Listening to Mathematics Psychologically: Themes of Interiority and Multiplicity

Abstract

The methodology for this work uses a psychological and phenomenological approach to listening, which emphasizes noticing affects and gestures as intimations of felt meaning in the researcher as she engages in the work. The initiating intimation called for listening into Western relatedness to mathematics across three significant discoveries in the history of Western mathematics: ancient Greek mathematics, the calculus of the seventeenth century, and non-Euclidean geometry in the nineteenth century. However, this was not to be a historical inquiry, but a listening within the present moment.
At the start, two significant intimations were noticed as necessary to hear into the moments involving these three discoveries. First was the notion of mathematics as epochal explications of the archetype of orderedness and relatedness. Further was the notion to think of the three moments both as separate and as together in the current epoch, which is based on the logic of transfinite numbers. These two opening intimations facilitated thinking of these moments as nonlinear bifurcations and psychological sublations within the whole of the Western psyche.
The mathematics of the ancient Greeks initiates our epoch as a response to the invention of phonetic literacy, which required sublating oral consciousness and expressing a new form of mathematics to sustain the emerging literate consciousness. The invention of the printing press further deepened the individual experience of a literate interiority by sublating the mathematics of the ancient Greeks into the writing of the calculus, which essentially represented nature as outside of the experience of interiority. The discovery of non-Euclidean geometry disrupted this development of a literate-focused interiority because it undermined its reliance on a single, absolute definition of orderedness and relatedness between self and other. Henceforth mathematics became a multiplistic expression of human thought and experience. The perspective prior to this bifurcation is still being sublated; that is, the psychological expression of orderedness and relatedness for this present moment is still mostly unknown.
By listening through these significant developments in Western mathematics as psychological stages in this epoch, it becomes possible to hear them as part of the individuation process of the archetype of orderedness and relatedness.