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Flatland

by Edwin A. Abbott

Reviewed by Ted Gioia

Mathematicians get little credit in the literary world.  Go
figure!  But when the history of conceptual fiction is finally
written, they may turn out to be the visionaries and pioneers.  

The use of storytelling as a means of experimenting with our
conceptions of reality—in essence the cult of the perversely
anti-realistic novel—didn’t become an important force in
literature until the twentieth century.  Most of the agents
provocateurs who made this happen came out of the blatantly
commercial world  of pulp fiction.  
Yet, in a strange turnabout, the
innovations of the sci-fi writers
eventually managed to influence
“serious” fiction, and even a
Philip
K. Dick could posthumously be
rehabilitated enough to join The
Library of America.  

But the mathematicians were
developing these literary concepts
even earlier—especially Charles
Lutwidge Dodgson (1832-1898),
whom you will know better as Lewis
Carroll, and Edwin A. Abbott
(1838-1926), author of the quirky
cult classic
Flatland.   The term
science fiction did not exist when
these authors were active, and their attempts to invent and
explore alternative universes built from their own vivid
imagination were, to a great degree, an extension of their
theoretical work with numbers.   

Fast forward to the modern era, and
you find that—once again—some of the
most conceptually advanced writers of
the contemporary era reveal an affinity
with conceptual thinking of a non-
literary nature.   Recall, Thomas
Pynchon applied to do graduate work in
mathematics at Berkeley in 1964—and
was turned down.  
David Foster Wallace's
senior thesis at Amherst was on the modal
logic.   

Most people today would struggle to
see the connection between numbers
and storytelling, yet from an anthropological point of view, the
linkage is far from arbitrary.  Calculations and stories both
possess functional value as means of grappling with our
surroundings, and securing our knowledge in a way that can
be passed on to others.   Before tales were recognized for
their aesthetic dimensions, they had “survival value”—to use a
Darwinian term—not dissimilar in this regard from quantitative
skills.  

If
Flatland demands recognition as one of the first major works
of conceptual fiction, it must rank even today as one of the
most ambitious.  Abbott, writing under the pen name of A
Square aims at nothing less than depicting life within a two-
dimensional universe. Our narrator lives on a geometrical
plane, where he can perceive only length and width, but not
height.   Here he and his family lead flat Euclidean lives, in a
rigidly hierarchical society, with circles at the top of the heap,
and women (who are straight lines) and the lower classes
(isosceles triangles and other irregular shapes) at the
bottom.   

But the book is not flat, even if the setting is.  Abbott is a
fascinating individual (in a surviving photo he looks like he
was destined to be cast in the role of Harry Potter headmaster
Albus Dumbledore).  His "geometry novel" presents a pointed
critique of Victorian attitudes and proves that, even at this
early point in the evolution of conceptual fiction, these kinds of
stories need not be limited by the formulas of escapist
literature.  In fact, the author may have found here a perfect
platform for exposing the narrow-mindedness and prejudices
of his day—after all what could be a better stick figure to
represent a narrow view than a two-dimensional sentient
square?

Flatland, it turns out, is a society built on questionable
dogmas.  Women are believed incapable of advanced
thinking, and are thus prevented from gaining an education,
or even learning how to read and write.   Triangles who fall
short of the equilateral ideal, are treated as akin to an
untouchable class—almost literally so, since their sharp
angles are potentially dangerous.   Parents are so caught up
in the geometrical symmetries of their offspring, that they will
resort to dangerous medical procedures with the hopes of
straightening out the angles of their progeny.  

Our narrator tells about his own dealings with one-dimensional
(Lineland) and no-dimensional (Pointland) societies.  He is
amazed at the inability of those in these settings to
comprehend his own, much richer universe.  Yet he is similarly
limited in imagination when a visitor from our three-
dimensional world (Spaceland in Abbott’s terminology) tries to
open up the Square’s mind to the possibilities of spheres,
cubes and other solid figures.   Yet A Square's epiphany
takes place when he is rudely dragged out of
Flatland and
allowed a brief glimpse into our world.  Our hero concludes,
however, that even three-dimensional space is itself a limited
perspective on the nature of things, and he hungers for the
wonders of the fourth, fifth and sixth dimensions, and so on
until infinity.

But this advanced knowledge does not come without a cost.  
In
Flatland—as perhaps in our own more elaborate world—
those who see more deeply into the things around them are
often branded as a threat by those whose positions of power
are built on complacency and dogma.   In short, even a
square can be a revolutionary in two-dimensional space,
contrary to what you might have heard from various hipsters
and beatniks.  

Yes, Abbott manages to deal with everything from politics to
theology in his story, and finds time to pause and reflect on
the nature of painting in a two-dimensional society, the history
of rebellions and uprisings among the lower geometrical
classes, the construction of houses, and various other matters
of import small and large.  Yet this tale has enough
mathematical and conceptual content to justify its cult status
among the slide rule and pocket protector folks.   In other
words, like any good book,
Flatland is one with many
dimensions—certainly more than the two that its inhabitants
recognize.
Edwin A. Abbott
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Conceptual Fiction:
A Reading List
(with links to essays on each work)

Home Page

Abbott, Edwin A.
Flatland

Adams, Douglas
The Hitchhiker's Guide to the Galaxy

Aldiss, Brian
Barefoot in the Head

Aldiss, Brian
Hothouse

Aldiss, Brian
Report on Probability A

Allende, Isabel
The House of the Spirits

Amado, Jorge
Dona Flor and Her Two Husbands

Amis, Martin
Time's Arrow

Apuleius
The Golden Ass

Asimov, Isaac
The Foundation Trilogy

Asimov, Isaac
I, Robot

Atwood, Margaret
The Handmaid's Tale

Banks, Iain M.
The State of the Art

Ballard, J.G.
The Atrocity Exhibition

Ballard, J.G.
Crash

Ballard, J.G.
The Crystal World

Ballard, J.G.
The Drowned World

Barth, John
Giles Goat-Boy

Bester, Alfred
The Demolished Man

Blish, James
A Case of Conscience

Borges, Jorge Luis
Ficciones

Bradbury, Ray
Dandelion Wine

Bradbury, Ray
Fahrenheit 451

Bradbury, Ray
The Illustrated Man

Bradbury, Ray
The Martian Chronicles

Bradbury, Ray
Something Wicked This Way Comes

Brockmeier, Kevin
The View from the Seventh Layer

Bulgakov, Mikhail
The Master and Margarita

Bunch, David R.
Moderan

Burgess, Anthony
A Clockwork Orange

Card, Orson Scott
Ender's Game

Carpentier, Alejo
The Kingdom of This World

Carroll, Lewis
Alice's Adventures in Wonderland

Chabon, Michael
The Yiddish Policemen's Union

Chiang, Ted
Stories of Your Life and Others

Clarke, Arthur C.
Childhood's End

Clarke, Arthur C.
A Fall of Moondust

Clarke, Arthur C.
2001: A Space Odyssey

Clarke, Susanna
Jonathan Strange & Mr Norrell

Crowley, John
Little, Big

Danielewski, Mark Z.
The Fifty Year Sword

Danielewski, Mark Z.
House of Leaves

Davies, Robertson
Fifth Business

Delany, Samuel R.
Babel-17

Delany, Samuel R.
Dhalgren

Delany, Samuel R.
The Einstein Intersection

Delany, Samuel R.
Nova

Dick, Philip K.
Do Androids Dream of Electric Sheep?

Dick, Philip K.
Flow My Tears, the Policeman Said

Dick, Philip K.
The Man in the High Castle

Dick, Philip K.
Ubik

Dick, Philip K.
VALIS

Disch, Thomas M.
Camp Concentration

Disch, Thomas M.
The Genocides

Doctorow, Cory
Down and Out in the Magic Kingdom

Donoso, José
The Obscene Bird of Night

Ellison, Harlan (editor)
Dangerous Visions

Ellison, Harlan
I Have No Mouth & I Must Scream

Esquivel, Laura
Like Water for Chocolate

Farmer, Philip José
To Your Scattered Bodies Go

Fuentes, Carlos
Aura

Gaiman, Neil
American Gods

Gaiman, Neil
Neverwhere

Gibson, William
Burning Chrome

Gibson, William
Neuromancer

Grass, Günter
The Tin Drum

Greene, Graham
The End of the Affair

Grossman, Lev
The Magicians

Haldeman, Joe
The Forever War

Hall, Steven
The Raw Shark Texts

Harrison, M. John
The Centauri Device

Harrison, M. John
Light

Heinlein, Robert
The Moon is a Harsh Mistress

Heinlein, Robert:
Stranger in a Strange Land

Heinlein, Robert
Time Enough for Love

Helprin, Mark
Winter's Tale

Herbert, Frank
Dune

Hoffman, Alice
Practical Magic

Huxley, Aldous
Brave New World

Keret, Etgar
Suddenly, A Knock at the Door

Keyes, Daniel
Flowers for Algernon

Kundera, Milan
The Book of Laughter and Forgetting

Kunzru, Hari
Gods Without Men

Lafferty, R.A.
Nine Hundred Grandmothers

Le Guin, Ursula K.
The Dispossessed

Le Guin, Ursula K.
The Lathe of Heaven

Le Guin, Ursula K.
The Left Hand of Darkness

Leiber, Fritz
The Big Time

Leiber, Fritz
Conjure Wife

Leiber, Fritz
Swords & Deviltry

Leiber, Fritz
The Wanderer

Lem, Stanislaw
His Master's Voice

Lem, Stanislaw
Solaris

Lethem, Jonathan
The Fortress of Solitude

Lewis, C. S.
The Chronicles of Narnia

Link, Kelly
Magic for Beginners

Malzberg, Barry N.
Herovit's World

Mann, Thomas
Doctor Faustus

Márquez, Gabriel García
100 Years of Solitude

Markson, David
Wittgenstein's Mistress

Matheson, Richard
Hell House

Matheson, Richard
What Dreams May Come

McCarthy, Cormac
The Road

Miéville, China
Perdido Street Station

Miller, Jr., Walter M.
A Canticle for Leibowitz

Millhauser, Steven
Dangerous Laughter

Mitchell, David
Cloud Atlas

Moorcock, Michael
Behold the Man

Moorcock, Michael
The Final Programme

Morrison, Toni
Beloved

Murakami, Haruki
1Q84

Murakami, Haruki
Hard-Boiled Wonderland and the
End of the World

Nabokov, Vladimir
Ada, or Ardor

Niffenegger, Audrey
The Time Traveler's Wife

Niven, Larry
Ringworld

Noon, Jeff
Vurt

Obreht, Téa
The Tiger's Wife

O'Brien, Flann
At Swim-Two-Birds

Okri, Ben
The Famished Road

Percy, Walker
Love in the Ruins

Pohl, Frederik
Gateway

Pratchett, Terry
The Color of Magic

Pynchon, Thomas
Gravity's Rainbow

Rabelais, François
Gargantua and Pantagruel

Robinson, Kim Stanley
Red Mars

Rowling, J.K.
Harry Potter & the Sorcerer's Stone

Rushdie, Salman
Midnight's Children

Russ, Joanna
The Female Man

Saramago, José
Blindness

Sheckley, Robert
Dimension of Miracles

Sheckley, Robert
Mindswap

Sheckley, Robert
Store of the Worlds

Shelley, Mary
Frankenstein

Silverberg, Robert
Dying  Inside

Silverberg, Robert
Nightwings

Silverberg, Robert
The World Inside

Simak, Clifford
City

Simak, Clifford
The Trouble with Tycho

Smith, Cordwainer
Norstrilia

Smith, Cordwainer
The Rediscovery of Man

Stephenson, Neal
Snow Crash

Spinrad, Norman
Bug Jack Barron

Stross, Charles
Glasshouse

Sturgeon, Theodore
More Than Human

Sturgeon, Theodore
Some of Your Blood

Swift, Jonathan
Gulliver's Travels

Thomas, D.M.
The White Hotel

Tiptree, Jr., James
Warm Worlds and Otherwise

Tolkien, J.R.R.
The Hobbit

Updike, John
The Witches of Eastwick

Van Vogt, A.E.
The Mixed Men

Van Vogt, A.E.
Slan

Van Vogt, A.E.
The Voyage of the Space Beagle

Van Vogt, A.E.
The World of Null A

Vance, Jack
Emphyrio

Verne, Jules
Around the Moon

Verne, Jules
From the Earth to the Moon

Verne, Jules:
Journey to the Center of the Earth

Vonnegut, Kurt
Cat's Cradle

Vonnegut, Kurt
The Sirens of Titan

Vonnegut, Kurt
Slaughterhouse-Five

Wallace, David Foster
Infinite Jest

Walpole, Horace
Hieroglyphic Tales

Wells, H.G.
The First Men in the Moon

Wells, H.G.
The Island of Dr. Moreau

Wells, H.G.
The Time Machine

Wilson, Robert Anton & Robert Shea
The Illuminatus! Trilogy

Winton, Tim
Cloudstreet

Woolf, Virginia
Orlando

Zabor, Rafi
The Bear Comes Home

Zelazny, Roger
Lord of Light

Zelazny, Roger
This Immortal


Special Features
Notes on Conceptual Fiction
When Science Fiction Grew Up
Ray Bradbury: A Tribute
The Year of Magical Reading
Remembering Fritz Leiber
A Tribute to Richard Matheson
Samuel Delany's 70th birthday
The Sci-Fi of Kurt Vonnegut
Curse You, Neil Armstrong!
Robert Heinlein at 100
A.E, van Vogt Tribute
The Puzzling Case of Robert Sheckley
The Avant-Garde Sci-Fi of Brian Aldiss
Science Fiction 1958-1975: A Reading List

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