Alien Geometries: Difference between revisions

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[[File:another world2 9367.jpg|link=M. C. Escher|frame|[[Of Mice and Men|Which way do I go]], [[H.P. Lovecraft|Jh'rj]], [[Looney Tunes|which way do I go?]]]]
 
{{quote|''"...but you start with parallel lines that ''intersect'' and you go from there."''|'''Black Mage''', ''[[8-Bit Theater|Eight Bit Theater]]'', [http://www.nuklearpower.com/2008/06/12/episode-1004-fun-house/ #1004]}}
|'''Black Mage''', ''[[8-Bit Theater]]'', [http://www.nuklearpower.com/2008/06/12/episode-1004-fun-house/ #1004]}}
 
A staple of [[Cosmic Horror Story]] and of [[Mind Screw]] artworks. [[Eldritch Abomination|Elder Gods, Old Ones, and other horrors]] tend to bend the laws of physics to suit them. Why make a triangle where the angles add up to 180 degrees, when you can make one where they add up to 200 degrees in a flat space and get some extra room? Even the very ''body'' of a particularly squamous thing may exhibit this, though more often it shows up in architecture as physically-impossible buildings—[[Genius Loci|occasionally sentient themselves]].
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* The third season of ''[[Sailor Moon]]'' does this when one of that season's miniboss squad accidentally breaks reality, resulting in the entire house becoming a zone of warped space.
* The [[Another Dimension|Reverse World]] in ''[[Pokémon: Giratina and The Sky Warrior]]'' is an [[M. C. Escher|Escher]]-like place where 'up' varies, but [[Fridge Logic|apparently only for landbound creatures]] (see the ''Pokémon Platinum'' note in Video Games below).
 
 
== Comic Books ==
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* [[Donald Trump]]'s hair, as portrayed in ''[[Doonesbury]]''.
 
== Fan Works ==
 
== Fanfiction ==
* ''[[Harry Potter and the Methods of Rationality]]'', in line with the original ''[[Harry Potter (novel)|Harry Potter]]'' series, has this: Hogwarts' corridors which can change when you aren't looking. The number of stairs you climb has only a passing correlation to your actual elevation when you look out the window. At least one corridor is tiled in pentagons.
* ''[[Aeon Natum Engel]]'' and its rewrite ''[[Aeon Entelechy Evangelion]]'' are the crossover fanfics consisting of ''[[Neon Genesis Evangelion]]'', ''[[Cthulhu Tech]]'' and ''[[First Encounter Assault Recon]]'', with the latter adding elements of ''[[Eclipse Phase]] and ''[[Alastair Reynolds|RevelationSpace]]'' to the mix, so they have this in form of Heralds/Harbingers who replace the Angels. Mot, the equivalent of Ramiel, cranks this up to eleven.
* In ''[[Fuck the Jesus Beam]]'', there is a city that literally ''does not exist'', as it is only a lie. Despite this, it is also a physical location. Given the name Αδιβ, when someone who can see in only three dimension looks at it, it appears normal, but in progressively higher dimensions, the architecture becomes more and more bizarre.
* In the Pokémon fanfic ''[[Ash's Return|Ashs Return]]'', the doors in Glitch City manifest this way to anyone trapped inside.
 
 
== Films -- Live-ActionFilm ==
* An indie black-and-white short film of ''The Call of Cthulhu'' by [https://web.archive.org/web/20071101063857/http://www.cthulhulives.org/toc.html The H.P. Lovecraft Historical Society] does a particularly good job of getting this idea across, in a scene (faithfully adapted from [[H.P. Lovecraft|HP Lovecraft]]'s story) wherein a victim falls into a crevice which an optical illusion has led the audience to believe is a convex crag of rock.
* ''[[Cube|Cube 2: Hypercube]]'' is a rare example of this trope being employed in a visual medium. The actual warped geometry shows up only a few times, due to the special effects required being rather expensive; the rest of the time it's showcased indirectly (e.g. duplicates of characters showing up).
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:Empirical Crescent, a row of terraced houses where every door and window leads somewhere other than where you'd expect it to lead. At least it makes it easier to get rid of rubbish—just toss it into the garden. After all, it might not be your garden.
:The reason for this corruption of dimensions occurs because the row of houses is crescent shaped on the outside only. Inside, it's supposedly laid out like a straight row. Presumably the two configurations conflict. Occupants had a tendency to leave in the middle of the night, often without stopping to pack...
** ''[[Discworld/The Colour of Magic|The Colour of Magic]]'' featured a parody of Alien Geometries: the Temple of Bel-Shamharoth (itself a spoof on [[Cosmic Horror Stories]]). The most striking feature of the Temple is that its walls, ceilings and floors are composed entirely of interlocking regular 8-sided tiles. Whilst is it possible to create octagonal tiles that be fitted in a regular, interlocking way, they must be concave polygons: there is a mathematical proof that no convex polygon of seven or more faces can tessellate on a Euclidean plane.
*** The first chapter mentions one of the gods using a 7-sided (but still cube-shaped) die to cheat.
** The buildings of the Unseen University, which have been rather strongly influenced by the vast amount of magic that has flowed through its halls over the centuries, have floors and rooms where logic says they simply could not exist. Magic is as much a part of the architecture as cement.
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* In [[Larry Niven]]'s ''Protector'' the Brennan Monster amuses himself by creating full scale replicas of some of Escher's art, using things like artificial gravity to make them work.
 
== Live -Action TV ==
* The ''[[Doctor Who]]'' [[Expanded Universe]] speculates that this is the default setting for the interior of a TARDIS, and that the Doctor's TARDIS projects a more easily comprehended interior so as not to [[Brown Note|freak out]] the Doctor's human companions. [[Genius Loci|She is just a sweet old thing.]]
:In "The Lodger" the Doctor uncovers an alien time-distortion device similar to the TARDIS in the upstairs flat of a British apartment building. Amy, poring over the building plans for the address, discovered that the building didn't even have an upstairs, it was a one-story building. Perception filters kept people from noticing anything out of the ordinary.
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== Tabletop RPGGames ==
* In [[Mortasheen]], this is where the [http://www.bogleech.com/mortasheen/xenogog.htm Xenogog] lives naturally, only coming into ours with a screw up in a time travel experiment.
* The near-universal hallmark of things made in the name of Chaos in ''[[Warhammer 40,000]]''. For example the [[Exclusively Evil|Dark]] [[Our Elves Are Better|Eldar]] capital Commoragh has spatial anomalies, "wandering shadows that tear apart the unwary" and many other dire things. It lies deep within a nest of extra-dimensional tunnels.
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** As you might imagine, this makes travel around Malfeas... interesting. Once you enter the dimension proper, you must cross Cecelyne, the Endless Desert, for five days to actually get to the Demon City. No, it doesn't matter if you're walking on foot, riding on horseback, and piloting a First Age airship. The trip ''always'' takes five days. Then you get to the Demon City, which is layers upon layers stacked on top of one another - but each layer has Ligier, the Green Sun, shining above it, no matter how deep down it is.
* ''[[Werewolf: The Apocalypse]]'' has the Black Spiral Umbral Realm. Being a [[Spirit World]] the Umbra is pretty odd at the best of times, but normally follows at least the guidelines of the laws of physics, [[A Form You Are Comfortable With|if only because vistors expect it to.]] But the Black Spiral... From the outside [[Exactly What It Says on the Tin|it looks like just a spiral pattern on the floor in black.]] Once you start walking it it seems longer, twistier and with entirely too many dimensions. In fact it's a path into the mind of [[Eldritch Abomination|the Wyrm.]] No-one's ever come out the other side sane.
 
 
== Toys ==
* The ''[[Transformers]]'' already skirt the trope, what with size and mass-changing and the oddness of the scales...but then we come to the Autobot Micromaster Countdown's playset. He's a deep space explorer. He has an interstellar rocket and a command base. The base is used to launch the rocket. But also fits inside the rocket: [[Your Head Asplode|mgnaaaaa!]]
 
 
== Video Games ==
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* ''[[Fez]]''. Gomez is a 2D man suddenly gifted with the ability to shift the 2D world on the third dimension.
 
== Web Comics ==
 
* In ''[[8-Bit Theater|Eight Bit Theater]]'', Black Mage's face is apparently so hideous as to be non-Euclidean—the hat keeping his features in shadow prevents people from [[Go Mad from the Revelation|being driven insane just by looking at it]], as seen [http://www.nuklearpower.com/2001/06/18/episode-044-what-the-hell-just-happened-in-survivor-8-bit-style-part-9/ here]. A more recent strip implied that revealing himself would ''[http://www.nuklearpower.com/2008/01/05/episode-939-total-protonic-reversal/ destroy the universe]'', but this was just an idle daydream.
== Webcomics ==
* In ''[[8-Bit Theater|Eight Bit Theater]]'', Black Mage's face is apparently so hideous as to be non-Euclidean—the hat keeping his features in shadow prevents people from [[Go Mad from the Revelation|being driven insane just by looking at it]], as seen [http://www.nuklearpower.com/2001/06/18/episode-044-what-the-hell-just-happened-in-survivor-8-bit-style-part-9/ here]. A more recent strip implied that revealing himself would ''[http://www.nuklearpower.com/2008/01/05/episode-939-total-protonic-reversal/ destroy the universe]'', but this was just an idle daydream.
:When the Light Warriors enter the [[The Very Definitely Final Dungeon|new-and-improved Temple of Fiends]], Black Mage criticizes it's infantile sense of twisted geometry (The room is merely upside-down for no reason), claiming that to "draw out ancient and malevolent forces of the underverse" you need to "[http://www.nuklearpower.com/2008/06/12/episode-1004-fun-house/ start with parallel lines that intersect]".
* ''[[Gunnerkrigg Court]]'', In Chapter 19: ''Power Station'', the buildings at {{spoiler|Zimmingham}} look pretty normal from nearby, but [http://www.gunnerkrigg.com/archive_page.php?comicID=461 long-distance shots] reveal that they are at crazy angles relative to each other.
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* The polygons in ''[[Triangle and Robert]]'' tend to have their own style of geometry, leading to strips like [http://tr.froup.com/tr.pl?412 this]{{Dead link}} or [http://tr.froup.com/tr.pl?2327 this]{{Dead link}}.
* The Toymania store that serves as the main setting for ''[[TRU-Life Adventures]]'' is bigger on the inside than it is on the outside. Subverted, though, in that it's a fluke of how the measurements were taken.
* In ''[[Adventurers!]]'', [https://web.archive.org/web/20100701193541/http://www.adventurers-comic.com/d/20020614.html when Imposis is just about to leave], Ardam points out that nothing he does seems particularly impossible. Imposis gives him a Penrose triangle and continues on his way, leaving Ardam to hold it in his hands and stare at it until he gets a headache.
* From ''[[Tales of the Questor]]'', we have the ''[https://web.archive.org/web/20121018200038/http://www.rhjunior.com/totq/00513.html Unseleigh castle...]''
** Yet another homage to [[M. C. Escher]]'s "Relativity".
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* A few arcs in ''[[Fans]]'' (notably the whole of Book 5) centered around a power-object called the 23-Sider, an RPG die with 23 identical sides. When the 23-Sider was formed in Book 5 it warped reality.
* Pip in ''[[Sequential Art (webcomic)|Sequential Art]]'' chose to prove his superiority in [[Bland-Name Product|Cubeminer]] by building "[http://www.collectedcurios.com/sequentialart.php?s=684 Escher's Staircase]". The next page shows that with a few tweaks you sometimes can build ''this'' in a 3D game. {{spoiler|But there's no guarantee that the physics engine will survive an attempt to process it.}}
 
 
== Web Original ==
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* Fredrik K.T. Andersson managed to [https://web.archive.org/web/20160329142210/http://www.elfwood.com/u/andersson2/image/45293a50-23da-11e4-9fb0-6fd3a883da45/naught-or-cross invert this].
* ''[[Bravemule]]'', the saga of a ''[[Dwarf Fortress]]'', gave the dwarves an utterly bizarre culture with [[Blue and Orange Morality]]. Among other things, any shape that is not rectangular is "unscrupulous". An accidentally-created ''octagonal'' room was thus treated as horrible and incomprehensible, giving dwarves [[Catapult Nightmare]]s and such.
 
 
== Western Animation ==
* ''[[Batman: The Brave And The Bold|Batmanand the Brave And The Bold]]'' has a standard-issue Escher magical library in the [[Batman Cold Open]] of "The Eyes of Despero". Batman is largely unfazed by the shifting gravity, and actually uses it to good effect.
* ''[[Looney Tunes]]'':
* The ''Foghorn Leghorn'' cartoon "Little Boy Boo" plays this for laughs. Foghorn is playing hide and seek with a child genius and hides in the coal bin. The kid performs a few calculations and then ''digs Foghorn out of the lawn''. A very befuddled Foghorn protests that he was in the coal bin, but the kid just shakes his head and holds up the calculations. Foghorn then goes to look inside the coal bin, but decides "No, I'd better not look. I just ''might'' be in there."
** Played for laughs in the [[Foghorn Leghorn]] cartoon "Little Boy Boo". While playing hide-and-seek with Junior, Foghorn Leghorn hides in a hay bin, [[Tempting Fate|claiming the kid would need a slide rule to find him]]. Junior writes out some equations, using a slide rule no less, then marks a spot in the grass before somehow digging Foghorn up from it. This leaves Foghorn irate, at which point the child shows him the equations; forced to admit that "figures don't lie", Foghorn is nevertheless curious and makes to open the lid, but stops himself midway through.
* The titular ''[[Foster's Home for Imaginary Friends]]'' sometimes exhibits a non-malevolent version of this combined with [[Bigger on the Inside]]. In one episode, Mac is attempting to leave for dinner but he and Bloo become hopelessly lost (and begin to go crazy from hunger), when, at one point, they exit on the roof, even though they clearly went downwards.
{{quote|'''Foghorn:''' ...No, I'd better not look - [[Logic Bomb|I just ''might'' be in there]]!}}
* The titular ''[[Foster's Home for Imaginary Friends]]'' sometimes exhibits a non-malevolent version of this combined with [[Bigger on the Inside]]. In one episode, Mac is attempting to leave for dinner, but he and Bloo become hopelessly lost (and begin to go crazy from hunger), when,- at one point, they exitend up on the roof, even though they clearly went downwards.
* Presumably alien geometries are how [[Scooby Doo]] and his gang perform their [[Scooby-Dooby Doors|strange chase routines]]. Perhaps something much more sinister than anyone suspected was going on the whole time.
 
 
== Real Life ==
* [https://web.archive.org/web/20120225002759/http://physicsworld.com/cws/article/print/23009 Studies] of the cosmic microwave background radiation suggest that it better fits a Poincaré dodecahedron than a sphere.
:To make the Poincaré dodecahedron more clear: you are floating inside a giant dodecahedron. When you get to an outer face you [[Wrap Around]] to the opposite face. Except the faces don't exactly line up, so you also rotate one tenth of a rotation.
:More aptly, it is to be observed that Euclidean geometry, mathematically speaking, is a ''special case'': it only applies to forms in a space with zero curvature (for the two-dimensional case, a perfectly flat plane); something that is, strictly speaking, an abstract concept (in light of the fact that time and space are demonstrably ''curved'' by gravity.) Consider that you cannot, in Euclidean geometry, draw a triangle with three right angles, ''but it is perfectly possible on the surface of a sphere.''
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{{reflist}}
[[Category:Alien Geometries{{PAGENAME}}]]
[[Category:Architecture Tropes]]
[[Category:Hyperspace Index]]
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[[Category:Geometry Tropes]]
[[Category:Horror Tropes]]
[[Category:Alien Geometries]]