The Mangle in Practice: Science, Society, and Becoming Book

Beautiful, thoughtful exploration of scientific epistemology, based on case studies. In particular, the question of where scientific models and concepts come from, presenting a challenge both to (a) the scientific orthodoxy that imagines an underlying stable physical reality to which scientific models hue ever more closely through the scientific process, and (b) the critique coming from the sociology of science, that scientific theories merely reflect the social context in which they are created and that they are designed to serve. Pickering argues that science is a kind of a partner dance between the physical world and the community of scientists, in which both exert influence on the outcome through a process of "tuning"/adjusting/"dialectic of resistance and accommodation" until the scientific and social objectives of the endeavor are met; and this outcome is not determined ahead of time (either by the physical world, challenging the scientific orthodoxy, or by the social world, challenging the sociological view), but emerges through the dance itself. To me the most useful idea has been the way this calls attention to the simultaneous creative freedom and constraint-by-physicality of the scientist: you are free to do whatever experiment / create whatever conceptual model / etc. that you want, but the world usually won't cooperate. Just a tiny few of the vast array of possible paths you take will work. This everyday truth is somehow clarifying, beyond its due, in a lot of areas of theory about how the world works. See for example the way Spatz uses it in What a Body Can Do to shed light on the problem of agency with regard to gender in leftist social theory!

I found Pickering's basic epistemological argument (chapters 1-2) about the structure of scientific thought convincing. When he applied it to math in chapter 4, as a mathematician I felt that he didn't press his theory fully; perhaps he was worried about being called a nutty theorist. (Throughout, he draws on continental theory, particularly Latour and Actor-Network Theory, but he is at pains to make sure you understand that he is saying down-to-earth / clear / concrete things that you can pin down, i.e. that you don't mistake him for one of those intentionally obtuse French dudes.) The question at stake is, when the science in question is mathematics, who is the scientist's partner in the dance? When the subject was physics, you could say "the physical world," but with math you can't say that. Pickering tries to give an account in which the partner is somehow "the discipline of mathematics" itself, but I thought this was weak. His whole point is that the scientist is facing an external agent. "The discipline" is insufficiently external. I found an email I wrote a friend where I elaborate on all this, so I'm including it below, slightly edited, in a PS.

NB: I read chapters 1, 2, and 4. I am curious about the later chapters, but got what I needed, and suspect that I am going to find Pickering's view in the later chapters less useful to me.

PS: Here's that email. Forgive the lack of capitalization. The Hamilton referred to is William Rowan Hamilton, the inventor of quaternions, which invention is the subject of chapter 4.

i read ch 1 and 2 of pickering and started on ch 4. i decided i will read the rest of ch 4 and after that put the book down for now. basically i find his main argument convincing regarding how scientific practice happens (dialectic of resistance and accommodation; interactive stabilization; both human and material agency emergent in time; etc.). i am not going to get to the part where he engages the metaphysics (in particular i'm curious about what he has to say about the "problematic of realism", which somewhere in ch 1 he beautifully characterized as "the nature of the purchase our knowledge has on the world and vice versa"), where i feel like there will be more room for his solutions not to totally match my sensibilities, but there is one significant thing that happened in ch. 4 where i see it differently from him.

the question is, what is the substrate that the mathematician engages in the dialectic of resistance and accommodation? pickering's answer is "the discipline" as in "disciplinary agency", vs. the "material agency" that happens when the physicists engage a "material" substrate. when he first used the phrase "disciplinary agency", i was excited, because he wants to draw a parallel between the mathematician's work and the physicist's engagement with something as obviously external and extrinsic to her control as the physical world. however, when he actually elaborates what disciplinary agency is made of, to me it felt way too thin, both to capture my own experience but even really to support his own case. once this happened, i realized that the word "disciplinary agency" is wrong anyway. "the discipline" is not the partner in the dance of resistance and accommodation because it is not external and extrinsic to the scientist's control in the way that the material world is. math has an equally extrinsic partner.

the substrate of mathematics is not the discipline itself. the discipline is a set of tools to probe a substrate external to it. it is the same for all disciplines. "materiality" is the wrong name for this substrate because math is not material. mathematician/educator paul lockhart calls it "mathematical reality" (he wrote something like "that's the thing about mathematical reality - when we push on it, it pushes back!"), but to me this is too narrow because it separates it artificially from all the other substrates it is connected to (such as the physical world). to me the actual substrate is "reality". when lockhart says "mathematical reality", all he means is "that part of reality that we tend to perceive when we use the tools of the discipline of mathematics to probe it."

i feel like i sorta know why pickering made this mistake. he's already sort of out on a limb with his talk of material agency, it's grouping him with the ANT people, who sometimes resort to "everything is signs!" nothingness [a propos of our earlier conversation about continental theorists and whether or not you're willing to stand behind your theory]. he's at pains to make sure nobody thinks he's talking about ghosts. (e.g. he's like, look, material agency for sure, but i'm not talking about material intentionality, are you crazy??) so it would be scary to him, and open up too much vulnerability, to try to impute the kind of substantiveness that is even capable of exerting agency on a mathematician to a "reality" that can't be located anywhere in the physical world.

the problem is that without this, he's talking in circles a little bit. on pp. 142-143, he notes the centrality to his case of the idea that hamilton's "transcriptions" were "forced moves" which hamilton didn't have control over. but he then immediately notes that hamilton exerted some discretion over which of the established conventions of disciplinary practice he was going to obey and which he was going to tweak. i am all for the idea that the discipline itself is emergent in time, and i think that's really right; but i feel that pickering has contradicted himself here. if hamilton is able to select which established disciplinary practices he's going to consider himself beholden to, then it is not these disciplinary practices that force his hand! he doesn't have to accommodate them! so pickering has failed to locate hamilton's partner in the dance of resistance and accommodation. the refusal to talk about reality apart from either material reality or the discipline itself has rendered the mathematician's actual dance partner invisible.