CINXE.COM

<!doctype html>     <html class="no-js" lang="en"> <head> <meta charset="utf-8"> <title>SFE: Mathematics</title> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <meta name="description" content="Welcome to the fourth edition of The Encyclopedia of Science Fiction." /> <meta name="keywords" content="" /> <meta name="viewport" content="width=device-width,initial-scale=1">  <script> window.ga=window.ga||function(){(ga.q=ga.q||[]).push(arguments)};ga.l=+new Date; ga("create", "UA-24275979-1", "auto"); ga("send", "pageview"); </script> <script async src="https://www.google-analytics.com/analytics.js"></script>  <link rel="icon" href="favicon.ico" type="image/x-icon"> <link rel="shortcut icon" href="favicon.ico" type="image/x-icon"> <link rel="apple-touch-icon" href="apple-touch-icon.png"> <link rel="stylesheet" href="/static/css/style.css?v=1"> <link rel="stylesheet" href="/static/css/media-queries.css"> <link rel="stylesheet" href="/css/cookie.css"> <script src="/static/js/libs/modernizr-2.0.6.min.js"></script> <style media="screen" type="text/css"> ::-moz-selection { background: navy !important; } html, body { margin:0; padding:0; height:100%; } #container { min-height:100%; position:relative; } #header { background:#ff0; padding:10px; } #body { padding-bottom:15px; /* Height of the footer */ } #footer { position:absolute; bottom:0; width:100%; height:15px; /* Height of the footer */ background:#6cf; } </style>  </head> <body style="overflow-x: hidden;"> <div id="container"> <div id="body"> <div id="minorNavWrapper"> <nav id="minornav" class="clearfix"> <ul class="clearfix" style="font-weight: bold;"> <li><a href="/">Home</a></li> <li><a href="/about-us">About us</a></li> <li><a href="/random.php">Random</a></li> <li><a href="/contact.php">Contact</a></li> <li><a href="/donate.php">Donate</a></li> </ul> </nav> </div> <div id="mainNavWrapper"> <nav id="mainnav"> <ul class="clearfix"> <li class="home"><a title="Home page" href="https://sf-encyclopedia.com/"><img id="sfeLogoSmall" src="/static/img/sfe.png" alt="SFE: The Encyclopedia of Science Fiction"><img id="sfeLogo" src="/static/img/logo.png" alt="SFE: The Encyclopedia of Science Fiction"></a><span class="logoArrow"></span></li> <li class="section-all"><a href="https://sf-encyclopedia.com/category/0">All entries</a></li> <li class="section-themes"><a href="https://sf-encyclopedia.com/category/theme">Themes</a></li> <li class="section-authors"><a href="https://sf-encyclopedia.com/category/everyone">People</a></li> <li class="section-media"><a href="https://sf-encyclopedia.com/category/media">Media</a></li> <li class="section-culture"><a href="https://sf-encyclopedia.com/category/culture">Culture</a></li> <li class="section-news"><a href="https://sf-encyclopedia.com/news/">News</a></li> </ul> </nav> </div> <div id="main"> <div class="colsWrapper clearfix"> <div class="column mainCol clearfix" style="background-color:white !important;"> <fieldset id="globalSearch"> <form name="srchenter" method="post" action="/search.php"> <select name="catfilter" class="searchFilter" style="width: 132px" title="Select entry category for headword or global search"> <option value="">Search all entries</option> <option value="chk">Checklist titles</option><option value="art">Art</option> <option value="author">Author</option> <option value="award">Award</option> <option value="character">Character</option> <option value="comics">Comics</option> <option value="community">Community</option> <option value="critic">Critic</option> <option value="editor">Editor</option> <option value="fan">Fan</option> <option value="film">Film</option> <option value="game">Game</option> <option value="house name">House Name</option> <option value="international">International</option> <option value="music">Music</option> <option value="people">People (media)</option> <option value="prelim">Prelim</option> <option value="publication">Publication</option> <option value="publisher">Publisher</option> <option value="radio">Radio</option> <option value="theatre">Theatre</option> <option value="theme">Theme</option> <option value="tv">TV</option> </select> <input name="search" type="text" value="" style="margin: 0 0 5px 0; width: 155px !important;" onFocus="this.select()" onClick="this.select()" onHover="this.select()" class="searchText" id="defaultOpen">  <input type="submit" value="Headwords" class="button primary" style="margin: 5px 0 0 0;; padding-left: 8px; padding-right: 8px">  <input type="submit" name="glob" value="Global search" class="button primary" style="margin: 5px 0 0 0; padding-left: 8px; padding-right: 8px"> <input type="text" name="eofmode" value="" hidden> <div style="display:none;"> <p style="margin: 0px; float: left;"><input type="radio" name="tomeselect" value="sfe" checked> <i>Search SFE</i>   <input type="radio" name="tomeselect" value="eof"> <i>Search EoF</i></p> <p style="margin: 0px; float: right;"> <input type="checkbox" Name="noxref">  <i>Omit cross-reference entries</i>  </p> <script> document.srchenter.search.focus(); document.addEventListener("keydown", function(event) { if (event.code == "PageDown" || event.code == "ArrowDown" || ( !event.getModifierState("NumLock") && (event.code == "Numpad2" || event.code == "Numpad3"))) { document.srchenter.search.blur(); } }) </script> </div> </form> </fieldset> <article class="entryArticle content STeditorial"> <header class="entryHeader icon-theme"> <h1 class="entryTitle">Mathematics </h1> </header><p class='tagLine'>Entry updated 1 January 2022. Tagged: Theme.</p><div class="browsingBtns"> <span> <input class="button PNI previous" type="button" onclick="window.location.href='/next.php?id=p&entry=mathematics'" value="Prev" /> </span> <span> <input class="button PNI next" type="button" onclick="window.location.href='/next.php?&entry=mathematics'" value="Next" /> </span> <span> <input class="button PNI incoming" type="button" onclick="window.location.href='/incoming.php?entry=mathematics'" value="About This Entry" title="What links to the entry; contributor initials explained; how to cite; other information" /> </span> </div> <p>The imaginations of pure mathematicians have provided sf writers with important motifs. For example, the notions taken from geometry and topology of a fourth and other <a href="/entry/dimensions">Dimensions</a> (which see for a listing of relevant sf stories) have the essential qualities of strangeness and mystery, making them an enjoyable struggle for the untrained intuition to accept. A surprising number of sf writers have been mathematicians, or at least have trained in mathematics; among them have been Lewis <a href="/entry/carroll_lewis">Carroll</a>, Arthur C <a href="/entry/clarke_arthur_c">Clarke</a>, Paul <a href="/entry/davies_paul">Davies</a>, A K <a href="/entry/dewdney_a_k">Dewdney</a>, Ralph Milne <a href="/entry/farley_ralph_milne">Farley</a>, Martin <a href="/entry/gardner_martin">Gardner</a>, Norman <a href="/entry/kagan_norman">Kagan</a>, Johannes <a href="/entry/kepler_johannes">Kepler</a>, Donald <a href="/entry/kingsbury_donald">Kingsbury</a>, H <a href="/entry/nearing_homer_jr">Nearing</a>, Larry <a href="/entry/niven_larry">Niven</a>, Esther <a href="/entry/rochon_esther">Rochon</a>, Rudy <a href="/entry/rucker_rudy">Rucker</a>, Bertrand <a href="/entry/russell_bertrand">Russell</a>, Ian <a href="/entry/stewart_ian">Stewart</a>, Boris <a href="/entry/strugatski_arkady">Strugatski</a>, John <a href="/entry/taine_john">Taine</a>, Vernor <a href="/entry/vinge_vernor">Vinge</a> and David <a href="/entry/zindell_david">Zindell</a>.</p> <p>In discussing the use of mathematical ideas in sf, the boundary between sf and fantasy must be drawn according to somewhat different principles from those used in the case of the natural sciences. Since many mathematical ideas derive their piquancy from the fact that they are definitely incompatible with the world we live in, a story illustrating such an idea cannot claim any credence as a record of possible events, and should perhaps be classed as a fantasy. Yet an important consideration in judging a story of this type is its fidelity to mathematical truth, in which respect it belongs not just to sf but to sf at the furthest remove from fantasy, to that subgenre comprising stories which turn on a point of established science.</p> <p>In the field of geometry these points are illustrated by the prototype of all stories which use the idea of space having other than three <a href="/entry/dimensions">Dimensions</a>, E A <a href="/entry/abbott_edwin_a">Abbott</a>'s <i>Flatland</i> (<b>1884</b> as by A Square). Written in a period when there was great interest among mathematicians in n-dimensional geometry, this fantasy offers an indirect approach to the problems we, as three-dimensional creatures, have in understanding four-dimensional space by examining the difficulties two-dimensional beings in <a href="/entry/flatland">Flatland</a> would have in understanding three-dimensional space – an explanatory device which was to become a standard feature of sf invoking a fourth dimension. With sentient lines, triangles and polygons as its inhabitants, the book's only three-dimensional character being a visiting sphere, Flatland makes no pretence of being related to the real world. The book has been made into a short animated film, <i>Flatland</i> (<i>1965</i>), directed by Eric Martin, with narration by Peter Cook. C H <a href="/entry/hinton_c_h">Hinton</a> developed Abbott's speculations, adding some of his own, in several pieces in <i>Scientific Romances</i> (coll <b>1886</b>) and <i>Scientific Romances: Second Series</i> (coll <b>1902</b>), and in his sequel <i>An Episode of Flatland</i> (<b>1907</b>). In <i>Bolland</i> (<b>1957</b>; trans as <i>Sphereland</i> <b>1965</b>) Dionys <a href="/entry/burger_dionys">Burger</a> wrote another sequel designed to explain in the same way Einstein's theories about curved space; there are further <a href="/entry/sequels_by_other_hands">Sequels by Other Hands</a>. Greg <a href="/entry/bear_greg">Bear</a>'s stylish story "Tangents" (January 1986 <a href="/entry/omni">Omni</a>) imagines the intrusion of higher-dimensional beings into our three-dimensional space, in a sophisticated reworking of the theme of Miles J <a href="/entry/breuer_miles_j">Breuer</a>'s "The Captured Cross-Section" (February 1929 <a href="/entry/amazing">Amazing</a>).</p> <p>Among the many stories using fourth and other dimensions, two deserve mention here for their emphasis on particular mathematical points. H G <a href="/entry/wells_h_g">Wells</a>'s "The Plattner Story" (April 1896 <i>New Review</i>) turns on the fact that a three-dimensional object, if rotated through half a turn in a fourth dimension, becomes its mirror image (in the story this happens to Gottfried Plattner, who afterwards finds his heart is on the right). The reception of this point by literary readers amusingly illustrates how, if science can lend credibility to sf, sf removes credibility from science: one critic (Allan Rodway, in <i>Science and Modern Writing</i> [<b>1964</b>]) told his readers that this was "neither scientific nor mathematical". In fact it is excellent mathematics. In "– And He Built a Crooked House" (February 1941 <a href="/entry/asf">Astounding</a>) Robert A <a href="/entry/heinlein_robert_a">Heinlein</a> describes a house of eight cubical rooms which fit together like the eight three-dimensional "faces" of a four-dimensional cube (a tesseract). The story ostensibly takes place in the real world, but Heinlein's main concern is not to persuade the reader that his house is physically possible but to show us something which is mathematically feasible though seemingly paradoxical. He is therefore careful to be mathematically correct in describing the structure of his house, while emphasizing its startling features. His one slip, as it happens, offends against both requirements; the mathematical truth is even stranger than he realized.</p> <p>Other writers have set stories in frankly imaginary worlds for the sake of unusual topological structures of space, but few have been so careful to define the structures as Heinlein was. It is common for the topological oddity to be revealed only at the last, as a shock ending, as in David I <a href="/entry/masson_david_i">Masson</a>'s "Traveller's Rest" (September 1965 <a href="/entry/new_worlds">New Worlds</a>) – though this is only one element of a subtle and complex story in which the structures of time and language undergo variations related to that of the structure of space (see <a href="/entry/relativity">Relativity</a>) – and 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>), which uses a similar idea. Christopher <a href="/entry/priest_christopher">Priest</a>'s <i>Inverted World</i> (<b>1974</b>) features (or appears to, for the whole thing could be a trick of perception) a hyperboloid world where variations of subjective experience take place according to one's position in the world. (Several mathematical stories, including Priest's, are discussed under <a href="/entry/perception">Perception</a>.) Topology is also likely to be abused as a catch-all explanation for any weird happening: in "A Subway Named Möbius" (December 1950 <a href="/entry/asf">Astounding</a>) by A J <a href="/entry/deutsch_a_j">Deutsch</a>, for example, it is supposed that a subway network has become so complex that trains mysteriously disappear and reappear, although no proper topological explanation is presented.</p> <p>This careless attitude to topology is comparable with the numerology (see <a href="/entry/pseudoscience">Pseudoscience</a>) of such stories as "Six Cubed Plus One" (in <i>New Writings in SF 7</i>, anth <b>1966</b>, ed John <a href="/entry/carnell_john">Carnell</a>) by John Rankine (Douglas R <a href="/entry/mason_douglas_r">Mason</a>), in which magical properties are attributed to special numbers. (A sardonic comment on cavalier attitudes to mathematics was made by L Sprague <a href="/entry/de_camp_l_sprague">de Camp</a> and Fletcher <a href="/entry/pratt_fletcher">Pratt</a> in <i>The Incomplete Enchanter</i> [May, August 1940 <a href="/entry/unknown">Unknown</a>; coll of linked stories <b>1941</b>], in which a series of propositions in mathematical logic is used as a magic incantation of transport to worlds of fiction and <a href="/entry/mythology">Mythology</a>.)</p> <p>Transfinite arithmetic shares with topology the appeal of the unfamiliar and the smack of <a href="/entry/paradox">Paradox</a>, and infinity has its own sensational connotations. For these reasons transfinite numbers are often called upon to establish an atmosphere of mathematical mysticism, but for many years few authors found it possible to do more with them. They appealed to the quirkiness of James <a href="/entry/blish_james">Blish</a>, who in "FYI" (in <i>Star Science Fiction Stories 2</i>, anth <b>1953</b>, ed Frederik <a href="/entry/pohl_frederik">Pohl</a>) seized on the fact that they do not and cannot count material objects and contemplated the Universe being reconstructed to accommodate them. Rudy <a href="/entry/rucker_rudy">Rucker</a> is a mathematician with a firm grasp of the issues: his <i>White Light, or What Is Cantor's Continuum Problem?</i> (<b>1980</b>) reifies the appalling tiers of mathematical infinities as an impossible mountain which the protagonist is required to climb, passing such relatively familiar benchmarks as aleph-null (the infinity of the integers or counting numbers) and C (the infinity of real numbers, which can have up to aleph-null digits after the decimal point) but reaching a setback at epsilon-zero (the point, in effect, at which all previous mathematical schemas for generating higher infinities cease to work). Here Rucker throws the reader in at the deep end of infinite set theory and other mathematical complexities; the background is more clearly explained in his nonfiction <i>Infinity and the Mind: The Science and Philosophy of the Infinite</i> (<b>1982</b>) and, in passing, in Douglas <a href="/entry/hofstadter_douglas">Hofstadter</a>'s <i>Gödel, Escher, Bach: An Eternal Golden Braid</i> (<b>1979</b>).</p> <p>The two other areas of mathematics which have provided material for sf stories are statistics and logic. The concepts of statistics and probability theory are easy to misunderstand, as has been demonstrated in many sf stories; also, being abstractions which can masquerade as concrete instances, they are easy to ridicule, and this can be seen in Russell Maloney's "Inflexible Logic" (February 1940 <i>The New Yorker</i>), which shows us monkeys producing famous works of literature by random manipulation of typewriters (a traditional <a href="/entry/thought_experiment">Thought Experiment</a>), William <a href="/entry/tenn_william">Tenn</a>'s "Null-P" (January 1951 <a href="/entry/worlds_beyond">Worlds Beyond</a>), in which an exactly average man is discovered and hailed as the ideal, and Jack C <a href="/entry/haldeman_jack_c_ii">Haldeman</a>'s "A Very Good Year" (December 1984 <a href="/entry/analog">Analog</a>) in which the absence of death for a whole year is statistically compensated for in the next. A rather more serious point about statistics was made by Robert M <a href="/entry/coates_robert_m">Coates</a> in "The Law" (29 November 1974 <i>The New Yorker</i>), which describes the "Law of Averages" breaking down and so prompts consideration of why human beings in large numbers normally do behave in predictable ways. Robert A <a href="/entry/heinlein_robert_a">Heinlein</a>'s "The Year of the Jackpot" (March 1952 <a href="/entry/galaxy">Galaxy</a>) extrapolates the phenomenon of statistical "clumping" to a scenario in which numerous unrelated <a href="/entry/disaster">Disasters</a> (predictable by study of cycles and trends) afflict Earth during the titular period. Perhaps the most famous if not the most plausible sf extrapolation of statistical theory is Isaac <a href="/entry/asimov_isaac">Asimov</a>'s predictive science of <a href="/entry/psychohistory">Psychohistory</a> (which see) in the <b>Foundation</b> sequence. Tom <a href="/entry/stoppard_tom">Stoppard</a>'s <i>Rosencrantz and Guildenstern Are Dead</i> (first performed 1966; <b>1967</b> chap) opens with a disconcerting breakdown of probability as 89 successive coin-tosses come up heads.</p> <p>The perennial fascination of logical <a href="/entry/paradox">Paradoxes</a> was exploited by Gordon R <a href="/entry/dickson_gordon_r">Dickson</a> in "The Monkey Wrench" (August 1951 <a href="/entry/asf">Astounding</a>). This story uses the paradox of Epimenides the Cretan ("All Cretans are liars": in effect, "this statement is false") to deflate a <a href="/entry/computers">Computer</a> engineer's pride in the perfection of his machine, thus giving a reassuring reminder of the insufficiency of logic which was to become a notorious sf <a href="/entry/cliches">Cliché</a>. An opposite effect was achieved by Frederik <a href="/entry/pohl_frederik">Pohl</a> in a number of stories, notably "The Schematic Man" (January 1969 <a href="/entry/playboy">Playboy</a>), which describes a man coding himself as a computer program (see <a href="/entry/upload">Upload</a>), and so raises the question of what makes the real world more than a mathematical model. Logical paradoxes in fictional form were a speciality of Lewis <a href="/entry/carroll_lewis">Carroll</a>, whose puzzle tales in <i>A Tangled Tale</i> (coll <b>1886</b>) and rulebook for <i>The Game of Logic</i> (<b>1887</b>) make some play with them, as – more familiarly – do the <b>Alice</b> books. Closer to our own time, Martin <a href="/entry/gardner_martin">Gardner</a>, whose mathematical-puzzle column appeared in <i>Scientific American</i> 1957-1981 and in <a href="/entry/asimovs">Asimov's Science Fiction</a> from 1977, has written many fictionalized mathematical diversions, such as those collected in <i>Science Fiction Puzzle Tales</i> (coll <b>1981</b>) and <i>Puzzles from Other Worlds</i> (coll <b>1984</b>). Those who have continued the immensely influential Gardner tradition in <i>Scientific American</i> include A K <a href="/entry/dewdney_a_k">Dewdney</a>, Douglas <a href="/entry/hofstadter_douglas">Hofstadter</a> and Ian <a href="/entry/stewart_ian">Stewart</a>; another author operating in a similar vein was Raymond <a href="/entry/smullyan_raymond">Smullyan</a>.</p> <p>Mathematics whose point is not primarily mathematical can also appear in sf; the use of an occasional mathematical formula is seen by some sf writers, as by some scientists, as conferring intellectual respectability. A rare example of a genuine mathematical argument occurs in a footnote to Fred <a href="/entry/hoyle_fred">Hoyle</a>'s <i>The Black Cloud</i> (<b>1957</b>): it is a nice calculation, and has probably added to a number of readers' enjoyment of the book. Hoyle also gave a mathematical explanation of an sf speculation in the preface to <i>Fifth Planet</i> (<b>1963</b>). Further examples of popular exposition of mathematical ideas in sf are the explanation of the calculus of variations in David <a href="/entry/duncan_david">Duncan</a>'s <i>Occam's Razor</i> (<b>1957</b>) and that of coordinate systems and relativity in Miles J <a href="/entry/breuer_miles_j">Breuer</a>'s "The Gostak and the Doshes" (March 1930 <a href="/entry/amazing">Amazing</a>). Both authors proceed to tell stories which have only tenuous connections with the mathematical ideas they have expounded. Sticking more closely to the subject, Leslie <a href="/entry/charteris_leslie">Charteris</a>'s action hero the <b>Saint</b> uncharacteristically takes up pencil and paper to lay bare the deceptive odds of various probability-based "sucker bets" in the non-sf "The Percentage Player" (August/September 1959 <i>Saint Magazine</i>).</p> <p>Though the mathematical genius Libby in Robert Heinlein's "Misfit" (November 1939 <a href="/entry/asf">Astounding</a>) proves resourceful, mathematicians as characters in <a href="/entry/genre_sf">Genre SF</a> have often been stereotyped as absent-minded, ineffectual and unworldly; they are clearly descended from the inhabitants of Jonathan <a href="/entry/swift_jonathan">Swift</a>'s Laputa in <i>Gulliver's Travels</i> (<b>1726</b>; rev <b>1735</b>). Sf is popular among mathematicians, however, and it is not surprising that there should have been some attempts to adjust this image. This can be seen particularly in the stories of Norman <a href="/entry/kagan_norman">Kagan</a>, whose portrayals of zany, hyperactive maths students, although they sometimes appear self-congratulatory, may be rather closer to reality. Kagan's stories make witty use of many parts of mathematics; while ostensibly concerned with sf speculations – in "Four Brands of Impossible" (September 1964 <a href="/entry/fsf">F&SF</a>) the use of a different logic to describe the world, in "The Mathenauts" (July 1964 <a href="/entry/if">If</a>) a physical journey into various mathematical spaces – they are really about the experience of doing mathematics. One important mathematical sf protagonist is Shevek, in Ursula K <a href="/entry/le_guin_ursula_k">Le Guin</a>'s <i>The Dispossessed</i> (<b>1974</b>), whose new mathematics is the basis for building the <a href="/entry/ansible">Ansible</a>, a <a href="/entry/faster_than_light">Faster-than-Light</a> <a href="/entry/communications">Communications</a> device.</p> <p>Another particularly interesting mathematician is the elderly protagonist of "Euclid Alone" (in <i>Orbit 16</i>, anth <b>1975</b>, ed Damon <a href="/entry/knight_damon">Knight</a>) by William F Orr, himself a mathematician. Here a student successfully proves one of Euclid's axioms to be wrong. His teacher is left with the moral quandary of whether or not to suppress the discovery, which may, ultimately, destroy the serenity of everyone in the world. Orr's story can be found in <i>Mathenauts</i> (anth <b>1987</b>) edited by Rudy <a href="/entry/rucker_rudy">Rucker</a>, the only <a href="/entry/anthologies">Anthology</a> of sf mathematical stories since the classic <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>. Similar in theme is Ted <a href="/entry/chiang_ted">Chiang</a>'s "Division by Zero" (in <i>Full Spectrum 3</i>, anth 1991, ed Lou <a href="/entry/aronica_lou">Aronica</a>, Amy Stout and Betsy Mitchell), in which the central character is horrified to discover a proof that mathematics is inconsistent with itself, and therefore meaningless. A further seeming inconsistency in mathematics is explored by the eponymous super-<a href="/entry/computers">Computer</a> of Greg <a href="/entry/egan_greg">Egan</a>'s "Luminous" (September 1995 <a href="/entry/asimovs">Asimov's</a>), where an anomalous zone of number theory proves to be the interface to a <a href="/entry/parallel_worlds">Parallel World</a> based on different mathematics; this crossover becomes more than theoretically disturbing in the sequel "Dark Integers" (October/November 2007 <a href="/entry/asimovs">Asimov's</a>).</p> <p>Mathematics has entered fiction in strange ways. Some of the oddest are discussed in the entry for the <a href="/entry/oulipo">Oulipo</a> group. Certainly stories of <a href="/entry/communications">Communications</a> can feature mathematics, through the idea of mathematics as a universal language. Some notable mathematical incursions into sf during the 1980s are the mathematical harmonies in Kim Stanley <a href="/entry/robinson_kim_stanley">Robinson</a>'s <i>The Memory of Whiteness</i> (<b>1985</b>), the cosmic message concealed in the endless series of numbers following <i>pi</i>'s decimal point in <i>Contact</i> (<b>1985</b>) by Carl <a href="/entry/sagan_carl">Sagan</a> – this was <a href="/entry/satire">Satirically</a> anticipated in John T <a href="/entry/sladek_john_t">Sladek</a>'s <i>The Müller-Fokker Effect</i> (<b>1970</b>), featuring the <a href="/entry/paranoia">Paranoid</a> theory that Commies have insidiously encoded their anti-US master plan into the digits of <i>pi</i> – and the sidebar disquisition on the Mandelbrot set in Arthur C Clarke's <i>The Ghost from the Grand Banks</i> (<b>1990</b>), at that time one of the few sf stories to use the mathematics of fractals (later to become a <a href="/entry/cliches">Cliché</a>). Greg <a href="/entry/egan_greg">Egan</a>'s "Unstable Orbits in the Space of Lies" (July 1992 <a href="/entry/interzone">Interzone</a>) features a mapping of migrant people's movements on to the kind of complex fractal path known as a strange attractor.</p> <p>But the most important mathematical sf writers since the late twentieth century have been Rudy <a href="/entry/rucker_rudy">Rucker</a> and David <a href="/entry/zindell_david">Zindell</a>, both mathematicians. Rucker's stories do not merely turn on mathematical points; they are often set in worlds generated by mathematical ideas, whose exploration is itself an act of mathematical intellection, in which the author delights, as he does in raunchy humour. Such tales comprise much of his early work, notably <i>White Light, or What Is Cantor's Continuum Problem?</i> (<b>1980</b>) – a crazed fantasia moving in physical (though afterlife) analogues of Hilbertian space, transfinite numbers and much else – <i>The Sex Sphere</i> (<b>1983</b>) and <i>The Secret of Life</i> (<b>1985</b>). Zindell's <i>Neverness</i> (<b>1988</b>) is one of the few successful books whose assumption is that mathematics is <i>romantic</i>. In this novel, to win an ice-race is to solve a theorem. The sequence where the protagonist can map the space windows only through mathematics – fountains and arpeggios of mathematics – is sustained and moving, and conveys with great conviction even to the nonmathematical reader what the high delight of mathematical thought must <i>feel</i> like. [TSu/PN/DRL]</p> <p><b>see also:</b> Augustus <a href="/entry/de_morgan_augustus">de Morgan</a>; <a href="/entry/basilisks">Basilisks</a>; <a href="/entry/information_theory">Information Theory</a>.</p> <p><b>links</b></p> <ul class="x"> <li><a target="_blank" href="http://kasmana.people.cofc.edu/MATHFICT/">Mathematical Fiction</a></li> </ul> <p><b>previous versions of this entry</b></p> <ul><li><a href='https://web.archive.org/web/*/http://www.sf-encyclopedia.com/entry/mathematics' 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; <a href="/updated.php">latest updates</a></p> <p style="line-height:1.6em;"><input type="button" value="In Memoriam" style="width: 150px !important;" class="button primary" onclick="window.location.href='/timeline.php?rip'">  Recent deaths</p> <p style="line-height:1.6em;"><input type="button" value="On This Day" style="width: 150px !important;" class="button primary" onclick="window.location.href='/today.php'">  Anniversaries; also <a href="/timeline.php">Timeline</a></p> <p style="line-height:1.6em;"><input type="button" value="Gallery" style="width: 150px !important;" class="button primary" onclick="window.location.href='/gallery.php'">  <i>SFE</i> Picture Gallery; <a href="/gallery.php?list&new">What’s New</a></p> <p style="line-height:1.6em;"><input type="button" value="Shopping" style="width: 150px !important;" class="button primary" onclick="window.location.href='/sfeshop.php'">  Affiliate settings</p> <p style="line-height:1.6em;"><input type="button" value="Random" style="width: 150px !important;" class="button primary" onclick="window.location.href='/random.php'">  Show a random <i>SFE</i> entry</p> <p style="line-height:1.6em;"><input type="button" value="SFE Facts" style="width: 150px !important;" class="button primary" onclick="window.location.href='/facts.php'">  Bar charts, awards and more</p> <p style="line-height:1.6em;"><input type="button" value="Entry Data" style="width: 150px !important;" class="button primary" onclick="window.location.href='https://sf-encyclopedia.com/incoming.php?entry=mathematics'">  Incoming links, who wrote it, etc</p> <p style="margin-bottom:15px;"><a href="/searching">Search help</a> | <a href="/rss.php" target="_blank">RSS feed</a> <img src="/static/img/external.gif"> | <a href="/fe/"><i>Encyclopedia of Fantasy</i></a> <img src="/static/img/external.gif"></p><div style="margin-bottom:10px;"></div></div> </aside><aside id="connect" class="widget"> <div class="content STeditorial clearfix"> <h2>Connect with <i>SFE</i> <span></span></h2> <ul> <li> <h3 style="text-align: left !important;"><a href="/donate.php">Donate towards <i>SFE</i> expenses</a></h3> </li> <li> <h3 style="text-align: left !important;"><a href="/contact.php">Send email feedback to the <i>SFE</i> editors</a></h3> </li> <li style=" display:none;"> <h3 style="text-align: left !important;"><a href="https://twitter.com/john_clute" target="_blank">John Clute on Twitter [X]</a></h3> <a href="https://twitter.com/john_clute" class="twitter-follow-button">Follow @john_clute</a> <script src="https://platform.twitter.com/widgets.js" type="text/javascript"></script> </li> <li style=" display:none;"> <h3 style="text-align: left !important;"><a href="https://twitter.com/sfencyclopedia" target="_blank"><i>SFE</i> on Twitter [X]</a></h3> <a href="https://twitter.com/sfencyclopedia" class="twitter-follow-button">Follow @sfencyclopedia</a> <script src="https://platform.twitter.com/widgets.js" type="text/javascript"></script> </li> <li> <h3 style="text-align: left !important;"><a href="https://www.facebook.com/pages/Sf-Encyclopedia/138995776178949" target="_blank"><i>SFE</i> on Facebook</a></h3> </li> <li> <h3 style="text-align: left !important;"><a href="https://www.facebook.com/john.clute.5" target="_blank">John Clute on Facebook</a></h3> </li> <li> <h3 style="text-align: left !important;"><a href="https://bsky.app/profile/sfencyclopedia.bsky.social" target="_blank"><i>SFE</i> on BlueSky</a></h3> </li> <li> <h3 style="text-align: left !important;"><a href="https://mastodon.social/@SF_Encyclopedia" target="_blank"><i>SFE</i> on Mastodon</a></h3> </li> </ul> </div> </aside> </div></div> </div> </div> </div> </div> </div> <div id="cookieConsent"> <div id="closeCookieConsent" onclick="hidepopup()">x</div> This website uses cookies.  <a href="/cookies" target="_blank">More information here</a>. <a class="cookieConsentOK" onclick="setcookie()">Accept Cookies</a> </div> <script type="text/javascript"> function hidepopup() { document.cookie = "hidecookiepopup=yes; path=/"; // session only document.getElementById("cookieConsent").style.display = "none"; } function setcookie() { document.cookie = "cookiesOK=yes; max-age=31536000; path=/"; // 1 year document.getElementById("cookieConsent").style.display = "none"; } var cookiestring = document.cookie; // document.getElementById("connect").innerHTML = cookiestring; // TEST only if ( cookiestring.indexOf("cookiesOK=yes") == -1 ) { if ( cookiestring.indexOf("hidecookiepopup=yes") == -1 ) { document.getElementById("cookieConsent").style.display = "block"; } } </script> <div id="footer" style="background:#fff; padding: 5px;"> <footer id="globalFooter" class="clearfix"> <div id="credit">Website design by Ansible Editions </div> <div id="credit" style="float: left !important; padding-left:20px;">Site and <i>SFE</i> content © 2011-2024 John Clute & David Langford</div> </footer> </div> </div> </body></html>