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Chapter 4 endnote 41, from How Emotions are Made: The Secret Life of the Brain by Lisa Feldman Barrett.
Some context is:

[James Russell] showed that you can describe your affect in the moment as a single point on a two-dimensional space called a circumplex, a circular structure with two dimensions, as in figure 4-5. Russell’s two dimensions represent valence and arousal, with distance from the origin representing intensity.

A circumplex represents the relation between things through the geometry of a circle, in this case, affective feelings.[1][2] The term ‘‘circumplex’’ literally means ‘‘circular order of complexity’’[3] to indicate that the feelings in question can be characterized on at least two more basic psychological features at the same time. The circle maps how similar the feelings are to one another; the dimensions (e.g., valence and arousal) describe the features of similarity. Dimensions can be placed anywhere in the circumplex structure to describe it, and scientists have debated which features are best.[4][2] All can be mathematically transformed into valence and arousal, however.[5][6]

Russell’s circumplex is so well accepted as fact that many scientists include it in their research without even referencing him. It’s even been used for mapping the sentiments in real-time tweets. You know you’ve hit the big time when someone has immortalized your work in a Twitter application.

Notes on the Notes

  1. There are hundreds of articles on this topic, but one of the best is also one of the originals. Russell, James A., and Geraldine Pratt. 1980. "A description of the affective quality attributed to environments." Journal of Personality and Social Psychology 38 (2): 311-322.
  2. 2.0 2.1 Barrett, Lisa Feldman and Eliza Bliss-Moreau. 2009. "Affect as a psychological primitive." Advances in Experimental Social Psychology 41: 167-218.
  3. Guttman, Louis. 1957. "A new approach to factor analysis: The radex." In Mathematical Thinking in the Social Sciences, edited by Paul F. Lazarsfeld, 258–348. New York: Columbia University Press.
  4. Russell, James A., and Lisa Feldman Barrett. 1999. "Core affect, prototypical emotional episodes, and other things called emotion:  Dissecting the elephant."  Journal of Personality and Social Psychology 76 (5): 805-819.  Also see the rest of the articles in this special issue.
  5. Carroll, James M., Michelle SM Yik, James A. Russell, and Lisa Feldman Barrett. 1999. "On the psychometric principles of affect."  Review of General Psychology 3 (1): 14-22.
  6. Yik, Michelle S. M., James A. Russell, and Lisa Feldman Barrett. 1999.  Integrating four structures of current mood into a circumplex: Integration and beyond. Journal of Personality and Social Psychology 77: 600-619.