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} }) </script> </div> </form> </fieldset> <article class="entryArticle content STeditorial"> <header class="entryHeader icon-theme"> <h1 class="entryTitle">Dimensions </h1> </header><p class='tagLine'>Entry updated 16 December 2022. Tagged: Theme.</p><div class="browsingBtns"> <span> <input class="button PNI previous" type="button" onclick="window.location.href='/next.php?id=p&entry=dimensions'" value="Prev" /> </span> <span> <input class="button PNI next" type="button" onclick="window.location.href='/next.php?&entry=dimensions'" value="Next" /> </span> <span> <input class="button PNI incoming" type="button" onclick="window.location.href='/incoming.php?entry=dimensions'" value="About This Entry" title="What links to the entry; contributor initials explained; how to cite; other information" /> </span> </div> <p>We perceive three spatial dimensions, but theoretical <a href="/entry/mathematics">Mathematics</a> is easily capable of dealing with many more. Conventional graphical analysis frequently represents <a href="/entry/time">Time</a> as a dimension, encouraging consideration of it as the "fourth dimension". The possible existence of <a href="/entry/parallel_worlds">Parallel Worlds</a> 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 <a href="/entry/cosmology">Cosmology</a> of Einstein's General Theory of <a href="/entry/relativity">Relativity</a> (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 <a href="/entry/multiverse">Multiverse</a>. Many modern occultists and pseudoscientists have followed in the tracks of Johann Zöllner (1834-1882), author of <i>Transcendental Physics</i> (<b>1865</b>), who borrowed mathematical notions to "justify" the idea of the "astral plane" beloved by spiritualists and Theosophists (see <a href="/entry/theosophy">Theosophy</a>). J W <a href="/entry/dunne_j_w">Dunne</a> 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.</p> <p>The possible dimensional limitations of human existence and perception were dramatized by Edwin A <a href="/entry/abbott_edwin_a">Abbott</a> in <i>Flatland</i> (<b>1884</b>) as by "A Square", in which <a href="/entry/flatland">Flatland</a> is 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 <a href="/entry/hinton_c_h">Hinton</a>, 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" (in <i>Stella and An Unfinished Communication</i>, coll <b>1895</b>) the afterlife involves freedom to move along the time dimension (see <a href="/entry/time_travel">Time Travel</a>) to relive and reassess moments of life; he also wrote a <a href="/entry/flatland">Flatland</a> novel, <i>An Episode of Flatland</i> (<b>1907</b>). H G <a href="/entry/wells_h_g">Wells</a> borrowed Hintonian arguments to "explain" the working of the device in <i>The Time Machine</i> (<b>1895</b>). The eponymous figure of E V <a href="/entry/odle_e_v">Odle</a>'s <i>The Clockwork Man</i> (<b>1923</b>) 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 <a href="/entry/blackwood_algernon">Blackwood</a>'s "The Pikestaffe Case" (in <i>Tongues of Fire</i>, coll <b>1924</b>) attempts to evoke the non-Euclidean geometry of a dimensional gateway lurking within a mirror, which has practical uses for its mathematician creator (he stores his books and equipment outside normal 3-D space) but is also a route to initially feared <a href="/entry/transcendence">Transcendence</a>.</p> <p>Early <a href="/entry/genre_sf">Genre-SF</a> writers who found the notion of dimensions fascinating included Miles J <a href="/entry/breuer_miles_j">Breuer</a>, most notably in "The Appendix and the Spectacles" (December 1928 <a href="/entry/amazing">Amazing</a>) and "The Captured Cross-Section" (February 1929 <a href="/entry/amazing">Amazing</a>); Donald <a href="/entry/wandrei_donald">Wandrei</a> in "Infinity Zero" (October 1936 <a href="/entry/asf">Astounding</a>); and Nelson S <a href="/entry/bond_nelson_s">Bond</a> in "The Monster from Nowhere" (July 1939 <a href="/entry/fantastic_adventures">Fantastic Adventures</a>), which makes play with the fact that a four-dimensional entity's various limbs or digits could appear as separate solid objects as the creature intersects our 3D world. (Wandrei's "The Monster from Nowhere" [23 November 1935 <a href="/entry/argosy_the">Argosy</a>] was wrongly cited as a dimensions-related story in past editions of this encyclopedia, almost certainly because the above-mentioned Bond story with the identical title is wrongly credited to Wandrei in the first edition of <i>The Best of Science Fiction</i> [anth <b>1946</b>] edited by Groff <a href="/entry/conklin_groff">Conklin</a>.) In E E "Doc" <a href="/entry/smith_e_e">Smith</a>'s <i>Skylark of Valeron</i> (August 1934-February 1935 <a href="/entry/asf">Astounding</a>; <b>1949</b>) the heroes briefly enter a four-dimensional reality, and in Clifford D <a href="/entry/simak_clifford_d">Simak</a>'s "Hellhounds of the Cosmos" (June 1932 <a href="/entry/asf">Astounding</a>), 99 men enter the fourth dimension in a single grotesque body to fight a four-dimensional <a href="/entry/monsters">Monster</a>. E E <a href="/entry/smith_e_e">Smith</a>'s <b>Lensman</b> universe features various <a href="/entry/aliens">Aliens</a> whose existence in ultra-frigid environments depends on their "extension into the hyper-dimension", as Smith phrases it in <i>First Lensman</i> (<b>1950</b>). In lower dimensionality, Madeleine <a href="/entry/lengle_madeleine">L'Engle</a>'s <i>A Wrinkle in Time</i> (<b>1962</b>) features a brief, uncomfortable visit to a two-dimensional planetary reality.</p> <p>As sf became more sophisticated, slick trickery often replaced rigorous thought. Henry <a href="/entry/kuttner_henry">Kuttner</a>'s and C L <a href="/entry/moore_c_l">Moore</a>'s classic "Mimsy Were the Borogoves" (February 1943 <a href="/entry/asf">Astounding</a>) as by Lewis Padgett features toys from the far future (see <a href="/entry/toys_in_sf">Toys in SF</a>) which educate children into four-dimensional habits of thought which remain carefully unexplored: like most stories of the period, this uses dimensional shenanigans casually to tie up its plot with a neat knot. Similarly, Mark <a href="/entry/clifton_mark">Clifton</a>'s "Star, Bright" (July 1952 <a href="/entry/galaxy">Galaxy</a>) and Alan E <a href="/entry/nourse_alan_e">Nourse</a>'s <i>The Universe Between</i> (stories March, September 1951 <a href="/entry/asf">Astounding</a>; exp fixup <b>1965</b>) both take it for granted that comprehending the fourth dimension will grant special powers, here <a href="/entry/teleportation">Teleportation</a>. Disguised perceptual training aids, respectively 4-D crossword clues and a perversely designed house, feature in Arthur <a href="/entry/sellings_arthur">Sellings</a>'s "One Across" (May 1956 <a href="/entry/galaxy">Galaxy</a>) and John <a href="/entry/brunner_john">Brunner</a>'s "The Analysts" (August 1961 <a href="/entry/science_fantasy">Science Fantasy</a>): in each case the protagonist is led to visualize the extra dimension and haplessly travels in that impossible direction. Greg <a href="/entry/bear_greg">Bear</a>'s "Tangents" (January 1986 <a href="/entry/omni">Omni</a>) is a knowing and sophisticated homage to this whole class of stories.</p> <p>The mathematical discipline of topology has inspired several dimensional fantasies: Möbius strips and related structure feature in Martin <a href="/entry/gardner_martin">Gardner</a>'s "No-Sided Professor" (January 1947 <i>Esquire</i>) and "The Island of the Five Colors" (in <i>Future Tense</i>, anth <b>1952</b>, ed Kendell Foster <a href="/entry/crossen_kendell_foster">Crossen</a>), Arthur C <a href="/entry/clarke_arthur_c">Clarke</a>'s "The Wall of Darkness" (July 1949 <a href="/entry/super_science_stories">Super Science Stories</a>), Theodore <a href="/entry/sturgeon_theodore">Sturgeon</a>'s "What Dead Men Tell" (November 1949 <a href="/entry/asf">Astounding</a>), A J <a href="/entry/deutsch_a_j">Deutsch</a>'s "A Subway Named Möbius" (December 1950 <a href="/entry/asf">Astounding</a>) and H <a href="/entry/nearing_homer_jr">Nearing</a> Jr's "The Hermeneutical Doughnut" (in <i>The Sinister Researches of C.P. Ransom</i>, coll <b>1954</b>). The Klein bottle (a one-sided self-intersecting surface with no edges) and the tesseract or hypercube (the four-dimensional analogue of a 3D cube) feature in "The Last Magician" (January 1953 <a href="/entry/fsf">F&SF</a>) by Bruce <a href="/entry/elliott_bruce">Elliott</a>, "– And He Built a Crooked House" (February 1941 <a href="/entry/asf">Astounding</a>) by Robert A <a href="/entry/heinlein_robert_a">Heinlein</a> and "Star, Bright" (July 1952 <a href="/entry/galaxy">Galaxy</a>) by Mark <a href="/entry/clifton_mark">Clifton</a>. <i>Occam's Razor</i> (<b>1957</b>) by David <a href="/entry/duncan_david">Duncan</a> also deploys some topological jargon – expressed through lively discussion of the properties of soap films stretched on wire frames – to shore up its dimensional speculations. The "adult" treatment in Ian <a href="/entry/mcewan_ian">McEwan</a>'s "Solid Geometry" (July 1974 <i>The New Review</i>) draws an analogy between paper-folding and human sexual positions, climaxing (as it were) with the folding of a woman into other-dimensional nothingness. George <a href="/entry/gamow_george">Gamow</a>'s popularization of ideas in modern <a href="/entry/physics">Physics</a>, <i>Mr Tompkins in Wonderland</i> (coll <b>1939</b>), dramatizes certain odd situations very well (although its contents are fictionalized didactic essays rather than stories).</p> <p>The notion that <a href="/entry/spaceships">Spaceships</a> might make use of a fourth-dimensional <a href="/entry/hyperspace">Hyperspace</a> in order to evade the limiting velocity of light is very common in sf, having been initially popularized by Isaac <a href="/entry/asimov_isaac">Asimov</a> 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 <a href="/entry/pohl_frederik">Pohl</a>'s "The Mapmakers" (July 1955 <a href="/entry/galaxy">Galaxy</a>), Clifford D Simak's "All the Traps of Earth" (March 1960 <a href="/entry/fsf">F&SF</a>), Madeleine <a href="/entry/lengle_madeleine">L'Engle</a>'s above-cited <i>A Wrinkle in Time</i> (which invokes the tesseract, though very loosely, as a <a href="/entry/faster_than_light">Faster Than Light</a> travel facilitator) and Bob <a href="/entry/shaw_bob">Shaw</a>'s <i>Night Walk</i> (<b>1967</b>). In Larry <a href="/entry/niven_larry">Niven</a>'s <b>Known Space</b> sequence, hyperspace appears or fails to appear as a sanity-threatening "Blind Spot" which human and other visual systems edit out. The dimensional chaos that might be associated with <a href="/entry/black_holes">Black Holes</a> has received closer attention, though these too are most often used as <a href="/entry/wormholes">Wormholes</a> permitting very long journeys to be taken more or less instantaneously. Among the more effective representations of experience in dimensionally distorted environments are Norman <a href="/entry/kagan_norman">Kagan</a>'s "The Mathenauts" (July 1964 <a href="/entry/if">If</a>), David I <a href="/entry/masson_david_i">Masson</a>'s "Traveller's Rest" (September 1965 <a href="/entry/new_worlds">New Worlds</a>) and Christopher <a href="/entry/priest_christopher">Priest</a>'s <i>Inverted World</i> (<b>1974</b>). Douglas <a href="/entry/adams_douglas">Adams</a> deals humorously with the notion in one <a href="/entry/space_flight">Space Flight</a> sequence of <i>The Hitch Hiker's Guide to the Galaxy</i> (<b>1979</b>), whose imagery is comically surreal.</p> <p>In the 1980s C H <a href="/entry/hinton_c_h">Hinton</a>'s ideas were entertainingly revived by Rudy <a href="/entry/rucker_rudy">Rucker</a>, who has used dimensional and other <a href="/entry/mathematics">Mathematics</a> very extravagantly in a number of his novels and short stories, including the afterlife fantasy <i>White Light</i> (<b>1980</b>), the comedy of fourth-dimensional intrusions <i>The Sex Sphere</i> (<b>1983</b>) and many of the shorter pieces first published in <i>The 57th Franz Kafka</i> (coll <b>1983</b>) and reprinted, with others, in <i>Transreal!</i> (coll <b>1991</b>). Rucker is perhaps the only modern author to have answered the challenge of "A Square" with authentic verve and authority, but A K <a href="/entry/dewdney_a_k">Dewdney</a>'s <i>The Planiverse</i> (<b>1984</b>) is an interesting drama-documentary about a two-dimensional world whose topography echoes Hinton's <a href="/entry/flatland">Flatland</a> rather than Abbott's: this addresses such seemingly insuperable 2D engineering difficulties as building houses with working doors, and even a plausible steam-engine. More in the arena of <a href="/entry/imaginary_science">Imaginary Science</a>, <a href="/entry/liu_cixin">Liu</a> Cixin's <i>Santi</i> (May-December 2006 <a href="/entry/kehuan_shijie">Kehuan Shijie</a>; <b>2007</b>; trans Ken <a href="/entry/liu_ken">Liu</a> as <i>The Three-Body Problem</i> <b>2014</b>) includes the bizarre notion of dimensionally unpacking a single proton into a vast 2D surface upon which the circuitry of a super-<a href="/entry/computers">Computer</a> is inscribed to produce – after restoration to 3D particle size – an inimical <a href="/entry/ai">AI</a>-controlled proton. The third book in this sequence, <i>Sishen Yongsheng</i> (<b>2010</b>; trans Ken <a href="/entry/liu_ken">Liu</a> as <i>Death's End</i> <b>2016</b>), introduces a dimensional doomsday <a href="/entry/weapons">Weapon</a> which – fatally to unprepared life – collapses entire solar systems into two-dimensionality.</p> <p>Vague references to other or higher dimensions – without concern for the mathematical aspect – have long been used in sf as a loose synonym for <a href="/entry/parallel_worlds">Parallel Worlds</a>. Thus <a href="/entry/superman_character">Superman</a> impish tormenter Mister Mxyzptlk hails from a fantasy "fifth dimension", and Superman's home world of Krypton exiled its criminals into a <a href="/entry/prisons">Prison</a> dimension known as the Phantom <a href="/entry/zone">Zone</a>, introduced in <i>Adventure Comics</i> #283 (April 1961). <a href="/entry/aliens">Aliens</a> from "higher dimensions" can be found as late in the twentieth century as Walter Jon <a href="/entry/williams_walter_jon">Williams</a>'s <i>Knight Moves</i> (<b>1985</b>).</p> <p>Relevant theme anthologies include <i>Fantasia Mathematica</i> (anth <b>1958</b>) and <i>The Mathematical Magpie</i> (anth <b>1962</b>), both edited by Clifton <a href="/entry/fadiman_clifton">Fadiman</a>, <i>Science Fiction Adventures in Dimension</i> (anth <b>1953</b>) edited by Groff <a href="/entry/conklin_groff">Conklin</a>, and <i>Mathenauts: Tales of Mathematical Wonder</i> (anth <b>1987</b>) edited by Rudy <a href="/entry/rucker_rudy">Rucker</a>. [BS/DRL]</p> <p><b>see also:</b> <a href="/entry/antimatter">Antimatter</a>; <a href="/entry/cthulhu_mythos">Cthulhu Mythos</a>; <a href="/entry/invasion">Invasion</a>; <a href="/entry/science_and_sorcery">Science and Sorcery</a>.</p> <p><b>previous versions of this entry</b></p> <ul><li><a href='https://web.archive.org/web/*/http://www.sf-encyclopedia.com/entry/dimensions' target='_blank'>Internet Archive</a></li></ul><br /><br /></article></div> <div class="sideBarsWrapper"> <div class="sideBarsColsWrapper clearfix"> <div class="column sideBar12 clearfix"> <div class="columnForm"><aside id="blogFeed" class="widget"> <div class="content STeditorial clearfix"> <h2>Recently visited entries<span style="background:url(/images/thingSFE2.png) !important"></span></h2><ul style='width: 50%; float: left;'> </ul> <p align=center style="float:right; padding-top:20px; padding-bottom:20px;">ISSN 3049-7612<br /> <a href="/facts.php?id=logo"> <img src="/images/VitMan.gif" width=150 height=150 title="Click for larger version of this SFE logo"></a><br /> <b><a href="/donate.php"><img src="/images/Paypal-Donate.gif" WIDTH="92" HEIGHT="26" BORDER="0" /></a><br /><a href="/">Home/Welcome page</a></b></p><div style="margin-bottom:10px;"></div></div> </aside><aside id="blogFeed" class="widget"> <div class="content STeditorial clearfix"> <h2><i>SFE</i> Special Features<span></span></h2><p style="margin-top: 10px;"><input type="button" value="What’s New" style="width: 150px !important;" class="button primary" onclick="window.location.href='/whatsnew.php'">  Latest entries; 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