Flatterland
Encyclopedia
Flatterland is a 2001 book by mathematician and science popularizer Ian Stewart
about non-Euclidean geometry
. It was written as a sequel to Flatland
, an 1884 novel that discussed different dimensions.
" children's toy with a gigantic grin, horns and a spherical body). The Space Hopper, more than being able to move between Flatland and Spaceland, can travel to any space in the Mathiverse, a set of all imaginable worlds. After showing Vikki higher dimensions, he begins showing her more modern theories, such as fractional dimensions and dimensions with isolated point
s. Topology
and hyperbolic geometry
are also discussed, as well as the Projective "Plain" (complete with intersecting "lions") and the quantum
level. Hopper and Victoria also visit the Domain of the Hawk King
to discuss time travel
and the Theory of Relativity
.
Ian Stewart (mathematician)
Ian Nicholas Stewart FRS is a professor of mathematics at the University of Warwick, England, and a widely known popular-science and science-fiction writer. He is the first recipient of the , awarded jointly by the LMS and the IMA for his work on promoting mathematics.-Biography:Stewart was born...
about non-Euclidean geometry
Non-Euclidean geometry
Non-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
. It was written as a sequel to Flatland
Flatland
Flatland: A Romance of Many Dimensions is an 1884 satirical novella by the English schoolmaster Edwin Abbott Abbott. Writing pseudonymously as "A Square", Abbott used the fictional two-dimensional world of Flatland to offer pointed observations on the social hierarchy of Victorian culture...
, an 1884 novel that discussed different dimensions.
Plot summary
Almost 100 years after A. (which we find out stands for Albert) Square's adventures that were related in Flatland, his great-great-granddaughter, Victoria Line (Vikki), finds a copy of his book in her basement. This prompts her to invite a sphere from Spaceland to visit her, but instead she is visited by the "Space Hopper" (a character looking somewhat like the "Space HopperSpace hopper
A space hopper, also known as a moon hopper, skippyball, kangaroo ball, bouncer, hoppity hop, or hop ball, is a rubber ball with handles which allow one to sit on it without falling off...
" children's toy with a gigantic grin, horns and a spherical body). The Space Hopper, more than being able to move between Flatland and Spaceland, can travel to any space in the Mathiverse, a set of all imaginable worlds. After showing Vikki higher dimensions, he begins showing her more modern theories, such as fractional dimensions and dimensions with isolated point
Isolated point
In topology, a branch of mathematics, a point x of a set S is called an isolated point of S, if there exists a neighborhood of x not containing other points of S.In particular, in a Euclidean space ,...
s. Topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
and hyperbolic geometry
Hyperbolic geometry
In mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced...
are also discussed, as well as the Projective "Plain" (complete with intersecting "lions") and the quantum
Quantum
In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...
level. Hopper and Victoria also visit the Domain of the Hawk King
Stephen Hawking
Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
to discuss time travel
Time travel
Time travel is the concept of moving between different points in time in a manner analogous to moving between different points in space. Time travel could hypothetically involve moving backward in time to a moment earlier than the starting point, or forward to the future of that point without the...
and the Theory of Relativity
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
.
Real-world references
Ian Stewart often includes puns and topical references in his popular writing, and "Flatterland" is no exception.- The heroine's name, Victoria LineVictoria LineThe Victoria line is a deep-level London Underground line running from the south to the north-east of London. It is coloured light blue on the Tube map...
, and her mother, Jubilee LineJubilee LineThe Jubilee line is a line on the London Underground , in the United Kingdom. It was built in two major sections—initially to Charing Cross, in central London, and later extended, in 1999, to Stratford, in east London. The later stations are larger and have special safety features, both aspects...
, are both lines on the London UndergroundLondon UndergroundThe London Underground is a rapid transit system serving a large part of Greater London and some parts of Buckinghamshire, Hertfordshire and Essex in England...
. - Her great-great grandfather's name is the fictional Albert SquareAlbert SquareAlbert Square is the fictional location of the BBC soap opera EastEnders. It is ostensibly located in the equally fictional London borough of Walford in London's East End. The square's design was based on the real life Fassett Square in Hackney, and was given the name Albert Square after the real...
in London, from the BBC soap opera EastEndersEastEndersEastEnders is a British television soap opera, first broadcast in the United Kingdom on BBC One on 19 February 1985 and continuing to today. EastEnders storylines examine the domestic and professional lives of the people who live and work in the fictional London Borough of Walford in the East End...
. Her father, Grosvenor SquareGrosvenor SquareGrosvenor Square is a large garden square in the exclusive Mayfair district of London, England. It is the centrepiece of the Mayfair property of the Duke of Westminster, and takes its name from their surname, "Grosvenor".-History:...
, is the square situated in the Mayfair district of London. - Hawk King is a simple pun on the surname of the famous astrophysicistAstrophysicsAstrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
Stephen HawkingStephen HawkingStephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
, whose research includes the Theory of Relativity and Hawking radiationHawking radiationHawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...
. - Vikki, while traveling in the Topological Dimension, also meets a one-sided cow named Moobius (derived from the Möbius stripMöbius stripThe Möbius strip or Möbius band is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface...
) who sells her milk in Klein bottleKlein bottleIn mathematics, the Klein bottle is a non-orientable surface, informally, a surface in which notions of left and right cannot be consistently defined. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a surface with boundary, a...
s (the strip and the bottle both being one-sided topological figures). - The Doughmouse, the Harsh Mare and the Mud Hutter are the counter-parts in Topologica (the rubber-sheet continent) of Carrol's Dormouse, March Hare, and Mad Hatter, respectively. The Doughmouse works with a dough tea set, dough being flexible.
Editions
- ISBN 0-333-78312-3 Original hardback from Macmillan
- ISBN 0-7382-0442-0 Hardback edition by Perseus
- ISBN 0-7382-0675-X Paperback edition by Perseus
- ISBN 0-330-39377-4 Mass-market edition by Pan