3.2 Elementary objects

Definition 3.2.1: The most simple objects (non-decomposable) which comply with the set of existence criteria P1…..P6 are called elementary objects.

According to criterion P1, the most simple object is the one which has a single component among the set of distributed attributes. The support attribute may be also multicomponent, multidimensional, such as the 3D Euclidean space, organized as a set of linear distributions with independent directions (axes). As regards the criterion P2, the most simple object is the one which is distributed on 1D support attribute (with a single dimension). We have noticed in chapter 2 that the distributions can be either simple or complex, and the most simple primary distribution is the uniform distribution. Therefore, as regards the criterion P3, the most simple object is the one who has an evenly distributed attribute. The amount of the support domain of an object may be either however big but finite, or however little but not zero (for the realizable objects)¹2. The minor support domain for a realizable object, as we have also seen in chapter 2, is the difference between two singular normal adjacent values (successive), with its geometric equivalent - that is a DP. The quanta DP of domain may be concatenated (jointed) in order to make-up domains of any size. As for the criterion P4, the most simple object is therefore the one which has a DP of 1D, that is an element of realizable primary distribution with an unidimensional support.

The inner reference system of an object shall be made-up from a number of elements equal to the dimensions of the support, and equal to the number of the distributed attributes within a set. In case of an isolated object (which does not have any relations with the outside), all these reference values are equal to zero (absolute reference). In case of the systemic set of objects which develop some relations between themselves, there will also be an inner reference system for the set (global) but which is external for the constitutive objects. In this case, the inner references of the objects are assigned with values against this common outer reference. This assignment process occurs only for those attributes which are involved into the relations between objects. As a conclusion, the most simple object which complies with the criteria P1…….P6 - elementary object - is an element of primary realizable distribution. This object is composable, either under the meaning of making-up some objects with higher support domains, or by means of properties combination (superposition), for the formation of multidimensional objects.

---

INDEX

---