(part two)

van Gelder holds that an algorithmic approach is simply insuitable for understanding the centrifugal governor. It just doesn't work, and there's no reason to even try. To understand the behavior of centrifugal governor, the appropriate tool to use are differential equations that describe its behavior as a dynamic system where the properties of various parts depend on each other.

Changing a parameter of a dynamical system changes its total dynamics (that is, the way its state variables change their values depending on their current values, across the full range of values they may take). Thus, any change in engine speed, no matter how small, changes not the state of the governor directly, but rather the way the state of the governor changes, and any change in arm angle changes the way the state of the engine changes. Again, however, the overall system (coupled engine and governor) settles quickly into a point attractor, that is, engine speed and arm angle remain constant.

Now we finally get into utility functions. van Gelder holds that all the various utility theories, no matter how complex, remain subject to specific drawbacks:

(1) They do not incorporate any account of the underlying motivations that give rise to the utility that an object or outcome holds at a given time.

(2) They conceive of the utilities themselves as static values, and can offer no good account of how and why they might change over time, and why preferences are often inconsistent and inconstant.

(3) They offer no serious account of the deliberation process, with its attendant vacillations, inconsistencies, and distress; and they have nothing to say about the relationships that have been uncovered between time spent deliberating and the choices eventually made.

Curiously, these drawbacks appear to have a common theme; they all concern, one way or another, temporal aspects of decision making. It is worth asking whether they arise because of some deep structural feature inherent in the whole framework which conceptualizes decision-making behavior in terms of calculating expected utilities.

Notice that utility-theory based accounts of human decision making ("utility theories") are deeply akin to the computational solution to the governing task. That is, if we take such accounts as not just describing the outcome of decision-making behavior, but also as a guide to the structures and processes that underlie such behavior, then there are basic structural similarities to the computational governor. Thus, utility theories are straightforwardly computational; they are based on static representations of options, utilities, probabilities, and so on, and processing is the algorithmically specifiable internal manipulation of these representations to obtain a final representation of the choice to be made. Consequently, utility theories are strictly sequential; they presuppose some initial temporal stage at which the relevant information about options, likelihoods, and so on, is acquired; a second stage in which expected utilities are calculated; and a third stage at which the choice is effected in actual behavior. And, like the computational governor, they are essentially atemporal; there are no inherent constraints on the timing of the various internal operations with respect to each other or change in the environment.

What we have, in other words, is a model of human cognition which, on one hand, instantiates the same deep structure as the computational governor, and on the other, seems structurally incapable of accounting for certain essentially temporal dimensions of decision-making behavior. At this stage, we might ask: What kind of model of decision-making behavior we would get if, rather, we took the centrifugal governor as a prototype? It would be a model with a relatively small number of continuous variables influencing each other in real time. It would be governed by nonlinear differential equations. And it would be a model in which the agent and the choice environment, like the governor and the engine, are tightly interlocked.

It would, in short, be rather like the motivational oscillatory theory (MOT) modeling framework described by mathematical psychologist James Townsend. MOT enables modeling of various qualitative properties of the kind of cyclical behaviors that occur when circumstances offer the possibility of satiation of desires arising from more or less permanent motivations; an obvious example is regular eating in response to recurrent natural hunger. It is built around the idea that in such situations, your underlying motivation, transitory desires with regard to the object, distance from the object, and consumption of it are continuously evolving and affecting each other in real time; for example, if your desire for food is high and you are far from it, you will move toward it (that is, z changes), which influences your satiation and so your desire. The framework thus includes variables for the current state of motivation, satiation, preference, and action (movement), and a set of differential equations describe how these variables change over time as a function of the current state of the system.