*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 G_{o} is garbage out, G_{i} 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).

where COMSYS_{o} is the assignable system output value and COMSYS_{i} 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 S_{o}, where P indicates the length of
the procedural or programmatic involvement during system activation and
S_{o} is the significance of the output of the system activation
occurrence.

Most generally, the relationship between P and S_{o} is given by

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

where P_{r} is the length in time units of the procedural determinations
and S_{so} is the significance of the substantive output.
For a computer system (COMSYS_{p}), the applicable expression is

where P_{g} is the length of the program and S_{do} is the significance of
the data output.

P, whether interpreted as P_{r} or as P_{g}, 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 S_{i} 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, C_{i}, and rates of effectiveness, E_{i}, are, of course,
given by

and

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, E_{a}, is given
by the equation,

Apparent change, C_{a}, likewise, is given by

For either system, So, the measure of output significance, is limited
to values equal to or less than S_{i}.

or rewritten

where P_{g} is the length of the program and S_{do} 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 gamma_{1}, gamma_{2}, . . .gamma_{n} are the
effectiveness ratings of the individual operators, each of which must
be given in within the limits

for any operator, gamma_{iota}.
Together with equation (5b1), the exact expression for S_{o} of COMSYS_{p} 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 C_{rho} 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 P_{g} 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.

or

where P_{r} is the length in time units of the procedural determinations
and S_{so} 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 C_{nu}+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
(H_{r}COMSYS_{p}), ancient operational rules exist for human relationships to
committees (H_{r}COMSYS_{m}). 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.

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 COM_{theta} 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,

and

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.

1. There is an analogy between COMSYS_{p} and COMSYS_{m} (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 COMSYS_{p} may have an analogue in COMSYS_{m}, 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 COMSYS_{p} and
COMSYS_{m} 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 t_{IA} 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. t_{CRA} can be shortened in a number of ways. The most
likely is through a merger of COMSYS_{m} with COMSYS_{p}. 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 S_{o} = k (S_{i}/P), and since no COMSYS exists without a
significant P factor, the entropic limit, S_{o} = S_{i}, can never in
practice be reached. In fact, the opposite limit, S_{o} = 0, is the more
likely prospect. Moreover, not only does P affect S_{o} adversely, so too
does beta, as noted in equations (17) through (19). likewise, COM_{0}, or
its equivalent, COM_{theta}, is unlikely to be permanently achieved for two
reasons. First, no COMSYS, once in existence, ever goes out of
existence. Hence, COM_{0} 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 COMSYS_{m}, let there be a COMSYS_{p} assigned each member such
that

a. each COMSYS_{p} is equipped with identical machines and languages;

b. RROO is made part of the COMSYS_{m} and the COMSYS_{p};

c. every computer of COMSYS_{m/p} (merged COMSYS_{m} and COMSYS_{p}) is
interactive.

2. Let operational rules 3 through 7 be programmed into every computer
of COMSYS_{m/p}.

3. Let each computer memory of COMSYS_{m/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 COMSYS_{m/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.