Early in my book on music, Beethoven’s Anvil, I set about conceptualizing group music-making at the neural level in terms of the collective neural state space (on neural state space, see this post). I argued, in effect, that the size of this collective neural state space could be no larger than the state space of an individual member of the group. By contrast, if the same group of people is just hanging around chatting in a coffee house or sipping piña coladas by the pool, their collective state space is likely to be considerably larger than that of any individual, as you would expect.
What’s the difference? When they’re making music, their actions are tightly coupled together, they constrain one another. Rather severely.
As this idea was central to my overall argument I called it a principle and gave it a name: Ensemble State Collapse (Beethoven’s Anvil, p. 61). The state space of the ensemble has no more (and likely fewer) dimensions than the state space of a single individual acting autonomously. “Dimension” is the key word. We’re dealing with spaces of very high dimensionality, millions upon millions upon millions.
I now discover that what I called ensemble state collapse has another name, dimensional compression. There’s that word, “dimension.” I discovered this in the following article:
Michael A. Riley, Michael J. Richardson, Kevin Shockley and Verónica C. Ramenzoni, Interpersonal synergies, Frontiers in Psychology, March 2011 2:38, pp. 1-7. doi: 10.3389/fpsyg.2011.00038
The opening paragraph gives a feel for the article:
We present the perspective that interpersonal movement coordination results from establishing interpersonal synergies. Interpersonal synergies are higher-order control systems formed by coupling movement system degrees of freedom of two (or more) actors. Characteristic features of synergies identified in studies of intrapersonal coordination – dimensional compression and reciprocal compensation – are revealed in studies of interpersonal coordination that applied the uncontrolled manifold approach and principal component analysis to interpersonal movement tasks. Broader implications of the interpersonal synergy approach for movement science include an expanded notion of mechanism and an emphasis on interaction-dominant dynamics.
“Degrees of freedom” (DF) is not the same concept as state space, but it performs similar conceptual work. Thus:
Bernstein (1967) identified the degrees of freedom problem – the notion that the large number of independently controllable movement system DF poses a computational burden to the CNS ... Bernstein’s solution ... was that rather than controlling each DF separately, the DF are coupled to form a synergy, enabling the DF to regulate each other. This reduces the need to control each DF, and allows compensation for variability in one component of the synergy by another. Two central features of synergies are dimensional compression and reciprocal compensation.
What’s dimensional compression?
DF [degrees of freedom] that potentially are independent are coupled so that the synergy has fewer DF (possesses a lower dimensionality) than the set of components from which it arises. The behavior of the synergy has even fewer DF, a second level of dimensional compression as one moves from structural components to the behavior enacted by the interactions among the DF. Dimensional compression at both stages results from imposing constraints, which couple components so they change together rather than independently.
So, I’m happy to discover that, in making up that concept, I wasn’t making up nonsense, though I’m a bit embarrassed that more or less the same notion has been in the literature since 1967, and from such a distinguished researcher as Nikolai Bernstein. The Wikipedia article on Bernstein gives a nice analogy to illustrate dimensional compression:
Bernstein suggested that the CNS is capable of "functionally freezing degrees of freedom." As an analogy, controlling the four wheels of a car independently is very difficult. Yet, by functionally freezing degrees of freedom (the two rear wheels are only allowed to rotate around one shared horizontal axis, and the two front wheels are also allowed to rotate in parallel around a longitudinal axis, controlled by the steering wheel) a car becomes much easier to control.
If, instead of the four wheels of a car, we think of, say, a pair of dancers, say, Fred Astaire and Ginger Rogers, you can see more or less how it works. If they’re simply chatting at a cocktail party Fred and Ginger can and do think and move independently of one another. But when you strike up the band, put them on the dance floor, and have them dance, their moves are tightly coupled and neither has time to think about much of anything, such as philosophy, household finances, or England. There’s a great deal of dimensional compression underlying that joy and grace.
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Now let’s consider the soccer game that was at the center of yesterday’s post on agency, ontology, and Rube Goldberg. Here’s the passage from Michel Serres:
A ball is not an ordinary object, for it is what it is only if a subject holds it. Over there, on the ground, it is nothing; it is stupid; it has no meaning, no function, and no value. Ball isn’t played alone. Those who do, those who hog the ball, are bad players and are soon excluded from the game. They are said to be selfish. The collective game doesn’t need persons, people out for themselves. Let us consider the one who holds it. If he makes it move around him, he is awkward, a bad player. The ball isn’t there for the body; the exact contrary is true: the body is the object of the ball; the subject moves around this sun. Skill with the ball is recognized in the player who follows the ball and serves it instead of making it follow him and using it. It is the subject of the body, subject of bodies, and like a subject of subjects. Playing is nothing else but making oneself the attribute of the ball as a substance. The laws are written for it, defined relative to it, and we bend to these laws. Skill with the ball supposes a Ptolemaic revolution of which few theoreticians are capable, since they are accustomed to being subjects in a Copernican world where objects are slaves.
If you’ve read my post, then you know that I expressed some skepticism about some of Serres’ formulations in that quite elegant paragraph and about some of the conclusions that Levi Bryant wanted to draw from it. That was yesterday.
Today we can talk about degrees of freedom and dimensional compression. But only loosely.
Caution: We must be careful of the word “freedom” in this context. We’re using it in the phrase, “degree of freedom”, where it’s a technical term from dynamics. Whether or not this technical term has any bearing in the question of freedom of will, that’s a different, though not unimportant matter. We’ll set that aside.
First, we have Serres’ contrast between the soccer ball just sitting around somewhere, on a shelf, on the ground, wherever, and then ball when in play. When sitting on the ground, it’s nothing. That is to say, it puts few constraints on anyone’s movement. When in play, though, that’s different. In that context the ball places severe constraints of the players’ movements, for they must follow it and attempt to control it in very specific ways as dictated by the rules of the game.
And, of course, the players must cooperate with one another in order to control the ball effectively and efficiently. How much dimensional compression do the players achieve as they pursue the ball (and one another), that’s an interesting question. Do better players and better teams achieve greater dimensional compression? an even more interesting question. As Serres says, the game doesn’t need selfish players who hog the ball, perhaps because they interfere with dimensional compression, and thus grace? Is following the ball a way to facilitate dimensional compression in the ensemble, the collective?
And what do these questions have to do with the much vexed question of agency?
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Bonus philosophy points: Near the end of the article the authors raise the question of causality, noting that the causal relations in such a system are not traditional one’s of efficient “billiard ball” causality. They’re circular. What is this circular causality? Does it fit into Aristotle’s scheme at all?
How might a structure of process be able to exert “control” over movements? This question raises another key point: The interpersonal synergy approach, with its roots in self-organizing complex systems, entails notions of “mechanism” and “causality” that are broader than the usual (Newtonian) sense of the terms as involving only efficient causes, the kinds of forceful interactions produced by colliding cogs or billiard balls ... Complex systems exhibit circular causality; bottom-up processes give rise to macroscopic patterns that simultaneously constrain the components from the top down. Constraints play the role of causal mechanisms in complex systems insomuch as constraints allow or deny certain states. Constraints limit the DF of a system, but do not cause the system to take on particular states by virtue of forceful “pushes” (local, efficient causes). Control (manipulation of the movement system) first entails coordination (organization of the movement system), as anticipated by Bernstein (1967).