[From Bruce Abbott (961127.1135 EST)]
Bill Powers (961126.0800 MST) --
Bruce Abbott (961126.0825 EST)
Other schedules (e.g., interval schedules) do not promote such high rates.
Fixed interval schedules produce a characteristic acceleration from low to
high rates that has been characterized as the "fixed-interval scallop"
because of its appearance on the cumulative record. The rate reaches its
peak as the fixed interval elapses. Thus observation does not support your
hypothesis that a high fixed rate of presses will occur regardless of
schedule.
I know that is what the traces on a cumulative record look like. I would
like to see what the rats are actually doing. After a reinforcement, and
after the collection time, do they sit before the lever, reach out, and go
tap ......... tap ........... tap .......tap ..... tap..... tap... tap..
tap.. tap.. taptaptap? That's what the record suggests (and what your verbal
description suggests), but somehow I doubt that this is what the rats are
actually doing. I was fooled once with respect to the fixed-ratio
experiments; I had a completely wrong mental picture of what I would see in
the operant cage, which your videos cured me of. I don't want to be fooled
again.
Nor do I. But there are two ways in which an accelerating pattern of
responding can appear in a cumulative record. One is the way you describe
above. The other is to be spending a higher and higher proportion of the
time pecking at the key as opposed to doing something else. Either way it
is clear that keypecking generally occurs more often as the fixed interval
elapses, and that this is a characteristic of responding on FI schedules --
one that develops, by the way, only after the animal has had sufficient
experience with the schedule.
After the second reinforcement there is a
much longer flat part of the curve and the rise to a steady rate is more
abrupt. By the fourth reinforcement, the transition from no pecking to
pecking at a steady high rate is still more abrupt, and continues to be
abrupt until the end of the tracing in the Figure. Once the high rate
appears, it seems to continue at a constant value for several minutes
(several hundred pecks) until the reinforcer appears. Skinner describes
these tracings this way:"The overall pattern of performance on a 'fixed-interval' schedule is a
fairly smoothly accelerating scallop in each interval, the acceleration
being more rapid the longer the initial pause." He then adds, "Local
effects due to separate reinforcements are evident, however, which cannot be
discussed here for lack of space."Evidently, Skinner decided he was seeing smooth accelerations, and from then
on, no matter what the actual behavior of the tracing, he saw all
transitions as examples of smooth accelerations -- even when there was an
instantaneous transition from no pressing to pressing at a constant rate, as
in the sixth segment.
No, he didn't. Here is a different example, from a 1952 article. Skinner
describes the performance of a single pigeon on FI 5-min.
The organism adjusts with a fairly constant rate of responding, which
produces a straight line with our method of recording. The rate -- the
slope of the line -- is a function of several things. It varies with
the difficulty of execution: the more difficult the response, the lower
the slope. It varies with the degree of food deprivation: the hungrier
the organism, the higher the slope. And so on. It will be seen,
moreover, that such a record is not quite straight. After each reinforce-
ment the pigeon pauses briefly -- in this case for 30 or 40 seconds. This
is due to the fact that under a fixed-interval schedule no response is ever
reinforced just after reinforcement. The organism is able to form a
discrimination based upon the stimuli generated in the act of eating the
food. So long as this stimulation is effective, the rate is low. There-
after the organism responds at essentially a constant rate. It would
appear that stimuli due to the mere passage of time are not significantly
different to the organism during the remaining part of the interval. The
organism cannot, so to speak, tell the difference between, say, three and
four minutes after reinforcement under these circumstances. At longer
fixed intervals -- of, say 15 minutes -- each segment of such a record is
a smooth, positively accelerated curve.
Skinner, B. F. (1952). Some contributions of an experimental analysis
of behavior to psychology as a whole. _American Psychologist_, 69-78.
I should point out that this text appears within a section of the article in
which experimental manipulations are described that lend support to
Skinner's explanation for the observed changes in responding across the
interval -- he's not just speculating, but offers evidence to support his
proposal. In _Schedules of Reinforcement_, Skinner notes departures from
the usual pattern (including an occasional _decelerations_) and discusses
their possible origins. For Skinner, these departures needed to be
investigated and understood, not swept under the rug.
The "cumulative record" is a very poor way to present the data. Human vision
tends to read large patterns into it which aren't actually there on close
inspection. I would say that a much more accurate general description of the
curves would be "periods of no pecking alternating with periods of pecking
at a constant rate."
That description is correct, but does not bring out the larger typical
pattern, which is that the periods of pecking come to dominate over the
periods of nonpecking as the interval progresses. I would say that the
cumulative record is an excellent way to present the data: look at the
details you have been able to discern in it, while also getting a somewhat
more global view of the changes in average rate over time.
It is not that the rats undergo "massive reorganization" that brings this
about, either. It's just that the rats learn something about the delivery
of food that they cannot learn on the ratio schedule, having to do with the
time following the previous delivery at which another press will again be
followed by the arrival of a pellet.I doubt that rats are smart enough to learn that. Your interpretation
depends on seeing the cumulative records as a gradual increase in pecking
rate as the time of reinforcement nears. If that isn't the case, if the
pecking simply comes to a constant rate which is maintained until the food
appears, then a different interpretation is needed.
You'd be surprised what rats can learn. I'm not assuming a gradual increase
in pecking rate as the time of reinforcement nears -- I'm assuming a gradual
increase in the average pecking rate as the time of reinforcement nears,
which could emerge from either pattern described earlier. But let's not
bicker about it: it's an empirical question; if we want to, we can
investigate it later.
And you're "proving"
that your hypothesis is right by pointing to what _doesn't_ happen -- you
say the rat would press even faster according to the hypothesis, except that
it can't, which is why we don't _ever_ see the rat pressing faster as the
hypothesis demands. You're turning a total lack of evidence into evidence
for your proposal!
Poppycock! I'm not "proving" that my hypothesis is right at all, I'm only
describing the hypothesis, which requires the assumption of rate limitation
if it is to explain the observed constancy in rate. I would find this a
very unsatisfactory, post hoc _explanation_, but as an hypothesis it is
subject to empirical test. What I'm doing is generating alternative
explanations that further experiments can be designed to evaluate. In my
book it's the smart -- not dumb -- thing to do.
Ah, Darth, Darth, there are dark days ahead. The Emperor is using you for
his own evil ends. You must save yourself before it's too late. May the
Force be with you, too, my old friend.
We are closer together on these issues than it would appear from our
writing, Obe-wan; what others may see as a light-saber duel to the death is
in fact no more than a friendly bit of sparring. As for the Emperor, he's
really not such a bad guy once you get to know him, and did bring about some
positive changes in the Empire during his early years. It is not so much
that I remain under his spell as that I still find his approach and the
findings it produced useful from time to time for my own nefarious purposes.
Unfortunately, the Emperor became set in his ways, unwilling to move beyond
the formula that had served him so well in the past, and became an
impediment to further progress. Today the Emperor's functional attack-style
is no match for the devastatingly effective mechanistic attack of the Rebel
Alliance, and so his days are numbered.
May the Force be with us both, old friend,
Darth