Digifesto

Tag: mathematics

the end of narrative in social science

‘Narrative’ is a term you hear a lot in the humanities, the humanities-oriented social sciences, and in journalism. There’s loads of scholarship dedicated to narrative. There’s many academic “disciplines” whose bread and butter is the telling of a good story, backed up by something like a scientific method.

Contrast this with engineering schools and professions, where the narrative is icing on the cake if anything at all. The proof of some knowledge claim is in its formal logic or operational efficacy.

In the interdisciplinary world of research around science, technology, and society, the priority of narrative is one of the major points of contention. This is similar to the tension I found I encountered in earlier work on data journalism. There are narrative and mechanistic modes of explanation. The mechanists are currently gaining in wealth and power. Narrativists struggle to maintain their social position in such a context.

A struggle I’ve had while working on my dissertation is trying to figure out how to narrate to narrativists a research process that is fundamentally formal and mechanistic. My work is “computational social science” in that it is computer science applied to the social. But in order to graduate from my department I have to write lots of words about how this ties in to a universe of academic literature that is largely by narrativists. I’ve been grounding my work in Pierre Bourdieu because I think he (correctly) identifies mathematics as the logical heart of science. He goes so far as to argue that mathematics should be at the heart of an ideal social science or sociology. My gloss on this after struggling with this material both theoretically and in practice is that narratively driven social sciences will always be politically or at least perspectivally inflected in ways that threaten the objectivity of the results. Narrativists will try to deny the objectivity of mathematical explanation, but for the most part that’s because they don’t understand the mathematical ambition. Most mathematicians will not go out of their way to correct the narrativists, so this perception of the field persists.

So I was interested to discover in the work of Miller McPherson, the sociologist who I’ve identified as the bridge between traditional sociology and computational sociology (his work gets picked up, for example, in the generative modeling of Kim and Leskovec, which is about as representative of the new industrial social science paradigm as you can get), an admonition about the consequences of his formally modeled social network formation process (the Blau space, which is very interesting). His warning is that the sociology his work encourages loses narrative and with it individual agency.

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(McPherson, 2004, “A Blau space primer: prolegomenon to an ecology of affiliation”)

It’s ironic that the whole idea of a Blau space, which is that the social network of society is sampled from an underlying multidimensional space of demographic dimensions, predicts the quantitative/qualitative divide in academic methods as not just a methodological difference but a difference in social groups. The formation of ‘disciplines’ is endogenous to the greater social process and there isn’t much individual agency in this choice. This lack of agency is apparent, perhaps, to the mathematicians and a constant source of bewilderment and annoyance, perhaps, to the narrativists who will insist on the efficacy of a narratively driven ‘politics’–however much this may run counter to the brute fact of the industrial machine–because it is the position that rationalizes and is accessible from their subject position in Blau space.

“Subject position in Blau space” is basically the same idea, in more words, as the Bourdieusian habitus. So, nicely, we have a convergence between French sociological grand theory and American computational social science. As the Bourdieusian theory provides us with a serviceable philosophy of science grounded in sociological reality of science, we can breathe easily and accept the correctness of technocratic hegemony.

By “we” here I mean…ah, here’s the rub. There’s certainly a class of people who will resist this hegemony. They can be located easily in Blau space. I’ve spent years of my life now trying to engage with them, persuading them of the ideas that rule the world. But this turns out to be largely impossible. It’s demanding they cross too much distance, removes them from their local bases of institutional support and recognition, etc. The “disciplines” are what’s left in the receding tide before the next oceanic wave of the unified scientific field. Unified by a shared computational logic, that is.

What is at stake, really, is logic.

Imre Lakatos and programming as dialectic

My dissertation is about the role of software in scholarly communication. Specifically, I’m interested in the way software code is itself a kind of scholarly communication, and how the informal communications around software production represent and constitute communities of scientists. I see science as a cognitive task accomplished by the sociotechnical system of science, including both scientists and their infrastructure. Looking particularly at scientist’s use of communications infrastructure such as email, issue trackers, and version control, I hope to study the mechanisms of the scientific process much like a neuroscientist studies the mechanisms of the mind by studying neural architecture and brainwave activity.

To get a grip on this problem I’ve been building BigBang, a tool for collecting data from open source projects and readying it for scientific analysis.

I have also been reading background literature to give my dissertation work theoretical heft and to procrastinate from coding. This is why I have been reading Imre Lakatos’ Proofs and Refutations (1976).

Proofs and Refutations is a brilliantly written book about the history of mathematical proof. In particular, it is an analysis of informal mathematics through an investigation of the letters written by mathematicians working on proofs about the Euler characteristic of polyhedra in the 18th and 19th centuries.

Whereas in the early 20th century, based on the work of Russel and Whitehead and others, formal logic was axiomatized, prior to this mathematical argumentation had less formal grounding. As a result, mathematicians would argue not just substantively about the theorem they were trying to prove or disprove, but also about what constitutes a proof, a conjecture, or a theorem in the first place. Lakatos demonstrates this by condensing 200+ years of scholarly communication into a fictional, impassioned classroom dialog where characters representing mathematicians throughout history banter about polyhedra and proof techniques.

What’s fascinating is how convincingly Lakatos presents the progress of mathematical understanding as an example of dialectical logic. Though he doesn’t use the word “dialectical” as far as I’m aware, he tells the story of the informal logic of pre-Russellian mathematics through dialog. But this dialog is designed to capture the timeless logic behind what’s been said before. It takes the reader through the thought process of mathematical discovery in abbreviated form.

I’ve had conversations with serious historians and ethnographers of science who would object strongly to the idea of a history of a scientific discipline reflecting a “timeless logic”. Historians are apt to think that nothing is timeless. I’m inclined to think that the objectivity of logic persists over time much the same way that it persists over space and between subjects, even illogical ones, hence its power. These are perhaps theological questions.

What I’d like to argue (but am not sure how) is that the process of informal mathematics presented by Lakatos is strikingly similar to that used by software engineers. The process of selecting a conjecture, then of writing a proof (which for Lakatos is a logical argument whether or not it is sound or valid), then having it critiqued with counterexamples, which may either be global (counter to the original conjecture) or local (counter to a lemma), then modifying the proof, then perhaps starting from scratch based on a new insight… all this reads uncannily like the process of debugging source code.

The argument for this correspondence is strengthened by later work in theory of computation and complexity theory. I learned this theory so long ago I forget who to attribute it to, but much of the foundational work in computer science was the establishment of a correspondence between classes of formal logic and classes of programming languages. So in a sense its uncontroversial within computer science to consider programs to be proofs.

As I write I am unsure whether I’m simply restating what’s obvious to computer scientists in an antiquated philosophical language (a danger I feel every time I read a book, lately) or if I’m capturing something that could be an interesting synthesis. But my point is this: that if programming language design and the construction of progressively more powerful software libraries is akin to the expanding of formal mathematical knowledge from axiomatic grounds, then the act of programming itself is much more like the informal mathematics of pre-Russellian mathematics. Specifically, in that it is unaxiomatic and proofs are in play without necessarily being sound. When we use a software system, we are depending necessarily on a system of imperfected proofs that we fix iteratively through discovered counterexamples (bugs).

Is it fair to say, then, that whereas the logic of software is formal, deductive logic, the logic of programming is dialectical logic?

Bear with me; let’s presume it is. That’s a foundational idea of my dissertation work. Proving or disproving it may or may not be out of scope of the dissertation itself, but it’s where it’s ultimately headed.

The question is whether it is possible to develop a formal understanding of dialectical logic through a scientific analysis of the software collaboration. (see a mathematical model of collective creativity). If this could be done, then we could then build better software or protocols to assist this dialectical process.