More than Three Dimensions

aka: Hyperdimensional

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 or even show 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. This is backed up by basic physics, since if these higher spatial dimensions existed, then forces that follow an inverse-squared law for effectiveness across space (in other words, their effectiveness decreases by the square of the distance) such as gravity or electromagnetism would follow an inverse-cubed law, or inverse-higher power law. Time, or any number of other variables, can be recognized as additional "dimensions", 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 Also, most if not all of these speculated dimensions are also believed to be very small (smaller than a Planck length) and curled up, meaning that even if we could perceive them there wouldn't really be much we could do with them.

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 From Greek roots meaning "up toward" and "down from" respectively, 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 Perpendicular angles are 90 degrees, parallel lines never intersect, squares have straight edges, the angles of a triangle add to 180 degrees, etc. 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

• The goddesses and other heavenly beings in Ah! My Goddess are 10-dimensional entities (in the "string theory" sense), not that it comes up very often. This means that, ostensibly, Keiichi can only perceive and interact with three dimensions of his ten-dimensional love interest.
• 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 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

• The Superman villain Mxyzptlk's realm has always been referred to as "the Fifth Dimension," but is usually depicted just as a typically weird comic bookity alternate universe (usually as a cartoon-style Wackyland). Occasionally, though, a writer will explore the implications of the name.
  • In Whatever Happened to the Man of Tomorrow?, Mzy reveals his true, five-dimensional 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.
  • One time, Superman has to rescue one of Mxy's people from a cosmic threat that is reducing him to only three dimensions. The entity attacks Superman, stripping away one of his dimensions and briefly turning him into a flat, two-dimensional image.

Fan Works

• Child of the Storm: The Spirit of the Fallen Fortress, being a minor Eldritch Abomination, enjoys playing with physics in its domain. When it possesses Hermione and unleashes her full reality-warping potential as a wielder of Chaos Magic and an Omega Class space-manipulating mutant filtered through its own sadism, the result is the kind of fractal-based physics warping that requires either multiple PhDs or some serious drugs to understand. Then it goes full Escher.
• In Equestria: Across the Multiverse, the Mane Six find themselves at an Inn Between the Worlds run by a Pinkie Pie from a universe where they ascended into 10th-dimensional beings. While she looks like an Alicorn Energy Being, Pinkie finds poking her feels like you're 'poking the universe' and her voice sounds like it's coming from everywhere at once, showing there's much more to her than that. Her true form turns out to be larger than a universe and even an Eldritch Abomination can't fully comprehend it.

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

• This forms the plot of "—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.
• Animorphs: 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.
• 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".
• This is how hyperspace works in The Culture. Realspace is surrounded by two layers of hyperspace, known as infraspace and ultraspace, one 'above' and another 'below'. These can be used not only to travel faster than light, but to move in four spatial dimensions, allowing hyperspace technology (such as scanners, teleporters, and weapons) to bypass normal three-dimensional barriers. Each hyperspace layer is also bounded by an 'energy grid', a region of infinite energy separating one universe from the next, which can also be weaponized in a process known as a hypergridintrusion, or 'Gridfire', essentially submerging a section of space into a bath of destructive energy comparable to the Big Bang.
• In Diaspora, 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.
• Dragaera: The Necromancer is a veteran Dimensional Traveler who understands death as merely a restriction on one's access to certain planes of existence. Her quarters in Castle Black are roughly the size of a closet in the conventional three dimensions, but she finds them quite spacious indeed.
• Eye of Terror, an early Warhammer 40,000 Expanded Universe novel, describes the Warp as an eight-dimensional space, none of which are the four dimensions of our home universe (three spatial and one temporal). As such, in the Eye of Terror, where the Warp bleeds into normal space, eight dimensions are overlaid onto four dimensions to become twelve-dimensional mayhem, very nearly impossible to navigate.
• Discussed in 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.
• "Gimmicks Three": Welby and Shapur, both having demonic powers, have the ability to travel in any dimension, and that includes time.
• Haruhi Suzumiya: 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.
• According to Mostly Harmless, the Whole Sort of General Mish-Mash is the sum total of everything that could exist and all the different ways one could look at it. So-called parallel universes (which are neither) are "slices" through the Whole Sort of General Mish-Mash in various dimensions — and since they're not parallel, these slices intersect.
• "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. The man later builds an actual Klein Bottle, which serves as a portal to the fourth dimension. He is Killed Mid-Sentence when something from there drags him in.
• The Number of the Beast features six-dimensional travel, enabled by pushing on a gyroscope in just the right way.
• Orthogonal rewrites 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.)
• Appears several times in Remembrance of Earth's Past. Notably, the Sophon is a proton-sized quantum supercomputer the Trisolarans created by unfolding two of its dimensions to the width of a planet and etching Strong Force-based circuitry into it before compressing it back down. This is further expanded on in Death's End when the crew of a human spaceship come across a "fragment" of fourth-dimensional space. This proves to be a dire warning, as the Solar System is later struck by a devastating alien weapon that collapses it into two-dimensional space. Guan Yifan speculates that the universe used to be made of 10 macro-dimensions, but billions of years of warfare between unimaginably advanced civilizations collapsed it down to 3 and lowered the speed of light. This is expected to continue until the universe is only one-dimensional, with the perpetrators engineering themselves to survive while they wipe out all possible rivals.
• The Space Odyssey Series 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!
• A Star Trek Expanded Universe novel has Picard encountering a four-dimensional joint Borg/Romulan station in subspace. The station appears to have a typical cube shape, except, as Picard circles it, he counts five sides instead of four. His brain is having trouble processing the information, as humans have a hard time thinking in four dimensions.
• The aliens in Stolen Skies exist in multiple dimensions, and UFO phenomena are the effects of them dipping into our perceivable universe. One character says it's like ripples in the surface of the pond when something falls in, if the surface was all you could perceive, and another explicitly compares it to the situations in Flatland.
• This is a plot point in 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 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 drop him somewhere else entirely from his starting point.
• In the 1914 short story "A Victim of Higher Space" by Algernon Blackwood, a man keeps accidentally falling into higher-dimensional space.
• In the Xeelee Sequence, the Xeelee trap the solar system inside a 4-dimensional hypercube to stop humanity from being a constant genocidal pain in their ass.

Live-Action TV

• Tesseracts are featured heavily as a plot device in Andromeda. Specifically as tools of the Abyss and also used to help Harper.
• An episode of Black Hole High features a tesseract.
• Doctor Who: Discussed briefly in the very first episode, "An Unearthly Child", demonstrating how strange Susan Foreman is. It's 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.
• In Earth: Final Conflict, Ma'el leaves behind a complex problem that has 10 components, one in each dimension. Thus, solving the entire problem requires thinking in 10 dimensions, and there's only one human in the world, who can do that. Even the Taelons aren't that smart.
• The Good Place implies that reality has nine dimensions. Humans just can't see them, hence why Michael apologises for the mess in his office despite it looking spotless.
• This is how Ford Prefect explains parallel universes to Arthur Dent in The Hitchhiker's Guide to the Galaxy segments of the Douglas Adams episode of The South Bank Show (tying into Mostly Harmless above), describing the five dimensions of height, length, width, time, and quantum uncertainty:
  Ford: Normally, human beings see landscapes of space, successive slices of time, and only one of slice quantum uncertainty. Rhinoceroses see landscapes of time^note As explained elsewhere in the programme, and in Last Chance to See, because smell is more important to rhinos than sight, and odours fade away more gradually than photons do. Cats, I believe, see landscapes of quantum uncertainty.
• 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 Twilight Zone (1959):
  • The first season opening narration starts as follows: "There is a fifth dimension beyond that which is known to man."
  • "Little Girl Lost" deals with a girl who falls through a portal to the fourth dimension that pops into existence next to her bed.

Magazine

• Analog: The February 1941 issue has an interior image on page 69, part of Robert A. Heinlein's "—And He Built a Crooked House—". The image includes two three dimensional models of a hypercube, which is incorporated as part of the titular house's design. Another model of the house's design appears on page 72, and the house itself collapses into itself on page 75.

Radio

• Journey into Space: In Journey to the Moon / Operation Luna, the Time Traveller states that, unlike humans, his people can control their movement through the fourth dimension: time.

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 (a.k.a. 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).
• GURPS: Powers has rules for 4-dimensional beings and 4D martial arts.

Video Games

• 4D and above variations of 2048 can also be found online.
• 4D Miner's entire concept is based around this. The game is very similar to Minecraft, but you can scroll the mouse wheel to shift your orientation in 4D space.
• 4D Toys is an early demo using the same engine that was designed for Miegakure, below.
• Half-Life 2: In a very arcane (and blink-and-you-miss-it) Genius Bonus, Dr. Judith Mossman quips about the resistance's superior, if somewhat unstable and homebrew, Extradimensional Shortcut technology. "If the Combine only knew what we were doing with the Calabi-Yau model..." 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 Wikipedia'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".
• Magic Cube 4 D is a fourth-dimensional variation of the Rubick's Cube.
• 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.
• In Portal, the sister franchise to Half-Life'', 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.

Webcomics

• In Girl Genius, the Castle Heterodyne discusses time as a thing with complex dimensions a human would have a very hard time visualizing while talking to Gil.
  "Just...accept that time, like space, has its planes and angles. It is not really a perfect analogy but it will suffice. [...] I believe you would have difficulty visualizing the complex dimensions of time."
• Coney the Cone-Ship's interior in The Inexplicable Adventures of Bob! is like this. Our heroes spend most of the story trapped in a space depicted as a flat plane surrounded by Acid-Trip Dimension imagery. As higher dimensional objects pass through the plane, Bob and his friends see them appearing out of nowhere and growing and shrinking. Touching the objects actually damages them, just as a 2D object touching a 3D one would slice into it like a knife.
• In xkcd strip #721, Cueball visits Flatland and apologizes to A. Square for having given him a hard time when he had trouble understanding three-dimensional space. Playing 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.
• Parodied in Aqua Teen Hunger Force when the Mooninites claim to have 5000 dimensions, although Frylock points out that he only sees 2 (due to the titular aliens being old computer sprites).
• The Simpsons parodies this trope in "Treehouse of Horror VI" when Homer ends up in a seeming Eldritch Location... one that renders everything, including himself, in computer-generated 3D graphics. When people try to rescue Homer and figure out what happened to him, Dr. Frink explains that Homer is trapped in "the third dimension", something baffling to the people of the two-dimensional Springfield.

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.
• Research shows the 3 spatial dimensions + 1 temporal dimension of our Universe is the only one where life -and technology- as we know it could exist^note Eldritch Abominations aside, that is. Mess with the number of dimensions and either complex systems will be impossible or orbits, either planetary or the ones of electrons around an atomic nucleus, will be unstable. Conversely mess with the number of time dimensions and watch how you either cannot predict the behavior of physical systems (meaning no way to develop technology) or protons and electrons, unless at temperatures low enough, go unstable.
• A tesseract is a classic example. It's a cube with four spatial dimensions. The name even means "four rays" because at the corners of the tesseract there would be four lines all at right angles to each other. Try and visualize that.

---