A Geometry of Moods: Evoked by Wujue Poems of the Tang Dynasty
Channel: Math 4 Wisdom
Date: 2023-03-12

Poems are used as data to study how they evoke moods by establishing and transforming the boundary between self and world.  37 classic four-line poems from the Tang Dynasty in China provide evidence for 6 geometric transformations. These are Möbius transformations. Thus the boundary between self and world is modeled by the boundary of a circle on a sphere.

Text and slides are available:
https://www.math4wisdom.com/wiki/Research/20230311AGeometryOfMoods

This is a rerecording, on March 11th, 2023, of an academic talk that I presented on August 14th, 2018, at the discussion panel on Philosophy and Literature at the XXIV World Congress of Philosophy in Beijing, China. I am Andrius Kulikauskas, host of Math 4 Wisdom.

0:00 Circumstances
0:55 Remarks about the end of the video, where I think of the six geometric transformations as Möbius transformations.
1:45 I will sketch a research program to model the thousands of moods we experience.
2:15 I start with six basic emotional responses (happiness, sadness, excitement, surprise, fright, disgust) documented by Oster and Ekman. I imagine how they arise from my expectations as I play with alphabet blocks.
3:10 The emotional distinction between self and world.
4:20 We feel but cannot observe suspense and peace. Cognition and imagination can evoke emotion. 6:15 Unhealty emotions (hate, anger, relief, depression) arise when we expect what we don't want.
6:40 We feel positive moral tones (beauty, love, intimacy) as the impossibility of negative moral tones.
7:05 This model relates the unconscious and the conscious, as with Kahneman and Tversky's system 1 and system 2.
7:35 Music, dreams, activities, and especially, poetry provide data for studying moods. Can we replicate a mood? Can two people have the same mood? Analysis of "Quiet Night Thoughts" by Li Bai, which creates a mood of conditional sadness.
9:45 37 wujue poems provided evidence for six transformations of the boundary between self and world: reflection, shear, rotation, dilation, squeeze and translation. They enrich four geometries - affine, projective, conformal, symplectic - which can be distinguished by how they view a triangle - in terms of paths, intersections, angles or oriented areas.
11:40 7 poems establish a mood by reflection. "Quiet Night Thoughts" by Li Bai.
12:05 4 poems establish a mood by a shear transformation, defining perpendicularity. "Grievance" by Li Bai.
13:15 5 poems establish a mood by rotation, turning our attention. "Listening to the Guzheng" by Li Duan.
14:35 7 poems establish a mood by dilation. "Climbing Up Crane Tower" by Wang Zhihuan.
16:10 9 poems establish a mood by a squeeze transformation. "Jiangnan River Song" by Li Yi.
17:15 6 poems establish a mood by translation. "Crossing the Han River" by Li Pin.
18:20 Classic poems let us believe that they can indeed evoke in us specific, comparable, well defined moods. 
19:00 Acknowledgements. Thank you to Shu-Hong Zhu, Rūta Jakštonienė, Rimvydas Krasauskas, Tong Zhu, Antanas Andrijauskas, Sylvain Poirier. 
19:15 These are Möbius transformations, bijective conformal maps from the Riemann sphere to itself. On spheres they map circles to circles. Apparently we think of the boundary between the self and the world as the boundary that separates a circle from what is beyond.
20:05 Inversions generate all of the Möbius transformations. In the poems, reflection is better understood as inversion.
20:50 Möbius transformations form the Möbius group, also known as the projective linear group, which is related to the special linear group.
21:10 We can think of a circle on a sphere as modeling a perspective. Operations on a perspective.
21:40 Conformal geometry based on complex numbers is the most fundamental. I believe there are affine and projective geometries based on real numbers, and symplectic geometry based on quaternions.
23:15 A next step is to study "Visual Complex Geometry" by Tristan Needham https://archive.org/details/visualcomplexana0000need and papers by Steven Lehar https://slehar.wordpress.com/2014/03/18/clifford-algebra-a-visual-introduction/ on Clifford algebras and geometric algebra. This is a route to Bott periodicity.

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Public Domain, 2023

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