do extraordinary things through training and meditation, like memorize huge amounts of information or play high-speed games of Tetris with invisible blocks. The idea of Kvothe learning to pull off similar mental feats would have been both more plausible and more entertaining; instead, we get mental powers which seem to suggest some very odd things about how brains work in Kvothe's world.
Later, Ben teaches Kvothe how to sympathetically bind objects together, so that moving one moves the other. Kvothe finds this underwhelming and unimpressive compared to Ben's earlier wind-calling:
This scene further highlights the strange and overly-complicated way these books handle magic.
Kvothe is clearly performing magic here--he's never seen or done anything like this, it should be just as strange and wondrous to him as it would be to us--but the book has to have him be inexplicably disappointed because sympathy isn't "really" magic and there's another, even more magical magic, that Kvothe will spend most of his University days pursuing. Why exactly Kvothe is so unimpressed with sympathy and the other "common" skills he learns early in the book, or why he finds Ben's wind summoning so mind-blowing, is never really explained; it's as if he's read ahead in the story and knows that he'll be encountering more impressive stuff in later years.
Nothing else happens in this section of the story except more in-depth explanation of the mechanics of sympathy and a scene where Kvothe sings a rhyme about a certain "Lady Lackless" and her mysterious lock-box, which his mother seems inexplicably upset about. The former is dry and boring and the latter is a bit of foreshadowing that doesn't pay off until the second half of The Wise Man's Fear, so we'll skip them for now.