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. 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."
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 18th 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.
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 and topography through the works of Bernhard Riemann, Henri Poincaré and others. 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.
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. As such, π was known as quantitas in quam cum multiflicetur diameter, proveniet circumferencia, until the 18th 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
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.
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.
 For future consideration, the poetry of Claude Royet-Journoud as mathematical operation.
 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.
 One consequence: The sum of all angles in a triangle equals to 180º.
 Just draw your triangle on a sphere.
 Their work also made possible the idea of Time And Relative Dimensions In Space being bigger on the inside than on the outside.
 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 20th century. Had he been from Québec, he might have used the word “donut.” Or not.
 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.
 To use Wordsworth’s expression. Analytical philosophers may or may not have a fit, which apparently happens very often.
 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.”
 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.
 Which might or might not be what Norma Cole talks about when she writes “all poetry is translation.”
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.