What’s Baruffio?

Baruffio is a blog for people who take silly things way too seriously. It’s where you can read ludicrously in-depth analyses of a single spell. It’s where the only argument against a conspiracy theory is that it’s not consistent. It’s where we’re still talking about Harry Potter, after all these years.

“Point me!”

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In Harry Potter, places like Hogwarts are hidden from unwelcome eyes with a number of protective enchantments. One of these enchantments makes the building unplottable, and so—apparently—incapable of being plotted on a map.

It’s not immediately obvious how this is possible. Some of the simpler and more obvious proposals as to how Unplottability might work turn out to be no good. Unplottability cannot not say anything about what I can and can’t draw on a piece of paper. It’s possible with magic to prevent the information from being transmitted, but this won’t be enough to prevent us from using maps to find Hogwarts.

What does work is something more drastic: Unplottability has to prevent us from inferring the location of a place from other information. The benefit of this radical solution is that it preserves the spirit of Unplottability, which is to prevent people from figuring out where Hogwarts is.

What we know about unplottability

The first mention of Unplottability is in Goblet of Fire:

“But Hogwarts is hidden,” said Hermione, in surprise, “everyone knows that … well, everyone who’s read Hogwarts: A History, anyway.”

“Just you, then,” said Ron. “So go on—how d’you hide a place like Hogwarts?”

“It’s bewitched,” said Hermione. “If a Muggle looks at it, all they see is a mouldering old ruin with a sign over the entrance saying DANGER, DO NOT ENTER, UNSAFE.”

“So Durmstrang’ll just look like a ruin to an outsider, too?”

“Maybe,” said Hermione, shrugging, “or it might have Muggle-Repelling Charms on it, like the World Cup Stadium. And to keep foreign wizards from finding it, they’ll have made it Unplottable—”

“Come again?”

“Well, you can enchant a building so it’s impossible to plot on a map, can’t you?”

“Er … if you say so,” said Harry (GoF, chapter 11).

I’m not really sure how disguising Hogwarts as a ruin will keep out Muggle archaeologists, but that’s beside the point. We’ve got one fact about Unplottability: it can apply to buildings and it makes it impossible to plot them on a map. But we learn in Half-Blood Prince that it applies to individual rooms as well:

“Harry Potter, sir,” squeaked Dobby, his great orblike eyes shining in the firelight, “the Malfoy boy is breaking no rules that Dobby can discover, but he is still keen to avoid detection. He has been making regular visits to the seventh floor with a variety of other students, who keep watch for him while he enters—”

“The Room of Requirement!” said Harry, smacking himself hard on the forehead with Advanced Potion-Making. Hermione and Ron stared at him. “That’s where he’s been sneaking off to! That’s where he’s doing … whatever he’s doing! And I bet that’s why he’s been disappearing off the map—come to think of it, I’ve never seen the Room of Requirement on there!”

“Maybe the Marauders never knew the Room was there,” said Ron.

“I think it’ll be part of the magic of the Room,” said Hermione. “If you need it to be Unplottable, it will be” (HBP, chapter 21).

Setting aside whether the Room is Unplottable or not, all the evidence we’ve got so far is compatible with Unplottability being nothing more than a restriction on what can be written down on a map. But if the point of Unplottability is to keep the location of a place secret, this hardly seems sufficient.

Fortunately there’s textual support in Order of the Phoenix for Unplottability being more than this sort of limited restriction:

“[Number 12, Grimmauld Place is] ideal for Headquarters, of course,” Sirius said. “My father put every security measure known to wizardkind on it when he lived here. It’s unplottable, so Muggles could never come and call—as if they’d ever have wanted to—and now Dumbledore’s added his protection, you’d be hard put to find a safer house anywhere” (OotP, chapter 6).

As a matter of fact, Sirius can’t be right when he says that Muggles could never come and call. Durmstrang—and, we’ll assume, Hogwarts—are Unplottable, but students have to be able to get there somehow. Likewise, if it weren’t for the fact that Number 12 is also protected by the Fidelius Charm, I don’t see how any sort of Unplottability could have prevented a Muggle from walking up to the front door, unaided by any map.

But if Unplottability can at least sometimes prevent Muggles from finding Number 12, then it’s clearly more than a restriction on what can be drawn on a map. But this leaves unexplained exactly what Unplottability is and how it works.

So let’s figure that out.

Maybe I can draw you a map, but you can’t understand it

We’ve seen that Unplottability can’t just be about what I can or can’t draw on a piece of paper. More precisely, it doesn’t just prevent me encoding certain information on a map. It has to also keep people from getting to the place that’s Unplottable. So the obvious idea is that Unplottability somehow prevents us from using a map to locate Hogwarts (or any other Unplottable location). How would that work?

When I read a map, I assume that the author intended to plot the locations of certain places on their map. I read the map with the belief that it is written with a communicative intention. When I find the location of a place on the map, I believe that I am recognizing the communicative intention of the author, which is to communicate to me the location of the place.

If I do not believe that there is this sort of communicative intention, I will probably not assume that I can use the map to find the locations of places. If I am a schoolteacher and I have my students create maps of imaginary places, I will not pore over them later to learn the locations of the places “plotted” on the maps. I know that they were not drawn with that sort of communicative intention, and so I would not—mistakenly—take them to be real maps of real geographic areas. I would not learn anything from the maps because I can’t imagine that there is anything to learn.

So here’s a possible explanation for how Unplottability works: it prevents us from recognizing the communicative intention behind maps of Unplottable locations. Even if a witch or wizard finds a map on which Hogwarts has been plotted, the effect of Unplottability would be to block the recognition of the mapmaker’s communicative intention. The reader would not believe that they are reading a map showing the location of Hogwarts, but will instead be in a situation similar to the schoolteacher looking over the students’ maps.

This kind of unplottability would play out in strange ways. If I plotted a map of Hogwarts, then pushed it across the table at you, saying “Look! I plotted Hogwarts on this map; you can use it to learn its location”, you would somehow nonetheless fail to recognize the communicative intention of the map. You might suppose that I believe I have plotted Hogwarts but haven’t, or that I am only pretending to plot a map, like the students were.

It’s hard to imagine what it would be like to experience this situation, but that’s no objection to the theory: it’s magic.

The problem is that there is an objection to this theory (which was brought to my attention by @helenoftroyius).

I can still find Hogwarts if I can’t read your map

The Marauder’s Map is a “internal” map of Hogwarts, so it doesn’t, strictly speaking, show the location of the castle. But since it shows the secret passages leading to Hogsmeade, it’s possible to figure out where Hogsmeade and Hogwarts are in relation to each other. Hogsmeade is almost certainly plottable, so using the Marauder’s Map to learn the location of Hogsmeade is unproblematic. But because Hogsmeade is plottable, we can easily find it on a map, and therefore—because we used the Map to find the relative location of Hogwarts—locate Hogwarts. We’re using maps only to find plottable locations, but by learning of the location of Hogsmeade relative to Hogwarts, this process allows us to bypass Hogwarts’ unplottability.

Now you might be thinking that this loophole probably only affects Hogwarts, because no other unplottable locations have (a) comprehensive internal maps and (b) passages leading out towards plottable locations. So who cares, right?

But things are actually much much worse than this. We can learn the location of Hogwarts relative to Hogsmeade by using the Marauder’s Map, but we can also figure it out by walking there. The Map isn’t actually the problem. I can just as easily walk from Durmstrang to the first plottable village. Boom, I know where Durmstrang is.

So Unplottability can’t just consist in preventing me from recognizing a communicative intention. It has to be something more, if it’s going to work.

A, and if A, then B, therefore … what?”

An earlier version of this essay concluded that Unplottability was impossible. Jacob T. Levy, Tomlinson Professor of Political Theory at McGill University, found that pessimism unwarranted and proposed a solution:

An S.E.P., or Somebody Else’s Problem, field, “utilizes a person’s natural tendency to ignore things they don’t easily accept” by causing them to simply ignore certain information:

Any object around which a S.E.P. [field] is applied will cease to be noticed, because any problems one may have understanding it (and therefore accepting its existence) become Somebody Else’s. An object becomes not so much invisible as unnoticed.

A perfect example of this would be a ship covered in a S.E.P. field at a cricket match. A star ship taking the appearance of a large pink elephant is ideal … you can see it, but because it is so inconceivable, your mind can’t accept it. Therefore it can’t exist, thus [you ignore it].

This proposal raises difficult and delicate questions in the philosophy of mind that I don’t know how to answer. But it also suggests an even simpler solution: whenever I try to infer from some pieces of information to the location of Hogwarts, the Unplottability enchantment blocks that inference.

When I walk from Hogwarts to Hogsmeade, measuring the distance, I may end up with this bit of knowledge:

  1. I walked 1km, northwest, from Hogwarts to Hogsmeade.

It may not be obvious at first, but just knowing that does not mean that one automatically knows this:

  1. Hogwarts is 1km southeast of Hogsmeade.

I can infer (2) from (1), but I have to know some other things as well. Things like:

  1. If I walk a certain distance from point A to point B, A is that far from B.

  2. If A is a certain distance from B, then B is the same distance from A.

  3. If B is northwest of A, then A is southeast of B.

Of course all these things are obvious, so we don’t usually think about how we rely on them for drawing equally obvious conclusions like (2). But we do rely on them, and we also rely on inference rules that allow us to move from our premises to our conclusion. For example, just to conclude that Hogwarts is 1km from Hogsmeade, I have to reason like this:

“Therefore” marks the point at which I make an inference. If I somehow fail to see that there is a valid inference to be made, I may be left with only the first two pieces of information, not knowing whether Hogwarts is 1km from Hogsmeade or not.

This, I suggest, is exactly the situation I will be in, because the Unplottability enchantment will prevent me from making inferences that would allow me to learn the location of Hogwarts. I will be like Lewis Carroll’s Tortoise, except unable—rather than simply unwilling—to see that if A is true, and A then B is true, that B must be true as well.

Thus, even if I know where Hogsmeade is, and know that I have to walk 1km from Hogwarts to Hogsmeade, because Hogwarts is Unplottable I cannot use this information to determine where Hogwarts is, because I simply fail to make the simple but necessary inferences. Likewise, after their adventure in the flying Ford Anglia in Chamber of Secrets, Harry and Ron might know both where King’s Cross Station is and how far they traveled to get to Hogwarts, but Unplottability prevents them from thereby deducing where Hogwarts is.

There’s no reason to think that this enchantment could only prevent inferences from map-based information; it would hardly honor the spirit of the spell to suppose that if I had learn where Hogsmeade is without using a map, that I could then determine the location of Hogwarts. If the purpose of Unplottability is to keep the location of a place secret, then a blanket ban on the sorts of inferences that would betray that secret seems entirely plausible.