19
In contrast, internal effects always form within
the system and influence the operation of the system. In the case of the climate system, the great
ocean conveyor (the system of surface and subsurface ocean currents) can be regarded internal
effect that has a significant role in the operation
of the global climatic system and also regarded
one element of the system.
For scientific purposes subsystems could be
determined within a system the boundary of which
cannot be defined using a geometric form. The
ecological system of a natural forest, for example,
is composed of plants, fungi, animals and microorganisms that are in connection with each other and
also with the soil which is the nutrient base and
even with the soil forming rocks. A system like
this is too complex to study every part comprehensively at one time. Generally, a subsystem is
selected for the study, for example, the animals in
the forest (or even only the arthropods), to understand the network of connections, food chains, etc.
In space animals in the forest combine with the
space defined by the plants (the forest itself);
therefore, it cannot be delineated by a geometric
boundary from the plant subsystem. Considering
the animal subsystem, plants will represent external effects like hiding places, food sources, etc.
while the number of individuals in animal populations, the ratio of carnivorous and herbivorous animals, etc. are regarded internal effects.
In order to decide between external and internal effects, the analysis of a particular system as
the object of the study is necessary.
Let us see how systems could behave as a
reply to external and internal effects.
Deterministic is the behaviour of a system
when there is a direct causal connection between
the effect and the reply of the system. At a first
glance, regarding scientific aspects (cognisability) this behaviour seems simple since its reply to
a given effect is calculable. Replies could be
either linear or exponential. Nevertheless, the
connection between cause and effect can be
always exactly calculated using mathematical
methods. The movement of a deterministic system is periodic.
In a mathematical sense, linear connections
can be described using first degree equations
while deterministic but non-linear connections
could be described using exponential equations in
which variables appear in the exponents (as well).
For example, in a heating system a given amount
of fuel with known heating value is burned over a
day the resultant temperature in a given building
can be calculated if the parameters of the building
are also known. For the calculation, however, an
exponential equation has to be used.
Stochastic, i.e. randomly behaving systems
give replies to external or internal effects that can
be described only with statistic methods. Such
replies also follow rules but the rules can be
found in the statistic relations of the law of large
numbers. The water system of a river is a fine
example. Precipitation is an external effect that is
random regarding time, spatial distribution and
quantity as well and the rate of flow in the river
will change accordingly. Using a century long
data series, however, the frequency of great
floods or extremely law flows can be calculated.
To describe random events and the reactions of
randomly behaving systems mathematical statistics was developed the application of which is
increasingly widespread.
The third type of systems behaves chaotically,
i.e. neither linearly nor periodically, furthermore
they are neither deterministic, nor stochastic. At
first, they could be called—using everyday
speech—“wayward” systems, however, incalculable behaviour is also based on mathematics.
Their behaviour can be described using chaos
theory that is described in short in the
followings.
Generally, Edward Lorenz mathematicianmeteorologist is regarded the founder of the theory (Gleick 1988). His chaos related work was
started in the early 1960s (Lorenz 1963, 1964),
however, his outstanding results had antecedents.
Computer simulations carried out by the
renowned physicist Enrico Fermi in 1950
described the vibration of an elastic chain composed of 32 loops using a non-linear equation
system. (His colleagues were John Pasta and
Stanislaw Ulam). The system got into a chaotic
state and its movement became unpredictable.
Fermi recognised the curious behaviour, however, did not publish the results (Strogatz 2002).
2.2 Operation of Material Systems
In contrast, internal effects always form within
the system and influence the operation of the system. In the case of the climate system, the great
ocean conveyor (the system of surface and subsurface ocean currents) can be regarded internal
effect that has a significant role in the operation
of the global climatic system and also regarded
one element of the system.
For scientific purposes subsystems could be
determined within a system the boundary of which
cannot be defined using a geometric form. The
ecological system of a natural forest, for example,
is composed of plants, fungi, animals and microorganisms that are in connection with each other and
also with the soil which is the nutrient base and
even with the soil forming rocks. A system like
this is too complex to study every part comprehensively at one time. Generally, a subsystem is
selected for the study, for example, the animals in
the forest (or even only the arthropods), to understand the network of connections, food chains, etc.
In space animals in the forest combine with the
space defined by the plants (the forest itself);
therefore, it cannot be delineated by a geometric
boundary from the plant subsystem. Considering
the animal subsystem, plants will represent external effects like hiding places, food sources, etc.
while the number of individuals in animal populations, the ratio of carnivorous and herbivorous animals, etc. are regarded internal effects.
In order to decide between external and internal effects, the analysis of a particular system as
the object of the study is necessary.
Let us see how systems could behave as a
reply to external and internal effects.
Deterministic is the behaviour of a system
when there is a direct causal connection between
the effect and the reply of the system. At a first
glance, regarding scientific aspects (cognisability) this behaviour seems simple since its reply to
a given effect is calculable. Replies could be
either linear or exponential. Nevertheless, the
connection between cause and effect can be
always exactly calculated using mathematical
methods. The movement of a deterministic system is periodic.
In a mathematical sense, linear connections
can be described using first degree equations
while deterministic but non-linear connections
could be described using exponential equations in
which variables appear in the exponents (as well).
For example, in a heating system a given amount
of fuel with known heating value is burned over a
day the resultant temperature in a given building
can be calculated if the parameters of the building
are also known. For the calculation, however, an
exponential equation has to be used.
Stochastic, i.e. randomly behaving systems
give replies to external or internal effects that can
be described only with statistic methods. Such
replies also follow rules but the rules can be
found in the statistic relations of the law of large
numbers. The water system of a river is a fine
example. Precipitation is an external effect that is
random regarding time, spatial distribution and
quantity as well and the rate of flow in the river
will change accordingly. Using a century long
data series, however, the frequency of great
floods or extremely law flows can be calculated.
To describe random events and the reactions of
randomly behaving systems mathematical statistics was developed the application of which is
increasingly widespread.
The third type of systems behaves chaotically,
i.e. neither linearly nor periodically, furthermore
they are neither deterministic, nor stochastic. At
first, they could be called—using everyday
speech—“wayward” systems, however, incalculable behaviour is also based on mathematics.
Their behaviour can be described using chaos
theory that is described in short in the
followings.
Generally, Edward Lorenz mathematicianmeteorologist is regarded the founder of the theory (Gleick 1988). His chaos related work was
started in the early 1960s (Lorenz 1963, 1964),
however, his outstanding results had antecedents.
Computer simulations carried out by the
renowned physicist Enrico Fermi in 1950
described the vibration of an elastic chain composed of 32 loops using a non-linear equation
system. (His colleagues were John Pasta and
Stanislaw Ulam). The system got into a chaotic
state and its movement became unpredictable.
Fermi recognised the curious behaviour, however, did not publish the results (Strogatz 2002).
2.2 Operation of Material Systems