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?

You see this book. Here is philosophy. For the present I think it would still be a little beyond you - plunging into Robert Musil's Young Törless

Not enough novels are about math; that is clear enough.

The Confusions of Young Törless, Robert Musil’s 1906 debut novel, has some math.

“I say, did you really understand all that stuff?”

“What stuff?”

“All that about imaginary numbers.”

“Yes.  It’s not particularly difficult, is it?  All you have to do is remember that the square root of minus one is the basic unit you work with.”

“But that’s just it.  I mean, there’s no such thing.” (105)

Young Törless is having an intellectual and emotional crisis, in part caused by a simple yet deep linguistic confusion.  He is having difficulty relating the name of a mathematical concept to the thing-itself.  Imaginary numbers are no more imaginary than real numbers are real; both are identically real and imaginary.  René Descartes is endlessly smarter than either Törless or me, but this particular confusion is apparently his fault.  If someone had at some point given the concept a less imaginative name – if imaginary numbers were called “Euler numbers” or “Cardano numbers” – Törless would have to go back to worrying about infinity, which he works on a bit earlier in the novel.

I remember – this is an aside – all of the confusion caused twenty or twenty-five years ago by so-called “chaos theory.”  Mathematicians have proven the world is chaotic, certain hasty non-mathematicians declared, which was as wrong as could be, since the “theory” suggested that certain processes that looked random were in fact perfectly orderly and predictable.  I suppose the great example of this kind of confusion is Einstein’s theory of relativity proving that all things – moral values, for example – are relative.  But that is history; I lived through the chaos confusion.

If only mathematicians would restrain their poetic impulses.

Törless, who attends a boarding school, visits his math teacher’s office, hoping for enlightenment.  He has apparently never been to the teacher’s office before.  It is “permeated with the smell of cheap tobacco-smoke,” and the teacher’s long underwear (“rubbed black by the blacking of his boots”) is visible over his socks.  Törless

could not help feeling further repelled by these little observations; he scarcely found it in him to go on hoping that this man was really in possession of significant knowledge…  The ordinariness of what he saw affronted him; he projected this on to mathematics, and his respect began to give way before a mistrustful reluctance.  (110)

Törless is in search of transcendent, not ordinary knowledge, beyond the scope of the teacher who urges Törless to trust math and be patient – “for the present: believe!”

But then the teacher makes a terrible error:

On a little table lay a volume of Kant, the sort of volume that lies about for the sake of appearances.  This the master took up and held out to Törless.

“You see this book.  Here is philosophy…  For the present I think it would still be a little beyond you.”  (112-3)

Which is not the right thing to say to this particular kid, although it might be good advice for me.  Nevertheless, we will see how far I can get this week with Robert Musil’s little book.

Page numbers refer to the 1955 Pantheon edition, titled Young Törless.  Eithne Wilkins and Ernst Kaiser were the translators.