Simplicity and Complexity of Systems Presentation's Means with Emergent Properties

Sergey V. Chebanov

Complexity and simplicity are not characteristics of the reality, but presentations about it. Any two fragments of the reality may be presented with an identical degree of simplicity and complexity. The means of presentation are distinguished on possession internal (I) and external (E) resolving structures (RS).

The grammar of presentation's means having IRS has the characteristics, isomorphic to described objects. So, the positional scales of notation have IRS on multiply calculation. The grammar of presentation's means having ERS has not the characteristics, isomorphic to described objects so for the description of properties of object to have to enter the special means in any each time. So, multiplication of numbers recorded by roman numerals has entered ERS.

On adequacy of considered object to presentation's means it is possible to divide on

- Reductive, having only ERS

- Systemic-reductive, having one or several local IRS

- Organic, having united global IRS.

The effect of complexity arises by use reductive and systemic-reductive means of presentation for element - structural presentation of considered object as components consisting from certain set. In the event that number and variety of components and connections between them are great so the object is qualified as complex. The increase in a system of number of similar elements and connections permits to qualify this system as bulky. So for example, description the mechanics of pellet as a material point through it kinematic and dynamic characteristics is simple as well as statement that Mark flies by a plane to girlfriend in Paris. The second situation will appear more complex only in the event that organic means of presentation absent, for example, description of this flight through the mechanics of material points will be applied.

Moreover, description of the second situation by means of presentation the mechanics of material points come across insuperable complexities - basic or technical. In this case the phenomena inherent to holistic object are qualified as emergent in relation to properties of components.

However, this situation is paradoxical as far as before to speak about existence of emergent properties of object in relation to the components, this object decomposes on these components by a way of very mediate analytical procedures. In practice usually this analytical procedure is realized as the relation 'to consist from'. The latter one is adequate only for relation of technical devices, which consist of details, made by human hands pursuant to beforehand existing idea. The transferring this relation on objects of non-technical nature and it ontologization derives a problem of genesis of emergent properties in reductive and systemic-reductive presentations.