Approach Gradient Paper Found

[From Rick Marken (2002.05.25.1000)]

The paper on approach gradients is by J. S. Brown (one of Neal Miller's grad
students, apparently). The reference is: Brown, J. S. (1948) Gradients of approach
and avoidance responses and their relation to level of motivation. Journal of
Comparative and Physiological Psychology, 41, 450-465. The relevant results are
measures of force exerted by hungry rat s at _two_ points as they proceeded down a
straight maze to a food goal. The force toward the food was measured when the
rats were 30 and 170 cm from the food. At these points in the rats' progress
toward the food a steel bead was engaged in a snap ring, connecting the rats'
harness to a spring. So the rats were "held up" by the spring at these points and
Brown measured the force exerted against the spring over a 5 second period.

The results presented are the _average_ force exerted by 20 rats at the 30 and 170
cm points as they proceeded down the maze to the food. The average force measures
(a graphically derived value so I don't know the units) at the two points were as

                 Mean Md SD
30 cm 56.5 47.5 33.7
170cm 40.9 36.1 26.3

So the _average_ force exerted by the rats is, indeed, greater when the rats are
closer to the goal (when, presumably, error is smaller). These, of course, are
statistical results. Brown does not report how many of the _individual_ rats
showed this effect. Since the medians are somewhat closer together than the means
it looks like the result could be driven, to some extent, by the behavior of a
couple of unusually high force measures at the 30 cm point (or unusually low force
measures at the 170 cm point) for a couple of animals.

I have replicated this experiment using a simple tracking experiment. The result,
for both me and a simple model control system, was that greater force was exerted
against the same disturbance the farther the cursor was from the target. But the
difference in force measures were relatively small (for me) when the cursor was at
different _far_ distances from the target. This was not true of me but not of the
model. Indeed, there were occasions when I exerted somewhat _more_ force
(acceleration) when the cursor started, say, 50 rather than 75 units from the
target. So, averaging over trials, it would be possible to observe a higher mean
force at the smaller distance (error) rather than the larger distance.

So the jury is still out on whether such a "positive" approach gradient actually
exists. It may be that the results obtained by Brown are, indeed, measures of a
component of a non-linear error curve. But I think they are more likely to be a
statistical artifact. I bet the error curve does max out at a certain distance
from the goal -- possibly around 30 cm or so; that's nearly three feet. So what
Brown was measuring was two point on a horizontal line. I bet if the experiment
were repeated (using the data from individual rats, of course) with force measure
taken at 20 10 and 5 cm from the goal the force measures at 10 and 5 cm would be
_much_ lower than the ones at 20, 30 and 170, the latter two probably being
nearly the same.

Best regards



Richard S. Marken
310 474-0313