Diachronic Analysis

Diachronic Analysis

(for French, click on the flag)

Starting from the fact that our model, presented in the "synchronic analysis" section, is able to describe every kind of game between a System in its whole and a part of it (an Actor), we will use this elementary model to build a multi-levels models, able to describe any multi-levels organization.
We will speak about "diachronic analysis".


  1. Two Levels Model :
  2. A 's freedom degree of the pilot's command set :
  3. S 's resolution degree as seen at pilot level :
  4. Definition of an application of A upon S at the pilot level:
    Control criterion of the Actor :
    Enslavement criterion of a System :
  5. Driving of Level 1 by Level 2:
  6. Transactions frequency :
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1/ Two Levels Model :

In the chapter about synchronic analysis, we review of all the different kind of transactions which can exist between A et S.
This review starts from the single perfect action (efficient action) between 2 players in a game with matrix gains and losses presenting an ideal strategy (presenting a "neck") up to the transaction failure, when the Actor cannot find a correct answer.
To overcome this failure implies a new definition of the states open to A and S.
We have seen, also, that a means for A to decrease his uncertainty is to reduce the number of states he takes into account to define the game between A and S.

We intent to show that a 2 levels Model allows :
  1. To decrease the uncertainty of the upper Level, by gathering the states of A and S
  2. To increase the efficiency of the lower level, when the upper level focuses their action.
We can schematize a Two Levels Model as follows :

This model is composed by 2 elementary "senaires" superposed, aligned following an oriented axis which indicates the system integration direction (counter-entropy axis).
We called :
pilot or command the Level 2 senaire
guided system, or enslaved system, the Level 1 senaire

2/ A's freedom degree of command set :

We take the hypothesis that both levels - master as well as slave one - follow the same logic pattern.
Each of them try to avoid undesirable states, and want to manage as far as possible his environment by means of the actions he has predetermined (i.e. they try to push S on a desirable state by means of one of the accessible states of A).

If the Actor succeed to define a neutral element (see synchronic analysis), then, every states sub-set of A is stable for Å.
Because each action is its self symmetric, every sub - set Hi = (a1,...., ak, e) of decisions (each one exclusive from the others) taken by A is a sub-group of (A, Å).

We can express (A, Å) as a sum of sub-groups in such a way that :

k is the freedom degree of A.


3/ Resolution degree of S at the pilot level :

On the same way, we can express S as a collection of sub-groups :

where Gi is a group of states which can be seen as very close, because, from the pilot point of view, there consequences are very similar.

r is the resolution degree of S at the pilot level.

4/ Definition of an application of A upon S at the pilot level:

A's willing to control the S's reactions, comes down, for the pilot to the search of an application of A's set of commands upon S's set of sub-groups:
We can, then, consider the following fonction F :

4.1/ Control criterion of the Actor :

A is able to manage S if :

F is injective because Hi ¹ Hj implies that resultant states are different (are not included on the same sub-group). So we have :

The command's freedom degree is lower than the system's resolution degree

4.2/ Enslavement criterion of a System:

S is enslaved to A if :

In other words, a system is enslaved if we are sure to have one command able to put S in any of its potential states.
The function F is surjective, so :

We can enslave a System, when the freedom degree of the command set is higher than the resolution degree of the System
This is the "requested variety" principle (in French : principe de "variété requise").
To continue our presentation, we will consider the case where S is both enslaved and under control, i.e. F is an application :
r = k


5/ Driving of Level 1 by Level 2 :

We can complete our 2 Levels Model on the following way :

at Level 2 :
The pilot takes only into account the sub-groups of A & S

at Level 1:
A pole is brought down to Hi and S pole to Gj:

Usefulness of a pilot level is double :
  1. Limiting the potential states that A have to take into account at Level 1 to Hi, the pilot increases the efficiency of the elementary actions. The action of A is more accurate.
  2. On the same way, restricting the description of S to Gj the pilot decreases the uncertainty for both Level 1 & 2, by limitation of the number of situations the Actor & the Pilot have to think about (see stability and information)

We call "strategy" the action of the upper level, and "tactic" the action at the lower one.
When the reaction from S is not within the sub-group expected by the pilot, the elementary transaction cannot be concluded, and we face a catastrophic situation, as yet defined (refer to synchronic analysis).
In order to finish the transaction, the pilot, at the upper level, have to define a new strategy, that means he has to choose another G and H.

6/ Transactions frequency :

When, at the tactical level, there is no interruption in the transactions flow, there is no necessity for the pilot to interfere on it.
As the Pilot works only to correct the lower level, then, its action is just requested when a "catastrophe" happens.

Consequently, the transaction frequency is decreasing when we go up on a hierarchy.

Our model can be developed with as much levels as necessary.
In such a multi layers model, we will characterized each synchronic level by its transactions frequency and present a theoritical relation defining the variation of these frequencies from one level to the other.

With this relation, it is very easy to point out a hierarchical dysfunction in an organization, just by the measure of the transactions frequencies variation along the hierarchical structure.

Just to illustrate our purpose, let us imagine a 3 levels hierarchy.
It is very common to observe two different kind of dysfunctions :
  1. If the intermediate level is not efficient enough in its job, it cannot pilot correctly the lower level which is too much times in a "catastrophic" situation in front of its environment.:
    This intermediate level have to correct very often the crisis occurring at the lower level.
    In other words, the transactions frequency of the medium level will increase.
    The medium level will evolve to the bottom of the hierarchy.
  2. In the reverse, the medium level could see itself more important has it is, an slow its transactions frequency. Medium managers want to play in the higher stage. They want to reach the clouds.
    In that case, the lower stage can stay too long time without any indication when it faces "catastrophic" situation in front of its environment.
    This is a very common case of dysfunction occurring in the army, with a big gap between the staff headquarter and the operational line.
It is easy to understand that a pilot, working only when its subordinates are in trouble, can manage several process in parallel. As a consequence of the frequencies decreasing rule, the number of people on each level must decrease from the bottom to the top.

Such an organization is of "pyramidal" type


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To come back to our introduction, our intend is greater than this :
the senaire model can describe any transaction, included the links of the Observer and his observation., or those of the Observer and his colleagues, when he explains his theory or reports an experiment, (including the present theory itself of course).

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page updated on 25/01/2000
author : Alain SIMON
© copyright 1998 Alain SIMON
adresse : isa.al.simon@wanadoo.fr

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