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.
This may seem impossible, and when we think through it carefully we’ll see that it basically is. A coherent notion of unplottability cannot not say anything about what I can and can’t draw on a piece of paper. Witches and wizards might, however, try to stop people from learning the location of Hogwarts from that piece of paper — the information can be encoded, but it may be possible with magic to prevent it from being transmitted.
But ultimately this won’t be enough to prevent us from using maps to find Hogwarts. Unplottability is a scam that doesn’t really work.
“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 121; page references are from the UK versions of the Pottermore ebooks).
I’m not really sure how disguising Hogwarts as a ruin will keep out Muggle archaeologists or whatever, but that’s not the point here. Just what on earth does it mean for something to be Unplottable? If I know where Hogwarts is, what stops me from drawing a map and marking “Hogwarts” on the relevant section? (I think it’s safe to assume that Hogwarts is unplottable if Durmstrang is.)
Well, drawing a map and marking “Hogwarts” on the relevant section requires knowing where Hogwarts is. One way that it would be impossible to plot Hogwarts on a map is if nobody actually knows where Hogwarts is. Maybe after the Founders build Hogwarts, they Obliviated each other to forget where they were and then brought in job candidates by Floo powder.
But how, in this case, could the rails for the Hogarts Express have been laid down centuries after Hogwarts was built? Even if some ingenious witch or wizard successfully cast the exceedingly difficult Build-a-Train-Track-From-Here-to-King’s-Cross-Station spell, you could then just follow the Hogwarts Express in the air, like Ron and Harry do in Chamber of Secrets, and record the castle’s location relative to King’s Cross.
So unplottability can’t consist simply in Hogwart’s location being unknown by everyone. If we know this much about the castle’s location, then a clever witch or wizard can certainly discover its whereabouts.
But even if that’s true, and it’s possible to discover where Hogwarts is, why can’t we be prevented from recording that information? Why did I say above that unplottability can’t mean that information about the location of Hogwarts is impossible to encode?
Let’s look at how someone might try to prevent us from encoding that sort of information. Whatever they do, I don’t think they’ll manage it:
Suppose a witch or wizard managed to cast an enchantment that had the following effect: whenever someone writes “Hogwarts” (or something sufficiently similar) at roughly the point where Hogwarts is located on a map, the enchantment erases what you’ve written. This obviously isn’t good enough, because you could refer to Hogwarts using a different name. This is a ban on using “Hogwarts” to refer to Hogwarts. It is not a ban on plotting Hogwarts on a map. If I am trying to make you a map with Hogwarts on it, I could tell you “I will write ‘Pigfarts’ instead of ‘Hogwarts’”, and then when I write “Pigfarts”, I am plotting Hogwarts on the map.
A second problem with this approach is that if the enchantment only detects when I’ve written “Hogwarts”, my writing will be visible until I finish that string of letters. If you are watching over my shoulder as I work, you will see me get at least as far as “Hogwart” and will probably infer my intention (to plot Hogwarts on this map), and the enchantment will be foiled. In order to work, the enchantment would have to determine our intentions and act before we can even start writing.
The subject of intention brings us to a second possible method to make it impossible to encode information about a place’s location.
Suppose it’s possible, somehow, to determine when I’m intending to plot Hogwarts on a map. Maybe an enchantment could figure out when I’m thinking about Hogwarts in a certain way while mapmaking, or whatever. When this happens, the enchantment makes me forget what I’m doing, or triggers something like the Tongue-Tying Curse except for writing, or in some other way prevents me from fulfilling my intention to plot Hogwarts on a map. Why wouldn’t this work?
This wouldn’t work because it’s possible for someone to make something that functions as a map showing the location of Hogwarts without intending to. Suppose a Muggle child is drawing fake maps for fun and accidentally draws one with a castle in just the right place on an accurate representation of the Scottish highlands. It’s even possible that — by a massive coincidence — the child could decide to label this castle “Hogwarts”.
Now, while there’s definitely a sense in which this Muggle child has not plotted Hogwarts on a map, the following scenario could still occur: the child drops their map while leaving King’s Cross, and it is picked up by a witch or wizard, who has been seeking the location of Hogwarts. They assume that someone plotted Hogwarts on a map and then dropped it. They guide themselves using this map, and as a result arrive at Hogwarts.
Our first solution was obviously insufficient, in part because it failed to account for a mapmaker’s intention. But in our examination of the second solution, we can see that accounting for the mapmaker’s intention won’t work either. Our scenario, involving the child serendipitously writing “Hogwarts” in exactly the right place on a map of the Scottish highlands, might be a scenario in which it’s strictly false that Hogwarts was plotted on a map, but the spirit of the idea has clearly been violated. The point of unplottability is to keep people from using maps to locate Hogwarts.
So we should look next at how a witch or wizard would use a map to find Hogwarts.
The crucial detail of our scenario above was that the witch or wizard who finds the child’s map assumes that the author intended to plot Hogwarts on their map. They believe — incorrectly, in this case — that the map was written with a communicative intention. The witch or wizard believes — again incorrectly — that they recognize the communicative intention of the author, which is to communicate to the reader the location of Hogwarts.
Suppose our witch or wizard had not made this mistake. Suppose they overheard the Muggle child taking about the map before dropping it, and realized that it was pure coincidence that led the child to label a map with “Hogwarts”. If the witch or wizard nonetheless picked up the map, they would not mistake it for a map showing the location of Hogwarts because they would not take themselves to recognize the author’s communicative intention. They would not think that the map was written with a communicative intent. They would not learn anything from the map because they wouldn’t imagine that there is anything to learn. Information transmission of this sort requires the belief in a communicative intention, and when this is missing it will not occur.
So if unplottability does anything at all, it prevents readers of maps from recognizing a communicative intention. Even if a witch or wizard finds a map on which Hogwarts has been plotted, the effect of unplottability will be to block the recognition of the mapmaker’s communicative intention. The reader will not believe that they are reading a map showing the location of Hogwarts, but will instead be in a situation similar to the witch or wizard who knows that they are looking at the scrawlings of a Muggle child.
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 Muggle child.
It’s hard to imagine what it would be like to experience this situation, but whatever, it doesn’t matter, it’s magic.
Everything seemed to be coming together nicely until I got this comment from an anonymous reviewer:
With all due respect my lord, there’s just one tiny flaw with this flawless plan … the Marauder’s Map.
Augh, you’re right!
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 Hogsmeaderelative to Hogwarts, this process allows us to bypass Hogwarts’ unplottability.
Now you might be thinking, “Whatever, Snape. This loophole probably only affects Hogwarts, because no other unplottable locations have (a) comprehensive internal maps and (b) passages leading out towards plottable locations. Who cares?”
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 what the hell?
My only guess at this point is that unplottability is a scam. There aren’t enough jobs in the wizarding world so the Ministry made up things like unplottability and the Trace in order to create positions for otherwise useless people who couldn’t pass their O.W.L.s. They go around making things like the World Cup stadium unplottable and get to feel good about themselves, because given the level of intelligence in the wizarding world they probably don’t realize that what they’re doing is useless.
Maybe unplottability still does prevent information transmission, and maybe it doesn’t. Either way it’s basically useless, but that shouldn’t be a big surprise.
I got valuable feedback from @helenrobynne and @zayalhawa. Let me know what I still got wrong on Twitter.