-
1
Unit II. SYNERGETICS
After completing this unit, you will be able to:
Define the terms Synergy and Synergetics Speak on the key
notions of Synergetics Use competently Past Participle Compose and
read off mathematical notation in English
Ex. 1: Check the pronunciation and translate the following
international words.
Algorithm Control Cybernetics Equilibrium Evolution
Generalization
Heurica! Heuristic Laser Macro Medium/Media Micro
Paradigm/Paradigmatic Tempo Thermodynamics
Ex. 2: Look up the possible translations of the following “false
friends» in a dictionary:
medicine: ......................................
besides:.........................................................
design: ........................................... besides:
........................................................
identical: .......................................
besides:.........................................................
original: ........................................ besides:
.......................................................
abstract: ....................................... besides:
.......................................................
radiation: ......................................
besides:.........................................................
construction: ................................ besides:
.......................................................
formula: ………………………... besides:
.......................................................
sympathetic: ................................. besides:
.......................................................
Ex.3: Translate the collocations into Russian. Then explain your
favorite ones in your own words in English to your groupmates so
they can guess which collocation you mean.
Enormous variety, new whole, mere sum, anticipatory design,
universal
applicability, entire system, mutual aid, black box, cooperative
behavior, starting
point, accelerated development, optimistic attempt, harsh
management.
Ex.4: Study the words to Text A « Synergy». Translate the
examples into Russian in writing.
1. 1 synergy, n [ˈsɪnəʤɪ]
Синергия, взаимодействие, совместная деятельность
Synergy may be defined as “increased effectiveness,
achievement, produced as a result of combined action.”
2. 2 literally, ad буквально The company has received literally
thousands of messages.
3. 3 denote, v обозначать Sigma is the Greek symbol used to
denote deviations from
-
2
the mean.
4. 4 joint, n сустав It felt as if he'd torn a muscle above the
joint.
5. 5 inspire, v
вдохновлять We are inspired by the creative solutions of
many
companies protecting their intellectual property.
6. 6 emerge, v появляться In the early 60's a new generation
emerged who attacked
that trend.
7. 7 recognize, v распознавать He learned to recognize the
panels that controlled lighting.
Ex.5: Text A.
Before discussing Synergetics - the main topic of the unit -
it’s worth learning the
term Synergy and its basic characteristics.
Read the text and present your own examples of synergy effect in
our life, in other
words, prove that 1+1=3!
Synergy The Greek word "synergy" means, literally, "working
together." In medicine, it
has long been used to denote the working together of two or more
drugs, or of two
or more muscles acting as a joint. Applied to the human mind,
"synergy" denotes
the working together of the enormous variety of functions that
comprise the mind,
producing a new whole that is greater than the mere sum of its
parts.
An early pioneer in synergy was Buckminster Fuller, whose
concepts of
anticipatory design for Spaceship Earth have inspired
generations of students.
Fuller emphasized the key role of synergy in producing a whole
that is greater than
the sum of its parts. Something new emerges - something that can
exist only at the
higher level of organization made possible by synergy.
Indeed, synergy is of universal applicability. It can be applied
not only to the
human mind, but also to human groups, to organizations of all
kinds, to industrial
enterprises, to entire economic systems, to international
relations, to any
functioning system. Its basic characteristics of improving
effectiveness by mutual
aid, and of producing emergent wholes, can be recognized in
every system to
which it is applied.
Text A Analysis.
Ex.6: Complete the sentences referring to the text.
1. Literally “synergy” means …
2. Buckminster Fuller was …
3. The key role of synergy is…
https://translate.google.ru/translate?hl=ru&sl=en&u=https://www.auburn.edu/~fordfn1/wh7cls05.ppt&prev=searchhttps://translate.google.ru/translate?hl=ru&sl=en&u=https://www.auburn.edu/~fordfn1/wh7cls05.ppt&prev=search
-
3
4. Synergy can be applied to…
5. Synergy has two basic characteristics: ……………. and ……………..
Ex.7: Write down as many cognate words as possible: to emerge –
…
to inspire - …
to apply - …
to produce - …
Ex.8: R. Buckminster Fuller has been called as "…one of the
greatest minds of
our times". Fuller wrote 28 books, coining and popularizing the
terms such as
"spaceship earth", ephemeralization, and synergetics. He also
created a large
number of inventions; the best-known is the geodesic dome.
It’s great to get acquainted with him, so find out the
information interesting to
you and make a report about B. Fuller.
Ex.9: Study the words to Text B «Synergetics». Translate the
sentences comprising them.
1. Synergetics, n [sɪnəˈʤetɪks]
синергетика - это междисциплинарное научное направление,
изучающее процессы самоорганизации,
устойчивости, распада и возрождения разнообразных
структур живой и неживой природы 2. self-organization,
n
самоорганиза́ция — процесс упорядочения элементов одного уровня
в системе за счёт внутренних факторов, без
внешнего воздействия.
3. complexity, n
сложность Each time interval greatly increases the
computational
complexity of the problem.
4. chaos, n [ˈkeɪɔs]
хаос A great example of a nonlinear system exhibiting chaos is
all
around you: the weather.
5. elaborate, v
разрабатывать The key idea of the book is expressed in the title
and
elaborated in the text.
6. self-control, n самоконтроль By constant self-discipline and
self-control you can develop
the greatness of character.
7. reveal, v
выявлять, обнаруживать Sometimes a second, closer examination
can reveal the things
you didn't see before.
8. dissipative structure
диссипативная структура A dissipative structure is a dissipative
system that has a
dynamical régime that is in some sense in a reproducible
-
4
steady state.
9. coherent, a когерентный The light from a laser is said to be
coherent, which means the wavelengths of the laser light are in
phase in space and time.
These three properties of laser light are what make it more
of
a hazard than ordinary light.
10. worldview, n
мировоззрение By advancing geographic knowledge, they broadened
people's
worldview and enhanced trade.
11. nonlinear, а нелинейный You can use it to solve nonlinear
equations.
12. auto-waves, n автоволны, автоволновой процесс The term «
auto-waves »is generally used in processes where
the waves carry relatively low energy, which is necessary
for
synchronization or switching the active medium.
13. deterministic, a детерминированный Chaos theory suggests
that even in a deterministic system, if
the equations describing its behavior are nonlinear, a tiny
change in the initial conditions can lead to an
unpredictable
result.
14. arise, v
возникать, появляться Considerable debate has arisen over their
origin and many
explanations have been given.
15. fluctuation, n
флуктуация, колебание Paranormal activity causes fluctuations in
the electro-
magnetic field.
Ex.10: Text B. Read the Text and select the appropriate heading
for each part.
Synergetics HEADINGS: From strict science to the philosophy of
life (IV); New science of
complexity (III); Various scientific schools (II); Synergetics
as a field of scientific research
(I).
I. The term «synergetics» was introduced by Hermann Haken, a
German
scholar. It has existed for over forty years already and it is
widely used, but still not
generally accepted. Instead, «theory of self-organization» is
used as a more
traditional term. Recently two other terms «studies in
complexity» and «theory of
chaos» have become widely used.
Synergetics can be considered as a current stage of development
within the
traditions of cybernetics promoted by N.Wiener & W.R.Ashby.
Cybernetics
investigates the functioning of complex systems 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».
Cybernetics elaborates
-
5
algorithms and methods of systems’ control; synergetics
investigates the processes
of self-control and self-organization of complex systems in the
world.
II. The focus of synergetic research program is to reveal
general laws of self-
organization and evolution which are common to processes of
quite different
nature: physical, chemical, biological, psychological, social.
The whole history of
development of the theory of self-organization shows that
significant theoretical
generalizations appeared from rather narrow, but fundamental
scientific results.
The non-equilibrium thermodynamics and the theory of dissipative
structures
developed by the Brussels school of the Nobel Prize winner Ilya
Prigogine started
with the investigation of processes in physical chemistry.
The theory of cooperative behavior, developed by H.Haken,
originated from the
investigations of the coherent radiation of lasers. Lasers
became an example of
synergetics. Another example of natural science starting point
for further
generalizations up to a worldview one can mention the
investigation of nonlinear
auto-waves as early as in the 1930′s by the Russian school of
L.I.Mandelshtam and
A.Andronov.
It’s worth mentioning the Polish-born French-American
mathematician B.
Mandelbrot who elaborated the so-called theory of deterministic
chaos, various
scenarios of transition to chaos and back. All these trends are
colored in specific
tones of the original disciplines, e.g. mathematics, physics,
chemistry or biology.
III. «Complexity» is one of the key notions in the field of
synergetics. The
theory deals with such questions as: 1) how does a complex
structure arise; 2) what
are the trends of a complex structure development; 3) how can a
complex
evolutionary whole be constructed?
Synergetics reveals the creative role of chaos in the process of
origin of complex
structures and their evolution. Chaos and fluctuations on the
micro-level play an
essential role in determining processes at the macro-level.
Complexity is closely
connected with the speed (tempo) of evolution. A complex
structure is an
integration of structures of «different ages», i.e. structures
at different evolutionary
stages of development. Structures of «different ages» start to
co-exist in one and
the same ‘tempo-world’. The principles of integration of such
«different ages»
structures into an evolutionary whole structure are revealed in
synergetics.
IV. Synergetics goes beyond the framework of strict mathematical
models and
narrow applications. In the current situation of accelerated and
unstable
development of the world, synergetics brings us new hopes. It is
an optimistic
attempt to understand the principles of co-evolution of the
complex social systems,
to reveal causes of evolutionary crises, instability and chaos.
How to manage a
complex system without harsh management is the major problem.
How can we
push the system in a favorable (for the subject) evolutionary
path with a small
influence? Synergetics can serve as a heuristic instrument in
searches of answers to
the questions.
Text B Analysis.
Ex.11: Find in the text the English equivalents to the
following: 1. Стать широко распространенным
-
6
2. Современный этап 3. Формирование сложных структур 4. Процессы
совершенно разного характера 5. Существенные обобщения 6. Теория
кооперативного поведения 7. Ключевое понятие 8. Сложное
эволюционное целое 9. Структуры «разных возрастов» 10. Принципы
интеграции 11. Выявить причины 12. Направить систему в подходящем
направлении 13. Эвристический инструмент
Ex.12: Follow the tasks. Part I is called
“_________________________________________”
a) Choose and write out all the terms relevant for the term
“synergetics”
___________________________________________________________
b) Find out at least 3 differences between synergetics and
cybernetics and fill in the comparative table:
SYNERGETICS CYBERNETICS
1. 1.
2. 2.
3. 3.
c) Agree or disagree with the statements: 1. Sometimes the terms
“synergetics” and “the theory of chaos” are used as
identical.(T)
2. Synergetics investigates the processes of self-controlling
and self-organization of universities. (F)
Part II is called
“_________________________________________”
a) Complete the sentences referring to the part: 1. The Brussels
school developed ….. 2. The German school presented …. 3. The
Russian school investigated… 4. The American scholar elaborated....
5. All these investigations are colored ...
b) Agree or disagree with the statements: 1. The focus of
synergetics is to hide some general laws of self-
organization which are common to processes of quite
different
nature.(F)
2. Lasers became an example of synergetics.(T)
Part III is called
“_________________________________________”
a) Fill in the missing parts of the sentences from the part: 1.
Synergetics reveals the creative role of ----- in the process of
origin of
----structures.
-
7
2. ------ is closely connected with the speed (----) of
evolution. 3. Complex structures are the ---- at different ----
stages of development. 4. Structures of «different ---» start to
co-exist in one and the same
‘tempo-----’.
5. The ---- of integration of such «different ages» structures
into an evolutionary whole structure are revealed in ---------.
b) Agree or disagree with the statements: 1. One of the key
notions specifying investigations in the field of
synergetics is similarity.(F)
2. Synergetics tries to explain how a complex evolutionary whole
can be constructed.(T)
Part IV is called
“_________________________________________”
a) Which sentence would you choose as the key sentence of the
part? Why? 1. Synergetics goes beyond the framework of strict
mathematical models
and narrow applications.
2. It is an optimistic attempt to understand the principles of
co-evolution of the complex social systems, to reveal causes of
evolutionary crises,
instability and chaos.
3. Synergetics can serve as a heuristic instrument in searches
of answers to the questions.
b) Agree or disagree with the statements: 1. Synergetics brings
us new hopes in managing a complex system
without harsh management.(T)
2. Synergetics can’t serve as a heuristic instrument.(F) Ex.13:
In the texts you can find the verbs «to evolve», «to create», and
«to exist», figure out as many ways of translation as possible and
write down the cognate words:
to evolve – …
to create - …
to exist - …
Ex.14: Refer closely to Texts A and B, and answer the
questions:
1. What does the term “synergy” mean? 2. Can you underline the
key role of synergy? 3. Is synergy of universal applicability? 4.
Who introduced the term “synergetics”? 5. What does synergetics
study? 6. What is the focus of synergetics? 7. Can you list the
main questions synergetics deals with? 8. What is a complex
structure? 9. Do chaos and fluctuations play an essential role in
complex
structures?
10. How can synergetics be applied in various situations?
-
8
Ex.15: Render the following text into English in writing, paying
attention to the terms
from the exercises above:
Синергетика – междисциплинарное научное направление,
изучающее
закономерности самоорганизации открытых систем в
неустойчивом
необратимом состоянии. Синергетика претендует на открытие
некоего
универсального механизма, с помощью которого осуществляется
самоорганизация как в живой, так и в неживой природе. Поэтому
объектом
синергетики могут быть только системы, которые удовлетворяют
двум
условиям:
- они должны быть открытыми, т.е. обмениваться веществом
и/или энергией с внешней средой;
- они должны быть существенно неравновесны, т.е. находиться
в
состоянии, далеком от термодинамического равновесия.
Важнейшим свойством самоорганизующейся системы является
бифуркация.
Бифуркация – это состояние системы, когда она находится перед
выбором
возможных вариантов функционирования и малейшие, случайные
обстоятельства могут кардинально изменить направление ее
дальнейшего
развития закрывая возможные альтернативные пути ее
изменения.
(Наглядно-образное представление о точке бифуркации дает картина
В.М.
Васнецова «Рыцарь на распутье»))). То множество траекторий, по
которым
возможно развитие системы после точки бифуркации, и которые
отличаются
относительной устойчивостью, называются аттракторами.
Синергетика
определяет хаос как многоликое материальное начало, которое не
только
разрушает и само является продуктом разрушения, но и
способствует
созданию нового. Во-первых, хаос необходим для исходного
структурирования нелинейной среды. Во-вторых, он
способствует
резонансному объединению простых структур в единую сложную
структуру,
согласованию темпов их эволюции, объединению «темпомиров».
В-третьих,
хаос может выступать как механизм переключения, смены
различных
режимов развития системы, переходов от одной относительно
устойчивой
структуры к другой.
Ex.16: You have learned that synergetics is an interdisciplinary
science explaining the formation and self-organization of
structures in open systems far from thermodynamic
equilibrium. So, we can discuss the main characteristics of
self-organizing systems: openness,
nonlinearity, fluctuations, bifurcation points, emergence of
order, dissipation, attractors and
chaos.
Below there are eight definitions determining each term,
identify the appropriate term
for each definition:
1. __________ Property of chaotic systems, characterized by
approximation, random behavior, and unpredictability. It is the
feature of
a system which cannot be decomposed into parts and reassembled
into
the same thing.
https://www.revolvy.com/topic/Self-organization&item_type=topichttps://www.revolvy.com/topic/Open%20system%20(systems%20theory)&item_type=topichttps://www.revolvy.com/topic/Thermodynamic%20equilibrium&item_type=topichttps://www.revolvy.com/topic/Thermodynamic%20equilibrium&item_type=topic
-
9
2. _________In a critical phase new qualities of a
self-organizing system emerge; this principle is also called order
from chaos or order through
fluctuation. Interactions between the components result in new
properties
of the system that cannot be fully predicted and cannot be found
in the
qualities of the components, therefore we say that a
self-organizing
system is more than the sum of its parts.
3. ____________ Small disturbances from inside the system
intensify themselves and initiate the formation of order.
4. ____________An open system is a system that has external
interactions. Such interactions can take the form of information,
energy, or material
transferred into or out of the system boundary.
5. ____________ Once a fluctuation intensifies itself, the
system enters a critical phase where its development is open,
certain possible paths of
development emerge, and the system has to make a choice. It’s
a
transitional phase from stability to instability.
6. ____________ Sometimes it looks like an exclusively
destructive element of the world, but it’s a necessary condition
for self-organization
and a way of evolutionary switching.
7. ____________The loss of energy from a physical system, most
often in the form of heat.
8. ____________ A set of states of a nonlinear dynamic system
toward which that system tends to evolve, regardless of the
starting conditions of
the system. They may appear, disappear or change stability
through
different bifurcations.
Ex.17: Now watch the video
https://www.youtube.com/watch?v=3ypBqxv_tz8 and present your
personal point of view towards synergetics in a written form.
Ex.18: Read the text below, fill in the gaps with the words from
the box and make up a summary:
essential reveals self-organization
destructive leads chaos
creative opens up regime
Up to now many people are afraid of chaos. It did resemble a
gaping abyss1 as
far back as in the ancient mythology. Chaos looks like an
exclusively ________
element of the world. It seems that chaos ________ to
nowhere.
1 зияющая бездна
https://www.youtube.com/watch?v=3ypBqxv_tz8
-
10
The classical view of chance is still sometimes valid. Chance
(randomness) is
considered as a secondary and subsidiary factor which is not of
principal
importance. Chances are being forgotten and washed away; they
leave no traces in
the course of events in nature, science, culture and
society.
Synergetics ________ the creative role of chaos (random
fluctuations) in the
evolutionary processes which occur in nonlinear complex systems.
There must be a
certain degree of chaos and destruction in the world. Chaos and
fluctuations on the
micro-level play an _________ role in determining the actual
trends, or “aims”, of
processes at the macro-level. Chaos manifests itself as a
“force”, as a mechanism
underlying an exit to one of several evolutionary
structure-attractors. The macro-
organization evolves from ________ on the micro-level.
Order and chaos, organization and disorganization, construction
and destruction
seem to be well-balanced in the world. Thus, it is senseless to
resist chaos, or to
tend to completely eliminate the negative, destructive elements
from the world.
Chaos is a necessary condition for ______________.
Besides this, chaos serves as a basis for integration of
relatively simple
evolutionary structures into more complex ones. It is a
mechanism of coordinating
their tempos of evolution. Chaos and fluctuations on the
micro-level, can also be a
way of evolutionary switching, allowing a periodical transition
from one
evolutionary regime to another one.
Synergetics reveals the sympathetic, ________ face of chaos.
Chaos is,
ultimately a field producing sparks of social and cultural
innovations. Because
chaos _________ the possibility for the appearance of something
completely new,
an element of chaos is desirable. Synergetics allows us to
understand destruction as
a creative principle. “A passion for destruction is creative”,
wrote the Russian
philosopher M.Bakunin. Thanks to the liberation from the old and
to the turn of
evolutionary processes to an opposing _________, something new
can emerge
from the remains of the old. (From “The Complex Nonlinear
Thinking” by H. Knyazeva)
Ex.19: Read the paragraphs and arrange them in their logical
order:
The possibility of synergetics to solve actual problems of oil
and gas industry
1. Let's consider the possibility of applying synergetics to the
problems of the oil and gas industry, where systems that can be
considered as self-
organizing, open and nonlinear are involved.
2. Summarizing these arguments, we can conclude that the use of
a synergistic approach is promising for solving problems in the
petroleum industry.
Applying synergetics to these problems will allow looking at
them in a new
way and, perhaps, will open up innovative ways to solve
them.
3. The problem of exploration of new fields and identifying the
patterns by which oil «returns» to the mature, already developed
deposits can absolutely
be considered through the prism of the synergistic method.
-
11
4. At the moment, the petroleum industry is in a very
complicated situation. This is directly related to the decline in
prices for hydrocarbon resources on
the world market. This is not the only problem, although it is
significant.
5. In the course of field development, there are difficulties
that are quite difficult to predict (for example, a water or gas
breakthrough). Therefore, it
is possible to consider the developed deposit as a
self-organizing system in
the development process, the impact on it at certain points
(pumping of
hydrocarbons, pumping of water/gas, processing of bottom-hole
zones of
wells, etc.) – as fluctuations, and the "critical" stages of
development as
bifurcation mechanisms, will create a clearer and more accurate
model of
development. This, in turn, will help solve issues related
specifically to the
development of deposits.
6. The processes of deposits’ formation and migration of oil in
the Earth 's crust can be examined as evolution of self-organizing
systems, connected
with geological structure of the Earth 's crust. The presence of
self-
organization in the geological structure can be judged from the
data of
seismic exploration and geochemical analysis of the core.
7. A number of problems related directly to the construction of
pipelines and transportation of hydrocarbons cannot be solved with
the help of
synergetics, since these processes are aimed at interacting with
systems that
are not self-organizing.
(https://research-journal.org/philosophy/vozmozhnost-primeneniya-metoda-
sinergetiki-k-resheniyu-aktualnyx-problem-neftegazovoj-otrasli/)
Grammar: Past Participle
We use the past participle to make the perfect tenses and for
all
the passive forms. Perfect tenses (have|/has/had drilled
etc.):
The company has drilled the wells. (present perfect)
They were still drilling. They hadn’t left. (past perfect)
Passive (is drilled/ had been found etc.):
He was woken up by a loud noise. (past simple passive)
This deposit has just been discovered. (present perfect passive)
Past Participle in a sentence has a passive meaning:
Some of the people invited to the party can’t come. (the people
have been invited to the party)
Most of the goods made in the factory are exported. (the goods
are made…)
When wounded, he was brought to the hospital. (when he was
wounded…)
Ex.20: Determine the grammatical past participle functions and
give exact Russian
equivalents to the following phrases:
-
12
Applied to the human mind, has long been used, have inspired,
can be applied,
was introduced, cybernetics promoted by Wiener, is widely used,
the theory
developed by the Brussels school, could be constructed, when
heated, is closely
connected, are being revealed, accelerated development, cannot
be mapped, are
being forgotten and washed away, to be well-balanced, might be
fully predicted,
had been determined.
Ex.21: Translate the sentences into Russian paying attention to
Past Participle:
1. Considered from the mathematical point of view, nonlinearity
signifies a certain type of mathematical equations. These contain
unknown quantities in
powers more than 1 or coefficients depending on properties of a
system.
2. Such events are to be forgotten, they don't leave any traces
in nature, science or culture.
3. The processes of simplification of organization and possible
transitions to chaos are considered by synergetics only as
necessary evolutionary stages.
4. An effect of localization, i.e. the structure formation, and
the appearance of extremely complicated structures may be observed
in these systems.
5. Certain human actions are doomed to failure. They fail
because they are not in step with the inner trends of the complex
system development. There are
evolutionary prohibition rules which are imposed on some kinds
of human
action.
6. Numerous conferences and publications have been devoted to
the role of synergetics for the last decades.
7. At this level we treat the liquid as being composed of little
droplets with certain temperature, density etc.
8. After the variables of the mesoscopic level characterizing
the system have been fixed, equations describing their temporal
change must be established.
9. Quite clearly a number of analogies between physical and
chemical processes on the one hand and processes in sociology and
economy on the
other can be worked out.
10. “Can we exploit the insights we have gained in synergetics
to either construct computers or to program them adequately? …” (by
H. Haken /
Synergetics and Computers)
11. Having reached specific critical values the system may
become unstable and adopt a new macroscopic state.
http://www.scholarpedia.org/article/Stability
-
13
12. The system can be brought by fluctuations to a critical
point called ‘bifurcation’. The term ‘bifurcation’ was coined by
the French
mathematician and philosopher of science Henri Poincare in
1885.
13. Nowadays, systems theory — which is partial to cybernetics
and feedback models — seems to have been temporarily eclipsed by
“complexity theory”.
14. Working on the theory of percussion drilling, the scientists
have designed a drill with a suspended pneumatic percussion.
15. If used in a business application, synergy means that
teamwork would produce an overall better result than if each person
within the group was
working toward the same goal individually.
Ex.22: Prepare to give a 5 minute talk on one of the following
topics and discuss these in
class:
The history of the concept of « Synergetics» Modern synergetics
The tasks of synergetics The principles of the theory of
synergetics The role of synergetics
https://libtime.ru/modelirovanie/sut-ponyatiya-sinergetika.html
Skills: How to read off mathematical notation in English
https://stemreader.org.uk/guidelines/
Once you start to read maths aloud, you quickly discover that
what seems like
simple notation results in a long stream of text. For example,
solve the equation 𝟑𝒙+𝟐
𝒙−𝟏+ 𝟑 = 𝟒 must be read as "solve the equation 3 x plus 2, all
over, x minus 1,
plus 3, equals, 4" where commas have been inserted to indicate
places to pause.
Often a person would use pauses, stresses and variations in tone
to communicate
groupings and semantics within maths notation.
Fractions are presented graphically with a numerator above a
denominator,
separated by a horizontal (or occasionally sloping line). When
reading aloud a
fraction, it is important that the listener understands what is
contained within the
numerator and denominator. The separator between them is purely
a graphical
representation and how it is drawn does not alter the structure
of the fraction. 𝟓
𝟐𝟓 numerator over denominator 5 over 25.
𝟏
𝟐 should always be read as one half. If the denominator is
between 2 and 10 then it
may be read in its colloquial form: 1
4,
2
4,
3
6, 3
2
15 one quarter, two quarters, three
sixths, 3 and two over fifteen.
https://libtime.ru/modelirovanie/sut-ponyatiya-sinergetika.html
-
14
Work out 𝟏
𝟕 ×
𝟐
𝟑 one seventh times two thirds.
Complex fractions should be read as [numerator] all over
[denominator]
Simplify 𝒙𝟐+𝟓
𝒙+𝟐 x squared + 5 all over x + 2.
A decimal point should be read as "point". Numbers following a
decimal point
should be read as individual digits. "0" is spoken as zero not
"oh".
0.125 zero point one two five.
When a plus sign on top of a minus sign appears between two
variables or numbers
then it should be read as "plus or minus".
Calculate 3±5 Three plus or minus five.
Where the multiplication sign × appears as an operator between
two variables or
numbers then it should be read aloud as "times".
Calculate 26×19 26 times 19
Where two variables or a variable and operator are displayed
consecutively as an
implicit multiplication, the multiplication should not be read
aloud.
Find the value of 3a+2b Three a plus two b.
Where the division sign ÷ appears as an operator between two
variables or
numbers then it should be read aloud as "divided by". It should
be noted that
division should not be typeset with a slash (e.g. 7/3).
Work out 110÷4 110 divided by 4.
Brackets can take different forms. The most common are round
brackets or
parentheses ( ). It is usual within the UK education system to
refer to these as
brackets. Brackets can be used to denote a number of
mathematical functions.
When a bracket is used to group an expression or to represent an
implicit
multiplication then the brackets should be read aloud as "open
bracket"…"close
bracket". Where there is a sequence of brackets, it can be
useful to pause between
the "close bracket" and following "open bracket" to signify they
are separate
expressions.
Simplify 3(x+2) + 5x 3 open bracket x + 2 close bracket + 5
x
Expand and simplify (y−2) (y−5) open bracket y minus 2 close
bracket, open
bracket y minus 5 close bracket.
When a mathematical exponent is written as a superscript number
or variable then
this should be read as "to the power of". If possible pause at
the end of the
superscript variable, operator or expression to indicate it has
finished. Where the
exponent is of value 2 this may be read as «squared» followed by
a pause.
-
15
Calculate (5×103) ÷ (2×10
-2) open bracket 5 times 10 to the power of 3 close
bracket, divided by, open bracket 2 times 10 to the power of
negative 2 close
bracket.
Where a variable, operator or expression is displayed as a
subscript, then precede
this with "subscript". If possible pause at the end of the
subscript variable, operator
or expression to indicate it has finished. It may be possible to
shorten "subscript" to
"sub" if the reader is award of this contraction.
Given that un=5un-1+1 u subscript n equals 5 u subscript n minus
1, plus 1
Where a root is not preceded by an index, it is assumed to have
an implied index of
2 and notate a square root. This should be read aloud as "square
root of". Where a
root is preceded by an index of 3 this should be read aloud as
"cubed root of".
For a root with an index with a number greater than 3, the
expressions should be
read starting with the index as "xth root of". If the radical
index is a variable then it
should be read as "x root of y".
Example: √𝟏𝟒𝟒𝟒
= √𝟐𝟖𝟖𝒙
4th root of 144 equals xth root of 288.
Where brackets are used to differentiate between the input of a
function, it should
be read aloud as "[function name] of [input]". Example
F (x) = 𝟐
𝒙𝟐 − 𝟑𝒙 f of x equals, 2 over x squared, minus 3 x.
Where the < symbol is used it should be read as "less
than".
Where the ≤ symbol is used it should be read as "less than or
equal to".
Where the > symbol is used it should be read as "greater
than".
Where the ≥ symbol is used it should be read as "greater than or
equal to".
When a colon is used between two numbers or variables to
represent a ratio it
should be read aloud as "colon". Write 25: 55:15 in its simplest
form 25 colon 55
colon 15.
Some examples:
x≈y x approximately equals to y.
3+7≠13 3 plus 7 not equal to 13.
Given that O is the centre of the circle and that ∠AOB=75°
Angle, capital A, capital O, capital B = 75 degrees
𝜋5 pi [pai] to the power of five
∫ 𝐹(𝑥)𝑏
𝑎dx integral [ˈɪntɪgrəl] from a to b of the F of x dx
52 % fifty-two per cent
Write the formula for each maths transcription:
1. Eight point two three times ten to the power of six 2. Seven
over eleven 3. Ten to the power of negative six
-
16
4. x greater than or equal to 16 5. Square root of 20 equals 2
square root of 5 6. One half open bracket a plus b close bracket, h
7. 4 over 3 pi r to the power of 3 8. One third pi r squared, h 9.
Open bracket 1 plus, i over n, close bracket to the power of n,
minus 1 10. Pi to the power of three over the fifth root of x 11.
Open bracket square root of 2 plus square root of 8 close bracket,
squared 12. 3 a to the power of 3 b + 12 a squared b squared + 9 a
to the power of 5 b to
the power of 3
13. For x equals 5, solve x squared, plus 3 14. Open bracket 7
to the power of 3, times 7 to the power of 5, all over 7 to the
power of 10, close bracket to the power of negative 1
15. Open bracket 5 times 10 to the power of 3 close bracket,
divided by, open bracket 2 times 10 to the power of negative 2
close bracket
REVIEW 2
I. Fill in the missing letters in these words.
1. The syn__rgetics deal__ with su__h quest__ons as:
2. How does a co__plex structure ar__se, i.e. the problem of
becom__ng;
3. __hat are the trend__ of a complex struct__re
developm__nt;
4. How c__n a complex evol__tionary w__ole be construct__d, the
problem of
rel__tion of parts to a who__e.
II. Write down the maths transcriptions of the formulas.
1. 5𝑥+2
𝑥−4+ 8 = 6
2. 1
4 ×
6
15
3. 214÷8
4. (y−7) (y+9)
5. S = v × t
6. √𝑐35
III. Circle the word or word combination in bold that fits the
best.
-
17
The Art of Complex Nonlinear Thinking
Some common patterns of the complex systems behavior are
revealed in
synergetics/synergy. The science makes steps towards a new
nonlinear/linear
evolutionary worldview as well as towards the stating of the
principles of complex
nonlinear thinking. The most essential elements/bifurcation
points of this
thinking are the understanding of:
1. The constructive role of chaos in evolution/degradation, the
connection of chaos on a micro-level with evolution of structures
on a macro-level;
2. The laws/principles of very fast, avalanche-like processes,
blow-up regimes in complex/ simple systems;
3. The existence of changing rhythms and regimes of evolutionary
processes, the nonlinear dynamics of evolutionary processes/
deals;
4. The patterns of constructing complex totalities from simpler
elements (or subsystems), that is the elaboration of a kind of a
new evolutionary
holism/interdisciplinary science;
The style of thinking of classical science is subjected to
radical criticism/
unanimous approval from the synergetic point of view. The style
is characterized mostly by patterns of
linear thinking. Some of them are not eliminated/ revealed up to
the present.
That's why it is worthwhile/ obligatory to consider in detail
the crucial shift of
paradigm/idea from linear to nonlinear thinking.
IV. Translate the following table «System Analysis versus
Synergetics» in writing to show your understanding of the Unit I
and Unit II.
Системный анализ Синергетика
1. Акцент делает на статике систем. 1. Акцентирует внимание на
процессах роста,
развития и разрушения систем.
2. Придает большое значение
упорядоченности, равновесию.
2. Считает, что хаос играет важную роль в
процессах движения систем, причем не только
деструктивную.
3. Изучает процессы организации систем. 3. Исследует процессы
самоорганизации.
4. Чаще останавливается на анализе
структуры систем, абстрагируется от
кооперативных систем.
4. Подчеркивает кооперативность процессов,
лежащих в основе самоорганизации и
развития систем.
-
18