2026/04/26 The Non-Euclidean World and Labyrinth
I look from my office window where I sit, and I see the sweet summer sunset. The gentle breeze brushing the tree leaves. Cars driving forwards keeping a set distance from one another. A tarmac drive which is flat and at rest. These are all simple facts of reality. I look out - and so could you - upon a world at peace and a world well-ordered. The trees are not dancing like ents, the cars walk not on their hind wheels, and neither is the ground undulating like the surface of the satellite Europa. Some take umbradge at this world's banality, though I have reason to think such sentiments give little thought to the alternative. The alternative to an ordered world is a chaotic world, a world without rules; a world where the wind, the rocks, and the trees have the agency of men, and the sinfulness of men to boot. Thank God, I say, we do not live in such a world.
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Yesterday, I was at the theatre with RiceIsNice to watch the film Labyrinth with a live orchestral performance of the soundtrack. It was quite smart how they did it: they had remixed the film without any of the music save the vocal tracks, and had the live band playing on the stage. A man in the back sat with the mixer, and dynamically mixed the musicians with the vocal track of the film. If you haven't seen the film before, I'll give a brief description as to what the film is like. Stylistically, it can be best summed up with two of its creative leads: Jim Henson, the creator of the Muppets, and Terry Jones, one of the Pythons. Now, if you were to blend together the Muppets and Monty Python, and then add to that a large helping of '80s cheese, you begin to approach quite a vivid sense for the aesthetic and feel of the film. The special effects used are simply marvellous. Even to an untrained eye like myself, it's clear that the techniques used to puppeteer the goblins is incredibly impressive, especially the scene with the fire-bird-creatures featured during the second insert song of the film, where these creatures were tossing around their appendages to one another. You really can't get effects like these in the era of CG; it's a dying art. The story, then, follows thus. A young girl, the kind who lives in fantasy and stories, is irritated at her parents burdening her with child-minding her baby brother. She wishes he be taken away by the goblins. But to her dismay her wish was granted, and Gareth the Goblin King - played by David Bowie - takes the baby Toby and hides him in his castles at the centre of his Labyrinth; and, if Sarah, the girl, is unable to retrieve her brother before the clock strikes 13 o'clock, Toby will be transformed into a goblin.
13 o'clock. We already see part of the nature of the Goblin Kingdom, that the goblin kingdom is not a place where the rules of our world are followed. Twelve is a number completeness - there are roughly twelve full moons in a year (each is a moonth of a year) - whereas thirteen most certainly isn't. Thirteen has a kind of imbalance to it, hence it being seen as a cursed number today. There are no easy divisions of thirteen as there are for twelve. The story proceeds with Sarah trying to get past the very first wall of the Labyrinth to begin her quest, and there she meets a dwarf named Hoggle who is spraying faeries with pesticides. Sarah is outraged - why was he killing such cute little faeries? That is, of course, until one of them bites her. Continuing around the perimeter of the wall, she meets a tiny worm. The worm teaches her, "things are not always what they seem in this place, so you can't take anything for granted", and then shows her how to walk straight across one of the walls and through.
After further wandering through the maze, using her lipstick to point the direction she's travelling. However, the tiles she's marking keep getting altered. She comes across two doors, each guarded by a two headed guard, one head atop and one below like a playing card. An abridged dialogue is below:
SARAH: Someone has been changing my marks, what a horrible place this is.....It's not fair B.LEFT GUARD: That's right, it's not fair (they both laugh) B.LEFT GUARD: But that's only half of it SARAH: (walks over to them) This was a dead end a minute ago B.RIGHT GUARD: No, that's the dead end behind you (they both laugh) SARAH: (turns to look at it) It keeps changing, what am I supposed to do? B.LEFT GUARD: Well the only way out of here is to try one of these doors B.RIGHT GUARD: One of them leads to the castle at the centre of the labyrinth, and the other one leads to.....certain death SARAH: Which one is which B.LEFT GUARD: Uh, we can't tell you SARAH: Why not B.LEFT GUARD: Uh, we don't know B.RIGHT GUARD: But they do (points to the top ones) SARAH: Oh, then I'll ask them T.LEFT GUARD: No, you can't ask us, you can only ask one of us T.RIGHT GUARD: Yes, it's in the rules....but I should warn you, one of us always tells the truth and one of us always lies that's a rule too, he always lies (points to t.left guard) T.LEFT GUARD: I do not, I tell the truth T.RIGHT GUARD: Oh what a lie SARAH: (to t.left guard) Alright, answer yes or no, would he (t.right guard) tell me that this door leads to the castle? T.LEFT GUARD: (thinking) Uh, yes SARAH: Then.....the other door leads to the castle and this door leads to certain death T.LEFT GUARD: How do you know, he could be telling the truth SARAH: But then you wouldn't be, so if you told me he'd say yes, I know the answer is no. T.LEFT GUARD: But I could be telling the truth SARAH: Then he would by lying, so if you told me he said yes I know the answer would still be no T.LEFT GUARD: Wait a minute...(to t.right guard) is that right? T.RIGHT GUARD: I don't know, I never understood it (laughs) SARAH: No, it's right, I figured it out, I could never do it before, I think I'm getting smarter (opens the second door and walks in) it's a piece of cakeAnd in a moment of dramatic irony, she falls into an oubliette. As Sarah points out, this world isn't fair. There's a grave injustice at having your surroundings change around you whilst you're trying to solve a puzzle. And neither is it fair if you're given a riddle, and come up with a witty solution, only for the riddlers to become confused; and to then have your answer be meaningless, and fall into a door-less dungeon anyway. In our world nature is fair. You can throw a rock into a river and know how hard to throw, what trajectory to aim given the wind and whatnot, and the rock will hit the river, should you have the skill. Then you will see the water ripple in ovals from the point of impact, just as expected, and perfectly justly. Taken a step further, one can use mathematics to calculate the force and trajectory of the throw to aim for a still more precise spot in the river. Mankind has taken this art so far we can send ICBMs into space and hit targets the other side of the Earth with pin-prick precision. This is the 'fairness' of nature: that these constants never change. Thrown into a far less fair dimension of the Goblin King's labyrinth, such assumptions of geometry and mechanics - that one turn will lead to another turn, and that the path from which you came won't morph into a dead end - are null and void. Anything can happen. The world's logic is non-Euclidean. We'll now pass ahead through the lion's share of the plot to the finale. I feel it's no spoiler to say that Sarah develops a posse of noble companions who fight and fumble their way into the Goblin King's castle. Sarah takes the final showdown with Jareth alone. She walks the stair to where the Goblin King is enthroned only to walk into an Escher illustration - the famous one with the winding stairs in all different directions. She walks into a non-Euclidean space. She's trying to run after her baby brother and retrieve him, but as she ascends each impossible staircase, her brother crawls away into a different dimension of.. gravity, I suppose you could call it, and gets away from her. In non-Euclidean space, it doesn't matter how far you run forward: running forward could even send you backwards! You aren't operating in a game with rules - that being nature - but instead you're at the mercy of chaos, of anarchy, of a lawless nature which just isn't fair. As an aside, for those in suspense, she does of course retrieve her baby brother. But not before a lengthy interesting scene where the Mephistophelean Jareth offers her everything she should ever want, and says everything he has done was for her sake. Sarah is unfazed, and repeats, "you have no power of me," to the demiurge of this pocket-reality, before awakening in the real world. I must now make a confession. Everything written thus far is but a preface to a Chesterton quote:
The sun rises every morning. I do not rise every morning; but the variation is due not to my activity, but to my inaction. Now, to put the matter in a popular phrase, it might be true that the sun rises regularly because he never gets tired of rising. His routine might be due, not to a lifelessness, but to a rush of life. The thing I mean can be seen, for instance, in children, when they find some game or joke that they specially enjoy. A child kicks his legs rhythmically through excess, not absence, of life. Because children have abounding vitality, because they are in spirit fierce and free, therefore they want things repeated and unchanged. They always say, "Do it again"; and the grown-up person does it again until he is nearly dead. For grown-up people are not strong enough to exult in monotony. But perhaps God is strong enough to exult in monotony. It is possible that God says every morning, "Do it again" to the sun; and every evening, "Do it again" to the moon. It may not be automatic necessity that makes all daisies alike; it may be that God makes every daisy separately, but has never got tired of making them. It may be that He has the eternal appetite of infancy; for we have sinned and grown old, and our Father is younger than we. The repetition in Nature may not be a mere recurrence; it may be a theatrical ENCORE. Heaven may ENCORE the bird who laid an egg. If the human being conceives and brings forth a human child instead of bringing forth a fish, or a bat, or a griffin, the reason may not be that we are fixed in an animal fate without life or purpose. It may be that our little tragedy has touched the gods, that they admire it from their starry galleries, and that at the end of every human drama man is called again and again before the curtain. Repetition may go on for millions of years, by mere choice, and at any instant it may stop. Man may stand on the earth generation after generation, and yet each birth be his positively last appearance.Our world has causality, and it's a jolly good thing it does. There's something deeply fair to causality, which we each day take for granted. We know not what it's like to live without causality, so we know neither to what extent we are indebted. That the griffin continues to lay eggs, that the rock repeats its trajectory, that the sun, and the moon too, rise day upon day, these are all causes over which to rejoice. It is God's encore. We don't live in a world where we are caught out by non-Euclidean planes, nor in a labyrinth of nonsensical happenings, and thank God for it. The very structure of reality, the logos which undergirds the falcon's glide, the rose's blooms, the volcano's eruption, and the bee's buzz, continues to be upheld by God out of love for His creation. It is cause to give thanks and worship.