**Poetry as Geometry**

The following is not a poetic or a personal
statement:

*i*is an imaginary number. Like poetry, mathematics contains infinities. Like poetry, it is difficult to define what mathematics*is*. Which might explain why Alfred North Whitehead and Bertrand Russell failed miserably when they tried to constitute a foundation for modern mathematics with*Principia Mathematica*, thus leaving them incomplete. Perhaps this failure stems from their attempt to find and justify a single basic unit of study, the way other sciences and logic had defined one at the turn of the 20th century (those have since lost their fundamental basis). This is of course a crude attempt to summarize a lengthy and complex work that spans over three volumes. But where other sciences are finite in their scope of inquiry, mathematics contains and studies the relationships between infinities[1]. To quote the Doctor in the recent episode*The Rings of Akhaten*: "There is only one of one, but there is an infinity of others."[2]
But mathematics is and remains the essence of
modern sciences. The scientific method finds its cradle in mathematics. To
summarize, based on previously made assumptions and questions, a hypothesis is
made. Following this hypothesis, an experiment will be devised and conducted,
in which the hypothesis may or may not be falsified and rejected. Out of this
conclusion may arise a new set of questions and entire new fields of inquiry.

Such examples can be found in geometry, which,
until the 18

^{th}century with the work of Carl Friedrich Gauss (*et al*.) had been defined by Euclid’s postulates, which state the following:
1.
A straight line is defined by any two points.

2.
A finite
straight line can be extended continuously into a straight line.

3.
Any circle
can be described by a center and a radius.

4.
All right
angles are equal to one another.

5.
If a straight
line falling on two straight lines make their interior angles on the same side
that sum to less than two right angles, the two lines, if extended
indefinitely, meet on that side on which the angles sum to less than two right
angles.[3]

This
fifth postulate is also known as the Parallel Postulate and its lack of
syntactic simplicity (among other things) has confounded geometers for centuries,
who tried to prove it false. Or not. Hence non-Euclidian (non-planar) geometry
where the sum of all the angles may or may not equal to 180º[4]
and topography through the works of Bernhard Riemann, Henri Poincaré and
others.[5]
This in turn made Einstein’s work on relativity and the postulate that any
three-dimensional object could be reduced to the shape of a three-dimensional
sphere or a three-dimensional donut.[6][7]

It
is difficult to find poetry that displays similar standards of experimental
rigor Christian Bök’s Xenotext Experimentcomes to mind. But since it is working from the principles of genetics and
molecular biology, it falls more into the realm of applied science and
technology. Simply put, the

*Xenotext Experiment*does not ask any question about genetics or language, except perhaps “Can it be done?”
Of
course, mathematics and poetry have never been mutually exclusive. Before the
modern mathematical notational system was devised, much of mathematics was
mediated through “natural” language[8].
As such, π was known as

*quantitas in quam cum multiflicetur diameter, proveniet circumferencia*, until the 18**[9]**^{th}century when William Jones and Leonhard Euler adopted the Greek letter now used in modern mathematics, a rather cumbersome notation that can lead to some rather pseudo-Oulipian tautologies:
Circumference
equals diameter multiplied by the quantity, which multiplied by the diameter,
yields the circumference

Or:

Circumference
= Circumference

Oulipo needs of course no introduction
as the best known nexus between literature and mathematics. But its most
mathematical operations do not stray very far from arithmetic, Euclidian
geometry and group theory. Mathews’ Algorithm, for example, finds its
historical precedent in the permutation theories of Renaissance mathematicians Pierre
de la Ramée (Petrus Ramus) and Ramon Llull.

Perhaps, however, mathematics provides
a salient metaphor for poetry in the French word

*translation*, which describes the transformation of a geometrical object by a vector. As such, a triangle ABC will be transformed by a vector W into triangle A’B’C’. A’B’C’ will possess the same angles, lengths, and orientation as ABC, but will be considered as a different triangle but its spatial coordinates have been transformed.**[10]**
Poetry operates the same way. It takes
a linguistic object and transforms it through the vector of writing. The
transformed object will have the familiarity of its original, stripped of its
operation context.[11]

[2] The Doctor might be
wrong on this one, as Wilfrid Sellars and Ludwig Wittgenstein might be tempted
to demonstrate there is an infinity of ones. He is also facing the problem of
three of one.

[3] One consequence: The sum of all angles in a
triangle equals to 180º.

[4] Just draw your triangle on a sphere.

[5] Their work also made possible the idea of Time
And Relative Dimensions In Space being bigger on the inside than on the
outside.

[6] Poincaré, being a distinguished French
mathematician, did not use the word “donut” or even “doughnut,” but the word
“torus,” not out of anti-Anglo-Saxon snobbery, but because the French didn’t
know what a donut was at the turn of the 20

^{th}century. Had he been from Québec, he might have used the word “donut.” Or not.
[7] Russian mathematician Grigori Perelman
demonstrated the Poincaré conjecture in 2007. He got the Fields Medal for it,
which is like getting the Nobel Prize in mathematics, but more nerdy.

[8] To use Wordsworth’s expression. Analytical
philosophers may or may not have a fit, which apparently happens very often.

[9] Which stopped being “’natural’ language” with the
sack of Rome in 461 CE and stands for “quantity which multiplied by the
diameter yields the circumference.”

[10] Which doesn’t have anything to do with textual
translation (

*traduction*) but is annoyingly translated as “translation” in English. No wonder a Russian demonstrated the Poincaré conjecture.
[11] Which might or might not be what Norma Cole talks
about when she writes “all poetry is translation.”

BIO:

Originally from Strasbourg, France, françois luong currently lives in San Francisco. He has translated into English the works of Esther Tellermann, François Turcot, and Rémi Froger, among others. His poetry and translations have recently appeared or are forthcoming in

*Lit*,*West Wind Review*,*Verse*,*Dandelion*(Canada), and elsewhere.
## 1 comment:

I'd like to clarify my comment on Christian Bök's

Xenotext Experiment. I am not attacking it. I actually think it asks fairly interesting questions about audience in the act of writing and it might lead to some advances in recombinant technology (but I am not a biologist).But I use this example to ask questions about what we mean when we talk about "experimental poetry" after Language poetry (in the US and maybe Canada).

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