Bruce sits down across from her, grapples with a similar problem, and eventually digs in to The Magic of Place and Space. It's a guide to everything from trunks and tents that are bigger on the inside to places like the Leaky Cauldron that fit between two buildings that share a wall to the ability of Unplottable locations to hide themselves from every surveying instrument muggles have devised. It has a lot of math, but the author made up a lot of her own jargon and notation, which means she explains it, which means Bruce can follow it pretty well for someone whose school had never mentioned cosines let alone the difference between a manifold and a lemniscate. He doesn't understand all of it but what he does understand is amazing.

Despite, the author explains, the understandable conflation of the two by the layman, stationary structures that are bigger on the inside and movable containers that are bigger on the inside are actually almost completely different phenomena! They're both really cool, though, so she bounces enthusiastically back and forth on explaining how each one works in her space-folding notation to show how you get a similar result with a different underlying mechanism. Tents are an especially good example of this because their function is to sort of be a building.

Moveable folded spaces work by changing the relationship of volume to the dimensions that make it up; stationary folded spaces work by changing the way that points in space connect to other points in space.

To understand the difference, consider a perfectly square box one meter on each side.(1) If you stationary-spacefold your box, it continues to take up the exact same amount of space, a single cubic meter, and to have the same dimensions, but the edges are now "next to" each other, so that you can move to the other side of the box as if the internal volume were not there. Crucially, though, it is still there: if you don't also carefully foil all possible surveying instruments, as described in detail in chapter 4, they may in fact detect that you have done something to your building even though walking across the border feels exactly like walking through nothing to a Muggle. (On the small scale that's all you need, but there's an aside in chapter 4 regarding the large project undertaken in the 40s by a fellow called Mercator to ensure that some of the uninhabited bits of Antarctica look suitably larger to the surveying instruments to cancel out the amount that various magical populations cause their locales to appear smaller, so that the total apparent volume of the planet retains consistency with its actual mass and density.) 

If, on the other hand, you moving-spacefold your box, the edges do not have any unusual behavior - you can set it down on a surface, pick it up and carry it, trip over it, etc. - and each of its constituent unit volumes is adjacent to the next in a perfectly normal way. There are simply more of them, all in a row, before you reach the other side. This extra volume does not, in a sense, exist: no surveying instrument will detect it. However, it has its own danger, which is that unlike a stationary spacefold, which by its nature cannot be entered without magic, a moving spacefold may in principle be interacted with by nonmagical creatures, so it is of especial importance to place defensive charms upon any such enchanted item to prevent it from becoming a Statute violation. Or, for that matter, from collecting an improbable volume of ants in your snack basket, a nearly equally undesirable state of affairs in the author's humble and unfortunately experienced opinion. 

(1) Editor's Note: Wizards don't actually use meters, they use a standard unit length called a flob which is approximately ten imperial inches and is defined by the remarkably consistent size of an adult flobberworm. This is not at any time explained in the book, which assumes that none of its reading audience is Muggle-raised first-years, but none of the math actually requires you to know the real-life magnitude of the standard unit vector, that being the entire point of a unit vector, you just end up feeling kind of intuitively puzzled about the example sizes of buildings, so Bruce can put a pin in that and look it up later.

Ghosts, meanwhile, form when a witch or wizard dies with a combination of personality and circumstances that leaves them totally unwilling to shuffle off the mortal coil and go on to whatever comes next. What comes next might be nothing or might be something: there are legends and rumors of an afterlife and of magics that enable the living to contact the dead, but nothing concrete or verifiable. Some murder victims become ghosts in pursuit of vengeance, but it's less common than one would naively expect, possibly because being murdered happens too quickly to form the requisite determination to stay on earth for as long as it takes to get revenge. Others become ghosts due to some great guilt they need to make amends for, or to care for dependents they can't bear to abandon. If a ghost finishes their unfinished business, they may become willing to move on and swiftly fade away. If the unfinished business is impossible to resolve, ghosts persist indefinitely; the oldest known ghost haunts a stretch of the Tigris river and speaks a language no-one living can identify.

Ghosts resemble their living selves at the time of death, both physically and mentally, and retain the knowledge and skills they had in life. However, they are very mentally rigid: they can form only shallow friendships, retain old grudges long after the one begrudged is dead, and do not grow in wisdom. They can learn new facts, but not new ways of thinking; their speech and manners become more and more archaic as language and culture evolve around them.

Muggles never leave ghosts. Scholars are divided on why this is: some claim it's because muggles don't have souls, or aren't really conscious; others that muggles' lives are so much worse that they're basically always willing to move on; others, that muggles have normal souls but the creation of a ghost requires the destruction of a magical core; still others, that a ghost is actually formed from the deceased's magical core and not their soul at all, and that if there is something else after death the people who left ghosts are there too. 

Huh! 

This adds several new questions to Hermione's queue (are there older wizards than that who just didn't leave unresolved ghosts? are there not older wizards than that? in either case, why not? what exactly is a magical core and what other behaviors does it have that might be related to the ghosts thing?) but that is the opposite of a problem. There are so many things to learn, and it turns out that learning new facts while sitting companionably with new friends is EVEN BETTER than just learning new facts by itself, which she did not previously know was possible to beat as the best activity.

And then, when it is dinner time, they can trade book summaries while their hands are full, yes?

Yes! Getting additional facts while eating! Telling interesting facts to someone who actually wants to hear them! He did not think life could be this good and yet here it is, being this good, so far totally failing to manifest a catch.

Some of the interesting facts are, so help him, going to be about the Chudley Cannons 1985 season! And also anecdotes from his brother Charlie's illustrious career as the Gryffindor seeker.

Bruce's taste in information is a lot like his taste in food, i.e. all of it should go in his face at speed.

Near-simultaneously emitting and absorbing information at speed is Hermione's favorite activity!! She loves her new friends. They are very good. This is everything she was hoping magic school would be like.

Next morning's Charms and History classes are much like the first, but after lunch they have, for the first time, Herbology.

There's gonna be MAGIC PLANTS. Normal plants are already so cool, some of them eat bugs and some of them can only be pollinated by one kind of butterfly and some of them look different in ultraviolet, and MAGIC PLANTS are even COOLER though hopefully they won't have to work with the ones that try to eat people yet, getting killed by a plant would be really embarrassing. 

The greenhouses are like stepping into yet another new world. It's warmer there, and more humid, and the light that comes through the glass is a different colour from the sunlight outside and more different yet by the time it's done filtering through the layers of leaves above. There are vines arcing above them, some on a trellis and some no less thin and delicate that appear not to need one. There are flowers clustering on the walls that slowly cycle from pink to blue a few times a minute, and a planter of moss that forms a pattern of tiny hexagons, and a plant whose leaves are almost as big as Bruce's torso and flap slowly like the wings of some ponderous bird.

Inhabiting the greenhouses there is a witch, who is so clearly precisely in the correct location that it's initially very easy to not quite notice she's there. Like a frog floating past on a lilypad, consciously unnoticed because that is simply Where That Creature Goes, the gardenwitch stands among the plants not as a visitor but as a part of the ecosystem.

"Good afternoon, my dears," she greets the first-years, with warm and sincere delight, as though each and every one of them is her beloved grandchild. "Welcome to Greenhouse One. Grab a stool, be careful of the chocolate mint." She pats a leafy brown-and-yellow spotted plant that sprawls, faintly wriggling, across several boxes and also a large fraction of the floor. "It doesn't like to stay in its box but it doesn't mind being stepped on and it won't hurt you unless you trip over it."

This is a much better way for a class to be. They're probably still not going to do any magic directly but the class won't be half safety lecture (he hopes) and they'll get to do something that actually involves the subject they're supposed to be learning. 

He didn't know people could be beautiful in that particular way and it's delightful and he's kind of envious. He avoids the mint and sits on a stool and twines a leg around one of its legs.

Other Gryffindors and Hufflepuffs shuffle themselves into various stools, and she observes each in turn, collecting new faces into memory. "Excellent. I am Professor Sprout," Dean Thomas giggles, and she smiles indulgently, "and yes, you're right, that is a very funny name for a Herbology teacher to have. I picked it myself when I turned seventeen. Now, the primary focus of this class is caring for plants, especially the sorts that are useful to keep in your personal garden for medicinal and potions-making uses, but we'll also spend some time on how to recognize dangerous plants you might encounter in the wild and how to protect yourself from them." She surveys her class, more than half of whom look kind of nervous, and adds, encouragingly, "but I should assure you that all of the latter kind of lesson will be theoretical for now, until you are a little older. Nothing in Greenhouse One will try to hurt you."

That sounds way more fun than mowing and weeding the Durselys' lawn assuming he can stay out of trouble. Maybe it will be fun enough, and he is now aware of magic enough, that he will not get tired and frustrated and make any of the plants shrivel up and die with his mind. When he isn't doing that (or is only doing it to the weeds) he's actually a pretty okay gardener.

He hopes there are also exciting plant facts.

Hermione, an indoor otter nerd who doesn't particularly like to touch things with her hands, is not hugely excited for this, but if there are plant facts that is at least 300% better than plant tasks and she can probably cope with a reasonable number of the latter in exchange for the former. 

"Now then! The first plant I like to show new students is this lovely fellow," says Sprout, reaching up above her head to nudge one of the hanging vines. When poked, it obligingly turns bright blue. "This is a skyvine, and you will no longer find it outside of registered greenhouses as of 1985. Does anyone know why that might be?"

Tentative handraise. "Is it an endangered species?"

"A very good guess, Mr. Potter, one point to Gryffindor! Indeed, many of the things you will find only in greenhouses are endangered. However, in this case it's because it's illegal."

"Illegal?" says Hannah, astounded. "Plants can be illegal? What for?"

"Well - "

"Oh there are so many illegal plants actually," contributes Susan, and then realizes she's interrupted Sprout and adds, "er, sorry Professor."

"It's all right, Miss Bones, I appreciate the enthusiasm. Yes, Miss Abbott, plants can be illegal to grow outside controlled environments, or at all, for a variety of reasons, typically because they are dangerous. Skyvine is friendly," she smiles in its general direction, and it wiggles slightly, "but it's used to make flying carpets. Now, we're allowed to have it because it is among other things a part of the regular maintenance performed on the Great Hall ceiling."

Bruce wants to know why having a plant used to make flying carpets is illegal. Are flying carpets illegal? Why is that? He's definitely not going to ask, though, because for one it's off topic and for two maybe the other ingredient in flying carpets is dead babies and everyone would look at him and ask why he would ask something so awful. And then he gets totally distracted thinking about the great hall ceiling and what its maintenance involves and forgets about the flying carpets entirely.

Sprout, meanwhile, cheerfully keeps talking about the care and keeping of skyvines and then assigns them all as their practical activity of the day to collect some spray bottles from this here box and water them. (The spray bottles contain a potion, not just water, but it's basically just magic plant nutrients.)

This requires of very gently poking a vine to find out if it is a skyvine before spraying it; none of the other vines here are dangerous if touched either, but for this purpose they're just going to water the skyvines, to get practice distinguishing, and they're going to all wear their gloves to get in the habit of doing that when touching plants, some of which may someday be less friendly than these ones.

The gloves are worse than not wearing gloves but better than muggle gardening gloves and the whole activity is soothingly repetitive and hard to fail at. It's pretty nice. If Sprout seems open to being asked questions he'll ask to know more about great hall ceiling maintenance.

Sprout is not quite as effusively Continuous Output Of Fun Facts With Exclamation Points as Flitwick but she is delighted by her students engaging with the lecture material and will very sunnily answer questions about it.

The Great Hall's ceiling, she will explain, (with regular interjections from Hermione, who is also curious, and also from Justin Finch-Fletchley, who lives at home in the sort of house that has big domed ceilings and has cogent questions about where the load-bearing columns are hiding) requires regular resurfacing - "Or, I suppose I should say, it prefers regular resurfacing, if neglected it doesn't so much stop working as start moodily displaying thunderstorms regardless of the actual outside weather" - using a combination of potions, charms, and a net woven of live skyvine. The last bit is easier to do the healthier and happier your skyvine, "which is true of most plants, really. It is common to think that plants are more like objects than like creatures but this is not really true even for plants that are not very magical, as I hope you can see from all of our lovely friends here in the greenhouse."

"It's alive the whole time it's on the ceiling? Wow!"

(He doesn't have the conceptual vocabulary to ask to what degree plants are moral patients so instead he merely strengthens his desire to be nice to them.)