Fri, 13 Feb 2004
In this essay, I'll describe Pickering's notion of "disciplinary agency". I'll use the same mathematical example Pickering uses. In the next essay, I'll use a coding example I stumbled over while happily hacking on the plane to San Francisco. My hope is that Pickering's notion gives some insight into the semi-common idea that "the code is telling us where it wants to go".
Let's define agency as "the capacity to do things". People have agency. I use my agency to write this essay. You have the ability - the agency - to read it or to turn aside.
Generally, we think of agency as being something that humans have. In his book, Pickering proposes that it's useful to think of nonhumans as having agency. For example, in an experiment a scientist creates a machine, turns it on, and watches it. While creating it, the scientist is exhibiting agency. But when watching the machine, the scientist is passive while the machine does whatever it is that it does. We can say the machine exhibits material agency. It's no longer manipulated by the human; instead, it's in control while the human sits back.
Another type of agency is disciplinary agency, in which a human gives up control to a routine way of reacting to patterns in the world. We can say that that routine has agency. It has the ability to do things in the world that the human doesn't expect, that the human can only observe and then react to.
This pattern of humans exercising agency, then sitting back and watching while something else exercises agency, Pickering rather fancifully calls the dance of agency. He claims it's a common pattern in intellectual practice.
as a case study. In the 1800's, mathematicians
had established a correspondence between algebraic equations involving
imaginary numbers, like
That's fine for two dimensions. What a mathematician named Hamilton
wanted to do was figure out how to link algebra and geometry in three
dimensions. How can we talk about a point
Hamilton first modeled 3D after 2D. If a point
That's fine, but does it work? One way to tell is to repeat what you already know how to do in the new context. That is, you apply - rotely - a discipline you already know. Hamilton knew the rules for algebra, so he started manipulating equations and seeing if the results corresponded to any sensible extrapolation (from 2-space to 3-space) of multiplying two vectors.
A first thing he did was consider the square of a point in
3-space. According to the normal rules of algebra, the square of
This is an example of disciplinary agency. Having decided on his
representation, Hamilton had no choice about how to proceed: the
rules of algebra controlled, and they produced the result that they
produced. Everything is straightforward, except there is a bit of a
question: what does
Now Hamilton turned to geometry. He needed to extrapolate the rules for 2D into 3D, keeping fixed the idea that multiplication means multiplying lengths and adding angles. A problem arises in adding angles. When you square, there are multiple points that satisfy the addition constraint. Which to choose? Hamilton chose the one that lay on the plane connecting the original point and the x-axis.
Hamilton has here taken back agency from the discipline of algebra. But once, he makes his decision, he surrenders again to the discipline of geometry. You can now square a point and, moreover, translate the result back into algebraic notation:
Since this formula and the previous one represent the same point (just gotten at by two different disciplines of multiplication), we know that:
Having given discipline free reign to get this result, Hamilton entertained two possibilities. The first was
I'll cut the story short here. The abbreviated version is that he
assumed either possibility held and kept multiplying. This time he multiplied
two different points rather than squaring the same point. He ran
problem that required him to accept that
So we see a pattern:
That's a dance of agency.