NETWORKS ORDERING
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(2) |
| ID | ◀ 2276 ▶ |
| Object type | Methodology or model |
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-levels 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.