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Overview
Product Details
| ISBN-13: | 9780738206752 |
|---|---|
| Publisher: | Basic Books |
| Publication date: | 04/18/2002 |
| Series: | Art of Mentoring Series |
| Edition description: | Reprint |
| Pages: | 320 |
| Sales rank: | 345,871 |
| Product dimensions: | 5.50(w) x 8.20(h) x 1.85(d) |
About the Author
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...
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 |
Interviews
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)