7.
Condition of systems of interactions existence
The evolution of concept
"information system" results in concept of "system of
interactions".
System of interactions (SI) is a
multitude of objects incorporated by general property to influence each other
and to cooperate with each other so, that in result the initial properties of
these objects change.
Let the group
of elements "à1", belonging to system of interactions A, co-operates
with group of elements "à2" of the same system. As a result of
interaction the set of elements "à3", also belonging to system of
interactions À, is formed
Having
designated interaction by the badge "«", this
statement can be written down as:
à1 « à2 = à3, [1]
Thus it should
satisfy the condition
à1+à2=/= à3 [2]
If à3=à1+à2,
then the algebraic equality of system elements takes place, so the objects of
systems formed from these elements, do not cooperate. There is only formal
addition of elements giving the sum not changed objects.
But if à1+à2 is
not equal to à3, the interaction takes place.
On the basis of
empirical supervision it is possible to put forward a hypothesis, that at
interaction of objects à1 and objects à2 the group of objects à4 can be formed,
which, in turn, can form new system of interactions B, which elements are the
objects b1 and b2, created from groups of objects belonging to system À.
Let's put
forward the following conditions, which any system of interactions should
satisfy with.
1. The first
condition of existence of any system of interactions is the opportunity of
creation of objects set with distinguished properties at a total sum of all
differences of objects equal to zero,
S ài Î À = 0 [3]
Under concept
"an opportunity of creation" we shall understand common property of
SI elements to form co-operating objects. The set of personal properties of SI
elements creates and forms that "constitution" or "of the laws
of nature" or "encoder", to which the co-operating SI objects
submit.
Under the
concept "set of properties of SI object" we shall understand those
reflections (real or probable, i.e. formal properties) of given object, which
distinguish it from other objects of this SI.
The opportunity
of SI creation appears together with formation of its quanta, i.e. is defined
by structure of the SI quanta.
2. The second
condition of SI existence should be "quantumability" of SI objects.
All objects of SI should be formed from elementary objects, which variety
should include object with the zero characteristics, which can be characterised
as vacuum of this SI and which exists formally for this system. The change of
properties of formal SI vacuum allows to create real identified quanta of this
SI, having the certain set of properties.
For example, if
to consider the letters, as quanta of the certain system of interactions, the
blank between words can be considered as vacuum of this SI, and, despite of
complete absence of any mark form in a place of a blank, the blank itself,
nevertheless, exists (both formally and really) and carries a semantic loading,
i.e. carries out the certain function in given SI.
The same can be
said both about physical vacuum and a temporary pause: if to consider sounds of
speech, as an element of original SI etc.
3. The third
condition of system of interactions existence is the presence of elements' set
of system of interaction forming space of elements of this system, which we
shall designate as "Ï". Thus, the elements' space of system A should
be equal to zero,
ÏÀ=/=0.
Let's consider,
that it is not necessary to the system element
to exist really. It can exist formally, i.e. as an opportunity of quanta
of this system of interactions to form this element in the future or as vacuum.
Nevertheless, usually the final and limited set of marks gets out of infinite
set of variants of ISI quantum changes, but sufficient for the description or
creation of all ISI with a richest set of objects and their properties. Though
thus the opportunity to design and to enter any new object in ISI is always
kept.
Thus, if there
is an opportunity even mentally to present formal existence of vacuum elements'
set of any formal space, the condition 3 will be executed for system of
interaction capable mentally to present this set of elements.
4. Proceeding
from definition of interaction [1], the property of the given SI to pass from
one status to another, distinct from the first, should be the fourth condition
of SI existence.
This property
in physical quantum SI derives time or set of personal times of SI elements.
Generally time
of SI characterises ability of system to pass from one status to another
consistently, i.e. to change at the expense of interaction of the elements'
set.
Return
statement is fair too - if there is no time, the elements of system never can
interact, i.e. change the status and condition 1 will be not executed.
The time
appears only in system of co-operating elements, and it can be determined only
for concrete set of space elements. It means, that in the same system the time
can be various (go with various relative speed) for two different objects
(subsystems) of this system and thus it will be the third in common system, to
which both objects (subsystem) belong. The time of common system will depend on
time of any subsystem, belonging to it, as though not enough elements she
include, only this system could change.
If to accept an
interval of time between two transitions of system A elements group from a
status "à1" to a status "à3" for a time unit
Ò(a1« à3)=Ò1,
That quantity
of transitions N of other interconnected group of elements of the same system A
from a status "b1" in a status "b2" will be relative time
of this change, i.e.
Ò
(b1 « b2) =Ò2.
Then it is
possible to write down, that
Ò2 = N * T1,
i.e. it is
possible to express this interval of time through individual.
If a cycle
between two transitions is a quantum of time, we come to a conclusion, that, if
according to condition 1, the various groups of SI elements have distinguished
properties, the transitions from one status to another can occur differently .
Hence, every group of elements of any SI, allocated on some attributes, can
have its personal relative "duration" of time quantum. This relative
group "duration" takes place for each group of SI elements and for
system as a whole. Probably, this property of ISI in physical system of
interaction derives weight or inertia of bodies and limits speed of light, as
link speed of minimally possible amount of the information.
It is
impossible to argue about current of time inside quantum of time, because
quantum of time was determined earlier as a cycle of transition (or interval of
time between two next transitions) of IS elements set from one status to
another. At an inside quantum level there is no time, and there is a simply
instant transition from one status to another and phase of stability of
discrete system. It is caused by step-type behaviour of systems of interaction.
Such systems can change only discretely or in steps. Hence, at a level of
transitions actually time is absent. And quantum transition can be considered
as instant only for the most varied object. But as soon as we pass to system of
elements of interactions, then there is a relative time having place for each
object of given SI. Thus, the time arises only in space of SI elements or in
aggregate of SI elements.
If a quantum
element of system B consists from set of co-operating objects "à1, à2...
àn" of more senior system A, and is capable to change itself, that,
according to conditions 1... 4, it will be also the object of system of
interactions A. In this case, it will have internal time Òâ, as is capable to
change at the expense of internal interaction of objects of system A, forming
this quantum. Thus, the real time of object is formed by system of the enclosed
temporary cycles of all set of objects of all systems of interaction forming
the given object.
It is possible
to define the relative time of any system of interactions, only having compared
this time to the time of other system.
The comparison
of time is possible only then, when there is an opportunity to distinguish one
status à1 of observable system A at the moment of time Ò1 of system of the
observer B from other status à2 of observable system A at the moment of time Ò2
of system of the observer B. If a status à1 is equal to a status à2 of system A
for an interval of time Ò=Ò2-Ò1, which is counted in system B, the comparison
of systems' times for an interval of time of supervision Ò will be impossible.
However, the concept
of supervision has a mathematically accurate information - reflection of
objects' space of system A on objects' space of system B. And observer itself
is an object, belonging to system B and realising process of supervision with
the help of the whole set of systems of interaction, created from system's B
elements (i.e. from the brain).
Thus, at
comparison of times of systems A and B, we have a process of reflection of
system's space A, distinguished from space of system B, through a chain of
systems of interaction belonging to system B. Such process occurs at the
expense of set of transformations - reflections, and each system of
interactions included in a chain of reflection A in B has a personal time and
personal laws of transformation, that results at the end in the certain
distortion of an image of system A in system Â.
If the observer
of system B observes at once two similar systems A and C, it compares two
equally deformed images of systems A and C in the system, that allows to
receive rather adequate results of supervision.
Let observer B
has an opportunity to compare statuses of systems A and C to such accuracy,
that if in system A or C even one element of system will change, it will be
fixed.
Obviously, the
change of a status even of one system element can be considered as a change of
a status of all the system.
Then, if the
observer in system B will wait changes of even one element of system A, and if
for this time N changes of a status of system C will take place, then it is
possible to tell, that for the observer B time in system A flows in N times
slowly, than in system Ñ.
It is obvious,
that the return statement is correct also.
If the observer
B has no opportunity to fix changes of statuses of any system A, then the time in
this system is absent for him, and this system will be constant and timeless.
The observer B would not fix any events (or interactions) in this system. This
system will be the system with zero personal interaction for him. However, it
does not mean at all, that the processes in the given system do not go on. Fact
of objects' system formation is the fact of the system's changes. If the system
exists, it means, that its observable status has arisen at once. So, its
previous status has changed. A conclusion follows: if there is or there were
some changes at once, this system has personal time.
From here it is
possible to make a conclusion, that there can not be a space without time, so
all systems of interaction, which we can distinguish from each other, should
have a personal time.
The return
phenomenon is interesting too. Let in the observer's system B a system A is
observed, which cyclically changes the status for the certain interval of time
of supervision That system A comes in an initial status. Let observer B due to
concrete properties of the system (quantization of personal time) can identify
(to observe) system A only through elementary intervals of time equal to quanta
of the system Òâ, as the observer itself is an object of system B. Let for this
period system A will change the status for some times and again will come in an
initial status. Then the observer B will not notice any changes of system A.
But, if the system repeatedly has changed the status and the observer has fixed
it other status, at the large distinctions of times in system A and B, the
observer B will fix a set of the most different statuses of system A, which, in
his opinion, couldn't be explained at all, either they are casual or
inexplicable. There will be statuses of system And, by the way, distinguished
only on a phase. At close concurrence of times' frequencies of two systems such
phenomenon is also possible, when the process will be represented to the
observer in a return sequence, as wheels of machines sometimes are moving
"back", opposite to their real direction in the cinema.
Maybe we
register the multitude of experimental processes in this way.
In some systems
the time can go with varied speed, because we determine the time by number of
changes of system's statuses for a standard unit of our time. And if the
observable system's changes are uneven, for example, the processes are
accelerated or are slowed down in it, or its time in relation to time of the
observer is either accelerated or is slowed down. Let's take a trivial example.
In the heated up body the speed of molecular interaction is higher, than in
cold, i.e. the changes inducing personal time of these bodies, occur faster,
than in cold, and it means, that the time in the hot body flows faster, than in
cold. For example, having put products in a refrigerator, we slow down their
own time. Therefore processes of decomposition of their components are slowed
down, and they are better kept.
The continuity
of time in system is defined by imposing of set of processes with different
duration of time quanta. Nevertheless, there can be a synchronisation of
interactions in SI. For example, all changes in some SI can occur
simultaneously tactfully to each other (as in computer objects). In other types
of SI different times of quanta provide simultaneous existence of generations
of quanta or quanta in a different phase of development, as in a society, where
the people of different age simultaneously live. By analogy it is necessary to
expect, that age or the phase statuses of quanta can be the factor, which
influences probability of interaction and its result.
With the
greater probability the quanta which are taking place in close or identical
phases (statuses) should cooperate.
If in SI there
is a process, for which the condition, that it occurs faster than all other
processes, is observed, it is possible to name this interval of time
"limiting period". It will define the maximal speed of the fastest
processes in given SI.
Let's imagine,
that there is a set of elementary objects forming the SI. We form all possible
combinations of objects' pairs from this multitude. (Pair of objects is a
minimum quantity of co-operating elements, because one element has nothing to
cooperate with). Let's complete set of objects' pairs simultaneously
starts interaction. As all objects
differ from each other, from all pairs of objects, there should be appear at
least one pair of objects, which will make a transition from status 1 to status
2, distinguished from initial, faster than others.
If it is so,
this pair will give the fastest transition, which is possible in given SI. This
implies the end of speeds of interaction for the external observer.
5. Fundamental
property of SI is that, as a result of interaction of objects of system A they
form new structures of elements, which can be considered as elements of new
system of interaction B. Elements of new system B are generated and derived by
system A and can cooperate with each other, but differently from elements of
system A. The formed affiliated system B, in its turn, can create new objects
from its own elements. This new objects form system of interaction C of the
third generation, which objects, probably, but not necessarily, can cooperate
with parental and preparential objects of systems B and A. It is possible, that
the amount of SI generations basically is not limited. Moreover, one system A
can form some systems of interactions, distinguished from each other. And it is
possible to speak not only about duplication of systems of interactions, but
also about mutation of affiliated systems of interaction.
It is possible
to make the following explanatory. Elementary SI forms SI of elementary
particles and fields. SI of elementary particles forms chemical system of
interactions. Chemical SI, in its turn, forms system of macrobodies and genetic
SI. Genetic SI gives SI mutations as a set of kinds of genetic objects with its
SI and, also forms SI of Reasonable Essences (SIRE). The system of interaction
of reasonable essences forms set of associative systems (linguistic,
subjective, financial and economic, computer SI, etc.), i.e. gives multiple
mutation. Computer's SI forms a set of SI mutations - linguistics, system,
program etc. Set of computers and advanced systems of communication derives
computer network SI, as a new kind of systems of interaction.
It is possible
to detail an example, but it is already obvious from the given text, that as a
result of occurrence of new generations and kinds of SI, arising SI objects
have properties perfectly distinguished from properties of the similar SI
objects of early generations. And the more SI generations lays between objects
of various systems, the more strongly these objects differ. It is a some kind
of reflection of time.
As a result of occurrence
of new generations of SI and their mutations, a supersystem of interactions
(SSI) appears, forming the space of SI, where the system of interaction
corresponds to each element of space. In this supersystem of interactions, all
new systems of interaction, which provide existence of each other and cooperate
with each other, i.e. "grow together", forming varied superspace of
interactions, are born and dead continuously.
This superspace
is capable to form such chains of connections, which we even do not suspect.
Therefore study of SI properties and structure of superspace or structure of
systems' space of interactions can give essentially new tools of transformation
of nature. The mathematical theory of
systems of interaction can give a technique of revealing of unknown chains of
SI co-operation, which realisation will open new opportunities of development
of our Civilization.
It is possible,
that the superspace of SI is capable to form new elementary or subelementary
systems of interaction, which can pass the same cycle of self-development, as
well as superspace, which has caused it. Thus cycle of self-development of
superspaces of interaction can be closed.