The idea of a fourth dimension has been a factor in the evolution of modern art, but use of concepts relating to higher dimensions has been little discussed by academics in the literary world.[1] From the late 19th century onwards, many writers began to make use of possibilities opened up by the exploration of such concepts as hypercube geometry. While many writers took the fourth dimension to be one of time (as it is commonly considered today), others preferred to think of it in spatial terms, and some associated the new mathematics with wider changes in modern culture.
In science fiction, a higher "dimension" often refers to parallel or alternate universes or other imagined planes of existence. This usage is derived from the idea that to travel to parallel/alternate universes/planes of existence one must travel in a direction/dimension besides the standard ones. In effect, the other universes/planes are just a small distance away from our own, but the distance is in a fourth (or higher) spatial (or non-spatial) dimension, not the standard ones. Fifth and higher dimensions are used in the same way; for example; the Superman foe Mister Mxyzptlk comes from the fifth dimension.
Early influence
Edgar Allan Poe wrote an essay on cosmology titled Eureka (1848) which said that "space and duration are one". This is the first known instance of suggesting space and time to be different perceptions of one thing. Poe arrived at this conclusion after approximately 90 pages of reasoning but employed no mathematics.[2]
Theoretical physicistJames Clerk Maxwell is best known for his work in formulating the equations of electromagnetism. He was also a prize-winning poet,[3] and in his last poem Paradoxical Ode; Maxwell muses on connections between science, religion and nature, touching upon higher-dimensions along the way:[4]
Since all the tools for my untying In four-dimensioned space are lying, Where playful fancy intersperses Whole avenues of universes.. Excerpt from Maxwell's Paradoxical Ode of 1878[5]
In the Brothers Karamazov, Dostoevsky's last work completed in 1880, the fourth dimension is used to signify that which is ungraspable to someone with earthly (or three-dimensional) concerns.[6] In the book, Ivan Karamazov laments to his younger brother:
"..I have a Euclidean earthly mind, and how could I solve problems that are not of this world? And I advise you never to think about it either, my dear Alyosha, especially about God, whether He exists or not. All such questions are utterly inappropriate for a mind created with an idea of only three dimensions."[7]
In the 1884 satiricalnovellaFlatland by Edwin Abbott Abbott, the two-dimensional protagonist (a square) is introduced to the concept of the third-dimension by his mentor (a sphere). After initially struggling with the idea, the square starts to speculate upon yet higher dimensions. After envisioning a tesseract, the square asks:
"..shall we stay our upward course? In that blessed region of Four Dimensions, shall we linger at the threshold of the Fifth, and not enter therein? Ah, no! Let us rather resolve that our ambition shall soar with our corporal ascent. Then, yielding to our intellectual onset, the gates of the Sixth Dimension shall fly open; after that a Seventh, and then an Eighth.."[8]
Oscar Wilde's The Canterville Ghost (A Hylo-Idealistic Romance) published in 1887 was Wilde's parody of a "haunted-house" story. The tale uses the higher spatial dimension as a handy plot device allowing a magical exit for the ghost:[9]
"There was evidently no time to be lost, so, hastily adopting the Fourth Dimension of Space as a means of escape, he vanished through the wainscoting, and the house became quite quiet."[10]
H.G. Wells famously employed the concept of a higher temporal dimension in his 1895 book The Time Machine. Wells had already covered the subject seven years previously in his tale of The Chronic Argonauts. In this 1888 short story, inventor Dr. Nebogipfel asks the Reverend Cook:
"Has it never glimmered upon your consciousness that nothing stood between men and a geometry of four dimensions - length, breadth, thickness, and duration - but the inertia of opinion? ..When we take up this new light of a fourth dimension and reexamine our physical science in its illumination.. ..we find ourselves no longer limited by hopeless restriction to a certain beat of time."[11]
In Wells’ 1895 short story The Remarkable Case of Davidson's Eyes, the main character sees visions of a ship – only to find out later that the ship in question was on the opposite side of the globe at the time. A doctor tries to explain how this might have happened through higher dimensions, though the narrator struggles with the concept.
"..his explanation invokes the Fourth Dimension, and a dissertation on theoretical kinds of space. To talk of there being "a kink in space" seems mere nonsense to me; it may be because I am no mathematician. When I said that nothing would alter the fact that the place is eight thousand miles away, he answered that two points might be a yard away on a sheet of paper, and yet be brought together by bending the paper round. The reader may grasp his argument, but I certainly do not."[12]
Joseph Conrad and Ford Madox Ford's 1901 work The Inheritors: An Extravagant Story uses the "fourth dimension" as a metaphor to explain a shift in society away from traditional values towards modern expediency and callous use of political power. The "inheritors" are a breed of materialists, who call themselves "Fourth Dimensionists", tasked with occupying the earth. The narrator tells how, "I heard the nature of the Fourth Dimension – heard that it was invisible to our eyes, but omnipresent.."[13]
In the first volume of In Search of Lost Time (or Remembrance of Things Past) published in 1913, Marcel Proust envisioned the extra dimension as a temporal one. The narrator describes a church at Combray being "..for me something entirely different from the rest of the town; an edifice occupying, so to speak, a four-dimensional space – the name of the fourth being time."[14]
Artist Max Weber's Cubist Poems, is a collection of prose first published in 1914.
Cubes, cubes, cubes, cubes, High, low and high, and higher, higher, Far, far out, out, far..
Billions of things upon things This for the eye, the eye of being, At the edge of the Hudson, Flowing timeless, endless, On, on, on, on.... Excerpt from The Eye Moment, a Weber poem published in 1914[15]
Poet Ezra Pound finishes his 1937 Canto 49 (often known as "the Seven Lakes") with these lines:
The fourth; the dimension of stillness. And the power over wild beasts.[16]
Science fiction author Robert A. Heinlein used ideas derived from multi-dimensional geometry in some of his stories. "—And He Built a Crooked House—" was first published in Astounding Science Fiction magazine in February 1941. In the story, a recently graduated architect constructs an eight-room home for his friend based on an "unfolded tesseract". An earthquake collapses or "folds" the structure, leading to all eight rooms being contained within just one. The stairs appear to form a closed loop, and there seems to be no way of leaving, as all the doors and even the windows lead directly into other rooms.[17] Heinlein's 1963 fantasy novelGlory Road (originally serialized in The Magazine of Fantasy & Science Fiction) features a device called a fold box which is bigger on the inside than the outside.[18] In his 1980 novel The Number of the Beast, a "continua device" formulated using "theories on n-dimensional non-euclidean geometry" gives the protagonists the ability to time-travel and to visit fictional universes.[19]
Arthur C. Clarke published the 1950 short story "Technical Error", which explored the effects on a man after he had been rotated in the fourth dimension.
In her 1957 novel The Strange World of Planet X -- adapted from her own screenplay for an earlier 6-part British television series -- author Rene Ray tells the story of a pair of scientists whose experiments with magnetic fields open what seems to be a pathway into a fourth dimension. One of the two researchers is driven by a lust for power and recognition to proceed without caution, while his colleague becomes increasingly alarmed at the forces with which they may be tampering -- with the wife of the former caught between them -- and this conflict and the dangers entailed in their experiments make up the major part of the story.
Published in 1962,[20]Madeleine L'Engle's award-winning[21]A Wrinkle in Time revolves around a girl called Meg whose scientist father disappears after working on a mysterious project. In a chapter entitled "The Tesseract", Mrs Whatsit and Mrs Who (both immortals) use the analogy of small insect making a long journey across a length of material in order to explain instantaneous travel across the universe: "Swiftly Mrs Who brought her hands, still holding the skirt, together. 'Now you see.. ..he would be there.. ..that is how we travel.'"[22] Meg declares herself to be a "moron" for not understanding the concept (known in the book as "tessering"). Luckily, her telepathic younger brother clarifies the matter, by telling Meg that the fourth dimension of time and the fifth of the tesseract combine, enabling Euclidean geometry-contravening short-cuts to be taken through space.[22]
In Kurt Vonnegut's 1969 work Slaughterhouse-Five, recurring character Kilgore Trout writes a book called Maniacs in the Fourth Dimension which relates how "three-dimensional Earthling doctors" were unable to cure people with mental diseases, "as the causes.. ..were all in the fourth dimension."[23] Trout also explains how "..vampires and werewolves and goblins and angels" reside in this alternative plane, alongside poet William Blake.[23]
The book "Surfing through Hyperspace" by Clifford A. Pickover specifically deals with fourth spatial dimensional creatures and contains a story involving two FBI agents musing over the implications of such beings existing.
"Death's End", the 2010 final novel in Liu Cixin's Remembrance of Earth's Past trilogy, begins with an introduction in which a woman gains the ability to reach inside closed spaces and remove the contents during the Fall of Constantinople. Later in the novel, two interstellar ships enter a four-dimensional fragment of space. While within this fragment, the crew of the ships can enter the fourth dimension. From the fourth dimension, they can see the interior and all sides of any 3D object, much like how humans can see every aspect of a 2D shape from the third dimension.
The 2019 novel "The Last Reincarnation of Steven Kinder" by Bernard K. Finnigan, and its subsequent 2021 sequel "The Human Sliver" deals with the fourth dimension as a series of parallel Earths, accessible to certain humans with an extra-dimensional sense. The extra spatial dimension is used as a hiding place for aliens preying on 3D humans, and for physics applications when battling 4D creatures immune to conventional human weapons.
In film and television
Aside from Hyperspace as a plot device for faster than light space travel, there are only a few examples of film or television productions that have explored the possible consequences of human access to a fourth dimension.
In the 1959 science fiction film 4D Man a scientist accessed the fourth dimension and gained the ability to move through solid objects at will, and to drain the future life out of other people.
In "The Borderland", a 1963 episode of the original television series The Outer Limits, an accidental four-dimensional rotation of a human hand heralded the beginning of an attempt by a scientific team to enter the fourth dimension.
In physics and mathematics, the dimension of a mathematical space is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.
Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.
In geometry, a tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4-polytopes.
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed, then there are affine planes associated with the planar algebras, which give rise to kinematic geometries that have also been called non-Euclidean geometry.
The Number of the Beast is a science fiction novel by American writer Robert A. Heinlein, published in 1980. Excerpts from the novel were serialized in the magazine Omni.
Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884 by Seeley & Co. of London. Written pseudonymously by "A Square", the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella's more enduring contribution is its examination of dimensions.
"'—And He Built a Crooked House—'" is a science fiction short story by American writer Robert A. Heinlein, first published in Astounding Science Fiction in February 1941. It was reprinted in the anthology Fantasia Mathematica in 1958, and in the Heinlein collections The Unpleasant Profession of Jonathan Hoag in 1959 and The Best of Robert Heinlein in 1973. The story is about a mathematically inclined architect named Quintus Teal who has what he thinks is a brilliant idea to save on real estate costs by building a house shaped like the unfolded net of a tesseract. The title is paraphrased from the nursery rhyme "There Was a Crooked Man".
A parallel universe, also known as an alternate universe, parallel world, parallel dimension, or alternate reality, is a hypothetical self-contained plane of existence, co-existing with one's own. The sum of all potential parallel universes that constitute reality is often called a "multiverse". While the six terms are generally synonymous and can be used interchangeably in most cases, there is sometimes an additional connotation implied with the term "alternate universe/reality" that implies that the reality is a variant of our own, with some overlap with the similarly named alternate history.
Charles Howard Hinton was a British mathematician and writer of science fiction works titled Scientific Romances. He was interested in higher dimensions, particularly the fourth dimension. He is known for coining the word "tesseract" and for his work on methods of visualising the geometry of higher dimensions.
A polycube is a solid figure formed by joining one or more equal cubes face to face. Polycubes are the three-dimensional analogues of the planar polyominoes. The Soma cube, the Bedlam cube, the Diabolical cube, the Slothouber–Graatsma puzzle, and the Conway puzzle are examples of packing problems based on polycubes.
Flatterland is a 2001 book written by mathematician and science popularizer Ian Stewart about non-Euclidean geometry. It was written as a sequel to Flatland, an 1884 novel that discussed different dimensions.
Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring and multiplying its length, width, and height. This concept of ordinary space is called Euclidean space because it corresponds to Euclid's geometry, which was originally abstracted from the spatial experiences of everyday life.
In science fiction, hyperspace is a concept relating to higher dimensions as well as parallel universes and a faster-than-light (FTL) method of interstellar travel. Its use in science fiction originated in the magazine Amazing Stories Quarterly in 1931 and within several decades it became one of the most popular tropes of science fiction, popularized by its use in the works of authors such as Isaac Asimov and E. C. Tubb, and media franchises such as Star Wars.
Sphereland: A Fantasy About Curved Spaces and an Expanding Universe is a 1965 translation of Bolland : een roman van gekromde ruimten en uitdijend heelal, a 1957 novel by Dionys Burger, and is a sequel to Flatland, a novel by "A Square". The novel expands upon the social and mathematical foundations on which Flatland is based. It is markedly different from the first novel in that it has a more prosaic ending and treatment of society.
Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions is the debut non-fiction book by Lisa Randall, published in 2005, about particle physics in general and additional dimensions of space in particular. The book has made it to top 50 at amazon.com, making it the world's first successful book on theoretical physics by a female author. She herself characterizes the book as being about physics and the multi-dimensional universe. The book describes, at a non-technical level, theoretical models Professor Randall developed with the physicist Raman Sundrum, in which various aspects of particle physics are explained in a higher-dimensional braneworld scenario. These models have since generated thousands of citations.
A five-dimensional space is a space with five dimensions. In mathematics, a sequence of N numbers can represent a location in an N-dimensional space. If interpreted physically, that is one more than the usual three spatial dimensions and the fourth dimension of time used in relativistic physics. Whether or not the universe is five-dimensional is a topic of debate.
The Fourth Dimension: Toward a Geometry of Higher Reality (1984) is a popular mathematics book by Rudy Rucker, a Silicon Valley professor of mathematics and computer science. It provides a popular presentation of set theory and four dimensional geometry as well as some mystical implications. A foreword is provided by Martin Gardner and the 200+ illustrations are by David Povilaitis.
Flatland: The Movie is a short animated film which was released to video in 2007. The cast includes the voices of actors Martin Sheen, Kristen Bell and Tony Hale. The story is based on the 1884 science fiction novella Flatland: A Romance of Many Dimensions written by Edwin A. Abbott.
New possibilities opened up by the concept of four-dimensional space helped inspire many modern artists in the first half of the twentieth century. Early Cubists, Surrealists, Futurists, and abstract artists took ideas from higher-dimensional mathematics and used them to radically advance their work.
Hiding in the Mirror is a popular science book by the theoretical physicist Lawrence M. Krauss. The text was initially published on October 20, 2005 by Viking Press. This is his seventh non-fiction book.
↑ Abbott, Edwin A. (1884). "19. How, though the Sphere showed me other mysteries of Spaceland, I still desired more; and what came of it.". 'Flatland'.
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