3.3 The objects’ hierarchical organisation

Considering the object O₁ from the figure 3.3.1, with an inner reference R₁ (assessed against the absolute outer reference R₀)¹3, which has few objects O₂ (out of which, only one is represented) in its composition (in its inner structure), which in their turn, contain several objects O₃ , so on.

Fig. 3.3.1

If the attribute we are dealing with is the spatial position (but this matter is also valid in case of other attributes), the position of an object O₃ against R₀ is:

(3.3.1)

where is the position vector of the inner reference R₃ against R₂, is the position vector of the inner reference R₂ against R₁, etc.

Let us consider that the object O₃ is non-decomposable, which means that either it does not have an inner structure any longer, or there are no available information on this kind of structure. Therefore, from analytical point of view, (in sense of its decomposability) this type of object has an unity level. But, the same object may be an element for a synthetic object (in sense of its composability) O₂. This synthetic object (composed, generated as a result of a synthesis) shall contain in its inner domain more objects of O₃ type whose external attributes are about to be determined against the reference R₂. This kind of object (O₂) shall have the analytical level equal with two (only a single level may be decomposed). The object O₂ can be also a component of another object O₁ which shall therefore have the analytical level equal to three, where there is another inner reference R₁ which is external to all O₂ components.

Definition 3.3.1: The integer number of hierarchical levels in which an object may be decomposed is the analytical level of the structure of that object.

The following remarks may be pointed out based on the aforementioned issues:

1. The objects are decomposable up to an inner informational limit equal to zero (null information), this limit being settled either by means of a convention (in case of the abstract objects), or by reaching the cognition threshold from a certain moment (for instance, in case of the abiotic material objects, as it was described in chapter 1).

2. The object’s hierarchical level coincides with the structure level of the reference system associated to these objects, the inner reference systems being abstract substitutes for those objects (the external relations between objects are in fact relations between their reference systems).

3. The reference which is external to all the objects from a series belonging to the structural levels, with the highest analytical level (that is R₀ in this case) is an absolute reference, any other reference from the set being relative (linked through a relation) against this reference. Without the existence of any other reference able to set its value, this reference shall have zero value. The level of the absolute reference (mostly for the models within the real processes) also depends on the level of knowledge existing at a certain moment.

4. Composition (synthesis) of the objects is made by respecting the object’s existence criteria, both for each component and for the composed object which was generated (criteria P1…P6).

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INDEX

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