MATHEMATICS Editorial

1 November 2017

Mathematics
Photograph by Tim Grey

I was already quite a few years into a creative writing PhD titled ‘Generic Engineering’ and flailing around quite spectacularly in a galaxy of words when an academic friend, perhaps hoping to spare me the indignity of a completed thesis and potential employment, flipped to the middle of the 526-page book he was reading. Wordlessly, pointed to a single sentence. ‘Due to a predilection whose origin I will leave it up to the reader to determine,’ it read, ‘I will choose the symbol ♀ for this inscription.’ The symbol had been summoned to designate what the writer called ‘generic multiple’. The generic, the writer noted, is ‘the adjective retained by mathematicians to designate the indiscernible, the absolutely indeterminate’. Another PhD student who was in the room sniggered, disparagingly, I thought, as if dubious that I could be capable of understanding what had been read aloud. In retrospect it was more likely a beleaguered exhalation, a stockpile for the future, of sympathy and despair.

I abandoned almost everything I’d been reading and writing so far and began trying to write my way through Alain Badiou’s Being and Event. Badiou’s grand (and, for some, controversial) innovation is to have substituted language for mathematics as the least compromised way of engaging with the philosophical problems of truth, being, and the infinite. Attempting to understand even the most basic implications of this move turned out to be an impossible endeavor, one that I was impelled to confront afresh on a daily basis for a number of years. In the midst of all of this, I began to write poems. I have heard that reading philosophy can sometimes have this effect.

I still don’t know how to ‘do’ mathematics but in reading through the twelve hundred or so poems submitted to this special issue of Cordite I was looking for traces of the various ways in which it can make its presence felt. Sometimes a physical reaction was all it took to make a decision. In other instances, where I couldn’t have quite articulated what was taking place, I relied on a kind of spatial recognition. Some of the more straightforward lyric poems were compelling for the subtle, inventive, and indirect ways in which they summoned mathematical formulations. Others tugged at long-buried memories of theoretical significances that only occurred to me later, randomly or upon considerable reflection. Certain poems were selected because I liked the way they sounded and it was only afterwards, following fortuitous discussions with their authors, that I discovered their intellectual scope.

Ann Vickery’s ‘In Confederates We Couple’ conjures an iconic poet’s ‘lexicons’ and ‘logarithms’ and offers additional rewards for code-cracking, archive-dwelling readers. Pascalle Burton’s ‘After Michael Winkler’s ‘Where Signs Resemble Thoughts” elaborates on the American conceptual artist’s graphological innovation in which letters of the alphabet are plotted around the circumference of a circle and particular letters are linked by lines to create seismographic word visualisations. Burton’s extension of Winkler’s premise invites the reader to perform a cognitive exercise, one that has physical and psycho-social resonances reminiscent of Yoko Ono’s instruction paintings.

In ‘The Pavanne for Hanne Darboven’, A J Carruthers draws on the precepts of Darboven’s ‘Mathematical Music’ in which accumulated series of numbers are assigned notes in the creation of musical scores. Carruthers supplements this technique with images from Darboven’s artworks to provide a contribution to the library of performable conceptual compositions. The homage can be viewed as a more complicated performance of Dickinson’s famous lines – ‘I died for beauty but was scarce / Adjusted in the tomb, / When one who died for truth was laid / In an adjoining room’. Carruthers re-makes Dickinson’s unimpeachable separation of poetry and mathematics and opens the field to more complex imbrications.

An article published recently in Quanta magazine reported on a 2016 advance made by mathematicians Maryanthe Malliaris and Saharon Shelah. The advancement solves two problems – one related to their initial inquiry into Jerome Keisler’s 1967 investigations into minimally and maximally complex mathematical theories, and another, the problem of ‘whether there exist infinities between the infinite size of the natural numbers and the larger infinite size of the real numbers.’ This problem is related to the continuum hypothesis, posed by Georg Cantor, the inventor of set theory, in 1878 and deemed unsolvable within set theory’s framework by Paul Cohen who invented the mathematical concept of forcing in 1963. As Justin Clemens writes, in ‘The Idea Takes Place As Place Itself, Expanded and Revised Edition with a New Foreword by the Author’

               Luckily 
                              no one was writing
poetry that year; it wouldn’t have come off well;
what poem can compare 
                              to something like that?

The article is well worth reading in its entirety but of particular interest to me here is the way in which Malliaris and Shelah stumbled onto their discovery. In his account of Badiou’s philosophical edifice, Norris explains how a subject’s fidelity to a generic truth procedure ‘can make room, via these concepts of the generic and indiscernible, for the advent of truths that as yet lie beyond the compass of achieved (or achievable) knowledge.’ What at first seems insoluble or paradoxical can be turned via Cohen’s technique of forcing ‘into a fully operative concept’. In proving that the two properties they were working on were both maximally complex, Malliaris and Shelah were also able to show that two infinities (p and t) that were thought to be of different sizes were in fact equal. They did this by ‘cutting a path between set theory and model theory’ in a move that deployed Paul Cohen’s method of ‘forcing’ to solve one of the remaining problems of the continuum hypothesis. The move is reminiscent (in terms of audacity if not scope) of Cantor’s realisation that ‘the scandal of the infinite – of a part that must somehow be conceived as equal to the whole – could in fact serve as its very definition or distinguishing mark.’1

  1. Christopher Norris, Badiou’s Being and Event: A Reader’s Guide, London; New York: Continuum, 2009, p137.
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