Cover image for Flatterland : like Flatland, only more so
Flatterland : like Flatland, only more so
Stewart, Ian, 1945-
Personal Author:
Publication Information:
Cambridge, Mass. : Perseus Pub., [2001]

Physical Description:
xi, 301 pages : illustrations ; 22 cm
Format :


Call Number
Material Type
Home Location
Item Holds
QA93 .S734 2001 Adult Non-Fiction Central Closed Stacks
QA93 .S734 2001 Adult Non-Fiction Non-Fiction Area

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In 1884, Edwin A. Abbott published a brilliant novel about mathematics and philosophy that charmed and fascinated all of England. As both a witty satire of Victorian society and a means by which to explore the fourth dimension, Flatland remains a tour de force. Now, British mathematician and accomplished science writer Ian Stewart has written a fascinating, modern sequel to Abbott's book. Through larger-than-life characters and an inspired story line, Flatterland explores our present understanding of the shape and origins of the universe, the nature of space, time, and matter, as well as modern geometries and their applications. The journey begins when our heroine, Victoria Line, comes upon her great-great-grandfather A. Square's diary, hidden in the attic. The writings help her to contact the Space Hopper, who becomes her guide and mentor through eleven dimensions. Along the way, we meet Schrödinger's Cat, The Charming Construction Entity, The Mandelblot (who lives in Fractalia), and Moobius the one-sided cow. In the tradition of Alice in Wonder-land and The Phantom Toll Booth, this magnificent investigation into the nature of reality is destined to become a modern classic.

Author Notes

Ian Stewart is Professor of Mathematics at the University of Warwick, where he is Director of the Mathematics Awareness Center. He has published over 60 books Stewart was awarded the Royal Society's Michael Faraday Medal for furthering the public understanding of science and he delivered the prestigious Royal Institution Christmas Lectures in 1997. He also writes science fiction and contributes to a wide range of newspapers and magazines in the UK, Europe, and the United States

Reviews 4

Publisher's Weekly Review

Higher mathematics and low comedy intersect acutely in this fuzzy follow-up to Edwin Abbott's 1884 classic, Flatland. Where Abbott's compact fable about a two-dimensional world discomposed by the discovery of a third dimension was a jeu d'esprit that slyly satirized rigid Victorian society, Stewart's sequel is an episodic ramble through the "flatterland" of modern mathematical theory that begins when teenaged Flatlander Vikki Line, great-great-granddaughter of Abbott's narrator, uses her ancestor's "hysterical document" as a passport to the Mathiverse. Accompanied by a Space Hopper guide, she tours landmarks of the post-Einsteinian universe that include fractal geometry, black holes, cosmic strings and quantum theory. Stewart (The Science of Discworld) keeps the tone light with incessant puns (a one-sided cow named "Moobius") and plays on names ("the Hawk King," who presides over a wormhole-ridden realm in the space-time continuum). The many line drawings that illustrate the text are both amusing and instructive. But the terrain Stewart sets out to explore is vast and abstract, and not all of the subjects he covers find a proper social analogue or cultural referent. The result is that lessons Vikki learns on some of the more abstruse principles still have a textbook stuffiness that even the author's Carrollian wit can't leaven. Though perplexing in spots, the tale is ever enchanting, and its user-friendly blend of fiction and nonfiction proves that the comic and cosmic need not be mutually exclusive. (May 1) Forecast: With advertising in Scientific American and the New Yorker and a 50,000-copy first printing, this should be a hit with the literate elite who also appreciate math and science. (c) Copyright PWxyz, LLC. All rights reserved

Choice Review

Edwin A. Abbott's Flatland has a special place in the hearts of many mathematicians. It is playful in its discussion of the problem of higher dimensions, a topic of considerable interest in 1884 to the scientific community. Abbott's clever depiction of Victorian life makes Flatland one of the most socially conscious works of mathematical sophistication ever written. Stewart (Warwick Univ., UK) has taken up the challenge of writing a sequel to this classic (a task not easily accomplished--others have tried). He revisits Flatland 100 years after A. Square, Abbott's protagonist, had written his travelogue through the dimensions. Stewart's protagonist is Vicki Line, an independent young woman who happens upon her great-great-grandfather's dusty old diary. She summons the Space Hopper from higher dimensions and what follows is a romp through topics in contemporary geometry, from higher dimensions to string theory, including non-Euclidean geometry, topology, and much more. The dialogue is engaging, the discussion of mathematical concepts always clear and accessible, and even the puns are worth reading. Stewart offers a worthy sequel to Abbott's classic and an account of contemporary geometry putting it in reach of all readers. This book is bound for the same kind of affection readers have for Abbott's Flatland. Highly recommended for every library. General readers. J. McCleary Vassar College

Booklist Review

Scientific American's math writer offers a sequel to Flatland, Edwin Abbott's late-nineteenth-century fantasy about a two-dimensional universe disturbed by a visitor from the third dimension, the Sphere. Since Abbott's era, mathematicians and physicists have latched onto fourth, nth, and fractional dimensions, which mandates an update. Stewart introduces Flatlander Vikki Line, who discovers a great-grandfather's book that mentions the third dimension. Apoplectic about such apostasy, Vikki's father destroys the book, but she has saved a copy in her computer. She summons the Space Hopper to guide her through the "Mathiverse," the set of all possible spaces and times. As they alight in Topologica, Hyperbolica, Planiturthia, and elsewhere, the Space Hopper surveys the inhabitants' horizons while Vikki, bright line though she is, sweats her way to understanding. She and the Space Hopper proceed to atomic physics, where a quantum cat talks about being dead and alive in Schrodinger's box, and to relativity, ruled by the Hawk King. Yes, the puns are groaners, but Stewart's Flatland-plus makes it fun to think in more than three dimensions. --Gilbert Taylor

School Library Journal Review

Adult/High School-During Victorian times, Edwin A. Abbott wrote the popular mathematical classic Flatland, in which he introduced readers to the concept of four dimensions, as seen through the eyes of two-dimensional A. Square, while cleverly inserting social commentary on class structure and women. In Flatterland, Stewart tells modern readers the story of A. Square's teenage great-great granddaughter, Victoria (Vikki) Line. She feels the typical adolescent mixture of familial love and rebelliousness. When she discovers a copy of her great-great grandfather's book, her parents forbid her to read it and actually burn it to remove the temptation. Of course, she finds a way to read the book anyway and manages to invoke a trans-dimensional being called a Space Hopper, who beckons her to explore the Mathiverse. In the tradition of Abbott's work, Stewart insinuates social commentary here and there; wry wit abounds and sometimes the puns can get quite merciless. Since Vikki is a mere two-dimensional being, she needs help visualizing different dimensions and gets plugged into a Virtual Unreality Engine (VUE). Instead of falling down a rabbit hole ? la Alice in Wonderland, she gets whooshed up into another dimension. Indeed there are references to Lewis Carroll's classic; Vikki encounters a twisted Topologist's Tea Party, and a Schrodinger's Cat complete with disembodied mouth. Containing plenty of illustrations and analogies to help readers through the Mathiverse, Flatterland is an accessible introduction to a number of the abstract worlds for students who have progressed beyond Euclidian geometry and have at least heard of modern physics.-Sheila Shoup, Fairfax County Public Library, VA (c) Copyright 2010. Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.



Chapter One THE THIRD DIMENSION Seen from space, it was a strange world, with the austere beauty of a page from Euclid. In fact it was a page from Euclid, geometry made flesh: a sprawling, humming world of two-dimensional shapes. Flatland. A land of lines, triangles, squares, polygons, circles ... people, of their own kind. They lived polygonal lives, ate polygonal food, drank polygonal drink, made polygonal love, bore polygonal children, and died (polygonally) in a two-dimensional universe -- and never thought it the least bit curious. Their flat world was all they could see, all they could hear, all they could feel. To them, it was all there was.     As long as nothing disturbed that perception, it was true .     But times were changing in Flatland. The house was dowdy and unfashionably pentagonal, but in an excellent location: just along the street from the Palace of the Prefect. It had been in the Square family for almost 150 years, and was now beginning to show its age. Nonetheless, it was a comfortable dwelling, with the typical large Flatlandish entrance hall, seven rooms for the male members of the household, two apartments for the females, a study, a large room that once had housed servants but was now used as a kitchen, with a dining alcove, and a musty, cluttered cellar. It had separate doors for women and men -- for safety reasons, women being rather sharp if encountered end-on. In the hall a middle-aged woman swept up after her two untidy square sons and her neat and lineal daughter, waving her body from side to side so that the males wouldn't accidentally blunder into an endpoint and cut themselves. She found it a comfortable life, though hardly a fulfilling one, and on the whole she was content with her lot.     In the cellar, her daughter Victoria was anything but content with hers. Flatland was a sexist subtopia in which women, seen by their menfolk as simple-minded one-dimensional creatures, performed only menial tasks. Even the lowest of the males, the isosceles triangles, had higher status, and each generation of males made sure everything stayed that way. Not exactly deliberately ... well, not consciously ... well, not with malice , anyway -- they really thought it was the only option ... Well, most of them. It just never occurred to the men that Flatland society might order itself differently. And it certainly never occurred to them that their most cherished beliefs about Flatland society might be based on prejudice and unchallenged assumptions. How could it be? In Flatland, your position in society was determined by how many sides you had and how regular your perimeter was. It was an objective test, hence unquestionable.     At the top of the tree were the Circles, priesthood-cum-nobility: glorious, almost transcendent beings -- perfection made flesh. And the biggest bunch of snobs you could imagine. They weren't even true circles, just polygons with an awful lot of sides. Like many aspects of Flatland, their name was a polite fiction. Behind the rigid façade of Flatland society, however, the winds of change were starting to whine. They had begun as a gentle breeze when the Six-Year War between the Axials and the Alignment had thinned the ranks of Flatland males and thrust women into the munitions factories and the civil service. To the surprise of the men, and the quiet satisfaction of the women, the lineal ladies carried out what had previously been men's jobs with aplomb -- maybe too much aplomb. There were mutterings in the Halls of Power -- but the catenary was out of the bag, and no amount of effort would ever get it back again. As the decades passed, the breeze had stiffened to a howling gale, as the advance of technology brought with it inevitable social spin-off.     If Vikki Line had her way, the gale would soon become a roaring hurricane. Not that she disliked boys, you understand -- as long as they knew their place. Once they stopped flaunting their vertices and comparing how many edges they had, some of them were even quite nice. In fact, that was what had brought her into the dusty recesses of the cellar: she was hoping to find some old discarded clothes of her mother's to wear to the disco that evening. Roger Rectangle was taking her on a date, the retro look was all the rage, and she was hoping to find a few items that would put a kink in the other girls' endpoints.     So far, all she'd found was a motheaten dishcloth and a box of her father's old string vests. (Literally: most Flatland garments were flexible lengths of string, which Flatlanders wrapped round themselves and secured with sticky tabs, leaving their faces uncovered.) Vikki had a feeling that her mother Jubilee would throw a fit if her daughter tried to go out wearing a string vest, however chic.     She noticed a cluster of rectangular boxes in a corner. One of them was battered and fraying at the corners, which looked promising; but she couldn't reach it easily, so she tugged at one of the nearer boxes. With a crash, the mildewed cardboard disintegrated and the contents scattered across the cellar floor.     `Victoria? Victoria! What was that? Are you all right, dear?'     She sighed. `Yes, Mother. An old box came to bits, that's all.'     `Oh. Well, it sounded like a herd of ellipses. Do be careful, dear. And clear up any mess you've made.'     `Yes, Mother.' Vikki started to pick up the junk that had tumbled across the cellar floor, stuffing it back into the now rather battered boxes. She had almost finished when she noticed a tattered book. (More properly, it should be described as a scroll, for on Flatland books are written on lines, not flat sheets, in a kind of Morse code; and the way to store a line compactly is to roll it into a spiral ... I can't keep explaining this kind of thing to you, my Planiturthian readers. So if I use a Planiturthian term that seems not to make sense, for instance, having Vikki -- who is a line , for heaven's sake -- pick something up or carry something, you'll just have to assume that there is some Flatland equivalent.)     Anyway, the book, for so we shall call it, had skated behind some cracked crockery, and nearly escaped her attention.     Curiosity impelled her to roll the book open. Even in the cellar, she had no difficulty seeing it, for in Flatland light manages to make its way into every nook and cranny. Where it came from was a complete mystery -- even to the greatest savants, even at the end of the twenty-first century -- but its ubiquity had an architectural consequence: houses did not need windows.     The book was handwritten, in an old-fashioned script. The title page bore the words Flatland, a Romance of Many Dimensions . The author was identified as A. Square . At first she thought it was some kind of child's primer on the geography, history, and sociology of Flatland, but as she skipped through the text it began to mutate into something darker and more personal. It was almost like a diary, except that it was not arranged by date. A bit past the middle she did come upon a date, however: From dreams I proceed to facts. It was the last day of the 1999th year of our era. The pattering of the rain had long ago announced nightfall, and I was sitting in the company of my wife, musing on the events of the past and the prospects of the coming year, the coming century, the coming Millennium. Why, that would make the book almost exactly a hundred years old! Vikki read on, hoping for more clues. The weird narrative told of a Stranger, a Circle who could change size -- a stranger from Space. It was some kind of science fiction novel, then. A lot of the boys seemed to be into that kind of thing. A phrase caught her eye: You see, you do not even know what Space is. You think it is of Two Dimensions only; but I have come to announce to you a Third -- height, breadth, and length. Ah. They'd done this in physics. Space was two-dimensional, of course -- how could it be otherwise? But there was a sense in which you could think of time as a third dimension, thereby getting a three-dimensional `spacetime continuum'. It wasn't real , of course, just a mathematical invention -- and she found the idea rather pointless because you couldn't draw pictures of three dimensions, anyway. Face it, you couldn't even draw pictures of two dimensions -- you had to project real space down onto a line if you were going to draw a picture. That was how the visual sense worked. Sculpture, though -- that was genuinely two-dimensional, like the tactile and auditory senses. So a moving sculpture could be considered three-dimensional -- and that was what the Stranger in the book was. A moving sculpture that spoke: what a strange idea!     She read on, and became confused. Whatever the Stranger's three-dimensional Space was -- and only now did the significance of the capital letter become apparent -- it was not the conventional three-dimensional spacetime continuum from her physics lessons. In the Stranger's mind, the Third Dimension wasn't time! What, for instance, could be made of this passage? You are living on a Plane. What you style Flatland is the vast level surface of what I may call a fluid, on, or in, the top of which you and your countrymen move about, without rising above it or falling below it. I am not a plane Figure, but a Solid. You call me a Circle; but in reality I am not a Circle, but an infinite number of Circles, of size varying from a Point to a Circle of thirteen inches in diameter, one placed on the top of the other ...     Above? Below?On top ? If A. Square had been writing about the spacetime continuum, surely he would have used words like before, after . These terms -- she could try to infer their content from their context, but the inference didn't really work -- were outlandish, meaningless nonsense words.     Vikki Line tucked the curious book away inside her edgebag, an accessory that had become very fashionable indeed, and not only among the young. Even males were wearing them, though they called them `sidesacks' to distinguish them from effeminate edgebags. She would take a closer look at the book later on. Right now there was a more pressing problem: finding something suitable to wear to the disco. `I don't understand why you young people insist on wearing your parents' old cast--offs', her mother fussed. `You know, your father gave me that jacket just after we got married. It used to fit me then. The colour suits you, dear, I must say.' Only a few generations ago, Jubilee would not have been able to make such a statement -- the rule had been `any colour as long as it's grey'. But the old colour prejudice, fallout from the political sabotage of the Universal Colour Bill, was slowly dying out (indeed, dyeing out), except for a continuing prohibition on body-paint -- and even that was coming under fire with the new fashion for lipstick among upper-class young women.     `It really needs an iron, though, dear,' Jubilee fussed. `Would you like me to--'     `New clothes are so ordinary , Mother. I want to look different.'     `Different from what, dear?'     `Well, just ... different. Like all my friends.'     `Different but the same, then, dear?'     `Ohhhh! You're making fun of me again!'     Her mother smiled (Flatland women do this by wiggling their front vertex in a special way). Vikki took the treasure away to her own little room, along with her other discovery. She kept her clothes in there, and her personal belongings -- a Parallelogram Bear and a dilapidated My Little Polygon which she had long ago outgrown but kept for sentimental reasons; a tape-player with hundreds of cassettes; letters from her friends; schoolbooks; and -- her pride and joy -- one of the new Home Computers, complete with key-strip, tape-reader, printer, and scanner. It had a 2D graphics accelerator, and twenty megs of RAM. Bundled with it had been a `free gift': a tiny electronic Personal Disorganizer, in which she kept contact information for her friends and an extensive diary. It communicated with the computer by invisible light. Not only that -- once she'd saved enough money she was going to add a modem, persuade Daddy to rent an extra phone link, and surf the InterLine. It wouldn't be hard to persuade him: all she had to do was to stay on the phone to her friends for hours and burst into tears and tell him he was ruining her life if he dared interrupt to make his own calls. Her friend Dilly had tried it on her dad a month ago, and a second phone connection had been installed within a day.     The Flatland phone system, by the way, was a triumph of technical ingenuity. In a two-dimensional world, you can't lay a network of cables without trapping people between them -- there's no underground and no overhead. But you can avoid cables altogether and use radio waves of a frequency to which most things in Flatland, especially houses and people, are transparent. With enough repeaters scattered around to boost fading signals back up to full strength and shunt messages past radio-opaque objects, the system worked surprisingly well. Fortunately, Flatlanders seemed to be unaffected by the radiation that sleeted through them, though some consumer groups were beginning to worry that overexposure to the phone system might be contributing to an epidemic of inflamed centroids.     At the very moment that Vikki was thinking about her father, he arrived home from work. Grosvenor was a huge, good-natured square ... well, actually he had gone a bit trapezoidal in his middle age, mostly because Jubilee was such a good cook. As usual, he had picked up their young sons Berkeley and Lester from primary school on the way home. Grosvenor gave Jubilee and Victoria a homecoming kiss and flopped against the big sofa in front of the fire. The soft, slightly springy cushions closed snugly around three of his edges. (The distinction between sitting on/in/against a piece of furniture and wearing it was often rather fuzzy in Flatland.)     The boys shot off into the yard, to play until dinner was ready.     `Vikki, love, be a dear and bring me a beer, will you? It's been a bisector of a day at work.'     Typical . But thoughts of an extra phone link stopped her saying what was on her mind: get your own beer, Dad . Instead, she padded off obediently and brought him back a rectangle of lager from the freezer.     He popped the tab at one end and sucked. `Thanks, sweet-centre.' Well, at least he's expressed gratitude . `Like the shoes. Nice jacket, too, love: it suits you.'     `It's the one you ... I mean, yes, it does, doesn't it? I found it in the cellar.'     `I keep meaning to clean that cellar out', said Grosvenor. `Nothing but a heap of useless junk. Some of it's been in there for generations. Give the lot to Boxfam, that's what we ought to do.'     Talk of junk reminded Vikki of her discovery. Innocently, she said, `That reminds me, Dad: I found a funny old book in the cellar. It looks really really interesting.'     `A book, eh? Well, that cellar holds an awful lot ... bound to be a few books down there--'     `It was handwritten, like a diary. By someone called A. Square.'     Her father sat bolt upright and popped out of the enveloping sofa. His beer slipped from his grasp and the fire hissed as a few errant drops hit it. ` What? '     `It was all about some weird Stranger from the Third Dim--'     Grosvenor's face turned an angry shade of grey. `Victoria Line: don't you ever mention that phrase in this house! God, I thought the family'd got rid of that pernicious little diatribe fifty years ago!'     Vikki didn't understand what she'd done wrong. `But Dad, it's just an old--'     Jubilee, ever the calm one, touched her daughter's side affectionately. `Wait till the boys have gone to bed, Victoria. Then your father will tell you a piece of family history.'     Grosvenor stared at his wife in horror. `Lee, are you sure that now is the right--'     `She's old enough to know the Facts of Life, Grosvenor dear, and how to deal with them on a practical basis. So she's old enough to know the truth about her great-great-grandfather.'     The Facts of Life bit was news to Grosvenor, and it threw him completely. `Dammit, Lee: great-great-grandad Albert's already caused this family too much grief!'     `Is that what the "A" stands for, Dad? Is the book by Albert Square? Was he my great-great-grandfather? What is the Third Dimension, Dad?'     `Victoria, I've just told you not to--'     `Grosvenor, it's too late. We can't hide our past from our own daughter', said Jubilee. `And it was all so long ago. Times are changing. She has a right to know. And you did promise--'     Grosvenor Square sagged back against the sofa. `Yes, but I thought she'd be a bit older than this before I had to ... Yes, yes, I'll tell her. I'm just finding it hard getting used to having a young woman in the house instead of a little girl, OK?'     `After dinner,' insisted Jubilee, driving home her advantage, `as soon as the boys have gone to bed.'     Grosvenor was a beaten man. `Yes, Lee -- after dinner. As you say.'     Jubilee was already dishing out the food into semicircular bowls. Vikki rushed to the door and flung it wide open. ` Berkley! Les! Grub's up! ' Faint sounds of childish prattle were wafting from the boys' bedroom. Ignoring them, Grosvenor took a deep breath and tried to find the courage to peel the wraps off an ancient -- and, he had hoped, forgotten -- piece of Square family history.     Jubilee saw her husband was having trouble, and offered a simple solution. `We don't talk about great-great-grandfather Albert because he died in prison, Vikki.'     `Lee!'     `There's no point in beating about the bush, Grosvenor. Albert did die in prison.'     `Yes, but he wasn't a criminal.'     `Did I say he was? Tell Vikki what he did to get himself imprisoned.'     `Uh -- well, you see, Ancestor Albert ... Lee, do I have to do this?'     `Yes.'     Grosvenor grunted, accepting the reality of his position. `Very well. Vikki, Ancestor Albert was ... he was the black shape of the family, so to speak. He ... he got some ridiculous nonsense into his head about what he called the Land of Three Dimensions. It was an imaginary world, different from ours, and he would have been all right if it had stayed imaginary, but his ... his mind went. He became convinced it was real. He claimed that he had received a visitor from the Land of Three Dimensions, which he called The Sphere.'     `What a funny word. Was the Sphere the Stranger I read about in Albert's book?'     `It was. Albert even claimed he had visited the Land of Three Dimensions himself, with the Sphere as his guide.'     `Wow! Hey, that's really neat!'     Grosvenor sighed. The naive enthusiasm of youth ... `A hundred years ago, Vikki, saying things like that got you sent to prison. For heresy, because you were contradicting the Priests, and because anyone who claimed to have visited another world must be a madman.'     `Oh.'     `So you see, sweetcentre, it's not something the family is proud of. To make matters worse, Albert's unfortunate brother was imprisoned too, supposedly because he witnessed something -- a Visitation, some such nonsense.' He paused, gulped for air, found none that helped. His voice came out half-strangled: `Do you really want all the neighbours to know that two of your ancestors were lunatics?'     Vikki wasn't sure. Being imprisoned for your beliefs was kind of romantic, like being a freedom fighter. And as for witnessing a Supernatural Visitation, that was cool `Crumbs, Dad, that was a hundred years ago.'     `The taint still lingers, Vikki. If your friends found out about old Albert, you might find that some of them weren't your friends any more. I admit that people aren't as obsessed by religion as they were in 1999, but they're still unhappy about any hint of mental instability.'     You mean they're still just as narrow-minded and unimaginative as they ever were , thought Vikki. It was a sobering thought.     `Did you read Albert's book, Vikki?'     `Only a few bits and pieces, Dad. I just ... glanced at it.'     Grosvenor sighed with relief. `Good, at least it hasn't had a chance to taint you too.'     `It looked kind of ... interesting. I was going to read the rest of it later.'     ` No! ' The cry was instant and automatic. `Sorry, love, but I don't think it's suitable material for you to read -- or anyone else.'     Vikki felt this was an infringement of her Polygonal Rights. `Why not?'     `Look what it did for Albert,' said Grosvenor, a wry smile flitting across his florid features. `Think what it might do for you, for us ... In your room, is it? Go and get it for me, there's a good girl.'     Vikki didn't like the sound of that. `But Dad, it's a historical document!'     `A hysterical document, more like. I'll get it, then. Where did you put it?'     Vikki gave her mother a pleading look. `Mum! He's going to destroy it! Can't you stop him?'     Jubilee gave a negative shake of her endpoints. Tm sorry, but your father's right, dear. Best not to wash our dirty strings in public. What's done is done, let's not dwell on the past. You had to be told about Albert because at some stage his name might come up, and you need to know how to react. But you don't need to read the rubbish that put him in prison. It's not fit for a young lady, anyway.'     Oh, Mum, if only you knew some of the books I've read ... But Vikki could tell when she was beaten. `Wait here, Dad, Mum: I'll go and get it. Give me a few minutes, though, OK? Just to be alone with my thoughts. I promise I won't try to read any of it before I bring it to you. Trust me? Please? Give me some dignity?'     Her father nodded, her mother gave a smug smile. Vikki slunk out of the room, defeated.     `That was very hard,' said Grosvenor, `I feel awful. Do you think we should--'     `She said to trust her, dear. So we shall.'     `Of course. Lee, you're so sensible about these things.'     They waited. After a quarter of an hour, Vikki was back. With a sulk, she put the book on the table in front of her parents.     Grosvenor rolled it partly open, checked the title, sampled a few lines here and there to be sure it was the authentic copy. There was trust -- and there was trust . `Should have been burned long ago,' he said. Then he tossed it into the fire. `Time you got yourself ready for young Roger, the lucky dog. Go out and have some fun.'     Vikki watched, damp-eyed, as the flames turned her great-great-grandfather's life's work into smoke and ashes. `Anything you say, Father.' Copyright © 2001 Joat Enterprises. All rights reserved.

Table of Contents

From Flatland to Flatterlandp. vii
1 The Third Dimensionp. 1
2 Victoria's Diaryp. 12
3 The Visitationp. 21
4 A Hundred and One Dimensionsp. 38
5 One and a Quarter Dimensionsp. 65
6 The Topologist's Tea-Partyp. 89
7 Along the Looking-Glassp. 107
8 Grape Theoryp. 118
9 What is a Geometry?p. 131
10 Platterlandp. 145
11 Cat Countryp. 165
12 The Paradox Twinsp. 187
13 The Domain of the Hawk Kingp. 202
14 Down the Wormholep. 223
15 What Shape is the Universe?p. 251
16 No-Branes and P-Branesp. 266
17 Flatterlandp. 288
18 The Tenth Dimensionp. 294