[From Bill Powers (960109.2315 MST)]
Bruce Abbott (950109.0930 EST) --
Mary discovered that during the year that I was subscribing to Behavior
and Brain Sciences I got the issue with Killeen's article, _Mathematical
principles of reinforcement_. I didn't give it much of a reading the
first time. I have gone through it again, swiftly, reliving some of my
original reactions as they come back to mind, and adding some new ones.
My sense of alienation from this whole approach is sharp. I don't want
to get into a long diatribe, however.
While lying in bed tonight, instead of sleeping I suddenly thought of an
illustration of what puts me off, probably a takeoff from your example
of starting the gasoline engine.
···
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Suppose the question were, "how does the engine of a car work?" Suppose
I thought about this for a long time, and had a sudden insight: what
makes it work is the rotation of the crankshaft! Immediately on having
this insight, all the facts I know about the engine would fall into
place.
The rotation of the crankshaft is coupled to the rise and fall of the
pistons, as well as to the opening and closing of the valves and, via a
drive belt, to the rotation of the armature of the alternator. In
addition, the crankshaft causes electrical contacts to close
periodically, causing sparks in the cylinders in a preset sequence. As
the crankshaft causes the pistons to fall, on every second rotation the
cam-shaft driven by the crankshaft opens the intake valve, creating a
vacuum which draws a fuel-air mixture from the carburetor. Then the
intake valve closes, and as the crankshaft rotates another 180 degrees
it makes the piston compress the mixture and at just the right time sets
off a spark in the cylinder, causing an explosion which delivers output
power to the drive train. The crankshaft then opens the exhaust valve
and causes the piston to rise, expelling the burned gases and completing
the cycle.
So clearly, it is the rotation of the crankshaft which draws in the
fuel-air mixture, compresses it, ignites it, and finally removes the
exhaust products in preparation for the next round. In this process the
crankshaft causes power to be delivered to the drive train, and also
operates the valves and runs the generator that supplies the electricity
for the spark and runs the water pump that cools the engine.
Now it becomes clear why the car must be started electrically, or by
putting it in gear and pushing it or rolling it downhill. Since the
rotation of the crankshaft is the cause of everything, the first thing
that must happen to get the car going is to make the crankshaft rotate.
Also, if the rotation of the crankshaft is inhibited by putting on the
brakes while the (stick-shift) car is in gear, the cycle will be
extinguished and the engine must be re-started by external means.
Some might say that it is the fuel that makes the engine go. But this is
clearly nonsense, because before any power can be generated, the
crankshaft must turn enough to draw the fuel into the cylinder, opening
the correct valve first and then closing it at the right time. If the
crankshaft doesn't rotate, nothing will happen. Everything critical to
the operation of the engine depends on the rotation of the crankshaft,
from operating the valves to drawing in the fuel to compressing and
igniting the fuel to clearing out the combustion products -- even to
charging the battery to provide for the next start. Once the cycle gets
going, it is true that the fuel provides the means of rotating the
crankshaft, but it is the _consequence_ of exploding the fuel, the
rotation of the crankshaft, that controls the fuel intake from then on,
as well as everything else. We can prove that when we prevent the
crankshaft from rotating, the power delivery to the drive train stops
and the fuel ceases to be pumped in. The fuel intake is controlled by
its consequence, the rotation of the crankshaft. We can even show that
increasing the speed of rotation of the crankshaft increases the
probability per unit time that a packet of fuel-air mixture will be
drawn into the cylinder and ignited.
The rotation of the crankshaft is contingent on the explosion of the
fuel. If this contingency changes, for example by changing gears while
going uphill or restricting the air intake to the carburetor, the result
is to cause the fuel intake to decrease, because the crankshaft rotates
more slowly. Clearly, the more engine rotation there is, the more fuel
is caused to be drawn in and burned, and vice versa. As the effect of
the fuel on the crankshaft rotation changes, the fuel consumption is
made to change and the power delivered to the drive train changes. So by
manipulating the contingency, we can control the flow of fuel into the
engine and the power output to the wheels. That is what the accelerator
pedal does: it changes the contingency by changing the consequence of
drawing fuel into the engine and igniting it, and this consequence in
turn controls the fuel intake and the rate of the explosions.
----------------------------
The point of this is that when you seize on a particular causal
explanation, you can make sense of any circular process by attributing
causation to any part of the process. The more you think about it, the
more sense it makes and the more supporting evidence you can find. We
could start all over and have the insight that the repetitive firing of
the spark plugs is the cause of the engine's rotation and the fuel
consumption. Or we could suddenly see that the fuel entering the engine
is causing everything. Then what we call the action, the contingency,
and the controlling consequence would shift around the loop, and
everything would still make sense, with all the evidence we want.
Killeen is stuck in the belief that behavior is controlled by its
consequences, by "reinforcements." This is a seductive concept, because
once you adopt it you can find endless evidence to support it. But the
result is no more meaningful than picking one spot on the rim of a wheel
as the cause of the rotation of the rest of the wheel, pushing on the
part ahead of it and as a consequence being pushed by the part behind
it. In any circular process, the language of causation is inappropriate;
every cause is at the same time an effect -- ultimately, an effect of
itself.
The real difference between PCT and reinforcement theory is that the PCT
explanation does not treat any event within the closed loop as "the"
cause of what is going on. Is reinforcement a cause? Yes. Is it an
effect? Yes, at the same time. Both reinforcement rate and behavior rate
are _dependent_ variables, and the variables on which they _both_ depend
exist outside the loop: the variables we call disturbances and reference
signals.
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The February Sky & Telescope arrived today. In it was a discussion of
the Standard Model in physics, and all its wierd problems. Here's part
of what the author, Sten Odenwald, said:
And it's worth remembering that mathematics can sometimes introduce
concepts that are only a means to an end and have no independent
reality. In the abstract world of mathematical symbolism, it isn't
always clear what is real and what's not. For example, when we do
long division on paper to divide 54,162 by 2 to get 27,081 we
generate the intermediate numbers 14, 16, and 2, which we then just
throw away. Are virtual particles, compact 6-dimensional manifolds,
and twistors simply nonphysical means to an end -- mere artifacts
of how we human beings do our mathematics? ... Even in superstring
theory, recent work suggests that it may be possible to build
consistent models entirely within ordinary four-dimensional space-
time, without recourse to higher dimensions.
Many of the concepts that Killeen uses, such as short-term memory,
backward effects of reinforcement, coupling of behavior to incentives,
activation, and constraint may be unnecessary intermediate steps given
more reality than they deserve. In the final system equations, they may
simply drop out, as we discard the intermediate numbers in long
division. Which of Killeen's concepts are real and which are not? Many
of them, surely, are simply means to an end and need not be thought
important in themselves. It may be possible to build a consistent model
without introducing all of the auxiliary concepts that Killeen uses,
without naming every intermediate relationship as it it corresponded to
something real.
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Best,
Bill P.