DIMENSIONS

   We perceive three spatial dimensions, but theoretical MATHEMATICS is easily capable of dealing with many more. Conventional graphical analysis frequently represents time as a dimension, encouraging consideration of it as the "fourth dimension". The possible existence of PARALLEL WORLDS displaced from ours along a fourth spatial dimension (in the same way that a series of two-dimensional universes might lie next to one another like the pages of a book) is a popular hypothesis in sf, and such worlds are frequently referred to as "other dimensions". The COSMOLOGY of Einstein's General Theory of Relativity (1916), which proposes a four-dimensional model of the Universe in which the notions of space and time are collapsed into a single "spacetime continuum", offered considerable encouragement to sf notions of a multidimensional Universe (or "multiverse"). Many modern occultists and pseudoscientists have followed in the tracks of Johann Zollner (1834-1882), author of Transcendental Physics (1865), who borrowed mathematical notions to "justify" the idea of the "astral plane" beloved by spiritualists and Theosophists. J.W. DUNNE used the notion to explain prophetic dreams, eventually constructing a theory of the "Serial Universe", and P.D. Ouspensky (1878-1947) built a more complex model of the Universe in which time"moves" in a spiral and there are six spatial dimensions.The possible dimensional limitations of human existence and perception were dramatized by Edwin A. ABBOTT in Flatland (1884) as by "A Square", which describes a world of two-dimensional beings, one of whom is challenged to imagine our three-dimensional world - encouraging readers, by analogy, to attempt to imagine a four-dimensional world. The challenge was taken up by C.H. HINTON, whose many essays on the subject attempt to "explain" ghosts and to imagine a four-dimensional God from whom nothing in the human world can be hidden. In his story "An Unfinished Communication" (1895) the afterlife involves freedom to move along the time dimension (TIME TRAVEL) to relive and reassess moments of life; he also wrote a Flatland novel, An Episode of Flatland (1907). H.G. WELLS borrowed Hintonian arguments to "explain" the working of the device in THE TIME MACHINE (1895). The eponymous figure of E.V. ODLE's The Clockwork Man (1923) could perceive many dimensions when working properly, but while malfunctioning could do no more than flutter back and forth in time, offering the merest hint of the quality of multidimensional life. Algernon BLACKWOOD's "The Pikestaffe Case" (1924) attempts to evoke the non-Euclidean geometry of a dimensional trap lurking within a mirror.Early GENRE-SF writers who found the notion of dimensions fascinating included Miles J. BREUER, most notably in "The Appendix and the Spectacles" (1928) and"The Captured Cross-Section" (1929), and Donald WANDREI, notably in "The Monster from Nowhere" (1935) and"Infinity Zero" (1936). In E.E."Doc" SMITH's Skylark of Valeron (1934; 1949) the heroes briefly enter a four-dimensional reality, and in Clifford D. SIMAK's "Hellhounds of the Cosmos" (1932), 99 men enter the fourth dimension in a single grotesque body to fight a four-dimensional monster. Henry KUTTNER's and C.L. MOORE's classic "Mimsy Were the Borogoves" (1943 as by Lewis Padgett) features toys from the future which educate children into four-dimensional habits of thought, but, like most stories of the period, this uses dimensional trickery casually to tie up its plot with a neat knot.The mathematical discipline of topology inspired several dimensional fantasies: Moebius strips feature in Martin GARDNER's "No-Sided Professor" (1946) and "The Island of Five Colours" (1952), Theodore STURGEON's "What Dead Men Tell" (1949), Arthur C. CLARKE's "Wall of Darkness" (1949) and Homer NEARING Jr's "The Hermeneutical Doughnut" (1954); Klein bottles and tesseracts feature in "The Last Magician" (1951) by Bruce ELLIOTT, "And He Built a Crooked House" (1941) by Robert A. HEINLEIN and "Star, Bright" (1952) by Mark CLIFTON. Occam's Razor by David DUNCAN (1957) also deploys topological jargon to shore up its dimensional speculations. George GAMOW's popularization of ideas in modern physics, Mr Tompkins in Wonderland (coll 1939), dramatizes certain odd situations very well (although its contents are didactic essays rather than stories).The notion that spaceships might make use of a fourth-dimensional HYPERSPACE in order to evade the limiting velocity of light is very common in sf, having been initially popularized by Isaac ASIMOV among others, but few stories actually attempt to describe it; it is usually imagined as a chaotic environment which utterly confuses the senses, as in Frederik POHL's "The Mapmakers" (1955) and Clifford D. Simak's "All the Traps of Earth" (1960). The dimensional chaos that might be associated with BLACK HOLES has received closer attention, though these too are most often used as "wormholes" permitting very long journeys to be taken more or less instantaneously. Among the more effective representations of experience in dimensionally distorted environments are Norman KAGAN's "The Mathenauts" (1964), David I. MASSON's "Traveller's Rest" (1965) and Christopher PRIEST's INVERTED WORLD (1974; vt The Inverted World US).In recent years C.H. Hinton's ideas have been revived by Rudy RUCKER, who has used dimensional mathematics very extravagantly in a number of his novels and short stories, including the afterlife fantasy WHITE LIGHT (1980), the comedy of fourth-dimensional intrusions The Sex Sphere (1983) and many of the shorter pieces first published in The 57th Franz Kafka (coll 1983) and reprinted, with others, in Transreal! (coll 1991). Rucker is the only modern author to have answered "A Square's" challenge with authentic verve and authority, but A.J. Dewdney's The Planiverse (1984) is an interesting drama-documentary about a two-dimensional world whose topography recalls Hinton's Flatland more than Abbott's.Relevant theme anthologies include Fantasia Mathematica (anth 1958) and The Mathematical Magpie (anth 1962), both ed Clifton Fadiman, and Science Fiction Adventures in Dimension (anth 1953) ed Groff CONKLIN.

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   See also: INVASION.