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Mathematics and the Humanities: Bridging the Divide

Posted in Digital Humanities, and Percolating Ideas

Photo taken by Flickr user Francesc González and used under CC BY-NC-ND 2.0 license.
Photo taken by Flickr user Francesc González and used under CC BY-NC-ND 2.0 license.

First of all, I love this image. Let me tell you why (and how it relates to this post)… It provides a wonderful pictorial representation of where we now stand – at the edge of a precipice with nothing but a flimsy rope bridge to reach the other side. On what precipice, you may ask, are we standing? That of the deep gorge between mathematics and the humanities. On each side is solid rock – the disciplinary knowledge and epistemology of each area. To make it personal, each side of the rocky cliff represents my background in mathematics and history. The flimsy rope bridge between the two represents the current linkages and potential connections between the two (not yet substantial enough to be built out of the same rock). The rope bridge, I must admit, calls to my sense of adventure and curiosity. As I metaphorically step off solid ground to test the strength of the connection, the bridge holds, but it sways with the stiff breeze blowing through the chasm. My stomach drops a little as I look down and the terrifying expanse below, yet a sense of wonder and thrill shoots through me at the same time, and I tentatively begin inching my way along passage.

This post represents that first step. I’m not sure where it will take me or if I will reach the other side, but I believe it’s a worthy endeavor, nevertheless. A great journey cannot begin unless the first step is taken, right?

The first link, I’d like to point out between mathematics and the humanities is one that some mathematicians may be loath to admit – research and argumentation in both require creativity and breakthroughs are often the result of intuition. Now, that intuition is finely honed and based on years of disciplined study, but frequently, it is a hunch (an educated guess and a move that ‘feels’ right) that will lead us down new and interesting paths until we find either what we thought we were looking for or discover something entirely new.

The second link, though, is what interests me today. Before applying to graduate schools, I had a decision to make: pursue a Ph.D. in applied mathematics with a specialization in graph theory or pursue a Ph.D. in history. You can read more about why I chose history on the Author Info page, but it was a difficult decision. With the rise of digital humanities, there are clearer paths between my two disciplines. The most interesting, to me at least, is the door to new questions, analytical tools, and answers that graph theory has opened for humanities scholars through network analysis.

In his exploration of the effect of applying network theory to Shakespeare’s Hamlet, Franco Moretti writes,

No, I did not need network theory; but I probably needed networks. I had been thinking about Horatio for some time – but I had never ‘seen’ his position within Hamlet’s field of forces until I looked at the network of the play. … Basically, I used (or mis-used) the theory in the same way I had used cartography in the Atlas of the European Novel, and charts in Graphs, Maps, Trees: as a way of arranging literary data that presupposed a principle of order – but not a full conceptual architecture. (“Network Theory, Plot Analysis,” 2011, p. 10)

Moretti is describing the process of “hacking” or reimagining the uses to which a mathematical construct might be put – repurposing and adapting a conceptual tool to suit the needs of a different field, a different set of questions, and a different epistemology. This is innovative and valuable, in and of itself. From a theoretical standpoint, though, I do think it worth examining the specific moves Moretti and other humanities scholars make away from the original underpinnings of theories and analytic tools from STEM fields, for what purpose, as well as the distance between the initial ideas/approaches and their application in the humanities. This analysis may very well lead to insights about how these constructs from STEM might be tailored for specific humanistic fields.

I am not proposing a search for a unifying theory, but rather some guiding principles that might assist scholars in understanding how, why, and when to incorporate analytical tools from mathematics, specifically. Ideally, research in this area would help scholars to understand the mathematical principles behind the theories and methodologies they find attractive. My hope is that such a study would also reveal both what is lost and what is gained in the migration and necessary transformations of these approaches from one field to another. Network analysis seems a fruitful place to start.

Now it’s time to brush up on my graph theory! If I’m able to move this investigation forward, I will continue to post my findings here. Stay tuned!

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