Saturday, January 9, 2016

the substantial realities of Flatland itself - Edwin Abbott's Flatland

Italo Calvino’s Cosmicomics (1965), among my favorite books, sent me to revisit one of its Victorian precursors, Edwin Abbott’s Flatland (1884), which is not so much science fiction as mathematics fiction, or even more narrowly geometry fiction, which cannot be too big of a genre.  A square, a resident of the two-dimensional Flatland, describes a revelatory visit by a sphere, and his own journeys to the one-dimensional Lineland and the three-dimensional Spaceland, where I live.

I remembered – everyone remembers – the clever shifts in perspective and diagrams that help youngsters visualize the differences between the dimensions, even, for readers with mathematically imaginative gifts beyond mine, into the fourth dimension.

The short visit to the Pointland, “the Abyss of No dimensions” (Ch. 20), seemed especially brilliant to me, especially strange:  “It is; and there is none else beside It,” a Buddhist existence.  Calvino had primed me for this vision in his magnificent but rather different “All at One Point,” when all of existence, in the moment or eternity before the Big Bang, is contained in a single point yet is somehow also an Italian apartment building:

There was also a cleaning woman – “maintenance staff” she was called – only one, for the whole universe,  since there was so little room.  To tell the truth, she had nothing to do all day long, not even dusting – inside one point not even a grain of dust can enter – so she spent all her time gossiping and complaining.  (p. 44)

I had effectively forgotten the first half of Flatland, the description of the laws and institutions of the two-dimensional world, which is in a more heavily populated genre, the Lucianic satire, a cousin of Utopia and In Praise of Folly.  Flatland is, for example, a deeply sexist and class-bound society, where the women are lines, the soldiers triangles, and the priests and rulers circles (or approximate circles).  Is Abbott reinforcing Victorian sexism or satirizing it?  Who knows!  Someone might know, but not from the text itself.

I had also forgotten the surprising beauty of the end of Flatland.  The square has become a martyr of science, imprisoned and disbelieved for his visions, and has even begun to doubt his own ideas, which only return to him in dreams.

It is part of the martyrdom which I endure for the cause of Truth that there are seasons of mental weakness, when Cubes and Spheres flit away into the background of scarce-possible existences; when the Land of Three Dimensions seems almost as visionary as the Land of One or None; nay, when even this hard wall that bars me from my freedom, these very tablets on which I am writing, and all the substantial realities of Flatland itself, appear no better than the offspring of a diseased imagination, or the baseless fabric of a dream.  (Ch. 22, last lines)

But I had forgotten- I had forgotten so much – that Edwin Abbott was a Shakespearean scholar.  See The Tempest, Act IV, Scene 1.

Does anyone have a strong opinion about Charles Howard Hinton’s Scientific Romances (1884-6)?  A mild opinion?  Or other mathematical fictions?


  1. my dad gave me flatland when i was young. i loved it but never could understand math. just finished "his majesty's voice"(lem)re a mathmetician engaged in attempting to decipher a message couched in a sliver of neutrino particles ; mostly re the philosophical and political machinations of the whole affair. probably lem's most brilliant book. he's an extraordinarily imaginative writer...

    1. "master's", not majesty's' grrr: the foibles of age!

  2. It's a fascinating little book, isn't it? I read it just over a year ago and while I didn't quite get all the maths, I loved the concept. And since Cosmicomics is one of my favourite Calvinos I guess that's inevitable!


  3. Your review/comment reminds me of the speculative alterations to laws of physics in S/F (e.g., 2001: A Space Odyssey in which gravity was "altered" as a centrifugal force on the rotation space station). Of course, I could be misremembering the example. And math has always baffled me. I could never get past the concept of functions in algebra. Yeah, I was that bad at math!

  4. I was wondering if this book could mean anything to people who can't see the geometry. I guess so. Good.

  5. Coventry Patmore was Abbott's contemporary. He wrote a poem, Magne Est Veritas which echoes and opposes the end of Flatland in its attitude to martyrs for "the cause of Truth":

    For want of me the world's course will not fail:
    When all its work is done, the lie shall rot;
    The truth is great, and shall prevail,
    When none cares whether it prevail or not.

    I can't tell which was written first, unfortunately.

  6. Yes, the square has become a kind of fanatic, embracing martyrdom, whether in the service of science or religion, even he does not know. Patmore has had not had the Truth revealed in a vision, and is thus sensible.

  7. Flatland maybe counts as the first "experimental" novel I ever read; it succeeded wildly in offering up to this 14-year-old a vivid new conception of literature. I was bowled over by it to the point that I created my own little Flatland using cut out shapes and segments and dots.

  8. My favorite mathematical fiction may be Harry Stephen Keeler's short story "John Jones's Dollar." There are probably stories with more interesting math in them, but none with such Keeler wackiness. Here it is, if you're curious:

  9. Keeler, there's a name I had forgotten. A compound interest gag - that's good for a math story.

    Scott, that is reading Flatlandin the right spirit.

  10. My 9th grade geometry class read Flatland. I guess I thought everyone had read this book in school.

  11. Almost no one has read this book in school.

  12. No, it is for the best. I am imagining my high school geometry teacher having to teach a Victorian satirical novel. Poor fellow. Maybe the pedagogical strategy is just to skip all of that stuff? Just go straight to the shapes.

    "when we asked them [math teachers] less than half said they'd heard of it"

    There are several film versions, as in that link. Maybe young geometers get to see one of those.