Unit Circle & Pilgrim’s Progress

You got your math in my poetics!
You got your poetics in my math!

Listening to a Cognition and Poetics Symposium last year, I recognized a tool both rigorous and flexible enough to help me with my writing. Since then I’ve been trying to learn all I can about cognitive poetics, so that I can apply these concepts and techniques to my fiction.

The focus of my interest is language (poetics, linguistics, rhetoric, etc.) but I’m also reading Where Mathematics Comes From by George Lakoff and Rafael Nunez. The potential to connect seemingly disparate disciplines, such as literature and mathematics, is one aspect of cognitive theory that intrigues me.

For example, I have been trying to correlate some of Lakoff’s mathematical analysis with the literary analysis of conceptual metaphor in The Emergence of Mind.

First, the mathematical (don’t be scared, there won’t be a test):

In addition to the innate ability to subitize, Lakoff identifies two types of metaphors humans use to do mathematics. Grounding Metaphors are closely associated with embodied activities and are obvious to most people, once you think about it.

Grounding Metaphors
source domain: target domain:
collecting objects ? ?> addition
measuring distance with sticks ? ?> multiplication

The second type, Linking Metaphors, are necessary for math beyond arithmetic. Linking Metaphors conceptualize one domain of mathematics in terms of another domain. The Unit Circle is a mathematical concept that requires a Linking Metaphor between geometry and coordinate algebra. Linking Metaphors are one or more steps removed from embodied activity and require some education to be understood. The Unit Circle only makes sense if you understand Euclidean geometry and the Cartesian coordinate system.

Linking Metaphors
domain: domain:
Euclidian plane, Center, Radius < ? ?> Cartesian plane, Origin, Distance 1 from Origin

These are the basic concepts Lakoff and Nunez use to analyze mathematics as an embodied human endeavor.

Now for the literary (also an embodied human endeavor):

In her essay Mind on the Move ?, Elizabeth Bradburn argues that the working out of metaphorical representations of consciousness by 17th century writers shaped the novelistic form as it emerged in the 18th century. She uses conceptual metaphors in the same way that Lakoff does, not merely as literary devices but as cognitive devices to indicate how thought itself is intrinsically metaphorical. ?

The first level of metaphor is the literary metaphor. Bradburn gives an example from Paradise Lost:

“seest thou what rage / Transports our adversaries”

The word “transport” is literal but also metaphorical. Like the Grounding Metaphors Lakoff and Nunez use in their mathematical analysis, the conceptual metaphor MENTAL STATES ARE LOCATIONS is obvious once it has been pointed out. The “calling attention to or formalizing the presence of metaphor in thought and language” is an aesthetic effect of the literary metaphor.

Bradburn also considers another level of conceptual metaphor that shapes narrative plot. John Bunyan’s allegory, Pilgrim’s Progress, can be read as a physical journey and as spiritual progression. Each level is self-coherent; they have the same morphology, but they do not mix. ?

Allegory – Pilgrim’s Progress
domain: domain:
mind or soul < ? ?> Christian (the character)
despair, tempation, faith, shame, etc. < ? ?> locations, objects, and characters

The richness of the allegory is the same richness of the Unit Circle; it is the play between different levels of conceptual metaphor. Readers of Pilgrim’s Progress must be educated in both the domain of spiritual writing and the domain of travel narratives to understand and appreciate the Linking Metaphor that connects them.

A mathematical analysis lends itself to precise categorization, and a literary analysis must be more subtle; math seeks precision in a way literature should not because the scope of literature is not limited the way math’s is. There can be no determinate matching between domains, especially for allegory according to Paul de Man, or meaning would be exhausted. In mathematical terminology, a literary text is not necessarily onto or one-to-one.

Bradburn elaborates on her reading to identify points of conflict between the allegorical level and the physical level. For example, the character Shame causes some consternation between Christian and Faith, not only in the aspersion Shame has for religion, but also in that Shame is both an external provocateur ? and internal feeling ?.

This method of analysis stays focused on the text but does not ignore that reading is done by people with minds. When I am writing, I forge pathways in my own stories by reading and revising. Recognizing domains that pervade my writing, I can find the freedom to play between them.

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