The virtual
abstract objects are those objects which cannot be realized not even
at the abstract level (an ISS including the entire information
associated to the virtual object cannot physically exist). It comes
out that people operate quite often with this kind of objects, being
named *ideal *objects. Such an object is, for example, the set
of real numbers {R}, but also other objects which represent some
*asymptotes* (limits impossible to be reached) for the
realizable objects. The realizable objects have characteristics which
are more and more closed with the virtual objects, once with the
increasing progress in the scientific and technological field, but
they will never attain the attributes of the ideal objects. One of
the fundamental roles of the virtual abstract objects, just due to
their asymptote character, is to delimit the highest existence domain
of a class of abstract objects.

A fundamental class
of virtual objects is represented by the class of *virtual
reference systems, *systems without which the assessment of the
existential attributes belonging to the object’s properties
could not be evaluated. For example, the reference system specific to
the *spatial position* attribute of the objects is made-up (in
3D space) from the three axes which represent the three possible
independent directions (**X**, **Y**, **Z**) into the
Euclidean space, axes which have only a single intersection point,
that is the origin of the reference system. Each axis is a set of
concatenated vector segments, all of them with the same direction
(the common value of the qualitative attribute), and quantitatively
speaking, each segment is a continuous distribution of virtual points
which owns an interval from the axis of real numbers as its support
(obviously, a virtual object as well). These axes (more exactly,
their directions) are a reference for the *rotations* (direction
variations), that is a reason why they make-up the reference system R
of each object which has a spatial distribution. The common
intersection of the three axes, the *origin of the spatial
reference system*, is also a virtual object (zero-dimensional)
where the rotations are null, this point being the reference for the
assessment of the object’s *translations*, therefore, T
reference.

It is worth mentioning that the virtual reference systems must not be mistaken with the realizable ones. When we are drawing some axes of reference on a piece of paper, these axes are similar with any realizable object, in terms of dimensions (they have a thickness which the virtual axes do not have it), and they are sets of 2D DP (pixels) with a different color than the support paper. This realizable representation of a reference system is also required by our visual perception system (to which is directed to) because it cannot operate with virtual objects (zero-thickness lines) either. However, starting from this representation, a series of derived abstract objects (such as the contrast lines) shall be projected into the brain, and they represent some limits towards which the objects which can be represented tend to. In our case, a contrast line is an abstract object which can be achieved only by means of computing (making the difference between two attributes which belong to some adjacent-disjoint domains), this calculus being performed by the neurons involved into the visual perception. Since the contrast line is a boundary, this means that not only the reference systems can be virtual objects but also the boundaries. For example, a virtual surface (mathematical) may be considered as a boundary between two adjacent-disjoint volumes.

Another example of fundamental virtual
object is the *axis of time*, entirely imaginary construction,
also arranged as an axis, but against the axis of the real numbers, a
single value from the axis of time being real, which is the so-called
*present value* (present moment), the rest of them being
considered as abstract even by the official science. Unlike the value
axis of a realizable attribute (such as, for instance, the spatial
position), where all the values have a simultaneous existence, in
case of the time axis, the existence of two values is not possible
(by definition), just for the simultaneity of the unique existence of
the values belonging to all the other known attributes to be defined.
The realizable time means a counting (numbering, increment) of a real
repetitive process (materially realizable). As for the realizable
time, the present is given by the real cyclic process which is in
progress (more exactly, by the number (index) of this process against
the adopted temporal reference). But, the counting is a __computing
process__ (information processing), because a *memorization *of
the number of previously-deployed processes takes place, number which
is *increased* by one unit every time the cyclical process is
terminated. Therefore, even the realizable time is an object
belonging to the *abstract process* type, process which is
carried out either by people (when they count the days, months, years
which went by) or by the intracellular IPS for the bio-system’s
fundamental processes.

Few observations may be drawn based on the above-mentioned issues:

The numerical values of the attributes belonging to the realizable objects tend to more and more high accuracy levels (the number of bytes of the artificial IPS is growing, as well as the accuracy of technical execution of the artificial material objects, the size of the observable universe is also increased etc.) whereas the civilization evolves. The time measuring methods tend to the utilization of more and more short cyclical processes, thus, towards higher counted numbers. These numerical values contain therefore, a more and more higher information amount. The limit towards which these values tend to (abstract or materially realizable) is the

__absolute accurate value__(AAV), the value which contains an infinite information amount. However, this limit was already foreseen by the mathematicians who operate for a long time with the set of “real numbers”, set which contains exclusively AAV (see annex X.3). This virtual object {R} comprise therefore the asymptotic limits of any realizable numerical value, regardless of the cognition or the technological progress level reached by a society. We might say that the numerical AAV are the components of the absolute reality because this virtual object also contains an infinite information amount which is both quantitative and qualitative.The asymptotic character (intangible, abstract or materially unachievable) of the virtual objects is also emphasized by the synthesis method of these objects carried out by IPS. Based on the above-mentioned issues, the virtual objects are extreme generalizations of some classes of abstract objects, generalizations which consist in the extraction of the common components from a set of abstract objects. We have found out that only the association of specific components provides particularity, as well as a recognizable and finally, an achievable character assigned to that object.

Comment
9.5.1: As for the notions of *reality *and *virtual*, as
they have been defined so far, now it is the moment to adopt a
position regarding a very frequent mass-media collocation named
“virtual reality”. The reader which has succeeded to run
through this paper up to this moment is certainly aware on the
absurdity of this collocation which contains an oxymoron (two
consecutive antonyms) which should be excluded one another, similarly
with expressions such as “idiot genius”, “fluid
solid” etc. In fact, that collocation denotes __a simulation__
of the reality (an illusion, a hoax on the visual and tactile sense)
achieved through images and artificial sensations, generated by an
AIPS, but the information fluxes are real; otherwise speaking, we are
dealing with an abstract representation (through ISS) but which is
abstract realizable rather than virtual. When we are able to
accurately differentiate the virtual area of the abstract world from
the achievable one, the reason why we made this comment will become
clear.

Copyright © 2006-2011 Aurel Rusu. All rights reserved.