To understand the importance of complex systems in the description of economics and society interactions as such requires a brief overview of the historical development of mathematical methods.

Originally, thee were only causing tasks that lead to developments of arithmetics and later to algebra that was used to plan and predict the economic evolution of companies on a small scale.

With the development of calculus and statistical methods, economics gained a new possibility in the description of larger economical segments, whole companies, and the whole economies.

From real economics, we see that our mechanistic and statistical understanding of it failed. What are the main reasons for this failure?

Currently, we are aware of the fact that mean field approximations used in differential equations and statistical parameters of the economy are insufficient in capturing the fundamental processes that are defining the evolution of the economies.

So what are those fundamental, for the evaluation and prediction of economy fundamental processes? It is one to one interactions of constituting elements of our models. Single people in companies, single companies in economies, single people in societies and their well defined mutual interactions.

Hence, we arrived at the core of complexity and its constituting parts and rules. Surprisingly, as was shown in many other disciplines, the very local and between individuals carried out interactions are fundamental for a description of the overall, global behavior of the systems.

We now for a relatively long time from physics that even by use of very simple models, which are capturing all fundamental local interactions as precisely as we can capture them, are surprisingly powerful in the description of the overall behavior of the systems.

That all including phase transitions, parameter sensitivity, order to chaos transitions, and many otherwise very difficult mathematical features of the observed natural phenomena.

Complex systems when well defined from the beginning, understand their local spatio-temporal interactions produce surprisingly robust and generic global responses that are easy to be identified with observed phenomena.

This leads us to the core of complexity: self-organization, emergent behavior, self-repair, creation of virtual entities and their interaction within the systems via emergence, multiscale emergence, etc.

This all is for a long discussion. By the way, the question is very important, so important that I decided to write down an overview of complex systems in biology and medicine. Many parts of this overview are relevant to your question. See, the review: Complex Systems and Their Use in Medicine: Concepts, Methods and Bio-Medical Applications.

No, because chaos theory is a part of classical physics. However there are two cases for deterministic chaos: Hamiltonian chaotic systems and non-Hamiltonian chaotic systems and they're qualitatively different.

Mr.Stam Nicolis I would like if you made clear your claim, that chaos theory is a part of classical physics.Thank You in advance.

"Will the chaos theory overcomes the centuries mechanic paradigm in economics, leadership and management?"

I do not know, but it surely is to be hoped for that the results from nonlinear dynamics will somehow make their way into economic sciences. Otherwise, we will probably remain helpless against the recurring return of economic crashes. Economies certainly are nonlinear systems and the typical behaviour of nonlinear systems under mild side conditions is chaotic. That means that it may be the normal situation for a free-running economic system to behave chaotically, i.e. to undergo a crash from time to time (aperiodically).

Hence, chaos theory suggests that generically the market does not regulate itself in a manner to stay away from these disastrous events, so economic systems should not rely on such a self-regulation. On the other hand, we know that chaotics systems can be controlled to stay near a desired trajectory in phase space by remarkably little external driving. Hence, if we had an economic theory at a level of predictive power similar to physical theories, we might know which minor measures (no fully planned economics, of course) would be sufficient to keep us away from the disastrous events (market crashes) on nice benign, almost periodic or constant orbits with a moderate increase in overall economic volume according to the growth of the planetary population.

On the other hand, if the fact is ignored that economic systems are nonlinear and hence prone to chaotic behaviour, we may not be able to do more than accept (unforeseeable) crashes, with the ensuing destruction of possessions, fortunes, and, in the worst case, supply with food.

It is a continuation of my previous answer to this question. Complex systems showed to be very powerful in the description of systems expressing self-organized critically. The term was founded by Per Bak and co-workers who wrote a paper about 1/f noise. There is a book of Per Bak on the topic too.

Very coarsely said, it can be explained on the sand pile model. You take a flat desk, put it at an elevated position and are putting one sand grain at a time in the center of it. After some time, the carrying capacity of the desk is exceeded and avalanches of sand are released from the desk. You measure the number and size of events.

When you make a logarithmic plot of a number of avalanches against their size, you get a straight line. It means that you are dealing with a power law dependence of a number of events on their size.

The ecology, society, and economy models are expressing the power law dependence too. Hence, you have a good prototypical model enabling you to study the economy. The avalanches can be associated with booms and crises. Think about the stock market and you immediately see avalanches there. There is a lot of physicists studying the stock market and econo.y in this way.

When interested, we can continue by some other examples of mathematics used in modeling of the economy. Quite of few of such complex systems, mathematical tools can be found in my latest review on complex systems use in biology and medicine (it is applicable outside of medicine too).

We testimony that economic models don't give good results in practice. One of the most important reasons is that the chaos ''obstruct'' precise future prediction. In addition to that, the problem is using mechanistic paradigm (linearity paradigm) for explaining non-linearity behaviour, as what are expectations of stakeholders, making decisions from management etc.

In that sense it is very important seriously studied of chaos theory, respectively studied of complex adaptive systems, which exist between order (Newton's paradigm) and disorder (chaotic paradigm).

Through studying chaos theory-complex adaptive systems, we will be in occasion to remarkably increase probability of predicting during making our decisions.That was essence of may question: Will the chaos theory overcome the centuries mechanic paradigm in economics, leadership and management? Overcome but not totally extract.

Nonlinear dynamics can open the path to enclosure-overcoming mathematics that allow science to become explicative, thus can help to overcome the traditional, mere descriptive since enclosure-confined rank of science: cf. Number form theory linked to Structure wave theory.

When I said that chaos theory will overcome, but not replaces mechanic paradigm too, I thought that managers have task to assess in which context they will use certain paradigm ( Newton or Complexity paradigm).The most mistake is made when managers use linearity for the resolving non-linearity problems.

On my opinion, this is often happened in the praxis. Do you have any comment, example or opinion about this?

The complex system enables building emergent and self-organizing structures in models. It is very difficult to achieve by older approaches (Newtonian based ones). Those features are inherent to biology, ecosystems, societies, and not surprisingly to economies.

When a complex systems model is built correctly at the microscopic level, it can often automatically reproduce observed macroscopic features. Agent-based models are proven to achieve such behavior in countless studies including economic ones.

What do you mean by ”self-organizing“ structures, Jiiri? Thanks so much.

Margaret Wheatley:''When simple relationships are created, patterns of organization emerge''.

Dear Jean, dear colleagues. Nature has a fascinating ability to utilize self-organization within its inner working. Simply said, self-organization is the tendency of the system to achieve the same or similar functional state irrespectively of its beginning.

The best is to provide examples. One example can be the von Karman path, which is created in the water after it passes around an obstacle. There are created whirlpools behind. Turbulent flow self-organize itself into a hierarchy of whirlpools of decreasing size and dissipate energy in this way.

Earthquakes are created by self-organized critically where the system is gradually fed by energy and its release happens suddenly in the form of avalanches. It is the same for stock markets where avalanches are sudden increases or decreases.

Cities grow according to some simple rules and tend to self-organize themselves into structures having certain properties.

Traffic flow self-organize itself into traffic jams, which occurrence suddenly occur above some critical density of traffic.

We can go on for a long time. Virtually almost all that we observe is based on self-organization and especially emergence. It is a fascinating world.

Thanks, Jiri for your ample reply!

What I actually meant with my question was: What is the source of self-organization given that we do not explain a property of an enclosure-confined system or mechanism by description: We merely describe a posteriori what has happened inside (cf. science paradigm!).

Therefore, my answer to my question is the following: Consciousness alone may justly be titled self-organizing inasmuch as it appears all-embracing, meaning i) acting non-locally and ii) enclosure-independently.

Indeed, no interdependent system can be held self-organizing. It is for this reason that the universe we are part of must not be thought self-organizing:

a) a universe is not everything since part of the (manifested) Mental generated by the Core of Consciousness thru dedicated releases of structure waves (cf. Structure wave theory);

b) nothing with a start (in time) can be everything.

Our truly fascinating world, among others, is actually governed by Consciousness explaining both any enclosure and the embedded mechanisms, all based on the DAT-mechanism (Discrete Amplitude Transform) applied to the structural oscillators populating any enclosure.

Hi Jiri again,

You wrote simplifying: "Self-organization is the tendency of the system to achieve the same or similar functional state irrespectively of its beginning".

This imperatively signifies that there is "something" at the start "knowing" where it goes. This definition already presupposes the work of Consciousness without explicating that!

And here is the point to be criticized: All our theories, naturally based on definitions, presuppose Consciousness without knowing their properties respectively how it works...

Hi Jiri,

As a result, what you call "Nature" is actually Consciousness from which standard science does not know much (since performing enclosure-confined) while presupposing constantly their work so that the established theories can hold.

To overcome enclosure-confined thus exclusively descriptive science, enclosure-overcoming mathematics are required: they are provided by Number form© theory. Number form metrics conjointly used with encoded structure waves provide explicative science instead...

Dear Jean Thill , Jiří Kroc , K. Kassner thanks for your comments.

As Jiří Kroc says: Nature has a fascinating ability to utilize self-organization within its inner working.Look at flocks of birds, fishes or people in the crowd. Nobody tells them how to behave together.All of them individualy(subconscious) understands and follow simple rules and selforganizing itself

Dear Jean Thill, can you provide a paper or other source of the term "number form theory". Without its understanding it is difficult or impossible to give a qualified answer.

Intuitively, from your answers I got understanding what is this theory about. When I got it correctly, it might be a mathematical link between spirituality and 'material' world.

I am really keen to read more about. Thank you for further information.

By the way, I do know that complex systems are not ultimate theory. It is just a step toward better description of biology and medicine, which sooner or later will be superseded by another deeper theory that tables us to link spiritual energy and matter.

Back to the original question. Unseen energies are playing a great role in biologicals systems, societies, and economies.

Dear Jiri, my papers on NFT & SWT are published on RG. Kind regards.

Dear Jiri, .....''mathematical link between spirituality and 'material' world''...What is with the thermodynamics (entropy)?The spirit of our time distinguished by the absence of awareness of the disappearance of the world...In establishing a coherent unity of inorganic and organic, also must considered and supernatural too (not as something mystical and esoteric, but as an integral part of the theory of knowledge about big chain of beings).So it would create an opportunity for discovering that unknown property of energy. Such property which allows the formation of higely organized matter capable of using this capacity. Regadless of the ways of our cognition, we must understand that in spite of our multi millenium ripening and evolutionary acumen, we cannot be smarter from the process which old a few trillion years.If we once see through the properties of the Universes that are oppose entropy, such as ordering, emergence, self -organization, increasing complexity...,then discovery even the greatest secrets will be, probably, possible...Just thinking...

After the fundamental discovery of a chaotic behavior in the n-body problem by H. Poincare, the theory of dynamical systems was developed with the significant contributions of George Birkhoff, Jürgen Moser, Andrey Kolmogorov and Vladimir Arnold. Today, the methods of this theory are applied in all areas of science. In meteorology, the concept of a "butterfly effect" was developed to reflect the chaotic behavior of the fluid systems studied by Edward Lorenz in the 1960s. As far as the economy is concerned, we should definitely mention Benoit Mandelbrot's contributions to the analysis of the stock market. Not surprisingly, this work has been fundamental for increasing our knowledge about the role of fractal sets in economy and social sciences. I would like to suggest the excellent book by Mandelbrot illustrating some aspects of a “financial turbulence”: “The Misbehavior of Markets: A Fractal View of Financial Turbulence”

In order to answer the question directly, the chaotic nature of the economic systems is taken into account in the daily practice of corporate management. This statement can be verified by studying the current literature. Please see for example, Bullard and Butler (1993): “Nonlinearity and Chaos in Economic Models: Implications for Policy Decisions”

https://files.stlouisfed.org/files/htdocs/wp/1991/91-002.pdf

Janusz Pudykiewicz Thank You for your comment.

Absolutely!