University of Liège, April 24-28, 2017
Geometry for the Poetry of Moods
The physical sciences leverage our ability to distinguish between thousands of colors, sounds, smells, tastes and other sense perceptions. Let us likewise consider the thousands of moods which we experience and how we might evoke, reproduce, compare, identify and name them, and in general, make sense of their variety. We start with a model of basic emotional responses which arise from our expectations. This model suggests a profound boundary between self and world. We further note the negative moral tones which arise when we expect what we do not wish. Positive moral ambiences resound when these negative moral tones are rendered impossible. We then study how the mood evoked by a poem can be accounted for by a specification of the boundary between self and world.
We proceed by imagining various circumstances and perceiving the emotional responses they evoke within us. A variant of Paul Ekman's basic set of innate emotional responses can be derived from outcomes of our expectations. In matters that are distant, that we locate outside ourselves, if our expectations prove wrong, then we are surprised, whereas if our expectations are met, then we are excited. If we try but fail to form expectations, then we are frightened. Analogously, in matters that are personal, and that we invest in ourselves, if our expectations prove wrong, then we are sad, whereas if they prove right, then we are content. If we try but fail to form expectations, then we are disgusted. Aside from these six outwardly observable outcomes by which we learn and know, we can also intuit two internal states by which we do not know but wait. Namely, we are in suspense when we are waiting if our expectations will be met, and we are at peace inasmuch as we do not try to form expectations.
Should we seek peace or happiness? We may avoid sadness by manipulating our expectations. However, negative moral tones arise when we expect what we do not wish, and thus experience not suspense but anxiety, not surprise but anger, not sadness but hatred, not excitement but relief and not happiness but depression. If we refuse to expect what we do not wish, then hate is impossible and we feel love. If we do not acknowledge any world outside of us, then fright is impossible and we feel intimacy. If we lose awareness of our selves, then disgust is impossible and we feel beauty. We do not feel love, intimacy or beauty directly, but as the lack of hate, fright and disgust, thus as afterglows.
Let us analyze the moods evoked by 37 Chinese wu-jue poems from the Tang dynasty. In each poem, the mood is defined by the boundary between self and world, for example, the bed that a traveler lies in. Beyond the bed is the beauty of the moon and the surprising illusion of frost, but also the traveler's happy home, which evokes a conditional sadness. Here we imagine ourselves reflected across the boundary. Mathematically, a geometry of paths-forward is enriched by reflection to become a geometry of lines-back-and-forth. We can have even richer geometries of angles-around and areas-encircled. The 37 poems each apply one of six specifications (reflection, shear, rotation, dilation, squeeze, translation) to enrich our geometry (affine paths-forward, projective lines-back-and-forth, conformal angles-around, symplectic areas-encircled).
We thus read poems constructed to evoke moods such as:
We may thus apply geometry and poetry to explore moods and share a regard for the boundary of self and world.