# Kaj_Sotala comments on Morality is not about willpower - Less Wrong

9 08 October 2011 01:33AM

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Comment author: 08 October 2011 10:29:47AM *  13 points [-]

To expand on this...

Tim van Gelder has an elegant, although somewhat lengthy, example of this. He presents us with a problem engineers working with early steam engines had: how to translate the oscillating action of the steam piston into the rotating motion of a flywheel?

(Note: it's going to take a while before the relationship between this and utility functions becomes clear. Bear with me.)

High-quality spinning and weaving required, however, that the source of power be highly uniform, that is, there should be little or no variation in the speed of revolution of the main driving flywheel. This is a problem, since the speed of the flywheel is affected both by the pressure of the steam from the boilers, and by the total workload being placed on the engine, and these are constantly fluctuating.

It was clear enough how the speed of the flywheel had to be regulated. In the pipe carrying steam from the boiler to the piston there was a throttle valve. The pressure in the piston, and so the speed of the wheel, could be adjusted by turning this valve. To keep engine speed uniform, the throttle valve would have to be turned, at just the right time and by just the right amount, to cope with changes in boiler pressure and workload. How was this to be done?

An obvious-to-us approach would be to break down the task into a number of subproblems. We might think of a device capable of solving this problem as implementing the following algorithm:

1. Measure the speed of the flywheel.
2. Compare the actual speed against the desired speed.
a. measure the current steam pressure;
b. calculate the desired alteration in steam pressure;
c. calculate the necessary throttle valve adjustment.
4. Make the throttle valve adjustment.

There must be some physical device capable of actually carrying out each of these subtasks, and so we can think of the governor as incorporating a tachometer (for measuring the speed of the wheel); a device for calculating the speed discrepancy; a steam pressure meter; a device for calculating the throttle valve adjustment; a throttle valve adjuster; and some kind of central executive to handle sequencing of operations.

Let's call this approach the computational governor. As obvious this approach might seem, it was not the way by which the problem was actually solved. After all, they didn't have computers back then. Instead, what they came up with was a centrifugal governor.

It consisted of a vertical spindle geared into the main flywheel so that it rotated at a speed directly dependent upon that of the flywheel itself (see figure 1). Attached to the spindle by hinges were two arms, and on the end of each arm was a metal ball. As the spindle turned, centrifugal force drove the balls outward and hence upward. By a clever arrangement, this arm motion was linked directly to the throttle valve. The result was that as the speed of the main wheel increased, the arms raised, closing the valve and restricting the flow of steam; as the speed decreased, the arms fell, opening the valve and allowing more steam to flow. The engine adopted a constant speed, maintained with extraordinary swiftness and smoothness in the presence of large fluctuations in pressure and load.

Now let's compare the computational governor and the centrifugal governor. Are they two entirely different ways of achieving the same goal, or are they on some level fundamentally the same?

One of the defining characteristics in the computational governor is that it relies on representations of its environment: it has a symbolic representation for the current speed of the flywheel, a symbolic representation for the current steam pressure, and so on. It manipulates these representations, and the results of those manipulations tell it whether to adjust the throttle valve or not. Does the centrifugal governor represent aspects of the environment in a similar fashion?

There is a common and initially quite attractive intuition to the effect that the angle at which the arms are swinging is a representation of the current speed of the engine, and it is because the arms are related in this way to engine speed that the governor is able to control that speed. This intuition is misleading, however; arm angle and engine speed are of course intimately related, but the relationship is not representational. [...]

A noteworthy fact about standard explanations of how the centrifugal governor works is, however, that they never talk about representations. This was true for the informal description given above, which apparently suffices for most readers; more importantly, it has been true of the much more detailed descriptions offered by those who have actually been in the business of constructing centrifugal governors or analyzing their behavior. Thus, for example, a mechanics manual for construction of governors from the middle of last century, Maxwell's original dynamical analysis (see below), and contemporary mathematical treatments all describe the arm angle and its role in the operation of the governor in nonrepresentational terms. The reason, one might reasonably conclude, is that the governor contains no representations. [...]

The temptation to treat the arm angle as a representation comes from the informal observation that there is some kind of correlation between arm angle and engine speed; when the engine rotates at a certain speed, the arms will swing at a given angle. [...]

For a start, notice that the correlation at issue only obtains when the total system has reached its stable equilibrium point, and is immediately disturbed whenever there is some sudden change in, for example, the workload on the engine. At such times, the speed of the engine quickly drops for a short period, while the angle of the arms adjusts only at the relatively slow pace dictated by gravitational acceleration. Yet, even as the arms are falling, more steam is entering the piston, and hence the device is already working; indeed, these are exacdy the times when it is most crucial that the governor work effectively. Consequently, no simple correlation between arm angle and engine speed can be the basis of the operation of the governor.

[...] For notice that, because the arms are directly linked to the throttle valve, the angle of the arms is at all times determining the amount of steam entering the piston, and hence at all times the speed of the engine depends in some interesting way on the angle of the arms. Thus, arm angle and engine speed are at all times both determined by, and determining, each other's behavior. As we shall see below, there is nothing mysterious about this relationship; it is quite amenable to mathematical description. Yet it is much more subtle and complex than the standard concept of representation can handle, even when construed as broadly as is done here. In order to describe the relationship between arm angle and engine speed, we need a more powerful conceptual framework than mere talk of representations. That framework is the mathematical language of dynamics, and in that language, the two quantities are said to be coupled. The real problem with describing the governor as a representational device, then, is that the relation of representing-something standing in for some other state of affairs-is too simple to capture the actual interaction between the governor and the engine.

(comment split into two, since LW says it's too long)

Comment author: 08 October 2011 10:30:33AM 10 points [-]

(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.

Comment author: 08 October 2011 10:59:09AM 3 points [-]

Kaj may be too humble to self-link the relevant top level post, so I'll do it for him.

Comment author: 08 October 2011 04:28:55PM 0 points [-]

I actually didn't link to it, because I felt that those comments ended up conveying the same point better than the post did.

Comment author: 08 October 2011 04:48:02PM *  -2 points [-]

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.

A set of differential equations that describe its behavior as a dynamic system where the properties of various parts depend on each other, would still be an algorithm. van Gelder appears not to have heard of universal computation.

(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.

I would say that the selection and representation of values is exactly this account.

(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

False.

and why preferences are often inconsistent and inconstant.

Perceived preferences are often inconsistent and inconstant. So you try to find underlying preferences.

(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.

Also false. The utility function itself is precisely a model of the deliberation process. It isn't going to be an equation that fits on a single line. And it is going to have some computational complexity, which will relate the relationships between time spent deliberating and the choice eventually made.

I hope - because this is the most charitable interpretation I can make - that all these people complaining about utility functions are just forgetting that it uses the word "function". Not "arithmetic function", or "regular expression". Any computable function. If an output can't be modelled with a utility function, it is non-computable. If humans can't be modelled with utility functions, that is a proof that a computer program can't be intelligent. I'm not concerned with whether this is a good model. I just want to able to say, theoretically, that the question of what a human should do in response to a situation, is something that can be said to have right answers and wrong answers, given that human's values/preferences/morals.

All this harping about whether utility functions can model humans is not very relevant to my post. I bring up utility functions only to communicate, to a LW audience, that you are only doing what you want to do when you behave morally. If you have some other meaningful way of stating this - of saying what it means to "do what you want to do" - by all means do so!

(If you want to work with meta-ethics, and ask why some things are right and some things are wrong, you do have to work with utility functions, if you believe anything like the account in the meta-ethics sequence; for the same reason that evolution needs to talk about fitness. If you just want to talk about what humans do - which is what I'm doing here - you don't have to talk about utility functions unless you want to be able to evaluate whether a particular human is behaving morally or immorally. To make such a judgement, you have to have an algorithm that computes a judgement on an action in a situation. An that algorithm computes a utility function.)

Comment author: 08 October 2011 05:41:10PM *  3 points [-]

A set of differential equations that describe its behavior as a dynamic system where the properties of various parts depend on each other, would still be an algorithm.

Sure, but that's not the sense of "algorithm" that was being used here.

If an output can't be modelled with a utility function, it is non-computable. If humans can't be modelled with utility functions, that is a proof that a computer program can't be intelligent. I'm not concerned with whether this is a good model. I just want to able to say, theoretically, that the question of what a human should do in response to a situation, is something that can be said to have right answers and wrong answers, given that human's values/preferences/morals.

None of this is being questioned. You said that you're not concerned with whether this is a good model, and that's fine, but whether or not it is a good model was the whole point of my comment. Neither I nor van Gelder claimed that utility functions couldn't be used as models in principle.

All this harping about whether utility functions can model humans is not very relevant to my post. I bring up utility functions only to communicate, to a LW audience, that you are only doing what you want to do when you behave morally.

My comments did not question the conclusions of your post (which I agreed with and upvoted). I was only the addressing the particular paragraph which I quoted in my initial comment. (I should probably have mentioned that IAWYC in that one. I'll edit that in now.)

Comment author: 08 October 2011 08:50:06PM *  3 points [-]

Sorry. I'm getting very touchy about references utility functions now. When I write a post, I want to feel like I'm discussing a topic. On this post, I feel like I'm trying to compile C++ code and the comments are syntax error messages. I'm pretty much worn out on the subject for now, and probably getting sloppy, even though the post could still use a lot of clarification.

Comment author: 09 October 2011 08:45:52AM 0 points [-]

No problem - I could have expressed myself more clearly, as well.

Take it positively: if people only mostly nitpick on your utility function bit, then that implies that they agree with the rest of what you wrote. I didn't have much disagreement with the actual content of your post, either.