Conclusion
C.1. Some general considerations
Few people are aware of the full implications of chaos science. Many people still believe that with enough data input (even a deluge of data), accurate long-term predictions are possible because it fits into their conventional thinking. As human beings, we are not at ease with the feeling that we are not in full control of our destiny. For some, this constraint questions our capability to exert our free will.
“Big data” is the notion that more information than ever can be collected about the world. It is the object of a lot of speculative ideas. The most controversial is that “big data” will result in algorithms that will know people better than they know themselves, and that this knowledge could be used by businesses or governments for manipulative ends, while undermining the very idea of individual freedom. The danger is certainly real. As more of the world may become tailored around individuals’ personality traits and interests, people will be subject to become passive recipients of AI decisions. However, in any case, accurate long-term forecasting will remain teemed with uncertainty.
The majority of the scientific community will come, sooner or later, to consider in one way or another that the scientific revolution brought about by the development of complexity and chaos science is to be compared with the upheaval brought about by the theories of relativity and quantum mechanics, but with a critical difference. Only theoretical physicists are exposed to the theories of relativity and quantum mechanics. The outfalls of complexity and chaos science will more and more affect our daily lives, because we are more and more depended on nonlinear systems of systems embedded in our environments.
The purpose of the scientific study of dynamical systems, after the first discoveries of Poincaré at the turn of the 20th Century and the use of computer power (butterfly effect discovered by the meteorologist Lorentz), is to explain how the future states of a system could be forecast from its initial states. In order for such a forecast to be reliable and useful, nearby initial states should lead to future states that do not take courses different from one another. However, it appears that in many cases when the situation is modeled by nonlinear equations, even close initial states lead, within short intervals of time, to future states that diverge quickly from one another. This can be qualified as time-chaos.
Some renowned scientists (de Broglie, Bohm, both of them Nobel Prize winners) put forward the idea that hidden variables could be imagined when trying to interpret the Shrödinger’s equation in terms of physical parameters accessible to human senses of perception. Darwin’s theory of evolution is a telling example of work successfully carried out within a framework of hidden variables. It is noteworthy to elaborate on this instance on the fact that penetrating analysis is a critical factor to assess any domain of knowledge successfully.
In the wide diversity of life on earth, Darwin distinguished a new principle for the organization of matter and the emergence of design. He was totally unaware of the existence of DNA. Yet despite his ignorance of the hidden variables of inheritance, he derived, through his shrewd analysis of the world around him, his theory of evolution in 1859 in an overwhelming convincing treatise titled “The Origin of Species”. It is a daunting question, when nothing was known about the molecular basis of genetics, to explain how a correct theory was delivered. The answer is rather straightforward.
The hidden variables of inheritance imprint their character on the relationships between all organisms. With minor changes, these variables endure through generations and are mixed like a multifold coin-toss in the game of life. The incessant experiment that is natural selection is constrained to produce results in which correlations inherent in the genotype are encoded in the phenotype.
Darwin arrived at his theory not by carrying out experiments but by simply observing and analyzing the phenomena of an experiment that had been running for billions of years. Each organism is a data point in the theory of evolution.
When these ideas are transposed in universes where human relations are involved, a strong stochastic factor plays a role that is difficult to assess. The second-order cybernetics approach can help provide a general modeling framework, i.e. the observed object and the observing object. Stochastic or deterministically chaotic, whatever the actual nature of unsmooth behaviors, long-range forecasting is unreliable. “Long range” has to be understood as a function of the phenomenon under consideration.
Another interesting example can be found when trying to understand the relationship between macroeconomics and microeconomics. At first sight, it can be reasonably thought that macroeconomics can be described as the behavioral aggregation of microeconomic agents, vernacularly called “homo economicus”. A priori teaching and learning macroeconomics should not generate any difficulty. Practically, they give professors and students the jitters. In fact, the subject is notoriously intricate, difficult to explain well and to convey macroeconomic intuition. Clear answers have to be delivered to muddled students, not to say laymen. Using math is an escape from thinking, and clear answers do not leap out of the equations.
In addition, theorists (classical, Keynesian, monetarist, new classical, new monetarist, etc.) disagree about so much and textbooks disagree about so little that different models are not always explained consistently with each other or even with themselves. The result is that many professors must teach concepts, notions and paradigms they do not believe in. Furthermore, it is full of faux amis, words that mean something else in every day parlance. The concept of equilibrium, for instance, is often used. Thermodynamics tells us that a living organism cannot survive in a state of equilibrium but must be open to its environment in a state of stability for securing its survival. The lack of semantic interoperability and coherence between the two disciplines explains why macroeconomics is often called the “dismal science”, disconnected from the common behavior of individuals and perceived as complex, namely not easily accessible to a wide public.
C.2. Complexity versus chaos
At the present time, the notion of a complex system is not yet precisely delineated as the idea is still somewhat fuzzy, and it differs from discipline to discipline and author to author. But the complex systems, those which we are keen to understand, are the biological ones, not only deal with our organic bodies but also deal with our lives as mindful beings in societal groupings. Living organisms are the iconic images of complexity in many people’s view.
Our purpose here is not to come to a precise definition, but to try to convey the meaning of complexity by enumerating what seem to be the most typical properties. It is noteworthy to be aware of the fact that the systems theory was pioneered by biologists, or scientists with direct or indirect connections to biology. Most of these properties are shared by many non-biological systems as well.
C.2.1. Complex systems contain many constituents interdependent and interacting nonlinearly.
Complex systems refer either to phenomena observed in nature or to man-made artifacts constructed on the basis of what we called the laws derived from the study of nature. The former systems refer to a decomposition approach (top-down) in line with the reductionist method proposed by Descartes, whereas the latter systems are built with a composition approach (bottom-up) integrating step by step subsystems. In both cases, systems are cognitively complex because they are perceived as being made of many constituents, generally interacting nonlinearly.
Interdependent implies interacting, otherwise systems constituents should be independent.
Recall that nonlinearity is a necessary condition for observing chaotic phenomena, and that almost all nonlinear systems whose “operational” phase space has three or more dimensions are chaotic in at least part of their phase space. This does not mean that all chaotic systems are complex: the logistic equation is a telling example. Chaotic behavior can appear with very few constituents; complexity does not. This establishes a decisive distinction between chaos and complexity.
Interdependence may mean different things according to the type of system envisaged. Consider first a non-complex system with many constituents – say a crystal slab. A crystal is made up of a spatial pattern of ordered rows of atoms. Cut away 10% of a crystal slab. On the whole, the very nature of the crystal system has not changed and the laws governing its properties remain the same.
Now carry out a thought experiment with a complex system where functional capabilities and roles are assigned to well-identified agents. Take a human body and just cut off a leg! The result will be drastically more spectacular than for the crystal. The new system will be entirely different from the previous one, because it will have to adjust its objectives with its new capabilities. A one-legged human being is not provided with the same mobility capabilities as a two-legged one!
C.2.2. A complex system possesses a structure spanning several levels
It is often helpful to have access to more than one level of understanding of a situation in our minds. The point is not to maintain different descriptions of a single system. What is confusing is when a single system admits a multi-description on different levels, which nevertheless resemble each other in some way.
Computer systems are a case in which many levels of description coexist for a single system, depending on the point of view and where all levels are conceptually interoperable between one another. When a computer program is running, it can be envisioned from a number of levels. At each level, the description is given in the language of computer science that makes all of the descriptions compatible. Yet they are important views we get on the different levels.
In data processing, all programs, no matter how large and complex and whatever the language in which it has been coded, must be transformed into compounds of instructions executable in machine language. These instructions constitute a repertoire of operations that are “understood” by the electronic hardware. Several intermediary languages are required to run a program written in a “high-level” language such as COBOL, Fortran, Pascal and C++. Two main translators into machine language have been developed, namely compilers and interpreters.
Compiler and interpreter programs convert a program written in a high-level language into machine language. It is written in a language which typically does not reflect the structure of the machines which will run programs written in them. When a compiler or interpreter language program is translated into machine language, the resulting program is machine-dependent.
While compilers translate all the statements first, before the machine code is executed, interpreters, instead of translating all the statements first and then executing the machine code, read one statement and execute it immediately. This technique has the advantage that a user need not have written a complete program before testing its execution.
As long as a program is running correctly, it hardly matters how it is described or is thought of in its functioning. When something is going wrong, it is important to be able to think on different levels. If, for instance, the machine is instructed to divide by zero at some stage, it will come to a halt and let the user know of this problem by telling them where in the program the questionable event occurred. However, the specification is often given on a lower level than that in which the programmer wrote the program. Here are three parallel descriptions of a program grinding to a halt:
Machine language level:
“Execution of the program stopped in memory location 111000101110001”.
Assembly language level:
“Execution of the program stopped when the DIV (divide) instruction was hit”.
Compiler language level:
“Execution of the program stopped during evaluation of the algebraic expression (A+B)/Z”.
The idea of assembly language is to “chunk” the individual machine language instructions by referring to them by a name instead of writing sequences of bits. Every level has a specific structure. This is an essential and radically new aspect of a complex system, and it leads to the next property.
C.2.3. A complex system is capable of emerging behavior
Emergence occurs at a bifurcation point when the pattern of inner-system interactions under the pressure of the environment or of a disruption in the inter-agent interactions is changed.
In a multi-level system, certain behavior, observed at a certain level, can be said to be emergent if it can be understood when you study, separately and one by one, every constituent of this level, each of which may also be a complex system made up of finer levels. Thus, the emerging behavior is a new phenomenon unique to the level considered and can impact the behavior of the whole multi-level system. If the observed behavior cannot be explained only by local constituents, influences from other levels have to be taken into account. An emergence at a certain level can trigger chain reactions in other levels resulting in a global emergence.
The human body is capable of walking. This is an emerging property of the highest level of human capabilities which can be decomposed into a hierarchy of capabilities. If you study only a head, or only a trunk, or only a leg, you will never understand the mechanism of walking. The combination of structure and emergence leads to self-organization, which is what happens when an emerging behavior has the effect of changing the current global structure or creating a new one.
There is a special category of complex systems which was worked out especially to accommodate living beings. They are the example par excellence of complex adaptive systems. As their name indicates, they are capable of changing themselves to adapt to a changing environment. They can also influence the environment to suit themselves. Among these, an even narrower category is self-reproducing: they experience birth, growth and death. Needless to say, we know very little that is general about such systems considered as theoretical abstractions. We know a lot about biology. However, we do not know much, if anything, about other kinds of life, or life in general.
C.2.4. Complexity involves reciprocal action between chaos and order
We already mentioned that complexity and chaos have in common the property of nonlinearity. Since practically every nonlinear system is chaotic part-time, this means that complexity implies the presence of hidden chaos. However, the reverse is not true. Chaos is a subject which has already received much attention from the scientific community. However, complexity has a much wider embrace and covers lots of cognitive situations which have nothing to do with chaos. Chaos requires mathematics to get a quantitative grasp of it, and by now much progress has been made to apprehend it. Complexity is still almost unknown when human agents are involved. The quote of Einstein “As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain they do not refer to reality” holds true especially in the realm of human organizations where individual and collective behaviors cannot be realistically modeled by equations.
The field of chaos may appear to be a subfield of the field of complexity. Perhaps the most striking difference between the two is the following. A complex system can always be analyzed by scaling levels. While chaos may reign on level n, the coarser level above it (level n+1) may be perceived as self-organizing, which in a sense is the opposite of chaos.
Many people have suggested that complexity occurs “at the edge of chaos”, but no one has been able to elicit this totally. Presumably, it means something like the following. Imagine that the equations governing the evolution of a system contain some “control” parameter which can be adjusted, depending on the context. We know that most nonlinear systems are not chaotic in all conditions: they are chaotic for some ranges of values of the control parameter and not chaotic for others. Then, there is the edge of chaos, i.e. the precise value of the control for which the nature of the dynamics switches. It is like a critical point in phase transitions, or the point where long-range correlations become most influential. Complex systems, such as biological systems, manage to modify their environment so as to operate as much as possible at this edge-of-chaos place, which would also be the place where self-organization is most likely to occur.
C.2.5. Complexity involves interplay between cooperation and competition
All complex systems that concern all of us very closely are dissipative systems (section 3.1, Chaos). All social systems and all collections of organisms subject to the laws of evolution belong to this category. Examples are plant populations, animal populations, other ecological groupings, our own immune system, and human groups of various sizes such as families, tribes, city-states, social or economic classes, and, of course, modern nations and supranational corporations. In order to evolve and stay alive, as Theilhard de Chardin noticed, living organisms tend to develop more and more complex structures. In order to remain complex, all the systems directly or indirectly linked to humanness need to obey the following rule:
C.2.5.1. Complexity implies interplay between cooperation and competition at different organizational levels
Once again this refers to interplay between system levels. The usual situation is that competition on level n is nourished by cooperation on the finer level below it (level n-1). Insect colonies like ants, bees or termites provide a telling demonstration of this. For a sociological example, consider the alumni of Oxbridge in UK. They compete with each other towards economic success and corporate top positions. They strive to find the most desirable spouses and to provide for their young heirs through the educational system with the same social status they enjoy. And they succeeded better in this strive if they have the unequivocal and earnest support of all their university fellows, and also if all their fellows have a chance to take part in their success by exchanging information, offering mutual help, etc. Once this competition–cooperation dichotomy is understood, the old cliché of Darwin’s “survival of the fittest”, which has done so much damage to the understanding of evolution in the public’s mind, is very far.
Complex systems, such as the weather, the economy and social organizations, face the problems dealt with in thermodynamics, namely understanding the relationship and interplay between order and disorder. For a closed system in thermal equilibrium, the transition between order and disorder is the consequence of a compromise: a part of the energy available tends to deploy order, while the other part, called entropy and associated with temperature, tends to break down the order. Thus, order and disorder can be associated respectively with cooperation to yield a compelling structured pattern of a sort and competition to gain a sort of freedom of action. This is a daunting challenge when we try to gain control of the split, especially when human behaviors are involved, all the more so that uncertainty is an integral part of the game.
If the approach to reality by systems thinking has been pioneered by Ludwig von Bertalanffy, a French sociologist Edgar Morin has carried out an extensive work on complexity thinking. He has produced the following definition: “the issue related to complexity is not completeness but incompleteness of knowledge. In some way complexity thinking tries to take into account of what truncating kinds of thinking get rid of and I call them simplifiers. Thus it fights not incompleteness but truncating… Complexity thinking in its core, although it endeavours after multidimensionality, has a principle of incompleteness and uncertainty” (Morin 1990, p. 164).
Considering its features of incompleteness and uncertainty, complexity thinking can be linked to what Abraham Moles calls “sciences de l’imprécis” (Moles 1995). According to him, recursive analytical analysis has proved explicitly or implicitly to be the most appropriate tool to tackle complexity. “It is always possible, and often helpful, to consider any phenomenon, object, being or message that we perceive in the world, as combining a certain number of simple elements of limited variety according a set of certain rules, called code or structure. This synthesis will be qualified as a model and its value draws on the accuracy with which its functioning mirrors the initial phenomenon. Identifying structural thinking and what can be called ‘atoms’ thinking in the etymological sense of this term is the essential epistemological fact of this approach. Reconstructing the world from these atoms is the very purpose of the structural methodology that is applied in three steps:
- 1) look for which atoms are involved
- 2) find out the rules of the assembly code for a certain number of these atoms for reconstructing a masquerade of reality
- 3) make an appraisal of the masquerade and if it appears not adequate, go back to step 1”.
C.3. References
Moles, A. (1995). Les sciences de l’imprécis. Éditions du Seuil, Paris, p. 148.
Morin, E. (1990). Science avec conscience. Fayard, Paris, p. 164.