More Than Three Dimensions

A popular idea in fiction that features Time Travel is the idea that time is not really any different from space—for whatever reason, we just can't perceive it as a spatial dimension or travel through it without technological assistance. Varying explanations are given for this.

In Real Life, it's (more or less) generally accepted that there are three spatial dimensions that we can perceive and interact with. Time is recognized as a fourth dimension, but with fundamental differences in how it works versus how space works; obviously, we can't just "turn around" and walk backward in time, or "turn around" and "remember" the future.

The idea of time as a spatial dimension has some roots in reality, as time is recognized by Real Life physicists and theoreticians as being closely tied to the dimensions of space, but not as a physically identical dimension. Additionally, string theory posits that there may be as many as eleven spatial dimensions that we just haven't evolved to perceive due to our inability to interact with them—a common (and very limited, but go with it for now) analogy is to imagine an ant that can only travel in two dimensions (barring its ability to climb up things, an ant cannot jump or fly), so the ant has naturally evolved to perceive the universe as two-dimensional.

Note that the most common way to play this trope is to have time portrayed as a fourth dimension, which explains why it's mostly encountered in fiction about Time Travel, but the core idea of the trope is simply that there are more than three spatial dimensions. A work that explores the ramifications of string theory's eleven dimensions, then, would be an unusual, but perfectly valid, example.

One of the earliest explorers of the idea of 4+ spatial dimensions was mathematician and Science Fiction author Charles Howard Hinton, who coined the term "tesseract", a four-dimensional cube. It's worth noting that any mention of a tesseract in fiction is practically a stock example of this trope. Hinton also coined the terms "ana" and "kata"note , now frequently used to refer to movement along the axis of a fourth spatial dimension (in the same sense as up/down for height, left/right for width, and forward/backward for length).

Note that this trope is not about just any work that features Time Travel, nor is it about a work that casually refers to time as a fourth dimension, unless it's made clear that time is being treated as "just another dimension like space".

Frequently found overlapping with Alien Geometries. The distinction between the two is that under normal circumstances (well, as normal as this sort of thing can be anyway) an object occupying more than four dimensions will still follow all standard rules of normal euclidian geometry note . If the additional dimensions are curved, however, normal geometry points to M. C. Escher and grabs a bucket of popcorn.

Not to be confused with Another Dimension or any of its Sub-Tropes—this is "dimension" in the sense of geometric dimensions, not parallel worlds or universes. Of course, the two may overlap.


Examples

Anime and Manga
  • Doraemon: There are at least four dimensions in existence, as the titular Doraemon's Bag of Holding is referred to as a "Fourth-Dimensional Pocket".
  • In The Melancholy Of Haruhi Suzumiya, Mikuru Asahina describes Time Travel as moving in a four-dimensional direction across a series of stills, as in an animation.
  • In the world of Tenchi Muyo!, there exist 22 dimensions, each with a 'supervisor' that oversees it. The Choushin Goddesses exist in the 'hyper-dimension' beyond dimensional space, and created the 22 dimensions as an experiment. This is a major plot point of the third OAV.

Comic Books
  • In Whatever Happened to The Man of Tomorrow?, Mxyzptlk, an inhabitant of the Fifth Dimension, reveals his true form. Lois Lane struggles to describe it afterwards:
    It had height, length, breadth, and a couple of other things. [...] Looking at it made my head hurt.

Fanworks

Film—Live-Action
  • Cube 2: Hypercube takes place inside what the film interchangeably refers to as both a "hypercube" and a tesseract. The film is not totally consistent with whether the fourth dimension is, in fact, time, or a fourth spatial dimension in addition to time; it's mostly a Timey Wimey exploration of Alien Geometries.
  • Interstellar features unseen higher dimensional entities going through a lot of trouble to provide higher dimensional travel for humans on a dying earth. One scene in particular has these entities attempt to illustrate their perception of time by mapping the timeline of a specific point of space three dimensionally as a tesseract that can be navigated ana and kata.

Literature
  • In The Andalite Chronicles Elfangor explains Z-space travel in an As You Know speech that includes a mention that normal space has ten dimensions. However, for most lifeforms only the first four (length, width, depth, time) are actually visible; the other six are curled up inside themselves in ridiculous fashion and can't be perceived.
  • Forms the plot of the Robert A. Heinlein short story "—And He Built a Crooked House—". An architect builds a house that is a series of connected cubes, designed to mimic the shape of an "unfolded" tesseract (a four-dimensional cube). The night before the architect and his friends are to visit the house, an earthquake hits. They arrive and enter, only to find that the house has collapsed back into a four-dimensional shape. They have a lot of difficulties trying to get around the unpredictable geometry of the house.
  • Robert A. Heinlein's The Number of the Beast features six-dimensional travel, enabled by pushing on a gyroscope in just the right way.
  • A plot point in Robert A. Heinlein novel Stranger in a Strange Land. Michael Smith, a human born on Mars and raised by Martians, has the ability to send objects to an unknown fourth dimension that is "ninety degrees away from everything else". He disappears two government Mooks by sending them to this mysterious dimension. Later, when he establishes a new religion with a Free-Love Future as one of its central tenets, he uses as part of his show a little stunt in which he makes people's clothes disappear, sent to the fourth dimension.
  • The title character of The Boy Who Reversed Himself is part of a family with a secret: they hold the knowledge of how to move in the directions of ana and kata, the fourth dimensional equivalent of up and down. The story deals extensively with the ramifications of what this would allow one to do: Just as a stick figure who learned to rise off a page and into the third dimension could step over two-dimensional barriers and access the inside of closed two-dimensional shapes, a three-dimensional person able to rise into the fourth dimension can access the insides of closed objects and pass through barriers with ease. The drawback? When you fold back into 3-space, you tend to inadvertently reverse yourself, down to the molecular level (which results in some strangeness like ketchup acting as a powerful mind-altering drug). The only way to fix it is a second exhausting trip into 4-space. And then there's the bigger problem: 4-space has residents.
  • "The Captured Cross-Section" by Miles Breuer is about a young scientist who builds a device that can rotate objects into 4-space. He accidentally uses it on his fiancée, and then has to rotate himself in order to rescue her.
  • This is all over the Cthulhu Mythos. Most of its famous monstrosities exists in many more dimensions than we humans can perceive, so what we do see are just limited projections of their true multidimensional forms onto the 3D "reality".
  • In Diaspora by Greg Egan, the protagonists discover that subatomic particles actually contain portals to a five-dimensional universe — whose subatomic particles contain portals to another three-dimensional universe, and so on.
  • Discussed Trope in the satirical novel Flatland. A. Square is a regular guy who happens to be a square, living in a two-dimensional universe. He is visited by a sphere who preaches to him the Gospel of Three Dimensions. The square is scornful of the idea initially, but eventually the sphere convinces him. When the square talks excitedly of the possibility of a fourth dimension, the sphere immediately dismisses the idea as ridiculous.
  • "No-Sided Professor" by Martin Gardner is about a mathematician who discovers a topological shape which doesn't have any sides (in the same way that a Möbius strip only has one). Folding something into this shape causes it to disappear into a higher-dimensional space.
  • Greg Egan's Orthogonal trilogy thoroughly Justifies this by rewriting the laws of physics to create an internally-consistent universe where there really are four spatial dimensions, one of which is perceived by the protagonists as time. An (oversimplified) explanation for why time seems so different from space is that the protagonist's momentum through the dimension of time is so great that it's impossible to change trajectory without technological assistance.
  • Played straight (in the "time is a fourth dimension" variant) and extensively explored in Pyramids. The shape of a pyramid allows it to be a dam in the flow of time, which causes the dimensions to get flipped around in strange ways in their vicinity; for example, one unlucky man becomes thinner than a sheet and begins to move continually to the right. All his dimensions have been shifted, so time became breadth. (They stop him aging by putting a large rock in front of him.)
  • H. G. Wells' classic, The Time Machine, is probably the Trope Codifier, as it is one of the first works to suggest this idea. The unnamed protagonist constructs the eponymous Time Machine, which allows him to jump forward in time, then return to his own time to tell the story of his adventure. Interestingly, while traveling through time, the machine doesn't travel through space, but eons of continental drift drops him somewhere else entirely from his starting point.
  • The Arthur C. Clarke novelization of 2001: A Space Odyssey explicates that the Monolith has sides in a proportion of 1:4:9, the squares of the first three integers. Then it suggests the Monolith extends in more dimensions, presumably by squares.
    "And how naive to have imagined that the series ended at this point, in only three dimensions!"

Live-Action TV
  • Discussed briefly in the first episode of Doctor Who, "An Unearthly Child," demonstrating how strange Susan Foreman is. Worth noting that she's supposedly a 15-year-old girl at this point.
    Susan: [About a math problem] It's impossible unless you use D and E.
    Ian: D and E? Whatever for? Do the problem that's set, Susan.
    Susan: I can't, Mister Chesterton. You can't simply work on three of the dimensions.
    Ian: Three of them? Oh, time being the fourth dimension, I suppose? Then what do you need E for? What do you make the fifth dimension?
    Susan: Space.
  • The Journey of Allen Strange: While wandering around a human high school, Allen overhears a physics class and walks in to "correct" the teacher with Xelan physics, which includes at least fifteen dimensions.
  • The first season opening narration of The Twilight Zone starts as follows: "There is a fifth dimension beyond that which is known to man."

Tabletop Games
  • Dungeons & Dragons, using "BD&D Immortals" rules. In-Universe, there are five known spatial dimensions. The first three are the standard ones (length, width and depth). The fourth is hyperspace (AKA the "shortcut dimension") and is used for teleportation. The fifth is a horrid alien space called the Nightmare Dimension. It is possible for an Immortal to see into or even enter the 4th and 5th dimensions. There are creatures that exist in the 3rd-5th dimensions: we view them as monsters (and vice versa).

Video Games
While this moment is easy to write off as mere Technobabble, Calabi-Yau manifolds are a type of N-dimensional shape/coordinate system/mathematical model with...strange...properties deeply related to the shape of space, time, and the curled up dimensions found in string theory. See The Other Wiki's article for more details, but for our purposes a Calabi-Yau manifold can be summed up as "a map of the Timey-Wimey Ball".
  • In the sister franchise Portal, there is a related Shout-Out to this same model in the swirling particles seen when the portal gun is fired: their paths trace out a simple 3d cross-section of a Calabi-Yau manifold. This would seem to imply that either Aperture Science independently stumbled across the same trick, or that the resistance has been attempting to reverse engineer their research based on incomplete notes.
  • Miegakure is an in-development (as of December 2014) Puzzle Platformer in which the player explores a world that has four dimensions, but only three are visible at any given time.

Web Comics
  • In xkcd strip #721, Cueball apologizes to a two-dimensional square named A. Square for having given him a hard time when he had trouble understanding three-dimensional space. Playing a four-dimensional game called Miegakure has made Cueball more sympathetic to Square's situation.

Western Animation
  • The Adventure Time episode "The Real You" centers on Finn gaining super-intelligence. He invents a bubble blower that can create two-dimensional bubbles with one-dimensional shadows, three-dimensional bubbles with two-dimensional shadows, and fourth-dimensional bubbles with three-dimensional shadows. That last one just existing creates a black hole.

Real Life
  • A real-life example of this trope is found in numerous attempts to explain how gravity works. To put it in layman's terms, gravity is quite weird. So weird, in fact, that the simplest way to explain the effects it has on time, space, and matter seems to be that it operates in additional directions than the three we can access. Theoretical models range anywhere from 5 dimensions (our three, time, and wherever the heck gravity is) to 11 (which would make our understanding of space look like a toddler's drawing if you could see all the dimensions that exist).
  • Going in the opposite direction, the holographic principle is a theory that there are actually only two spatial dimensions, and either the third or time are an illusory byproduct of the universe existing.
  • If wormholes are conclusively found to exist, they would essentially prove the existence of additional spatial dimensions. One especially interesting theorized form of wormhole is a Timelike Curve, which would allow the type of Time Travel which we here at TV Tropes know as a Stable Time Loop. This has led to physicists spending large amounts of time trying to prove they do not exist—mostly in the hopes of ending the migraines caused by thinking about all the horrible things a Timelike Curve could do to physics.

Alternative Title(s): Hyperdimensional

http://tvtropes.org/pmwiki/pmwiki.php/Main/MoreThanThreeDimensions