Flatterland: Like Flatland Only More So


The brilliant "sequel" to one of the all-time classics of popular mathematics. First there was Edwin A. Abbott's remarkable Flatland, published in 1884, and one of the all-time classics of popular mathematics. Now, from mathematician and accomplished science writer Ian Stewart, comes what Nature calls "a superb sequel." 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 ...

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Flatterland: Like Flatland Only More So

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The brilliant "sequel" to one of the all-time classics of popular mathematics. First there was Edwin A. Abbott's remarkable Flatland, published in 1884, and one of the all-time classics of popular mathematics. Now, from mathematician and accomplished science writer Ian Stewart, comes what Nature calls "a superb sequel." 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 tempts her away from her home and family in Flatland and becomes her guide and mentor through ten dimensions. In the tradition of Alice in Wonderland and The Phantom Toll Booth, this magnificent investigation into the nature of reality is destined to become a modern classic.

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Editorial Reviews

From Barnes & Noble
The perfect homage to the classic Flatland, this fanciful book describes the adventures of A. Square's hip great-great-granddaughter Victoria Line. Guided by the Space Hopper, Vikki visits the fourth dimension and beyond -- spending time in the Fractal Forest with Helge the Snowflake and in Topologica with the Doughmouse, among many others -- with the aid of her Virtual Unreality Engine.
From The Critics
Valuable both for the exhilarating range of ideas it plays with and for the deep questions it poses.
New York Times
Flatland challenged the familiar conception of three dimensions; Flatterland challenges the familiar conception of dimension itself.
A. S. Byatt
The most exciting book I have read this year…truly amazing.
A book in which the hard science is as gripping as the fiction…one for anyone with an interest in where science comes from and where it is going.
Stewart achieves what other popular mathematics writers merely strive for: an accurate, informative portrayal of contemporary mathematics without a single equation in sight.
David Brin
Flatterland topples every cozy assumption about what the very concept of dimension means. Get ready for a dizzying ride!.
Rudy Rucker
Filled with jokes and word-play, Flatterland is a joyous tour of more new kinds of spaces than you ever expected..
Thomas Banchoff
Flatterland challenges readers to go beyond Flatland to encounter and deal with phenomena in many exotic geometric realms that stretch our imagination and powers of visualization..
Clifford Pickover
Flatterland is sure to be an instant classic. [Stewart] takes the reader on an engaging and infinite journey to the very fringes of space and time..
Publishers Weekly - Publisher's Weekly
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. Copyright 2001 Cahners Business Information.
School Library Journal
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 Copyright 2001 Cahners Business Information.
Edwin Abott Abott's 1884 instantly became a classic of popular science and has not been out of print since. Contributing to a long line of sequels, Stewart (mathematics, U. of Warwick) tells of the narrator A. Square's great-great-granddaughter Vikky in a society rather like Britain and the US in the early 1960s, though with the Internet thrown in. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780738206752
  • Publisher: Basic Books
  • Publication date: 5/28/2002
  • Series: Art of Mentoring Series
  • Edition description: Reprint
  • Pages: 301
  • Sales rank: 386,396
  • Product dimensions: 5.40 (w) x 8.20 (h) x 0.90 (d)

Meet the Author

Ian Stewart is Professor of Mathematics at the University of Warwick and is well known for his writing and broadcasting about mathematics for nonspecialists. He has written over 140 research papers on such subjects as symmetry in dynamics, pattern formation, chaos, and mathematical biology, as well as numerous popular books, including Letters to a Young Mathematician, Does God Play Dice?, What Shape Is a Snowflake?, Nature’s Numbers, The Annotated Flatland, and Flatterland. He was elected a Fellow of the Royal Society in 2001. He lives in Coventry, England.

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Read an Excerpt

Chapter 1: The Third Dimention

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 facade 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...

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Table of Contents

From Flatland to Flatterland vii
1 The Third Dimension 1
2 Victoria's Diary 12
3 The Visitation 21
4 A Hundred and One Dimensions 38
5 One and a Quarter Dimensions 65
6 The Topologist's Tea-Party 89
7 Along the Looking-Glass 107
8 Grape Theory 118
9 What Is a Geometry? 131
10 Platterland 145
11 Cat Country 165
12 The Paradox Twins 187
13 The Domain of the Hawk King 202
14 Down the Wormhole 223
15 What Shape Is the Universe? 251
16 No-Branes and P-Branes 266
17 Flatterland 288
18 The Tenth Dimension 294
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Interviews & Essays

Exclusive Author Essay
When I was a student I read a curious little book called Flatland, by "A. Square," first published in 1884. The real author was a teacher called Edwin Abbott Abbott. Flatland is a two-dimensional world, and its people are geometric figures -- lines, triangles, squares. Abbott's aim was to explain the Fourth Dimension -- hot intellectual property in his day -- and he made his readers receptive to the idea by getting them to imagine how A. Square would respond to a visitor from the Third Dimension. And Flatland society satirized the rigid social conventions of Victorian England, especially the lowly status accorded to women.

At the start of the 21st century, mathematics and science have moved on, and so have social issues -- though not as much as I'd like. I was reading Flatland again, and I got the idea of writing a sequel, to bring it up-to-date. Clearly the sequel had to be about one of A. Square's descendants, but Abbott doesn't tell us what the "A" in "A. Square" stands for, and I found that I just could not start writing the book until I knew his full name. I was stuck. For years.

Then it suddenly dawned on me that the "A" must stand for "Albert." In the U.K. there is a TV soap called EastEnders, set in a fictitious region of London called Albert Square. Prince Albert was Queen Victoria's consort; Abbott was writing in Victorian times, satirizing Victorian values -- the name fit. What of the womenfolk? On Flatland, women are lines -- and it followed as night followed day that my central character should be female, and her name should be Victoria Line -- which in reality is part of the London Underground.

Now everything came to me in a rush. Young Vikki is Albert's great-great-granddaughter, a thoroughly modern young woman in a society rather like the USA in the early '60s. Flatland's male-dominated culture is falling to bits as its women break away from their traditional restraints. Vikki finds an old notebook, Albert's original manuscript of Flatland, and is bitten by the 3-D bug. She tries to visit the Third Dimension and succeeds -- with some outside help.

Flatterland has a serious purpose, but most of the characters are outrageous. For instance, there's Moobius the cow, who explains topology, and Superpaws -- Schrödinger's cat -- who introduces quantum theory. My previous books provided some inspiration, too: fractals (Does God Play Dice?), symmetry (Fearful Symmetry), number patterns (Nature's Numbers), complexity (The Collapse of Chaos), evolution (Life's Other Secret), the human mind (Figments of Reality)...even aliens (Wheelers).

I had a lot of fun writing Flatterland, but I realize that anyone who insists on putting on a solemn face to talk about science will probably be annoyed by my irreverence.

Tough. (Ian Stewart)

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Sort by: Showing all of 6 Customer Reviews
  • Anonymous

    Posted April 12, 2008

    This Book Explains the Complicated Simply

    The first time that I opened this book I could not put it down. I thought that the characters made this more than just a 'science report'. The language is easy to understand 'save a few paragraphs and explanations - some things are just too complicated to simplify'. Overall, if you are confused by the thought of extra dimensions and want an easy way to understand it, while at the same time being entertained, read this!

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  • Anonymous

    Posted December 8, 2005

    Read Sphereland instead

    I put this book down two chapters in. There is more useless character development and less intelectual structure.

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  • Anonymous

    Posted March 14, 2003

    Not as good as I had hoped

    I was expecting something of a little bit higher caliber. The book was written in too simple of a style. Abbot would be embarashed to read this 'sequel.'

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  • Anonymous

    Posted January 9, 2003

    This book rocks!

    I real Flatland a few months ago and I though it was great. I just finished reading Flatterland and it maybe one of the greatest books ever written. I loved it and would recomend it to everyone I know.

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  • Anonymous

    Posted September 30, 2002


    An interesting book. It isn't quite as good as Flatland, but holds your interest. It presents a much greater number of ideas. It is somewhat amusing as well. It is worth a read.

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  • Anonymous

    Posted January 7, 2002


    great book I liked it alot I was so cool and I bet others books by him are jus as good I'm bugging my library for his books

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