The Differing Roles of Mathematics in Engineering
I’m presently making my way through Roads: An Anthropology of Infrastructure and Expertise by Penny Harvey and Hannah Knox. It’s a study of road construction in Peru over the first decade or so of the 21st century. It scales in and out between global factors like trans-national trade and modernist desires for ease and connectivity, and very local ones like soil composition and personal beliefs about ghosts at certain mountain passes. The work is fascinating and I heartily recommend it.
In this post I want to focus on the book’s third chapter, Figures in the Soil. It is here that Harvey and Knox dwell on the topic of mathematics and data in the work of producing a road. I think this is important because it says something about how agents and institutions use math, and numbers more generally, and thus reveal something about their cultural values. It serves as a great touchstone, for me, as I consider how software engineers and their organizations use numbers.
Politics
To frame the discussion, we need to consider two phases of road construction. The first is manifesting the political will and dedicating the resources to the project. The second is the on-site work of literally building the road. The authors note that there are two distinct ways and means by which numbers are mobilized, corresponding to each phase.
The first consists of government employees, including engineers, in off-site locations like Lima writing of several large documents consisting of “pre-feasibility” and then “feasibility” studies. These formally scope the project, for example considering possible sites and explaining the factors deems relevant to a bureaucratic and legislative audience. They also consist of projections of the possible range of impacts along numerous dimensions, like economic and environmental. The projections are often a combination of figures (charts and graphs, often with numbers) and text (natural language sentences and the like). The numbers are calculated using various national and international standards drawn from existing national and international bureaucratic institutions like fellow government agencies or the World Bank.
The point of this document and the numbers contained within are to convince the Peruvian state to mobilize resources under its dominion. This is a political act. Harvey and Knox write:
The political force of the figures produced through this work of analysis and description should not be underestimated. In democratic polities, public infrastructures need proven public utility. The public good has to be demonstrable, and the “public” itself also has to be conjured up as a material presence alongside, and in relation to the figures.
Thus we see that engineering does very much consist in some part of politicing. Engineers need to organize themselves into a coherent entity and engage in collective action, persuade others to support their endeavor and dissuade opposition, etc. What role do the numbers specifically play here?
The authors cite Annelise Riles and her work with The Philosophy of ‘As If’ by Hans Vaihinger. Vaihinger looks at the general epistemological problem of future knowledge and present action; the problem is that people don’t know what’s going to happen but want the justification of good outcomes to account for their present actions. Since people can’t actually know how things will turn out, they work off assumptions constructed from past experience. (Side note: Kwame Anthony Appiah has an interesting lecture series on this topic.) Riles’ study looks at how financial speculators construct those assumptions, and Harvey and Knox argue that the numbers and whole of the feasibility studies act in the same manner. That is, they reassure and give confidence to present actors in the face of an unknown and unknowable future.
Structuration
Harvey and Knox find that numbers play a quite different role in the second phase. Assuming that the project is deemed feasible and is selected to go forward, the numbers previously produced are now largely set aside. It’s time for ‘practical people’ and ‘practical numbers’ to get to work.
At this point, a usually quite different set of engineers are mobilized to the sites selected for road construction. They’re probably private contractors from whom the state has purchased engineering services. These folks get to work surveying the landscape, collecting samples of materials like soil, creating their provisional buildings, and establishing social relations with local residents. A big chunk of their work is understanding the terrain, in this case through collecting samples of big chunks of earth. These they take to field labs where they will test and document their properties.
The authors witness and record the tests and the impressions of the practitioners. They note the engineers have specialized techniques that distinguish them as experts, both within specific domains of civil engineering and from ‘the general public’. These techniques consist of engaging with the material and doing something to it, like sorting or mixing it with something else, and observing the results. They then record the results, typically in paper notebooks, but usually translate the qualitative data they sensibly engage with into numbers. To give an example, one engineer added water to soil to understand the threshold when it would change from acting like a dusty solid to a muddy liquid; that point was denoted as a number according to a particular unit of measure.
Harvey and Knox also view this as a form of knowledge production, but instead of one that works “‘as if’” they see it as better characterized as “‘as long as’”. To explain this, they turn to Mathematics as Sign: Writing, Imagining, Counting by Brian Rotman. Rotman has studied how mathematicians work with numbers as three distinct personae. These are as “person,” as “subjects,” and as “agent.” The person persona is the flesh-and-blood historical person of the mathematician, the subject is an abstracted and universalized will which engages with Platonic forms, numbers, and their transformations (my characterization), and the agent is an idealized aggressor who tests the subject’s proofs and findings.
The knowledge produced by creating and calculating with these numbers are used by the people who produce them for the sake of building an artifact. It will exist for some duration, and its qualitative properties will change over that time. For example, wear and tear means that it will need upkeep. The knowledge therefore has a particular temporality and conditionality, hence the ‘as long as.’ This is in stark contrast to the knowledge produced in the first phase, which allowed a one-time action and then became unimportant (and maybe obsolete) once that action was taken.
Conclusion
That’s about as far as I’ve gotten in the chapter, so perhaps there’s more to come from the authors. However, I thought this disjunction within the practice of engineering was interesting enough to pause on.
In terms of software I’ll be thinking about when engineers turn to numbers, and why qualitative data and knowledge are transformed into quantitative. The thing that will unite them both, I think, is that math and numbers will play a role when uncertainty is high and trust is low. It’s in these sorts of situations that people will probably feel most uneasy and I think that numbers have the force in our culture of communicating precision and rigor, which makes people feel more comfortable and restores confidence. That confidence puts them in a position to act and feel good about what they’re doing or have done.