From F=ma to the Hamiltonian I have glossed over 200 years of development in physics, several textbooks of explanatory material, and that which comprises several years of study for the aspiring physicist.  It is time to take a breather and ask what these equation mean.

Equations 8.13 and 8.14 imply

      .                                                     (3.19)

The key issue of interpretation in the real world centers on this equation.  The potential or its gradient, the force, is the basic cause and effect relationship.  It expresses the forces at work that cause a change in the entity relationship structure of an organization.  One way to view this is to think of each person within a society attempting to adjust his or her relations to increase want satisfaction.  Each person adjusts his or her relations such as to move from high potential to lower potential, or acts, as if, they were moved by a force toward relations that increase their want satisfaction.  (Note that I will make this more explicit when I discuss wants, mimetics, and decision making.)

The next step in Relation Dynamics is to apply individual human behavior to equation 8.19.  This will need to consider.

1. How the two potential gradients created by the wants dynamics of two persons interact.  This is to include
   1. the situation where what each person wants of the relation is different and even contrary,
   2. what a person will offer in the relation to attract the other, and
   3. how changing (or acquiring) the relation feeds back to the want satisfaction dynamics and thereby alters the potential gradient of equation 8.19)
2. How groups establish a potential gradient that interacts with other groups and individuals so as to attract some and repel others. 

For the most part these steps will be taken later in this document, however we can give, at least, a glimpse of what is involved.

The following diagram gives a graphical view of the systems relationship of selected parameters that depict 2-person interactions based on a given a set of wants, intelligence, and memes.  The diagramming technique is referred to as a Diagram Of Effects (DOE).  When we get to creating computer based simulations of organization behavior I will define the technique more formally.  For now what we require from the diagram should be intuitive.  There are two purposes of a DOE; 1) make the general relationship between system parameters more apparent and 2) aid in the creation of a simulation from a decomposition of some aspect of the real world into a series of algorithmic relationships.  It is similar in construction and purpose to electronic diagrams, both show how things are ‘wired’ together.  If the technique is not relatively obvious then it does not meet it’s purposes.  The boxes represent characteristics of some component of the system that is, at least in principle, measurable.   The arrows represent the direction of cause and effect.  The + signs and the – signs indicate if increasing the cause parameter tends to increase the effect parameter.  The numbers are simply notation referring to the algorithm that defines the cause-effect relationship precisely.  The colors are an aid to visualize the relationships.  In more complex diagrams it is often difficult to follow all of the interconnections. 

Diagram 8.2: Simple Person-Person Interaction without Other Entity Involvement

The diagram shows how 2 persons affect their shared relation distance.  There are 4 algorithms in the diagram.  Let us consider each from right to left.

Algorithm 1: There are two forces acting on the relation distance, one from each entity.  Each entity may be trying to increase, decrease, or leave it the same.  We make the simple assumption that the effect on the second time derivative can be combined by addition.  Note that each person acts only on his or herself to change the relation distance.  There is no mysterious attraction or repulsion.  Each person simply decides to act insofar as their ability allows in such as way as to change the relation distance to what they want of the relations.  They may both act to either increase or decrease the distance, or one may act to decrease and the other to increase. 

Replacing  with and with in equation 8.10 and noting that , and assuming that we can sum the effect of n and j on .  We have

,       (3.20)

where O is other factors.  As noted in the last section a  can change as a result of changes to other ’s.  For a relation to exist it is necessary that both persons spend time in the relation activity, thus if other factors prevent this the relation distance will increase.

I use the proportional symbol () because I have not addressed scale factors yet.

Algorithm 2: The efficacy or effectiveness of action depends on intelligence and memes known.  In these algorithms we are not concerned with specifics of what a person does.  Our focus is on the efficacy of that action, whatever it may be, to achieve wants.  I make the simple assumption that the efficacy is the product of intelligence, memes known, and time spent.  Additionally if anyone of these is zero then the change efficacy must be 0.

                                                                     (3.21)

Where   = i(jnk) or the intelligence of n for acquiring want k

            = f(njk) or the meme action fitness of n for acquiring want k with person j

            =t(njk) or the time spent on this relations.

Intelligence is not specific regarding the individual one is attempting to change a relation; whereas the acquired memes about that individual are important and clearly impact our ability to effect the relation.  Time spent is a constraint.  Time spent changing one relation implies less time spent changing or maintaining another relation.

Algorithm 3: Unsatisfied wants are simply wants minus want satisfaction.  In the following equation I assume that wants are expressed in terms of relation distances.

                                                (3.22)

Algorithm 4: Based on intelligence and experience a person’s meme action fitness will increase with time via an evolutionary search.  There are two types of experience; 1) that represented by the relation distance between n and j and 2) that represented by other experience.  Fitness can be expected to improve in the form of a logistics curve, thus we can write

,                                                          (3.23)

where F is the maximum value of the fitness function and  is a scale factor.

Diagram 8.2 and its associated algorithms are a simplification that is likely to occur rarely.  Most of the time person-to-person relations involve other entities.  This makes the application of the individual entity dynamics to a large ensemble somewhat more difficult than trying to track the individual movements of molecules in a gas.  In a gas we are generally only concerned with the effect of 2 molecule interactions.  We will find some occasions where tracking a single entity, especially where that entity is an organization, both useful and practical, however for the most part we will find the relation thermodynamic properties more useful. 

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(C) 2005-2014 Wayne M. Angel.  All rights reserved.