Learning Curves and Free Energy considerations on them. LO30802

From: Richard Karash (Richard@karash.com)
Date: 11/24/03

Replying to LO30786 --

In At de Lange's recent essay, I placed two graphics on the web page
and inserted URLs for them in the message.

However, I overlooked a third graphic... Here is the last part of At's
message with the URL for the graphic.

Sorry for the mixup.

   -=- Rick

.. snipped most of the original message...

>But when some more of one of the products is added to the reaction,
>the opposite happens. Look at the third, inner, right hand graph. It
>is like lifting the RH which holds the string. Note how the minimum
>point (equilibrium) of the string shifts to the left, stopping at a
>25% progress. However, when removing some of one or several of the
>products of the reaction, the converse happens. Look at the fourth,
>outer, right hand graph. It is like lowering the RH which holds the
>string. Note how the minimum point (equilibrium) of the string again
>shifts to the right, stopping at a 80% progress. In other words,
>adding a reactant or removing a product have the same effect --
>shifting the equilibrium to the right.
>Let us now return to the free energy graph of mastering a topic such
>as in the middle graph of figure 1. This graph is reproduced in the
>upper, outer, left hand graph of figure 3.


>Let us now think of a complex topic which consists of four topics A,
>B, C and D. An example which many of you fellow learners experienced
>in this list, is irreversible self-organisation. Topic A would then be
>the definition of entropy. Topic B would then be the production of
>entropy by force-flux pairs. Topic C would then be the derivation of
>the concept free energy. Topic D would then be the optimisation of
>free energy in living systems by following as organising path the
>punctuated equilibrium.
>Look at the upper, outer, left hand graph of figure 3. In the
>objective of topic A some properties are taken (as reactants) from the
>world of experiences of a learner and combined to define topic A. (For
>example, should the topic be entropy, the properties temperature and
>heat will be used to define it. Most people will have sufficient
>experiences of temperature and heat to define entropy.) Within topic A
>these experienced properties result in new properties of which the
>learner has little, if any, experiences. Thus the learner still has to
>seek experiences in these new properties. Let us call them
>unexperienced properties.
>Next to this graph is the upper, inner, left hand graph. In this graph
>some of these unexperienced properties are combined together with
>others into topic B. They result within topic B into even more
>unexperienced properties. In other words, topic B is experentially
>alien to the learner from its beginning (the formulated objective) to
>its end (the mastery of the objective). The same for topics C and D.
>However, most importantly, topic B is presented as if it has little to
>do with topic A. Furthermore, since topic B is not backed up by
>experiences, it has to rely on the learner's mastery of topic A. But
>since the learner is neither aware of this connection nor concerned
>about it, he/she has to begin with much less mastery and thus free
>energy of the outcome properties of topic A serving as input to the
>properties of topic B. Consequently, the free energy of the LH side of
>topic B lowers, shifting its equilibrium to the left (40% progress).
>What will happen when the learner is aware and concerned that topic A
>and topic B are tightly linked? Compare the upper graph to the outer
>left with the lower graph also to the outer left. The upper graph
>shows a progress of 65% whereas in the lower graph the progress
>increased to 83%. Why? In the lower case the unexperienced properties
>of topic A have been used in topic B. It is like removing the products
>of a chemical reaction A by using them as reactants in a reaction B,
>thus shifting the equilibrium of A to the right. Note how the free
>energy of the mastery of topic A is lower in the lower graph than the
>upper graph, resulting in this shift of the equilibrium to the right.
>Now compare the upper graph to the inner left with the lower graph
>also to the inner left. In the upper graph the progress stops at 40%
>whereas in the lower graph it stops at 70%. Why? In the loose
>(unlinked) case the unexperienced properties produced in topic A are
>not added to the defining properties of topic B. Hence the objective's
>free energy of topic B (see left axis) is lower in the upper graph
>than the lower graph. It is like removing the reactants of a chemical
>reaction B by not supplying them as the products of reaction A, thus
>shifting the equilibrium of B to the left.
>Should we compare all four upper graphs with their counter lower
>graphs, the decrease in progress is profound. In topic D, not linked
>to topics C, B and A, the upper graph shows a progress of only 10% at
>D. But when topics D, C, B and A have been linked all together to form
>one complex topic, the lower graph shows a progress of still 52% at D.
>In other words, seeking for the wholeness among a number of related
>topics like A, B, C and D results in a far better progress for each of
>them than being ignorant to wholeness or unconcerned about it.
>I have observed this trend thousands of times when marking the tests of
>chemistry students. In these tests i always linked a number of topics
>together in one problem with subproblems for each topic. The solution to
>subproblem A is needed as data to solve subproblem B, etc. I used to
>call the complex problem a "moncat" problem. Here the "mon" and the
>"cat" are derived from wholeness and sureness which are two of the 7Es
>(seven essentialities of creativity. In those days i described them as
> sureness ("identity-categoricity")
> wholeness ("monadicity-associativity")
>But presently i prefer the description
> sureness ("identity-context")
> wholeness ("unity-associativity")
>The progress of students who had an affinity for sureness and
>wholeness was much better than for students who did not care for them.
>In fact, their progress was so extraordinary that they left the others
>behind to form a "bell curve" of their own in front of the "bell
>curve" for the other students. Perhaps most striking was their
>enthusiasm for chemistry and its complex topics. This enthusiasm is a
>sign of their free energy after they have completed a complex topic.
>This is shown by the endpoints of each of the last three lower graphs
>which are higher than the endpoints of their corresponding upper
>When did i became aware of this trend in performance curves? As a
>student (1964) in chemistry 2 i was intrigued, but also horrified, by
>a certain complex problem in physical chemistry. It was the only one
>of its kind which i had encountered at university. In 1968, after
>having finished a MSc degree, i began to study this problem. It
>intrigued me more and more. In 1972, as a high school teacher, i began
>to design such complex problems myself. It is then when i became aware
>of this trend. However, i did not understand it until much later near
>the end of the eighties. I first had to learn a lot of irreversible
>self-organisation, especially in learning.
>As an application, think of giving a presentation of the five
>disciplines of a LO (Learning Organisation). When it is done such that
>wholeness is neglected and hence that they are considered as
>independent, the progress in the fifth disicpline presented will be
>profoundly less than in the first discipline presented. I would not be
>surprised should the whole audience be sleeping at the end of the
>presentation. But when they are presented as linked together to form
>the complex topic "managing the LO", the audience ought to be
>attentive up to the very end.
>With care and best wishes
>At de Lange <amdelange@postino.up.ac.za>
>Snailmail: A M de Lange
>Gold Fields Computer Centre
>Faculty of Science - University of Pretoria
>Pretoria 0001 - Rep of South Africa


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