Replying to LO21375
LO21272 (The Digestor, At de Lange)
LO21315 (The Digestor, At de Lange)
LO21463 (Language, Obfuscation, Steve Eskow)
LO21482 (Language, Obfuscation, John Zavacki)
LO21485 ("Junk" Science, John Gunkler)
Greetings LOrs!
Greetings At, Steve, John Z., and John G.,
First of all, At - Thank you for taking the time to articulate Ostwald's
digestion and making connections to evolutionary changes. I especially
wanted to thank you for the effort you made to make explicit the role that
the essentialities play in determining the possibility of a new level of
order emerging from a system that may have used its free energy for one
level of organization and may now be rich in free energy for another path.
I am still not fluent enough in the essentialities to make these
connections on my own.
Winfried Dressler,
Greetings to you also! I also wanted to thank you for the time that you
have taken in some of your recent postings to articulate your reaction to
the Digestor model. The issues and questions that you have raised did
much to help me as I wrestled (diversity of becoming) with these ideas.
In LO21272, At wrote,
>Obviously, up to now the Digestor is only valid for the competition
>between crystals in the inanimate world. Thus we may have to speak of
>it as the Crystal Digestor. Rather than looking for digestors in all
>hierarchies and establishing the validity of each one, we will simply
>consider one in one of the highest levels of human affairs, namely
>education. In other words, we will accept the bridge between the
>material and the abstract world. We will call it the Educational
>Digestor. We will then observe how apt the correspondence is between
>the crystal and the educational digestors. Von Bertalanffy has
>already anticipated in general systems theory how important such
>correspondences (isomorphisms, adjunctions, metaphors) will become.
>Chomsky and Prigogine (1980) are also very sensitive to this problem.
...snip...
>Such descriptions are not only possible, but are also metaphorically
>sensible.... Once we make sure that this isomorphism
>(correspondence, adjunction) does make sense, we have established a
>powerful categorical identity (see the essentiality sureness.) We may
>then speak of Digestors in general rather than typical Digestors such
>as the Crystal Digestor or the Educational Digestor. Furthermore, we
>also have a new way of introducing and understanding dynamical
>quantities such as enegry E, entropy S and free energy F, originally
>refering to the material world of brain, to the abstract world of mind.
At, again I have to thank you. Your attempt to draw the parallels between
entropy production and the world of the mind have opened up a new level of
understanding for me. The parallels that I have been able to see between
the mechanisms of the physical world and behavior have been for me an
extraordinary source of energy - to the point where I feel almost
obligated to share the thoughts that I have with others so that they may
experience what I have been able to experience (and give me feedback on
these ideas, so that my learning may continue).
Prior to the past six months or so, I felt as if I had nearly reached
equilibrium in my own thinking about behavior, organizations, and
learning. As I have experienced it, I had reached a state of equilibrium
where the free energy for further organization at that level was almost
depleted. But, unbeknowst to me, the free energy for a new level of
organization was plentiful. By connecting (essentiality fruitfulness)
with the thinking that you and others on the list have shared, I have been
able to experience emergences of thought that I may never have had on my
own. At times (like recently) the postings have been filled with so much
new food for thought (producing entropy at a very high rate), that I have
almost felt overwhelmed trying to absorb it all. Not that I haven't been
able to understand the ideas (the dialogue has been at a very high level,
but very clearly communicated), but rather because of how it impacts and
informs my understanding of organizations and behavior.
Greetings Steve, John Z., John G.,
Obviously, you do not share my enthusiasm for the extension of these ideas
into the world of the mind as At has been advocating. I will admit that I
initially had similar views as I began thinking about these ideas. For
example, I was not overly impressed with Meg Wheatley's book, Leadership
and the New Science, because I could not determine which of her
metaphorical conclusions and points were "obfuscation" and which were of
some value. I think that some of the more recent works in this areas have
been of greater value (for example, The Complexity Advantage, by Susanne
Kelly and Mary Ann Allison, I found to be much more useful and
purposeful), but there is still a great deal of ambiguity and uncertainty
(at least) as to how these ideas will impact our understanding of
organizations. I do not think that this is the same necessarily as
obfuscation. I think that it is too early to tell which is the case at
this point regarding these ideas. However, I feel certain that these
ideas are worth investigating.
After reading through At's description of the Ostwald Digestion model,
particularly the equation that you presented for the change in free
energy, and giving it some thought, I think that there are some very
strong parallels to systems of behavioral energy that may be worthwhile to
add to the dialogue. and might serve to validate these ideas in an area
that is not nearly as far afield of the study of organizations as the
ideas that At, Leo, and Winfried have been sharing. In vein, I would like
to continue to articulate the parallel relationships that I see between
systems of energy in the physical world and systems of behavioral energy.
I would like to start off this contribution by introducing the work of
Richard Herrnstein (who is now deceased), and his matching law for
behavior. Richard Herrnstein was a behaviorist (in the Skinnerian
tradition) who many (in the world of behavior analysis) consider to have
made nearly as large a contribution to behavior analysis as Skinner
himself did.
Herrnstein was able to show in numerous settings and contexts that the
probability of a given behavioral response was directly related to the
availability of reinforcement for the behavior (in relation to the
availability of reinforcement available for competing behavioral
responses). This relationship that he articulated and demonstrated has
been replicated by many other researchers as well, and forms the
foundation of much of what I have written about over the past 6 months.
Herrnstein's matching law, in its general form, can be expressed in the
following equation:
Pr(A) = k( Ra/Ra+Re )
Where
Pr(A) = probability of behavioral response A
k = highest # of possible behavioral responses available (total # of responses)
Ra = Reinforcement experienced for response A
Re = Reinforcement experienced for extraneous behavior (behavior other
than the response of interest)
This relationship, has been reliably demonstrated to account for over 90%
of the variance in responses. One point of interest, this relationship is
not necessarily a reinforcement maximization rule, and, at times, will
predict patterns of behavioral response that are counterintuitive.
In order to further explain, allow me to illustrate the matching law first
in the simplest of settings. The simplest expression of the matching law,
modeling a choice between 2 possible behavioral responses, is as follows:
Proportion of responses on A = Responses on A/ (Responses on A + Responses
on B) = Reinforcements on A/(Reinforcements on A + Reinforcements on B
or
Pr(A) = Ra/Ra+Rb = rA/rA+rB
[Host's Note: Hmm... I think there should be (..) in the denominators here
and in the similar fractions below? ...Rick]
giving us the proportion of responses which will be accounted for by
response A.
To give an example, we can place two schedules of reinforcement against
each other and see if the relationship expressed in the equation holds
true (it does). So if we had a constrained choice between two equivalent
responses A and B, with choice A being reinforced on an VR3 schedule, and
choice B on a VR6 schedule (see LO20774 for an explanation of schedules of
reinforcement), we can plug these values in the equation and see what
split of responding might be expected.
Pr(A) = (1/3)/(1/3)+(1/6) = .667
So we would predict that choice A would be preferred over choice B by a
ratio of 2:1 (choice A would be chosen 66.7% percent of the time). And,
as it turns out, this is very consistent with what has been demonstrated
empirically. Notice that the prediction isn't in line with a maximization
prediction which would predict that Choice A would receive all of the
responses, resulting in the maximum possible reinforcement.
Another example: Choice A on a VR4 schedule and Choice B on a VR11
schedule
Pr(A) = (1/4)/(1/4) + (1/11) = .25/(.25 + .09091) = .733331
or, Choice A would be chosen 73.3% percent of the time and Choice B chosen
the remaining 26.7% of the time.
This first example allows us to see that the relative frequency of
reinforcement given a response is an important dimension in understanding,
and even predicting, behavior. This is the source for my assertion that
the first dimension which effects a consequences ability to act as a
reinforcer for behavior is the probability (or certainty) of the outcome
to result given the behavior.
One way that this variable can be "controlled" is to change the schedule
of reinforcement, given equivalent responses (for example, in many lab
experiments of the matching law, this has taken the form of bar pressing
behavior for rats and key pecking for pigeons, with each of two different
bars or keys with differing schedules of reinforcement available for
pressing or pecking). However, this variable also gives us a means for
capturing the effect of the relative effort required to perform the two
competing responses. A response requiring greater expenditure of effort
than a competing response, when placed on an identical schedule of
reinforcement, will respond similarly to an identical response placed on a
"thinner" schedule of reinforcement. This line of thinking moves us in
the direction of the flow of units of behavioral energy required to attain
the reinforcer.
But this isn't the whole picture. Another characteristic that impacts the
ability of an outcome to reinforce is the delay of the reinforcement from
the time of responding (we can't forget the decay of delay). In my
previous discussion of the impact of delay, I mentioned that the decay is
not a linear one. Research using the matching law suggests that relative
frequency of responding matches the reciprocals of the delays (given that
the delays are expressed in the same units of time).
Pr(A) = Ra/Ra+Rb = (1/Da)/(1/Da)+(1/Db)
To illustrate, lets consider an example where 2 equivalent responses, A
and B, are both on an equivalent schedule of reinforcement, but, with
Choice A, the delivery of reinforcement (occurrence of the outcome) is
delayed by 2 seconds, and, with Choice B, the delivery of reinforcement is
delayed by 4 seconds. In this situation, we have the following:
Pr(A) = Ra/Ra+Rb = (1/2)/(1/2)+(1/4) = .5/(.5+.25) = .667
Again, according to the matching law, we see that Choice A is preferred
over Choice B 2/3 of the time. And, again, if we were to test this out,
this is essentially what we would find.
The third dimension which effects the ability of a consequence to
reinforce behavior is the magnitude of the reinforcer. In my discussions
of behavior to this point, I have brought up this dimension only in the
form of discussing whether the outcome is perceived to be positive or
negative by the performer. Actually, to be accurate, we would have to
consider to what extent the outcome is perceived to be positive or
negative, relative to the outcomes for other, competing behaviors. The
more positive the outcome, the greater its ability to attract the
behavioral response, and the more negative the outcome, the greater its
ability to repel the behavioral response. This dimension we could call
the magnitude of the available reinforcement (m), giving us:
Pr(A) = Ra/Ra+Rb = Ma/Ma+Mb
controlling for our other dimensions (holding them constant).
In order to illustrate this, we need to have some unit of reinforcement.
This is possible in a lab setting, but it becomes more difficult outside
of that environment (perhaps we might use some form of currency, but even
this relationship is not perfectly linear (perhaps it is on some kind of
logarithmic scale). For our example here, we can again contrast two
equivalent responses, A and B, on identical schedules (cancelling out),
with identical delays (again cancelling out), but with different
magnitudes of reinforcement. Choice A gets reinforced with 2 units of
reinforcement (for example, 2 food pellets, or 4 seconds of pleasureable
electrical stimulation), while choice B gets 1 unit of reinforcement (for
example, 1 food pellets, or 2 seconds of pleasu reable electrical
stimulation).
We would then have the following:
Pr(A) = Ra/Ra+Rb = 2/2+1 = .667
Again, Choice A is preferred 2/3 of the time over Choice B. And we have
the source of the third dimension of a consequence that effects its
ability to reinforce/attract a behavior that I have articulated in
previous posts, the extent to which the consequence is seen as positive
(or, in the case of punishing/repelling, negative). This constitutes the
magnitude of the consequence.
So we have the following three dimensions:
1) A measure of effort in the form of the frequency of reinforcement given
a response (the probability/certainty of reinforcement.
2) The delay of the occurrence of the reinforcement from the occurrence of
the behavior
3) The magnitude of the reinforcer (extent to which it is perceived as
positive or negative).
Giving us the following equation for the matching law given 2 competing
responses, A and B:
Pr(A)= Ra/(Ra+ Rb) =
(rA*(1/Da)*Ma)/(rA*(1/Da)*Ma) + (rB*(1/Db)*Mb)
The matching law was originally articulated in sometime in the 50's or
early 60's, and has been the focal point of an enormous amount of
research. I have tried to illustrate the relationship by providing
examples of its application to 2 competing responses. However, the
research that has been done regarding the matching law has not been
limited to 2 choices, but has extended the relationship to many competing
choices with similar success. And the application of the relationship has
been explored in areas far outside the animal lab, including consumer
choice behavior in internet shopping. The system becomes more and more
complex as we extrapolate into "reality", but the relationship has
continually demonstrated its utility (does this make me a pragmatist? ;-).
Using the matching law, we can then begin to apply the lens to the world
around us and seek to understand many behaviors that are seemingly
"irrational" (which I would propose falls closely in line with a
reinforcement maximization model, as opposed to a matching model).
I hope that I have been able to demonstrate that the ideas conveyed in my
posts over the past 6 months have not been made up by me (I am not nearly
this imaginative), or pulled out of a hat, but rather are based on 50+
years of research conducted by many different researchers in many
different contexts. Most of the information that I have shared regarding
behavior analysis can be read for oneself in any graduate level text on
learning and behavior (should you be curious). If anyone has spotted any
problems with my articulation of these ideas and concepts, please let me
know.
This brings us back to the general form of the matching law that I
originally stated:
Pr(A) = k( Ra/Ra+Re )
and the Digestor model that At articulated in LO21272 in the form of free
energy:
/_\F(un) = -/_\n*mSU*[E(mSY, Msy) - E(mSU, Msu)]
where
F = free energy
n = basic building blocks of system (ion pairs)
m = size of the crystal - quantitative summary in units of lowest orders
of the surroundings (e.g., the number of ion pairs - the basic building
blocks - that have been digested by the crystal, making up its size). The
variable m is expressed in n units.
M = qualitative assessment of the perfection of the lattice structure/the
regular pattern of arrangement of ions in the crystal.
E = energy
I would propose that the matching law is the equivalent of the Digestor
model as it would apply to behavior with the following "translation":
The variable n, in the translation, is the variable k in the general
matching law equation converted into units of behavioral energy (the basic
building blocks of the system of behavioral energy).
The variable m is the proportion of behavioral energy allocated to the
various potential responses (attracted by the competing "crystal seeds" -
mSY and mSU), or the measure of the size of the "behavioral crystal".
The M variable for behavior is a perfection measure of the "bond" between
the behavioral response and its consequences, consisting of the three
dimensions that I have articulated above - ratio of reinforcement to
response, delay of reinforcement, and magnitude of reinforcement.
The combination the m variable and the M variable for behavior form the
Madelung forces which attract behavioral energy towards a potential
response (yes, this explanation is a bit teleological). On an individual
level, the consequences/reinforcement for a given behavioral response form
the "sy" portion of the equation, and the consequences for all other
potential responses (the extraneous reinforcement in the matching
relationship) form the "su" portion of the equation.
Or maybe the Digestor model is the matching law for behavior extrapolated
to the world of crystallography. Is this obfuscation? IMHO, I don't
think so. In both cases, the relationships were uncovered independently.
Which relationship was "discovered" first? What should we do with this?
IMHO, the efforts that At has made to show the difference between
spontaneous changes and nonspontaneous changes and empowered systems, the
attempt that Leo Minnigh made to illustrate how the digestor model might
be applied in an organizational setting (LO21360), and the wrestlings of
Winfried Dressler to reconcile the model with his own thinking are, at the
very least, excellent examples of the learning process that we have been
able to witness, and, at most, important forays into a world that may have
enormous impact on our understanding of organizations, learning, and their
interaction.
With the Digestor model/Matching law, we have a lens through which we may
understand evolutionary change that results from low entropy production in
systems close to equilibrium. We have a lens for understanding CONTINUOUS
changes and improvements. With the Brusselator model, and the parallels
that I have attempted to convey in the relationship between behavior and
its consequences, we have a lens for understanding DISCONTINUOUS,
revolutionary changes and improvements that result from high rates of
entropy production in systems far from equilibrium. To bring this home to
roost with a thread from months ago, these models together give us a means
for understanding the process of CONTINUAL improvement (advocated by
Deming). We really haven't gone that far off the course set for us by
Senge, Forrester, Deming and others. But we are extending the line beyond
what has been drawn before.
Which begs another question: At what point does
generalization/extrapolation of any theory become obfuscation? I'm not
sure that the conclusion can be drawn with foresight. As far as I can
tell, the difference lies in the utility of the model. Maybe after the
fact this differentiation can be made, but if we are indeed after the fact
in this case, and these ideas have been conclusively disproven, please
show me where the evidence is so that I can quit wasting my time.
Hypotheses generated by the theory/model must be articulated in a way that
they can be tested and disproven. From what I have read on both sides,
these ideas have withstood much rigorous examination and been shown to be
robust. I am not an expert in the physical sciences. The Ph.D. that I
hold is not in physics, or chemistry, or biology. But I have read
numerous texts on chaos theory, relativity, quantum physics, and 3 books
by Ilya Prigogine on thermodynamics, entropy and entropy production. The
accounts that At has given of these ideas are representative of what I
have read in these other sources. I have read numerous works by Skinner
and Herrnstein and numerous other behavioral theorists. I have read
Senge, and Forrester and other systems thinkers. I believe that if anyone
else has studied in these areas, they would vouch that my portrayals of
these areas are representative as well.
I, for one, find these parallels to be compelling, and I have invested a
considerable amount of time articulating the connections that I have made
for others to examine. To me, the obvious next step is to see how much
further the model can be extended. Is this really a step into oblivion?
Regards,
Jon Krispin
--"Jon Krispin" <jkrispin@prestolitewire.com>
Learning-org -- Hosted by Rick Karash <rkarash@karash.com> Public Dialog on Learning Organizations -- <http://www.learning-org.com>