| THE
PECULIARITIES OF THE STOCK EXCHANGE INDEX FOR THE MASS
MEDIA SPHERE
The analysis of the economic parameters
of the Massmedia Sphere in the USA, European countries
and Japan, shows that this sector came close to the
economic parameters of the Material Sphere.
In the Massmedia Sphere, millions of people and billions
of US dollars are involved. Is the index of business
activity for the Massmedia Sphere is absent to this
day?
The absence of the exchange index in the Massmedia Sphere
of the USA and other economically developed countries
has a negative effect on everything. It is difficult
to talk definitely about the tendencies on the market
of informational and entertainment services.
Today, it is imperative that we create the index of
business activity for the Massmedia Sphere which would
resemble that of the Dow-Jones index. But, for the exchange
index of the Massmedia Sphere, I suggest using another
logic that differs from that logic used in 1897.
Firstly, at creating the index of stock activity of
the Massmedia Sphere, I proceed from the fact that the
Massmedia Sphere represents the economic system, the
resources of which are moving in economic space.
Secondly, in the index of stock activity of the Massmedia
Sphere, I suggest taking into account complex numbers.
MACROECONOMY OF THE MASS MEDIA
DOUBLE ACCOUNTANCY WITH THE USE OF COMPLEX NUMBERS
Introduction
«For the past 30 years now the
state power has been shifting itself towards mass media».
«The sphere of mass media has been challenging
the traditional branches of power». Prof. A. Reevs.
The Massmedia often informs us of the
leftist parties who come into power in Latin America
and try to change the total vector of state development.
In other cases a rightist party to come to power and
change the inclination angle of the total power vector
is reported.
All such assertions should be provided by estimates
confirming the shift of the power vector to the left
or to the right.
However we cannot take advantage of the marine orders
such as «two compass points left» or «three
compass points right». They are estimations of
navigational character, and cannot help to solve the
problem of defining inclination angles of the power
problem.
Where does the power vector shift?
What happens with state power sphere?
I suggest to consider the shifting of power vector graphically
as follows:
- by placing total vector of the three basic branches
of power «R1» on axis «X»;
- by placing total vector of the mass media «R2»
on axis «Y».
The position of the vector indicates
that there has been a shift of power towards the mass
media.
The position of the vector testifies to the equality
between the total mass media vector R1 and vector of
the three main branches of power R2.
The position of the vector Z3 proves that the shift
occurred towards the three branches of power.
We shall investigate this problem at a greater length.
CHAPTER 1
It is difficult to picture the general
model of a state structure without taking into consideration
the press industry, radio and TV. These three components
of the mass media are of utmost importance for the life
of society and state. The mass media represent a new
branch of economy with inherent technology, economic
relations and financial schemes.
Without the mass media present statehoods would actually
resemble the democratic set-ups of some 150 years back.
The sphere of mass communication (mass information)
can be interpreted at greater length provided its economic
theory has been elaborated. The lack of theory makes
all deliberations on the subject vague and pointless.
The mass media sphere can be considered as being detached
from the state. However, such an approach has a number
of significant shortcomings:
Firstly: why consider the mass media sphere as being
disconnected from the legislative power service if the
former exists in the frames of the «law»?
Secondly: is it justified to investigate the mass media
sphere beyond the executive power service if it is dependent
on and subject to it to a certain extent?
Third: why consider the mass media sphere as being disconnected
from the judicial power service?
The investigation of the mass media sphere without taking
into account the services of these branches of power
is a major logical mistake.
The mass media sphere develops in the framework of the
state together with the services of the three branches
of power.
I suggest that they be considered in the Cartesian three-dimensional
system of coordinates in which the aggregate vector
of the services of the above branches can be represented
as follows:
where
a1 – vector of legislative power service (±
leg);
b1i - vector of executive power service (± exe);
C1j - vector of judicial power service (± jud).
Z = ± leg ± exe ±
jud
In every state service the vectors
a, bi, Cj have different values depending on the degree
of development of each branch of power.
On reading the title of the book you may ask some questions:
why did the author decide on using complex numbers?
Is there a shortage of real numbers?
Or does he suggest a new system of estimates?
These questions need to be answered right from the first
pages of the book.
Indeed, the calculations of the economic estimates of
the mass media sphere prove that the limits of real
numbers seem rather tight. It reveals the lack of a
fraction of numbers, that is of imaginary, complex numbers.
Judge it for yourself.
The mass media services are being created and consumed
in one and the same stretch of time. They momentarily
disappear as soon as they are produced. That is the
peculiarity about the media services which represent
specific economic products. Such a particular nature
of the media services is prompting the need to use unconventional
technologies in calculating the cost of the services,
i.e. imaginary, complex numbers with their operational
systems.
CHAPTER 1. «NUMBER» AS INSTRUMENT OF RESEARCH OF ECONOMIC PROCESSES
Numbers, numbers, numbers – they are present everywhere, both in traditional and untraditional economy.
We don't ponder on the kind of numbers we use in economic calculations, although a lot depends on them. Real numbers reflect one depth of the economic processes; imaginary numbers show the other.
We should not be afraid of using untraditional numbers. If we look realistically, we can see that social sciences meet with exact sciences and they «go together» – next to real numbers, imaginary numbers and complex numbers quaternions.
Researching economic processes, we should not be afraid of fresh ideas and new horizons. Both in the area of the traditional and - even more importantly - untraditional economy, we should not find ourselves in the zone of old approaches, old opinions, thoughts and definitions.
In the hall of mirrors which we all visited one time or the other in our childhood, the mirrors’ surfaces were distorted: some of them were convex, others concave. That affected our reflection in the mirror. These various transformations entertained us. Of course, it was funny.
I have mentioned the hall of mirrors in connection with different numbers the fact that a researcher of the economic processes who uses in his research – natural, irrational, real, imaginary, compound and super-compound (quaternions) – finds himself in an analogous situation. The numbers can be treated as a specific mirror that reflects economic processes.
It has taken thousands of years to define numbers. The numbers' theory has been widening and developing. For example, the ancient Greek mathematicians thought that only natural numbers were real.
In the times of Pythagoras a discovery was made in the area of numbers. Its essence consisted in the fact that there were not enough natural numbers, if one tried to put into practice the arithmetic calculations connected with the diagonal of a square (see Pythagorean Theory). There, the necessity of using real numbers came up.
I am not going to go deeper into the theory of the development of numbers' definition. It is enough if I say that in our daily life we use real numbers and basic arithmetic calculations such as addition, subtraction, multiplication and division. Only in some exceptional situation, do we raise a number to the nth power or extract the square root. In other words, we use one type of numbers (real) and primitive mathematical apparatus (in our daily life).
If we raise (A + B) to the third, fourth power, some very complex problems arise. Their essence consists in the fact that there are not enough real numbers (the ones that we use in our daily life) to solve the equations. Part of the equations can be solved only with the utilisation of complex numbers.
This situation partly explains the necessity of using new numbers and new methods of technology in calculations. There, everything looks the same as in daily life: some things can be measured by a simple ruler, some only using a logarithmic ruler. This is clear for everybody.
Because of this, mathematicians give the following example. The system of the simple equations does not have a solution in the framework of real numbers:
This system of equations looks simple. But the solutions for these equations lie beyond the borders of real numbers. Beyond the border of existing, traditional definitions, opinions and axioms. If we cross the line of «impossibility» imposed on us by real numbers, we will find solutions, but the journey towards these solutions leads through an arithmetically impossible operation - extracting the square root of negative number. The solution of the equation is as follows:
3. DEFINITION OF THE COMPLEX NUMBERS
In 1545 Italian mathematician G. Cardano made the first steps towards development of a theory of complex numbers.
1n 1572 R. Bombelli established rules of an arithmetic operation on numbers.
In 1637 R. Decart offered a name for new numbers – «imaginary numbers».
In 1831 K.Gauss introduced a concept of an imaginary unity.
In the list of those who worked out complex numbers there are many well-known names – G. LaGrange, P.Laplas, Y.Bernulli, K.Vessel, G.Argan, and W.Hamilton.
The scope of usage of complex numbers is expanding with every passing year.
Complex numbers have incorporated the logic of the dialectical method.
Dialectic logic of construction of complex numbers.
Thesis Real numbers –«a»
Antithesis Imaginary number – «bi»
Synthesis Complex number – Z = «a + bi»
The principal feature, being at the same time its advantage, of the «complex number» (complexus) is that with the help of complex numbers it is possible to reveal combination of several concepts, phenomena and processes as a whole. That is, the complex number reveals the idea of compositions of concepts, compositions of processes and compositions of phenomena.
Definition 1. Numbers - a + bi, where a and b – are real numbers, i – an imaginary unit – we will call them complex numbers.
Number a we will call a real part of a complex number, bi – an imaginary part of a complex number, b – a factor at an imaginary part. There are cases when it is possible that real numbers are equal to zero. If a = 0, a complex number bi refers to only imaginary. If b = 0, a complex number a + bi is equal to a and refers to only real. If a = 0 and b = 0 simultaneously, a complex number a + bi is equal to zero. So, we have got that real numbers and only imaginary numbers are special cases of a complex number.
Record of a complex number as a + bi is called an algebraic form of a complex number.
A complex number is represented either as a point with coordinates (a, b) or as a vector beginning in the center of coordinates (0,0) and ending in the point with coordinates (a, b) (see fig. 1).
Axis X is called a real axis, axis Y – an imaginary axis and a plane Z itself – a plane of complex numbers or Z-plane. Real numbers can be represented by points of a direct line as it is shown in figure 1.
Segments OA OB, can also represent these numbers, taking into account not only their length but the direction as well.
Two complex numbers a + bi and c + di are considered equal in only case when separately their real parts and factors at imaginary unit one are equal, that is a + bi = c + di, if a = c and b = d.
4. OPERATIONS ON COMPLEX NUMBERS IN ALGEBRAIC FORM
Addition, subtraction, multiplication of complex numbers in algebraic form are carried out according to the rules of corresponding operations on multinomial.
a) addition of complex numbers;
b) subtraction of complex numbers;
c) multiplication of complex numbers;
d) division of complex numbers.
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