## 3.5 Reference objects

Based on the above-mentioned issues, we have noticed that any quantitative value (existential attribute) of a property is determined through a difference against other invariant value - reference value. This evaluation is made (as we are about to see further on) by a information processing system (IPS), the only type of material system able to distinguish the object’s attributes one from another, and to establish their existence degree. We have seen in chapter 2 that a distribution consists of a set of value-assignment relations of an attribute distributed on a support domain, without establishing the way how the assigned value may be evaluated. Now, it is time to assert that each of these values are evaluated (by an IPS) against the reference value, therefore, this kind of value shall be required for each assignment relation. Thus, we are dealing with another distribution - reference distribution - in which the distributed attribute is even the reference value, this distribution clearly having the same support as the distribution meant to be evaluated. The value allotted within the reference distribution is invariant, and is equal to zero, in case of the absolute reference. This uniform distribution with the reference value makes-up a reference axis (why it is called axis we shall see later on, when we will focus on processes). Since an object generally has a set of distributed attributes, each attribute from this set will have its own axis of reference on the inner domain of the support attribute.

Definition 3.5.1: The set of reference distributions for the model attributes of an object makes-up an abstract object known as the inner reference system of the object.

Because we are dealing with an invariant set of distributions on a common support, this means that the inner reference system of an object is also an object itself (obviously, an abstract one), which is called the inner reference object.

According to the approach way - either virtual or realizable - the inner reference object may be a virtual object, respectively, abstract realizable. In a virtual case (ideal, mathematic), this object is made-up from a set of continuous even distributions (with absolute accurate singular values), whereas in case of the realizable reference, it is a set of evenly realizable distributions with normal values, as reference values.

It is worth mentioning right even in this exposition stage that both the model of a real object and its reference object are abstract objects which exist only in the internal or external memory of an IPS (either natural or artificial one), in us, in our mind of human beings, but these make us able to perceive and evaluate our instant reality. This subject shall be broadly approached in chapter 8 and 9.

The distributions of the inner attributes against the inner reference values remain invariant in case of an invariant object. These reference values may be therefore considered as common components for a set of values assigned on the object’s inner domain (as it was mentioned at the par.3.4). Since they are common components, any variation in the value of these references is equally transmitted to all the dependent values from that distribution, as we have already noticed in case of the compound objects. In case of the objects’ composition, each object is represented in the outside by its reference object, the relations deployed between the objects which are included in this composition are relations developed between the inner reference objects belonging to these objects.

Comment 3.5.1: The reader will be able to better understand the truth and generality of the above mentioned issues if an analogy with the situation of relations between two objects belonging to the category of the current existing world’s states is being made. It is a well-known fact that the political relations between two states are actually relations developed by their governments, more precisely between the ministries of foreign affairs belonging to these governments. In other words, the government of a state is an inner reference system of this object, against which both the inner attributes of the state’s components and the outer attributes, revealed by the relations with other states, are determined. As for the human relationships within a community, there is a particular inner reference system for each individual in the evaluation of his conduct - that is the individual conscience - but there is also a reference system which is external to the individual but internal to the society - that is the moral conduct, ethics, good manners rules etc. - which makes-up the reference system for the behavior of all the society’s members. The individual conscience of an element of society, as an inner reference, is granted (through education) with the proper values right from the set of conduct norms which is the society’s global reference.

Because the spatial position attribute of a real object is very important in this paper, we shall focus a little bit on the reference object for this kind of attribute. We know since the schooling years that in order to define the position of a point in space, a system of reference made-up from three equally orthogonal axes (in case of a 3D space) is required, and these axes have a single intersection point- that is the system origin. According to the objectual philosophy, the axes of reference are some independent reference distributions which have only one element in common, which is their intersection (origin, common component of the three axes). This unique element for a certain object has a special denomination in this paper - T reference - because it is the element of the inner reference system involved in the translation processes (which shall be approached in the following chapter).

The other elements of the inner spatial reference system - the axes of reference (more exactly, their directions, invariant along their entire length) - make-up the second reference, that is R reference (which is involved in the evaluation of the object’s rotation processes).