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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.
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.
| conceptual fiction |
Edwin A. Abbott
