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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

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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

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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

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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

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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

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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.

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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?

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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

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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

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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.

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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:

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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

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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

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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.

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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

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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.

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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.

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