7.3 Движение декабристов (стр. 3 )

f) Complexity theory came after cybernetics but prior to catastrophe theory.

2 Answer the questions:

a) Where can complex systems be applied? Give examples.

b) What doesn’t mechanical approach fit today?

c) Are complex systems easy to define and model?

d) Can you consider human brain and a society as a complex system?

e) Do complex systems need linearity or non-linearity?

f) What is the main concept of a complex system?

g) When and where were the complex system applied first?

h) What are “c-theories” that the humanity gained in the 2nd half of the 20th century?

i) What was the role of Friedrich Hayek in the complexity theory development?

j) Can complex systems be predicted?

3 Try to define the nouns below:

simulation, definition, computation, prediction, equation, execution, distinction, action.

4 Fill in the gaps with the proper prepositions:

1 The scientific field ______ discussion is also called complex systems theory.

2 The consensus related ______ one universal definition of complex systems doe not exist yet.

3 Scientists often seek simple non-linear rules which lead ____ complex phenomena.

4 The evolution processes of certain economic systems can be carried

_____ also _____ sets of linear equations.

5 Complex systems is a new approach ____ science that studies how relationships ____ parts give rise _____ the collective behaviors of the system.

6 People can predict the behavior of complex systems _____ modeling.

5 Enlarge on the topic covered in the text by giving brief presentations about

1 Keynesian economics

2 Karl Popper’s and Warren Weaver’s main ideas and views

3 cybernetics

4 catastrophe theory

5 chaos theory.

Unit 4

1What basic principles of synergetics do you remember? Give some examples of synergetic approach.

2 Make sure that you can read and understand the words and word combinations below. Memorize them.

cybernetics qualitative changes bifurcation theory

emergence macroscopic scales chaos theory

neuron strong interplay catastrophe theory

hormone cooperative behavior stochastic process

fluctuation paradigmic example instability point

variable theoretical treatment to obey

cognition macroscopic state to elaborate

interdisciplinary order parameters macroscopically

spatial slaving principle irrespective of

temporal circular causality

spontaneous phase transition

3 Read the text

SYNERGETICS

Synergetics (Greek: ‘working together”) is an interdisciplinary field of research originated by Hermann Haken in 1969.The term “synergetics”is widely used, but still not generally accepted. Instead, “theory of self-organization” is used as a more traditional term.

Synergetics can be considered as a modern stage of development within the traditions of cybernetics (N. Weiner, W. R.Ashby) and system-structural analysis (attempts to elaborate the general theory of systems). However, while cybernetics investigates the functioning of complex using an abstract model of “black box”, synergetics studies some physical mechanisms of the complex structures formation, i. e. it tries to look into the “black box”.

Synergetics deals with material or immaterial systems, composed of, in general, many individual parts. It focuses its attention on the spontaneous, i. e. self-organized emergence of new qualities which may be structures, processes or functions. The basic question dealt with by Synergetics is: are there general principles of self-organization irrespective of the nature of the individual parts of a system? In spite of the great variety of the individual parts, which may be atoms, molecules, neurons (nerve cells), up to individuals in a society, this question could not be answered in the positive for large classes of systems, provided attention is focused on qualitative changes on macroscopic scales. Here “macroscopic scales” means spatial and temporal scales that are large compared to those of the elements. “Working together” may take place between parts of a system, between systems or even between scientific disciplines. Characteristic of synergetics is the strong interplay between experiment and theory.

The development of the theory of cooperative behaviour, made by H. Haken and called by himself synergetics proper, originated from the investigation of the coherent radiation of lasers. Lasers became a paradigmic example of synergetics.

The systems under experimental or theoretical treatment are subject to control parameters which may be fixed from the outside or may be generated by part of the system considered. An example for an external control parameter is the power input into a gas laser by an electric current. An example for an internally generated control parameter is hormones in the human body or neurotransmitters in the brain.

When control parameters reach specific critical values the system may become unstable and adopt a new macroscopic state. Close to such instability points, a new set of collective variables can be identified: the order parameters. They obey, at least in general, low dimensional dynamics and characterize the system macroscopically. According to the slaving principle, the order parameters determine the behavior of the individual parts which may be still be subject to fluctuations. Their origin may be internal or external. Because the cooperation of the individual parts enables the existence of order parameters that in turn determine the behavior of the individual parts, one speaks of circular causality. At a critical point, a single order parameter may undergo a non-equilibrium phase transition with symmetry breaking, critical slowing down and critical fluctuations.

Synergetics has a number of connections with to other disciplines, such as complexity theory, dynamic systems theory, bifurcation theory, chaos theory, catastrophe theory, the theory of stochastic processes. The connection with chaos theory and catastrophe theory is in particular established by the concept of order parameters and the slaving principle, according to which close to instabilities the dynamics even of complex systems is governed by few variables only. Synergetics goes beyond the framework of strict mathematical models and narrow applications. Scholars are trying to apply synergetics not only to new fields of natural sciences, but also to humanities. There are some attempts to use synergetic models in understanding human artistic and scientific creativity, cognition, health, education, communication, etc.

1 Say if the statements below are TRUE or FALSE.

1 The term “synergetics” is still being discussed today.

2 Synergetics is being developed and applied by mathematicians.

3 Lasers happened to become quite important for synergetics development.

4 Fluctuations are typically caused from outside.

5 Synergetics can help investigate human abilities and behavior.

2 Answer the questions.

1 What is the origin of the term “synergetics”?

2 How is synergetics related to cybernetics?

3 What is synergetics focused on?

4 What meaning does the term “macroscopic scales” acquire in the synergetic context?

5 What systems can be investigated by means of synergetics?

6 What is the contribution of Hermann Haken into synergetics development?

7 What is the difference between types of control parameters?

8 What are order parameters?

9 When does circular causality take place?

10 What are connections and newest trends of synergetics?

3 Comment on the terms from the text:

interdisciplinary field phase transition

coherent radiation spatial/temporal scales

instability point stochastic process

4 Complete the chart by forming nouns and adverbs from the adjectives enlisted:

Noun Adjective Adverb

__________ qualitative ____________

___________ traditional ____________

___________ stochastic ____________

___________ critical ____________

___________ artistic ____________

___________ creative ____________

___________ natural ____________

___________ cooperative ____________

___________ paradigmatic ____________

5 Add negative prefixes to the words below and sort them out into three columns as in the examples:

in - im - ir-

instability immaterial irrespective

regular, possible, moral, finite, migrant, dependent, capable, movable, mobile, rational, adequate, accurate, resistible, responsive

6 Fill in proper prepositions.

1 Synergetics tries to look _______ the black box”.

2 Synergetics focuses its attention ______ the spontaneous emergence of new qualities.

3 Synergetics proper originated _______ the investigation of the coherent radiation of lasers.

4 According _____ the slaving principle, the order parameters determine the behavior of the individual parts.

5 _____ a critical point, a single order parameter may undergo a non-equilibrium phase transition.

6 Close ____ instabilities the dynamics even of complex systems is governed by few variables only.

7 Scholars are trying to apply synergetics not only _____ new fields of natural sciences, but also ____ humanities.

Unit 5

1 Say what you remember about fractals. Give examples of fractals.

2 What scientists investigated fractals? Try to remember names and countries.

3 Make sure that you can read and understand the words and the word combinations below. Memorize them:

magnification reduced copy Brownian motion

snowflake Hausdoff dimension Levy flight

coastline mountain range fractal landscape

artifact lightning bolt aggregation cluster

triangle true fractals blood vessel

set iterated functions pulmonary vessel

sponge recurrence relation to derive

aggregation complex plane to exhibit

broccoli replacement rule to denote

replica deterministic process to take shape

to coin

4 Read the text

FRACTALS

A fractal is generally “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced copy of the whole,” a property called self-similarity. The term was coined by Benoit Mandelbrot in 1975 and was derived from the Latin fractus meaning “broken”. A fractal often has the following features: