The Rhetoric of Mathematical Programming

Jennifer Juszkiewicz, Indiana University
Joe Warfel, Northwestern University

(Published November 22, 2016)

Introduction

At nearly the same time we learned we were accepted to the Indiana Digital Rhetoric Symposium, the Winter 2014 issue of RSQ arrived. It included a review by G. Mitchell Reyes in which he petitioned for more rhetorical studies of mathematics. The fields of rhetoric and mathematics, Reyes claims, have an inherent kinship. He argues that the “meaning and significance of a mathematical statement comes not from its infallibility . . .but from its meta-Code” (479). Elizabeth Losh, Annette Vee, Ian Bogost, James T. Brown, William Hart-Davidson, and many others have also advocated for a deeper analysis of the meta-code underlying much of the technology we use. Even as we submitted our final revisions of this article, Computational Culture released its special issue on rhetoric and computation.

But what many have advocated and few have done is to build disciplinary bridges with mathematicians, rather than just with what they do and make. Understanding the rhetorical nature of mathematics and, as a result, technology, requires working with mathematicians directly. Losh chastised rhetoricians more than five years ago because “the discourses of computer scientists themselves . . . tend to be conspicuously absent in scholarly books and articles about digital rhetoric” (89). The advantages of working with practitioners directly are numerous. After all, few rhetoricians are sufficiently skilled in complex mathematics to fully comprehend the way its practitioners think and invent.

What our conversation has uncovered is an underlying and generally incorrect belief by rhetoricians: that math offers certitude. This misconception begins with Aristotle, who assumed that math provides definite knowledge, that it is episteme rather than techne. In application, math is a genuine rhetorical art, a techne. As evident in the conversation here, mathematicians compose within traditions, constraints, and conventions. Their work, as Estee Beck claimed at IDRS, is persuasive and situational. A mathematician, like a rhetorician, is responsible for topoi of the sort described by Quintilian. Linear programming, which we discuss below, is one such topoi: it’s a branch of mathematics that enables particular forms of knowledge-making (5.10-14).

A note on the text:

For the purposes of this project we decided to choose a specific mathematical text, linear programming, which is the foundational logic undergirding much of mathematical modeling. This example allowed us to show how both mathematics and rhetoric embrace contingency and multiple valid solutions to a problem. However, equally if not more important to us, was showing our modes of dialogue, one based on examples and patience. Therefore, we staged a dialogue at the Symposium, and we continue that practice here. This iteration of the project, however, has depended on digital tools to facilitate composition. We revised this project via conversations on an online video-streaming service, embedding links and responding somewhat asynchronously to each other on a draft of the script. We then streamlined and reenacted it. We worked with a digital cinema scholar and producer, who contributed his own perspective and skills in representing dialogue. His contributions also reshaped our script and our overall approach. We repeated this process when we revised as a result of our reviewers’ helpful guidance. The reviewers particularly encouraged us to foreground the consequences of our argument. Therefore, our final addition was closing messages to each other reflecting on how the discussion can cast new light on our respective fields.

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Jennifer’s Letter

Dear Mathematicians (and especially Joe),

I write because I’d like to request for a further conversation. Rhetoricians, specifically digital rhetoricians, have been interested in your work with algorithms, programming languages, and how you make knowledge with math and how this math then affects the world. This is because rhetoric is the study of how we make meaning in an effort to communicate with others. Math becomes rhetorical when it affects an audience. Mathematicians then become rhetors when they make choices that will adjust the audience’s response. For example, Annette Vee, a digital rhetorician, has pointed out that those writing computer code choose between writing within or around legal strictures. Vee also brought Jeannette M. Wing’s definition of computational thinking to the table, a definition that could further inform rhetoricians’ understanding of how mathematicians create knowledge. Wing writes that “Computational thinking is using abstraction and decomposition when attacking a large complex task …It is separation of concerns. It is choosing an appropriate representation” (33). Our discussion aimed to further show how the choices mathematicians make are sometimes the result of mathematical strategy, but they are often the result of convention and convenience as well. 

We have also explored how computers are more than tools for those in your field. Computers are able to complete calculations that are too laborious for a single person or even a team of people. This is becoming a factor of increasing interest for rhetoricians as well: N. Katherine Hayles and Richard Lanham have considered how technology has changed how we read and view text. That makes us all the more curious about how you work with solvers. From our discussion, I posit that they co-invent with you; they make possible some of the work that you do. 

So the rhetorical aspects of your work are not only in the choices you make but also in your inventional process. The next step, the one on which many digital rhetoricians focus, is how that information is then communicated to an audience of non-specialists via data visualizations, statistics, or computer programs. Let’s take this step together and become cross-disciplinary rather than just interdisciplinary. Let’s discuss how you envision the audience of your work. To what degree does your consideration of them affect how you formulate your processes? If we address such questions together, we may be able to examine more fully the way that mathematical knowledge is made, to show that it is not a remote, impersonal method. Rather, there are scholars such as yourselves at work in a complex situation of tradition, processes, and collaboration. 

So, let’s talk more. Maybe we’ll go out for some Italian? 

With thanks,

Jennifer 

 

Joe’s Letter

Dear Digital Rhetoricians (in particular, Jennifer),

Since we talked, I’ve been thinking much more about the rhetoricity of my work.  

The common perception of math is as a source of absolute facts; as a domain free of human bias; as, perhaps, the unique human activity in which statements can actually be proven. The base angles of an isosceles triangle are congruent; the rationals are dense in the reals; if a linear program is unbounded, then its dual is infeasible. Mathematics contains many such unequivocally true statements that can be logically demonstrated, step by step, from a small set of carefully defined axioms.  

However, when we use mathematical objects to model reality, our mathematical work gains an audience—the users of the solutions of the model—and it becomes rhetorical.  As rhetors, then, we have to make choices about how to describe systems that are a result of our own objectives and biases. Given a linear program, I can obtain an optimal solution, but optimization in this sense is a purely mathematical activity. I cannot “optimize” a true, living system in the world, because I cannot formulate a model that contains the world (for, if so, the model would contain itself). We talked about this—when we were modeling the factory, we had to make choices about what to include.

I’ve been thinking more about what we include in models, and why—and, above all, about why we mathematicians do so much linear programming. Often, we don’t even consider other techniques; we simply discuss which variants of linear programming to try. But other techniques do exist. In particular, heuristic methods allow you to describe any type of relationship, not just those that can be expressed linearly; to model huge systems, including those with stochasticity; and to influence or control the structure of the solution in a way that is difficult or impossible in linear programming. However, they do not provide an “optimal” solution in the sense that linear programming does. We mathematicians have a deep desire to present “optimal” solutions to the user, even though we must admit that their “optimality” ceases as soon as they are applied outside the limits of the linear program from which they were obtained.

I would like to know more about how to understand the conversations that take place in my community as rhetorical acts; I want to be more aware of the rhetorical choices I am making, and better able to uncover the reasons for them; I hope to demonstrate to my colleagues that their choices are rhetorical, and to understand with them what the implications of that statement might be. As such, I hope that we continue this conversation.

How was the lasagna?

-Joe