International Encyclopedia of Systems and Cybernetics

The limit of a system's size, either inferior, or superior, which impedes its survival.

Any system, individual or social, has size limits: a minimum one below which it cannot organize itself and a maximum one beyond which it is not anymore able to sustain itself.

These size limits are defined by various interconnected conditions, namely:

SIZE (Minimum accretion)

Systems need a minimum number of coordinated elements in order to acquire sufficient variety by their possible interactions.

M. BUNGE calls this the "treshold size" "below which the aggregate does not form a system" (1979, p. 37).

Only when a critical mass is obtained does the system-forming process become able to dominate centrifugal forces or to polarize the uncoordinated behavior of free elements. For example, according to D. GORDON: "The size of the (ant) colony determines the number of interactions between individual ants, which results in a change in the dynamics of the colony" (1995. p.55).

A satisfactory surface-volume relationship: This necessity has been explained in a quite exhaustive manner by d'ARCY WENTWORTH THOMPSON in his great classic "On Growth and Form" (1916-1952, p.22-27) (in the chapter "On Magnitude").

From a systemic viewpoint, each form of organization implies a specific interrelation between invironment and environment. As the environment grows, the inputs of the system must grow proportionally and this increasingly taxes the environment, as well as the more or less permeable boundary. As for similar shapes the surface increases as the square when the volume does it as the cube, there is a definite limit beyond which the interfaces between the system and its environment is not anymore able to provide the system with sufficient inputs.

Density: A minimum density is needed for the system to be coherent, lest communication becomes too difficult and costly, or even downright impossible. However, when density turns excessive, communication becomes blocked by the sheer crowding effects in space and time.

M. RIDLEY emits the hypothese that, for human beings, there is a "natural group size" of about 150 individuals.

This is roughly "… the number of people in a typical hunter-gatherers band,… in a typical religious commune,… in the average address `book,… in an army company……

It is, in short, the number of people we each know well" (1996, p.69).

Once over this natural size, the organization of the group could show a lessened fitness. This could lead to the necessity to integrate various groups into a wider supergroup, i.e. lead to emergent hierarchy.

It would be interesting to research this model as a general systemic condition in other types of groups, as for instance, networks of neurons in the brain, or networks of participants in an Internet site.

Communication rate: The coherence of a system depends on a communication between elements and subsystems at a rhythm sufficient to maintain their interactions.

The communication time is directly proportional to the media's velocity and inversely proportional to distances. The first factor, may compensate the second one: Modern telecom munications are quickly "shrinking" the world. Regulation and control cost: As a system grows and differentiates, the interrelations between its elements and subsystems must be growingly monitored and regulated in order to avoid internecine conflict. Moreover, complex systems tend to need and built hierarchies and pyramidal controls, which absorb a growing part of the available resources.

When the cost of regulation and control becomes overtaxing, the system finds itself exposed to self-destruction by sclerosis.

Moreover, an old or aging system loses much of its adaptability which causes communication and control problems. As a result, while its size remains unchanged, it may become unmanegeable.

M. BUNGE relates the maximum possible size with a number of components "above which the system breaks down" (1979, p.37).

Ian I. MITROFF and Harold A. LINSTONE explain: "… all processes have an upper limit to their efficiency. At some point bigness boomerangs on itself. Instead of leading to greater end benefits, it produces negative end effects. These negative benefits are almost impossible to foresee and go completely counter to the hypothetized benefits of bigness" (1993, p.13).

Limits to size is thus a general functional and structural rule.