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Spawned from a discussion in the comments of: Why didn't Harry use the right-hand-rule (or other methods) to solve the Triwizard maze?

In the 4th book of the Harry Potter series, Harry uses the Four-Point spell to supposedly know which direction to go in order to get to the maze:

Harry had soon mastered (...) the Four-Point Spell, a useful discovery of Hermione that would make his wand point due north, therefore enabling him to check whether he was going in the right direction within the maze.

How, exactly, would knowing which way is North help him to find the center? He might know where the center is in relation to where he's started, sure. So if for example he started on the southern edge of the maze, he knows he has to go north. But then what? He travels north for a while, or at least as north as he can go given the maze walls and obstacles. At some point, he will have passed the center of the maze, and it will be somewhere south of him. But he has no way of knowing when that happens. He has no way of knowing when "north" is any longer the direction to be going, and is instead taking him farther away from the center rather than closer to it.

Forgive my exceedingly crude illustration:

enter image description here

At the point he enters the maze, he can know he has to go North. When he reaches a barrier, he randomly chooses to go left (West). Then another corner forces him to go North again. At the point of the dot near the North-West corner (assuming I was better at drawing and he couldn't actually see the cup from where he was), how would knowing which way is North help him to decide to go left or right? It would only work if Harry knew he had already passed the point where the cup was directly East of him. Without knowing that, there's no way of knowing if North or South is correct way to go.

Is this just an error in the reasoning by J.K. Rowling, or is there some fundamental aspect of compasses and mazes I'm not understanding?

  • he actually has a few more turns then that, and at one point rounds a corner, as we dont even know if the paths are straight they could be diagonal as well, or even curved and rounded. – Himarm Jun 2 '16 at 14:31
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    "Is this just an error in the reasoning by J.K. Rowling" Yes. Always. I love her, I just don't go pulling at the threads. – Anthony Grist Jun 2 '16 at 14:44
  • @Himarm I didn't intend for it to be an accurate representation of the actual maze in the book. Just to demonstrate that someone who doesn't know where he is in a maze can't find "North" useful to locating the center – Paul L Jun 2 '16 at 14:56
  • Most people have a rough sense of direction and spatial distance. But when everything looks the same, and you can't distinguish your surroundings, you get lost. A functional compass gives you a single reference that you can work with to get that sense back. It's nowhere as good as a map, but it helps. – Radhil Jun 2 '16 at 20:04
  • I don't know if you've ever actually been through a maze. I haven't had much experience, but what little I've had suggests to me that having some way of orienting yourself does indeed help, presumably by making it easier for you to build a mental map of the parts of the maze you've already been through. – Harry Johnston Jun 3 '16 at 1:29
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While the Four-Point Spell tells Harry where North is, he also has other important pieces of information:

  • the maze occupies the area of the Quidditch Pitch (an oval 500 feet long and a 180 feet wide)
  • the goal is to reach the center of the maze

How does he use this information?

  1. At the get-go Harry knows the distance from his position to the cup (of course, the other champions know this too).

    For example, if the champions enter the maze from South and the longer axis of the pitch runs N-S Harry knows that the cup is 250 feet North (this is probably not the case, but bear with me).

  2. Now, Harry need to keep track of the distance he travels in the North-South direction and in the East-West direction:

    For every step he is forced to take East or West, he knows he will have to later take a step in the opposite direction.

    Moving North decreases his distance from the cup; should he move North more than 250 feet, he would have to start moving South when possible.

  3. Every time he meets a fork, he can make a decision according to the cup's relative position (i.e. choosing the path that seems to go in the direction of the cup, or avoiding the one going in a completely different direction).

In order to have an (approximate) idea of the length he is walking, he can either count his steps or look at the end of the "segment" and estimate that distance (being a Quidditch player, he is probably quite good at it).

However, knowing the cup is currently 50 feet West and 20 feet South would have no use if he didn't know anymore where West and South are due to all the turns he took.

Vice versa, knowing where North is would not give him a clue if he didn't know the direction of the cup. So, the spell is a helpful tool, but it is not enough to guide Harry effortlessly to the cup (otherwise, it would probably be considered cheating).

Bottom line:

The Four-Point Spell tells Harry in which direction he is moving, so that he can correctly update his mental record of the cup's relative position.

2

The point of the spell was for Harry to know which direction he was traveling in relation with his goal. With it being dark out, it will be extremely easy for Harry to wander in part of the maze thats in the wrong direction from his goal.

Harry is shown using the spell repeatedly.

‘Point me,’ he whispered to his wand, holding it flat in his palm.The wand spun around once, and pointed towards his right, into solid hedge. That way was north, and he knew that he needed to go north-west for the centre of the maze. The best he could do was to take the left fork, and go right again as soon as possible.

The second time he uses it he had been traveling generally in one direction for a while,

Left ... right ... left again ... twice he found himself facing dead ends. He did the Four-Point Spell again, and found that he was going too far east. He turned back, took a right turn and saw an odd golden mist floating ahead of him.

How does he determine he went too far east, when his wand points north? Most likely his current path he was on was leading east, and he determined he had been generally traveling east for a while now.

The third time he uses it we dont actually know where Harry is, or what direction he's headed,

He took a left path, and hit a dead end, a right, and hit another: forcing himself to stop, heart hammering, he performed the Four-Point Spell again, backtracked, and chose a path that would take him north-west.

He still believed he was south and east of his goal, most likely he had hit the south eastern corner some time ago and had been lost in the maze in that corner for a while.

After this he seems to start using it at every turn or fork,

Harry moved on, continuing to use the Four-Point Spell, making sure he was moving in the right direction. It was between him and Cedric now. His desire to reach the Cup first was now burning stronger than ever, but he could hardly believe what he’d just seen Krum do.

This leads me to believe the paths are not square and that he isnt taking just straight paths that lead N, S, E, W, but that the maze has curves and angles, which is why his point me spell is far more effective, in telling him which paths lead where.

Finally

He had a choice of paths up ahead. ‘Point me!’ he whispered again to his wand, and it spun around and pointed him to the right-hand one. He dashed up this one, and saw light ahead. The Triwizard Cup was gleaming on a plinth a hundred yards away. Harry had just broken into a run, when a dark fig- ure hurtled out onto the path in front of him.

The first time he clearly knew where he was in relation to the center. The second time we can be reasonably sure he knew he was still south of the center and had been headed east for a while. The third time we can still be reasonable sure he believed he was south of his goal.

Then she spoke, in a deep, hoarse voice. ‘You are very near your goal. The quickest way is past me.’ The sphinx smiled more broadly. She got up, stretched her front legs, and then moved aside for him to pass. ‘Thanks!’ said Harry, and, amazed at his own brilliance, he dashed forwards. He had to be close now, he had to be ... his wand was telling him he was bang on course; as long as he didn’t meet anything too horrible, he might be in with a chance ...

We can see that Harry clearly believed he was still on the south side of the maze so when his choice between a north and a south path came up after the sphynx he choose north and it paid off.

As you've said this could lead him to go the wrong way if he had passed it, but luckily he seemed well aware of where he was in relation to the center.

JKR seems to have given Harry excellent spatial awareness, so that he could visualize how far in any given direction he had gone in relation to the middle and the start of the map.

In reality the use of a compass would not be much help deep in the maze for finding the middle, but it would allow you to know which direction you were currently traveling.

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    Yes, and I'm asking how the wand pointing north tells him anything about the direction he's traveling in relation with his goal. "I'm going north" doesn't mean squat when you don't know if the goal is north, south, east, or west of you. – Paul L Jun 2 '16 at 14:03
  • @PaulL he knows where the goal is – Himarm Jun 2 '16 at 14:04
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    When he starts the maze he does, sure. He knows it's in the center. As he travels the maze, he has absolutely no way of knowing where it is in relation to him. – Paul L Jun 2 '16 at 14:05
  • okay, so after your latest edit, you're now changing your answer to "It didn't", correct? You're saying the second time we see him use the spell, it was of no use at all, and he simply just randomly decided to go north, and happened to be correct. Have I interpreted you correctly? – Paul L Jun 2 '16 at 14:10
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    @Himarm To be fair Harry does seem to develop a good knowledge of Hogwarts' shortcuts and hidden passageways pretty quickly. Obviously his night time wanderings and the Marauder's Map contributed a lot to this. But by his fifth year, Harry presumably has the best knowledge of the school's layout among the students apart from the Weasley twins. Hogwarts' interior layout is quite extensive and labyrinthine and Harry does seem to learn it fairly quickly. So we can assume that his sense of direction is not too shabby. – ʀᴇᴅ_ᴅᴇᴠɪʟ226 Jun 3 '16 at 5:12

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