Unlike
the abstract distributions (virtual or realizable) which are
synthetic, mathematic models (“build” by an IPS), the
properties of the sets of real objects have also some distributions,
but these are self-settled^{9}4^{
}by means of repeated interactions
deployed between all the objects of the set. However, a specification
is required: the properties whose distributions are self-settled
within a set of real objects must be *transmissible*
(namely, it is required to be carried by a flux), and the
interactions are even the property interchange (transactions)
processes between the two objects which are interrelated one
another^{9}5.

The natural distributions are evaluated by the human IPS by means of a complex mixed process, made-up from a series of real (experiments) and abstract processes (information processing obtained by means of experiments). This way has allowed that the attribute distributions of the real objects to be known, such as the distribution of the molecular velocity into gases, the frequency of the thermal photons, of the richness or education level of the individuals belonging to a society etc.

It
was found that for most of the attributes distributed on a set
made-up from real objects, the Gauss-type distribution may be applied
(also named *normal distribution*):

(X.5.4.1)

where
is the population of the distribution’s elementary support *dx*
(fraction, number of objects from the set which own the value *x *of
the support property, *C* is a normalization constant,
is the mean value (internal reference of the distribution object),
represents the variance and *x* is the internal reference of the
support element *dx*.

If we are talking
about the distribution of the velocity within a gas^{9}6,
*x* is the velocity value (more exactly, its modulus),
is the fraction from the molecule population which reaches to that
particular velocity, and
is the mean velocity, that is a calculus value depending on the
conditions in which the gas may be found (temperature, pressure
etc.). This mean value is the reference against which the gas
molecules are divided in two complementary classes: the molecules
with a velocity surplus (as compared to the mean values) and the ones
with a velocity deficit. In this case, the positive or negative
character of the two complementary properties is given only by the
symbol of the difference between the value of the molecular velocity
and the mean value, therefore, by a quantitative value. However, for
people, this symbol is a qualitative attribute because any school boy
knows that positive numbers are different in terms of quality as
compared to the negative ones, although they are different (at the
same modulus) only by the symbol which is placed in front of them.

Comment
X.5.4.1: If the reader has already read the chapter 2, he will
probably notice a discrepancy between the denomination for some of
the Gauss-type distributions presented in the current scientific
papers (or of other distributions of an attribute on a set of
objects, such as the Maxwell or Plank distribution) and the name of
the distributions given according to the model used in the
mathematics field (which is also used in the present paper). In
chapter 2, we saw that a distribution has a distributed attribute
(dependent variable displayed on the vertical axis) and a support
attribute (independent variable displayed on the horizontal axis),
with a set of assignment relations deployed between their values
(relations which can be symbolically invariant - functions - such as
the case of the above-mentioned distributions). The name of a
distribution must specify the distributed attribute and its support.
It is clear that as regards the Gauss-type distribution, the support
(mathematic) attribute is the variable *x*, and **
(number of the elements which own that value) is a distributed
attribute (__this__ should be put at the genitive in order to show
the affiliation to all the support objects). On the other hand, the
elements belonging to the set of objects are material supports (ISS)
of the information regarding the existence of the property *x*,
but they are not the distribution’s support and their number is
the distributed attribute. It is compulsory that a clear distinction
to be made between the notion of __distribution’s support__
(as an independent variable), and the one of material support of an
information (ISS). Because the denominations of the above-mentioned
distributions are quite frequent in the specialized papers, we shall
further tolerate them although they are inaccurate in terms of the
distributions definition.

94 Self-settle means that the quantitative values of the attributes are not imposed by an IPS, but they are distributed on the set of the involved objects, by means of a simple interaction between the real objects, through real, natural processes.

95 For instance, the distribution of the individual kinetic energy of the molecules on the set of the gas molecules, or the distribution of the material assets which are owned by an individual (richness) belonging to a human population.

96 Distribution known as Maxwell distribution but which is similar with Gauss distribution.

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