[…]


Eleanor Johnson

Two from Non-Linear Geometric Translations: or, Imagining the Mad Mind of a Soviet Non-Euclidian Mathematician, based upon a Russian textbook found in a mushroom dale in Oakland, California

Introduction to the First Edition: Asymptotic methods and theories


             Naturally, one would expect herewith a recapitulation,or perhaps it is best to say,
a precapitulation, of Chapters forthcoming. But to do so, equally naturally, violates the
principal truth contained in them, namely that linearity exists only in the mind. Therefore,
by way of warning, we will simply say these pages warp forth dreams whose outsides
their insides dwarf by comparison.
             Or, to put it otherwise, no two-dimensional diction, no flat syntactic inky verbal
wash, however wrought, could mime even the barest graph. Systems, as we now know,
cannot be spoken; the tongue being a univariable, rigid, unplastic wielder of a uselessly
sliding language—a baseball bat propelling rain sideways, through frozen air.
             Duly disclaimed and queerly qualified, we humbly represent the contents of this
work, which will be thickly curved, bent thickly around edges of swollen axes, falling
between limp and unlimpid oozing prose which our editors have seen fit to obtuse.
             Best of luck in this your journey unseeable. Recognize the reality that maps are
non-existent, and that only recursivity is absolute. And remember: this is the real
geometry.

                                                                                                 Yours et cetera, with
                                                                                                 something like Love,
                                                                                                 though perhaps more like
                                                                                                 Exasperation,
                                                                                                 N. N. Bogolyov,
                                                                                                 lately of Moscow,
                                                                                                 and I. A. Mumrobolyski,
                                                                                                 his companion.


Chapter One: Describing the Surface of a Sphere: Non-linear, Atemporal Exercises

In my subsequent essay, I had described the perplexity of the surface of a sphere in
terms
at once voluptuous and strangely muonic, gluonianism having not yet to be discovered
from the quark wash of last year’s curdled milk.

Now that’s a task for you.  Describe the Surface of a Curdle.

Exercise 1:
Describe the surface of a curdle.
Conditions: do not use the terms “curd” or “le,” and avoid descriptors of color.

Example answer:
“The surface of a qvorsh-popplet equals one times the differential equation separating
you from my lemon-drop dripping nipples.”

Back to spheres: Girard’s Theorem states that the problem of lunes is one of antipoding
not wisely but too well.

History: Girard lay compassing cow-pies and pine cones under a yew tree.  Euler came
along, trying angles in the sky.  Blinded by his protractor and ruler, Euler prostrated
himself unpremeditatedly, tripping over Girard’s tool.  “Fool!  I was describing pies and
cones, and now all is vexed.”  Euler, curved to raging humiliation, threatened vertex.
Girard edged back.  They faced each other, fell mathly in love, conceived and bore the
snarkiest of snaking shapes: the twisting triangle, and its smaller sibling, the lune.

Since this time, lunes have become increasingly problematic:

Far too many lunes loom at large, without area, threatening circles and harassing
rectilinear triangles in subway cars.  What is to be done?  Ours is not to solve the
problems of the world, but merely the problems of the word.

But I digress. A natural response to stimuli, in the universe that inherits Chiron’s
suffering: the wound that will not heal, accidentally inflicted by a supposed hero, seeking
the death that will not die, spelunking into contracted mortality, con-cave.

His mother lies mewling in a dark, dark concavity where she can be no further
chronically-compassed, toppled by Time, knowing her best-beloved has lost his ear for
tune and hooves now the far, far madder stamping dance of rage and pain.

He, strumming out stampeding strophes and stanzas in the crumbling loam beneath,
describes circles that swell spherical in his sight as the coursing venom coaxes his
watering eyes to wild warpings.  In this universe, digressivity is direction.

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