[From Bill Powers (960215.0100 MST)]
Bruce Abbott (960214.1730 EST) --
Your treatment of the feedback function for variable-interval schedules
is the right way to do it -- as opposed to assuming that the loop is
open just because the slope of the function approaches zero.
If the operant is assumed to be emitted at a steady rate (not
too unreasonable on variable interval schedules), the feedback
function can be modeled as follows:
(1) R = 1/(1/B + VI)
(2) g = 1/(1 + VI*B).
Killeen offers this as the formula for the feedback function ( in terms
of interresponse intervals):
R = [1 - exp(-IRT/T)]/IRT
where T is the mean interval
I think your formula is an approximation of this, based on the series
expansion of the exponential; if so, it isn't a valid approximation for
all values of IRT/tau as it drops the terms with exponents greater than
1. You might want to plug this formula into your program to see if the
numbers change very much.
It would be very interesting to see where, on interval schedules, the
maximum of the R vs B curve occurs, in terms of the effective loop gain,
g. Keep in mind that we have not established the reason for the low
behavior rates at the lowest reinforcement rates -- whether the animal
is "emitting operants" at a steady low rate, or at a very high rate, but
interspersed with long periods of doing something else. It is possible
that the maximum of the R/B curve represents the point where a
significant proportion of the time is spent not pressing the lever but
engaging in other behaviors. If this turnover region tends to occur
where the loop gain has fallen close to 1 (or some low number), we might
have a regularity that will tell us something interesting.
You can estimate the output gain from the R/B ratio for the shortest
intervals. If it's the same as on ratio schedules, it would be fairly
high, 30 or more.
Remi Cote 960214.2230 EST
If control system are efficient they should evolve gradually in
cohesion with environment. How could we explain that control
system evolve to find themselve is unstable relationship with
environement, where they cannot control and yet survive???
I suspect that the higher levels of control in human beings evolved very
recently. This is why we are not very good at controlling perceptions at
these levels (just as the first birds were probably not very good at
flying). Homo Sapiens is still not very good at the "sapiens" part.
Other animals, which have much less ability at the levels of programs,
principles, and system concepts are not trying to control social
relationships or build social systems; their social systems are simply
the outcome of controlling variables at lower levels, and are not really
objects of control. And here I mean spontefaction: if something begins
to disturb the social system of an ant colony, the colony will not take
steps to oppose the disturbance and restore the system to its former
state. That is because ants _have_ a social system, but do not
_perceive_ it. So the social system is largely in the eye of the human
observer, who _can_ perceive social systems.
There must have been some drastic development in the brain that suddenly
gave rise to history -- to the deliberate recording of social events.
Perhaps it was just an invention, writing, but there must have been a
time when human beings, or proto-human beings, would have been incapable
of grasping the principle of writing or other forms of symbolic
communication. It's very interesting to try to imagine how the world
would seem without the higher levels of perception -- a world, for
example, in which specific logical procedures could be learned, but in
which no general principles could be perceived, and no system concepts
such as "society" could be comprehended. Or a world in which
relationships could be perceived and controlled, but not categories or
sequences. Somewhere in the process of evolution, these capacities must
have first developed. What was life like before they developed?
Me: If we are in all this jam about authority, confrontation,
conflict, murder, war, psychological trauma, high anxiety, it is
because we were allowed to be by a natural cause: fire. The chance
where 1/100000000 that a living control system meet this kind of
thing, and we got the winning ticket. Of course, if we had not get
the winning ticket we wouldn't have develop conscience to be aware
This is a chicken-and-egg problem: which came first, fire, or the
ability to control fire? Actually, vast numbers of fires occur naturally
every summer day without any human help, and this has probably always
been true. Even a single individual would have a very good chance of
encountering fire at some time; when we consider a population of
hundreds of thousands of individuals, it is essentially a certainty that
every generation would have many experiences with naturally-occurring
fires. So what is unusual is not an experience with fire; it is the
sudden thought that it would be nice to be able to make a fire occur
when one needed it instead of waiting for lightning to strike or looking
for an active volcano. To have such an idea, one's brain must have
evolved to the necessary level of complexity. And once that level of
complexity has been reached, it is not just fire that one would try to
reproduce, but EVERYTHING useful that previously occurred without human
intervention. The invention of fire-making methods is only a symptom of
a general new ability which would not be limited to the making of fire.
I think you are exaggerating when you see control as resulting in the
destruction of the human race. Don't forget that there are close to 6
billion of us now, and every other creature is at our mercy. My view is
that we, as a species, have developed some powerful new abilities that
other species possess only in a limited way, and that we are still
trying to learn how to ride this bucking bronco. One of our great
mistakes was to assume that we could control other human beings in the
same way we control animals, plants, and non-living objects. We can't
truly comprehend social systems until we see the difference; until we
realize that trying to control other control systems that have abilities
equal to our own simply can't work the same way.
Also, people's ability to comprehend ALL the consequences of their
actions is still very limited; or perhaps it would be better to say that
people have a limited comprehension of the fact that their actions have
consequences in addition to the ones they intend. So people tend to see
their worlds through small windows where only immediate effects are
considered, and less direct effects (in space and time) are ignored.
This is one of the reasons we have environmental problems, and why we
often progress from simple goal-seeking actions to world wars.
You are pointing out that control can have bad consequences. This is
true. But by pointing this out, you become part of the powerful forces
that are always at work to correct our mistakes. The human species is
actually trying to correct its errors, trying to learn to use higher
levels of control to its benefit instead of its detriment. If you get
too pessimistic about the future of the human species, you will forget
that there are many, many human beings who are trying to learn to deal
with these problems, trying to teach and influence others to deal with
them better. They don't necessarily go about this in the best possible
way, but the intention is there, and learning always happens.
I think that teaching control theory is one of the ways we can help
improve the higher levels of control in human beings.
Best to all,