On Socio-Cybernetic Modeling

L. B. Cebik

Since the original private publication of this paper in the early 1970s, the work of refining the correlations between the entropic system pair that is the subject of the original work has proceeded to reveal an ever tightening cohesiveness to the fundamental premises of the study. Advances in computer hardware and programming since the 70s have permitted fuller realization of all of the facets and features of a committee system that have been categorized to this date (January, 1999). For example, as computer speed and storage have increased, programming (or procedural counterparts) have enlarged to fill the space and extend the time to its original limits and beyond. Ostensibly designed to speed results, the end result is often slower than with older, slower machines that somehow managed to get their work done. Likewise, the interactions of task-specific programming and the overall operating system reflect virtually all of the interactions of committees in almost any organizational hierarchy. Inter-committee and inter-program relationships--both beneficial and detrimental when viewed from a perspective of the goals of each--reflect more detailed correlations than were ever thought possible in the beginning. The list might go on indefinitely.

Therefore, it has seemed useful to make the original paper once more available to those interested in modeling entropic system pairs in a rigorous manner. Much research remains to be done, but here is where it began.

LBC, January, 1999

This paper presents the fundamental stages of modeling two equivalent entropic frames of reference. As with any paired frames, one may analogize from one to the other and back. This procedure proves especially profitable in developing suitable symbolic and mathematical models of computer systems and committee systems.

A simple example illustrates the principle. The notorious expression,

which translates for computer programmers as "garbage in, garbage out," may be expressed more rigorously as

where Go is garbage out, Gi is garbage in, and k is a constant of proportionality (as it will be throughout this exercise). The comparable, but non-equivalent, expression for a committee system is

where V means "any input." A little thought over the difference yields the realization that equation (2) applies to computer systems without reference to the operator. Since a computer system consists of one or more computers plus one or more operators, equation (2) is a limited subsystem case. A full computer system answers to equation (3).

1. Entropic Frames of Reference (COMSYS)

For either system (COMSYS), the equivalency of the output value equations leads to the conclusion that

where COMSYSo is the assignable system output value and COMSYSi is the assignable system input value. Moreover, equation (4) defines both systems as entropic frames of reference.

If the conclusion expressed in equation (4) is to hold, it must have consequences that are valid for either system. Consequences of the precise order required abound. Of most central interest for modeling is the relationship between P and So, where P indicates the length of the procedural or programmatic involvement during system activation and So is the significance of the output of the system activation occurrence.

Most generally, the relationship between P and So is given by

For each system type, there are closely related but separable interpretations. For a committee system (COMSYSm), the applicable expression is

where Pr is the length in time units of the procedural determinations and Sso is the significance of the substantive output. For a computer system (COMSYSp), the applicable expression is

where Pg is the length of the program and Sdo is the significance of the data output.

P, whether interpreted as Pr or as Pg, is essentially a time measure. The change of output significance, C, for notable periods of system activation is given by

where t is an applicable general time measure and Si is a measure of the input significance. The rate of change provides a measure of system effectiveness, E, and is given by

An accompanying graph (Fig. 1) provides an illustration of the results. Given an arbitrary significance of 1 to the input for any COMSYS activation, C and E will vary as shown. Besides the steep decline of efficiency in a short time, the net result is the leveling off of change and effectiveness at a level which approaches 0. Instantaneous rates of change, Ci, and rates of effectiveness, Ei, are, of course, given by


Real effectiveness (the rate of change of significance) and apparent effectiveness mirror each other. Graphically, this is shown in Fig. 2. Apparent effectiveness represents the measure assignable to the system self-appraisals of output significance, which is in no case to be confused with the self- or system appraisal of any individual element in the system. In general terms, apparent effectiveness, Ea, is given by the equation,

Apparent change, Ca, likewise, is given by

For either system, So, the measure of output significance, is limited to values equal to or less than Si.

2. Computer Systems Modeling (COMSYSp)

The general equations governing systems are subject to individual refinement. In the process of refinement, variations arise between expression appropriate to each system just to the degree that either a. the two systems are dis-analogous or b. the development of suitable categories is lacking. For computer systems (COMSYSp), equation (5b) holds, namely,

or rewritten

where Pg is the length of the program and Sdo is the significance of the data output. For real systems, this equation is modified by a measure of operator efficiency, epsilon, such that

where n is the number of operators and gamma1, gamma2, . . .gamman are the effectiveness ratings of the individual operators, each of which must be given in within the limits

for any operator, gammaiota. Together with equation (5b1), the exact expression for So of COMSYSp is

This equation, of course, provides a significance measure of the output of the special case including one and only one computer. Its limiting value is the instance (real or hypothetical) of a single operator with an effectiveness rating of 1, which forces the equation to the form

For rho computers which are interactive, the equation becomes

where all factors are as previously defined and Crho is the total possible combinations of computers.

Even equation (15) makes certain assumptions. First, it is assumed that operators within any given system are exclusive; that is, no operator forms part of a system with more than one computer. Interactive operators would require a correction factor within equation (15). Second, any necessary interaction programming is absorbed within the Pg measure for each computer. Precision in this regard would also require a correction factor. However, equation (15) will be sufficiently accurate for most purposes, and the derivation of corrective factors is left as an exercise for the reader.

The interactive computer super-system presents many difficulties for accurate modeling. For example, under some forms of standard programming, computers will assume data not in evidence. Different CPUs with alternate instruction sets, even operating under the same operating system, may do this without necessarily alerting the operator to the altered data. Variations occur due to differences both at the level of translating program language into machine processes and in the conduct of machine processes.

Without suitable correctives, the assumptions and the possible errors stemming from them complicate the evaluation of the output of a super- system. Analogously, members and subcommittees make similar operational variations which complicate the evaluation of a committee's output. Moreover, such members and subcommittees often make assumptions in the absence of data without informing either the chair or the hierarchical "user" (administrator, executive, etc.) of the committee.

The resultant errors are closely related to the concept set or language processed by the COMSYS, whether computer or committee. In complex machines with sub-units and multiple computing units (CPUs), the analogy to committees, with subcommittees and individual members--all active language users--is close to exact.

3. Committee Systems Modeling (COMSYSm)

For committees,


where Pr is the length in time units of the procedural determinations and Sso is the significance of the substantive output. More generally and as a limiting case,

However, committees, as previously noted, have both subcommittees and members. Thus, the limiting case is more precisely specified for real circumstances as

where beta accounts for subsystem activation.

where mu is the number of members, nu is the number of subcommittees, and the expression Cnu+1 represents the total combinations of subcommittees plus the committee as a whole. The final equation is thus

As with computer systems, equation (19) is limited by assumptions. If, for example, subcommittees have unique procedures of their own, a correction factor will be needed within equation (19). This derivation is left to the reader as an exercise.

The nature of the correction factor will depend in part upon the nature of the subcommittee procedural activities. Robert's Rules of Order (RROO) is the most common committee program. If used uniformly throughout proceedings of all subcommittees and of the committee itself, then a generalized accounting correction factor is possible for equation (19). If, on the other hand, special procedural rules are introduced into one or more of the subcommittees, two analyses become required. first, the effects of the deviant procedure on the subcommittee output must be evaluated. Second, the compatibility of the sub-outputs with each other--when produced under differing procedures--must be evaluated. Just as some deviants of the same program may turn out to be incompatible, so too may be outputs resulting from the use of variant procedures. The analogy of FORTRAN and RROO is more than accidental.

An interesting historical phenomenon is that although there exist no operational rules for human relationships to computer systems (HrCOMSYSp), ancient operational rules exist for human relationships to committees (HrCOMSYSm). This fact owes probably to the antiquity of committees and the recentness of computers. The more recent the development of a system, the more complex the rules, which is evident from a comparison of the operating instructions for a computer with its mix of procedural and relational matters and operational rules for committees.

Operational rules, of course, are imperatives often representing the accumulated experiential wisdom of a group and may be passed from one generation to the next in aural or written form. When distorted due to accident in the transmission or by virtue of motivated obscurity, such operational rules may comprise one core of magic and witchcraft. In more pure form, they undergird what has become modern science. To this day, we persist in calling them "laws."

Perhaps the most ancient extant operational rules come from a collection of sayings originating--or at least aggregating--along the Danube River. The following list is freely translated and updated in light of RROO.

Laws (Operational Rules) Governing Human Relationships to Committees

1. If asked to serve on a committee, refuse.

2. If forced to serve on a committee, be absent.

3. If forced to attend committee meetings, be silent.

4. If forced to speak, move for a termination of discussion.

5. If the motion to terminate is defeated, move to remand the issue to its source for action.

6. If the motion to remand is defeated, move for adjournment and/or disbandment.

7. If all else fails, leave the meeting on the grounds of having another committee meeting to attend.

The historical list of operational rules contains numerous additional rules,, laws, and advice, much of it ad hoc at first sight. for example, there is a cryptic note:

8. What you chair, you must sit in.

More problematical is the rule,

9. To be absent is to be elected,

which seems initially to contradict rule 2., unless interpreted as an implicit power which may force attendance. A recent (1970s) New Yorker cartoon has perhaps made the only significant summary contribution to this ancient list with its caption:

10. There are no great individuals, only great committees.

For socio-cybernetic modeling, perhaps the most mathematically interesting rule is 7. Whatever the case among those who created this aggregate of rules, in modern institutions, following this rule will never create ethical guilt for lying. It follows from adherence to this rule that the existence of some certain number of committees will have identical consequences of there being no committees, since the number will effectively preclude the conduct of business, indeed, preclude even strictly procedural activation. In the abstract, the equation for this situation is

For the real world, some finite time, t, is required even to record presence, convene, and adjourn. Therefore, there is an empirical equivalent of the abstract equation which takes the form

where COMtheta is a quantity of committees so large that the effective t allowable to each is less then the t required to convene, record, and adjourn, or

which thus defines the threshold for the maximum possible number of real committees.

The threshold condition leads to some interesting consequences, namely,


etc., or more generally,

This result may be of only historical interest for inter-cultural studies, since for any given time and place, there is one and only one number x such that x is theta.

4. The Future of Socio-Cybernetic Modeling

Every set of models must have empirical application if it is to have more than idle interest. The present case is no exception. The application of these models rests on certain fundamental principles.

1. There is an analogy between COMSYSp and COMSYSm (and any other COMSYS member). In other words, all members of COMSYS are equivalent entropic frames of reference.

Several points follow from this principle alone. First, every equation for COMSYSp may have an analogue in COMSYSm, and vice versa. In exact form, such equations will be equivalent. Thus, every extant relationship within one member set provides a potential insight into another member set. Likewise, every inexactitude in one member set may find a means of correction in another member set. Second, the analogy may be systemic rather than particularistic, thereby permitting individuality to the equations describing elements of the system.

2. Equivalent frames of reference are convertible.

Since what is herein modeled is an empiric reality, convertibility extends beyond the generation of conversion equations. There is, in effect, a potential for converted reality. Since both COMSYSp and COMSYSm are social realities with the same conceptual foundations, the possibility of merging adds itself to mere conversion. This fact makes possible the creation od scenarios of futuristic import.

For example, we earlier noted the limit theta to the possible number of committees. By principle 1, above, we should also seek an equivalent limit phi to the number of interacting computers. This limit may be a function of time tIA such that the addition of further computers does not permit passing beyond the ENTER-EXIT procedure into data processing. Future generations of computers may suppress the effect by increasing computer speed and by bypassing ENTER-EXIT procedures through common machine and program languages.

Such speed elevating procedures hold promise for committees in accord with principle 2. tCRA can be shortened in a number of ways. The most likely is through a merger of COMSYSm with COMSYSp. Thus, rather than requiring the physical co-presence of members, committees may convene via CRT terminals. Conference telephone calls already accomplish such ends. Computer terminals provide enhanced speed by automatically recording proceedings. Thus, the limit theta for committees can be increased by several orders of magnitude.

3. Every problem contains the seeds of its own solution.

The enhancement of the limit "theta" is close to reality. The next step, however, requires a review of the model equations set out herein. First, since So = k (Si/P), and since no COMSYS exists without a significant P factor, the entropic limit, So = Si, can never in practice be reached. In fact, the opposite limit, So = 0, is the more likely prospect. Moreover, not only does P affect So adversely, so too does beta, as noted in equations (17) through (19). likewise, COM0, or its equivalent, COMtheta, is unlikely to be permanently achieved for two reasons. First, no COMSYS, once in existence, ever goes out of existence. Hence, COM0 is unobtainable directly. Second, tactical gains in pressing the limit "theta" have appeared whenever needed throughout history. Hence, exhausting the mechanical gains of computer terminal meetings is not likely to exhaust theta.

The solution lies in a systems merger of a more complete sort. Systems merger would include the following steps.

1. For every COMSYSm, let there be a COMSYSp assigned each member such that

a. each COMSYSp is equipped with identical machines and languages;

b. RROO is made part of the COMSYSm and the COMSYSp;

c. every computer of COMSYSm/p (merged COMSYSm and COMSYSp) is interactive.

2. Let operational rules 3 through 7 be programmed into every computer of COMSYSm/p.

3. Let each computer memory of COMSYSm/p contain a large quantity of random discussion statements, key word selected by rapid scan of the preceding discussion statement in the meeting record such that

a. for any point of discussion, every system scans;

b. scanning proceeds from end to beginning, with the first to hit a key word being the next to discuss; and

c. in the event of identical timing, discussion goes to the memory with the longest elapsed time since its last recorded discussion.

4. Let all meetings occur via preset timing and system keying.

5. Let adjournment be a function of completion of business or of falling below a quorum due to other meetings.

6. Let the program and the procedure be as long as human intervention can make them, with all terminals dedicated in non-meeting hours to extending both and to automatically introducing extensions as meeting topics.

7. Let the "off" switch be removed from each terminal.

The immediate consequences of these procedures will be to place all matters of substance and action into the hands of individual humans. However, since COMSYSm/p would no longer require human relationship in order to function, there ought to be plenty of time to perform these simple tasks of substance.

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