International Encyclopedia of Systems and Cybernetics

Networks are, by definition, sets of a number of elements and their interconnections. This is amenable to factorial combinatorics.

When the elements are very few, the number of all possible interconnections is quite limited. For ex., 3 elements can combine in 1x2x3 = 6 different ways (AB – BA – AC – CA – BC – CB)

However, when elements become more numerous, the number of possible combinations grows inordinately. For ex. for 8 elements, we have 1x2x3x4x5x6x7x8 = 40.320 ones. If all these interconnections – or corresponding interactions – are admitted, the net loses any specific definition and the number of operations gets out of control.

A natural solution is to introduce constraints (ASHBY, 1958, 1960 – GREY WALTER, 1953, p.27-28). This can be done:

- by creating a meta- (or hierarchic) level in the network in order to define a reduced number of "blocks" grouping a number of elements with a common positional value characteristic of the "block". For ex. A, B and C form a group L; D, E, and F form the group M and G and H form the group N. In this way the interconnection and communication problem is again reduced to factorial 3. The process can be repeated by creating meta-meta-Ievels and so on.

- by cutting some links between some elements., for ex. inhibiting direct communication between C and G, between A and F, etc… In this way, the network needs no hierarchical nodes. But it needs those constraining rules, that must be somehow stated or imposed.

- both devices could moreover coexist. This seems for ex. to be the case for the neuronal network in the brain. Not all connections are possible or effective, and more or less specialized centers of activity shape up.

Obviously, hierarchic meta-levels signal the emergence of increased complexity. Meanwhile inhibition rules have somehow equivalent effects as hierarchization, with some more leeway. Ashby reformulated these interconnections rules, speaking of richly or poorly joined systems.