# Bifurcation diagram of the logistic map

Dans le document Complexity Theory: Applications to Language Policy and Planning (Page 56-0)

(A)n0=0.2 andr=0.8. (B)n0=0.2 andr=1.8.

(C)n0=0.2 andr=2.8. (D)n0=0.2 andr=3.8.

FIGURE(1.12) Cobweb plots withn0 = 0.2 and various val-ues forr.

dies out (A) or stabilizes at some specific value (B) within a few iterations. In panel C, which displays the trend forr = 2.8, the population stabilizes at a specific value, but it gets there in a very different way with respect to B, i.e.

by oscillating around it for numerous iterations. In cases A, B and C, the fact that the population stabilizes is showed by the fact that the it converges to a value were the parabola crosses the 45 line, that is, wherent+1 =nt. This is not the case for the trend depicted in panel D, wherer=3.8. The population never reaches a stable point. Rather, it keeps jumping across different values, displaying chaotic behaviour.

### 1.4.4Feedback loops

The presence of feedback mechanisms is a necessary condition for a system to be complex. A feedback loop is defined as a loop in which the output of a system turns itself into an input for that same system. A very intuitive example is that of heating systems. The system generates heat and the tem-perature rises. This higher temtem-perature is “fed back” to the system which interprets it as a signal to stop generating heat when the temperature reaches a certain threshold (normally set by the user). Feedback loops are of two types: negative, in which the effect of the input is reduced (as in the example of the heating system), orpositive, in which the input effect is amplified (as, for example, in the case of lactation, where consumption by the new-born stimulates the organism of the mother to further produce milk). Those fa-miliar with economics (especially financial economics) can think of a selling panic in the investment market as an example of feedback mechanism, or to expectations leading to a boost of the financial markets that, in turn, has a positive impact on expectations. It should be noted that the words “nega-tive” and “posi“nega-tive” are not meant to indicate, respectively, “worse/lower”

or “better/higher”, as common sense might suggest, but only whether the di-rection of the output is opposed to that of the input or not. In the case of the heating system, we would still speak of a negative feedback if we considered the case of a lower threshold being surpassed indicating that the temperature should be increased.

### 1.4.5Spontaneous order and lack of central control

One might be tempted to believe that complex systems should not display any sort of order or self-organizing dynamics. However, it should be noted that pure randomness and total order would equally imply no complexity at

all (Ladyman, Lambert, and Wiesner,2013). If we were to plot order against complexity on two axes, the resulting function would approximately resem-ble a concave parabola (that is, opening downwards). Complex systems are characterized by internal patterns which arise naturally as a response to ex-ternal inputs. However, these patterns are not defined at a central level. This order, being distributed rather than centralized, is said to be robust, in that it is not vulnerable to the malfunctioning of some key elements (Ladyman, Lambert, and Wiesner,2013). This, however, is a necessary yet non-sufficient condition for complexity as also non-complex systems may have no form of central control.

It should also be noted that complex systems are located in what some scholars name “the edge of chaos” (Langton,1990), which is the subtle zone between complete randomness and perfectly structured order.21 Therefore, neither total lack of order nor its opposite could define a complex system.

### 1.4.6Emergence and hierarchical organisation

Emergence is probably one of the (if not the single) most important charac-teristic displayed by complex systems and would probably deserve a whole discussion to itself. Here, however, I only offer a general introduction.

A system is characterized by emergence if it exhibits novel properties that cannot be traced back to its components (Homer-Dixon,2010). Some scholars call these properties “emergent properties” (Bunge, 2003; Elder-Vass,2008).

The adjective “emergent” refers to the fact that such properties are not present at the individual level, but only “emerge” as we move on to consider higher levels of aggregation. To understand this idea one could think of utterances as sets of words. Words have their own properties (such as meaning and syntactic function) and, put together, they can form sentences. However, a sentence is more than the simple sum (or succession) of the words that it con-tains. It has its own meaning that emerges only when its components are put together and is also dependent on extra-verbal contextual elements.22 For a quick (and very unsophisticated) example, think of the profound difference

21Some have noted that the “edge of chaos” areas abound in the natural world, such as the transition area at 0Cbetween ice and water. These situations are constantly falling away from equilibrium and require continuous injections of energy to remain stable (Prigogine and Stengers,1984).

22Note that a language is a complex system in that it is also located in the “edge of chaos”

previously mentioned. Words have to respect precise patterns of expression, which are pro-vided by the grammar and are generally shared and understood by all speakers. Neverthe-less, they are at the very same time subject to arbitrary use by the speakers.

between the words “yeah” and “right” and the utterance “yeah, right” (es-pecially if accompanied by a sarcastic intonation).

A good example from the natural sciences is the saltiness of sodium chlo-ride (i.e. table salt), which is not attributable neither to chlochlo-ride nor to sodium individually. Saltinessemerges as a consequence of a (1 to 1) combination of the two elements. Elder-Vass (2008) goes on to stress that an emergent prop-erty is not only one that is not possessed by any of the parts individually, but also one that would not be possessed by the compounded entity if there were no structuring set of relations between the individual parts (and it is therefore not due to the mere co-presence of these elements). This reasoning echoes what Nobel laureate Herbert Simon argued much earlier:

“Roughly, by a complex system I mean one made up of a large number of parts that interact in a non-simple way. In such sys-tems, the whole is more than the sum of the parts, not in an ul-timate, metaphysical sense, but in the important pragmatic sense that, given the properties of the parts and the laws of their interac-tion, it is not a trivial matter to infer the properties of the whole.”

(Simon,1962, p. 468)

One could conclude that all other characteristics of complex systems are in-deed emergent properties. As a matter of fact, that is far from being incorrect.

Spontaneous order and self-organisation, discussed in the previous subsec-tions, are indeed emergent properties. They emerge only as a consequence of the existing interactions between parts and they are not inherent to any of them. Talking specifically about spontaneous order, Hayek defined it as

“orderly structures which are the product of the action of many men but are not the result of human design” (Hayek,2013, p. 36). Market dynamics lead-ing to equilibria (in the absence of a central coordinatlead-ing body) are quite an eloquent example of emergent (orderly) behaviour (Petsoulas,2001).

Discussing emergence, one should also mention the hierarchical organisa-tion of different levels of observaorganisa-tion. When we adopt a “micro” perspective, we are focusing on the individuals, on the rules that direct their behaviour, and on the efficiency, efficacy, and socio-psychological rationale underlying the origination and adoption of these rules. Conversely, when we switch to a

“meso” perspective, we move away from such a detailed vision and focus on

“meso units”, which can be defined as a population of actualizations (Dopfer,

Foster, and Potts,2004).23 In other words, we are looking in a unitary way at a collection (or population) of elements sharing a similar characteristic (such as belonging to a determined category) or behaviour (e.g. having a specific preference). To put it in algebraic terms, we could say that a meso-unit is equal to:

MEj =

### ∑

n i=1

MIi (1.22)

where MEis a meso-unit, MI is a micro-unit. This means that a meso-unit is the sum ofn micro-units. Therefore, in this specific case, we would have a meso-unitjmade up ofnobservationsisharing a similar characteristic (or behavioural rule). We can also say that there exist as many meso-units as there are rules. Summing up over meso-units we obtain a macro-unit:

MAz =

The relationship linking the macro and the meso level is of the same kind as the one linking the meso to the micro-level. If we put together a number of meso-units sharing a characteristic, we could say, of higher order (in other words, a characteristic that is the same for everyone, even though they are different as we reduce the scale), we obtain a macro-rule. It should be noted that this algebraic representation describes only the number of elements, and not their characteristics.24 Therefore it should not be confused with another statement that I made elsewhere, i.e. that a higher-order complex system is not just the sum of its elements. This latter statement clearly refers to the novel characteristics that the elements display when added up together.

To take a simple example, we could think of individuals as micro-units, the sum of individuals attending the same educational institution as a meso-unit, and the sum of the schools in the same level of education as a macro-unit. It is obvious that there is no strict positioning of the micro, meso, and macro-levels. Reconsidering the same example, we could switch the school

23The authors use the term "actualization" to refer to various ideas. In our case, the term can be described as the sum of "carriers of a rule", where a carrier is an agent whose be-haviour follows some specific rule. The aggregation of these carriers, that is, of the multiple realizations of a specific behavioural rule, is then seen as the actualization of such rule.

24In this regard, we should note that numerosityof elements has also been mentioned as a basic characteristics of complex systems (Anderson,1972), in that complex dynamics can only arise from the interaction between more than a bunch of individual elements. Besides, this is a major difference with respect tochaotic systems, which can have very few interacting sub-units, whose interactions, though, are such that they produce very intricate dynamics highly dependent on initial conditions (Rickles, Hawe, and Shiell,2007).

to the macro-level and make all students belonging to the same class a new meso-unit. What I would like to stress here is not that there exist three levels of observation that always correspond to the same kind of entities, but rather that there are levels of observation that fall along the micro-macro contin-uum, which I call meso-levels. This is always true, in that even an individual can be seen as a macro-unit made up of atomic and sub-atomic particles, be-ing, respectively, the meso and the micro-level. When we move to a higher perspective we are able to concentrate on the dynamics concerning aggre-gations of elements rather than the details characterizing individuals. Pool (1991a, p. 7) notes that some detail tends to disappear while other character-istics of the issue at hand appear or become much more evident as we move from a micro perspective to a more macro scale. Alternatively, from the op-posite perspective, some crucial detail risks being overlooked when we are at a macro-level but becomes evident once we switch to a micro perspective.

However, we should also understand that meso and macro-level dynamics can be embodied in individuals that we could be tempted to consider micro-level actors (this idea will be clarified in a moment). Besides, one may be tricked into believing that the determinants of interest (and, therefore, of op-timal behaviours) are the same at all scales, basically replicating their struc-ture as we move up and down the scale levels (in the same way as fractals have a recursive self-replicating structure). What distinguishes higher-order units (i.e. the macro from the meso and the meso from the micro) is the fact that, as often stressed throughout these pages, they are not just the sum of their constituent parts. Therefore, complex systems are not fragmentable, in that a decomposition into smaller parts would inevitably amount to a loss of properties (particularly, those appearing only at the highest levels of aggre-gation).

### 1.4.7A definition of complexity

After this in-depth examination of the various characteristics of complexity, I can now propose a definition of complex system, which is largely based on the one provided by Mitchell (2009) and takes into consideration all the aspects discussed above: “A complex system is a system in which large net-works of components with no central control give rise to (i) non-trivial emer-gent behaviour at different levels of aggregation, (ii) sophisticated informa-tion processing, (iii) non-linear and/or unexpected effects, (iv) processes of self-regulation, and (v) adaptation via learning and evolution”.

### 1.5How does complexity arise in socio-economicsystems?

In this section I look at real-life manifestations of complexity in social sys-tems. As often mentioned in the previous pages, reality is rich in examples of complexity in all sorts of domains, ranging from the physical laws governing the natural world to the social conventions governing interactions between humans. Concerning social systems, it is easy to see that they are made up of heterogeneous elements, whose conditions are highly dependent on the conditions of others. Therefore, they can be seen as complex environments, where interactions can bring about global dynamics that are more than the sum of individual behaviours.

So far I have considered examples from different spheres. Henceforth I limit the discussion to cases which might be of interest to the social sciences to see why and how complexity came to be considered by policy makers. I briefly discuss how complexity arises in business contexts and then I move on to consider the case of the public sphere in greater detail. In general, I pay greater attention to language-related cases.

### 1.5.1Complexity in business and management

The issue of complexity has largely been explored by scholars in business and management since the early 1990s, especially from an organizational be-haviour perspective (see, for example, Simon 1962; Stacey 1996; Levinthal 1997; Anderson1999; Kelly and Allison1999; McKelvey1999; Chiles, Meyer, and Hench 2004; Gruhn and Laue 2006; Gharajedaghi 2011; Straub 2013).

Complexity theory is of particular interest for strategy choices in large corpo-rations characterized by interconnected structures. However, some authors noted that complexity theory is still struggling to become a fully accepted approach to business management. Straub (2013) suggests that this is in part due to the reluctance of managers to accept a complexity approach in that it would inevitably make their job dramatically harder.

Traditionally, corporate strategy has been treated as a centralized activity, under the responsibility of corporate executives who are often supposed to be in possession of all critical information and to have the right incentives to make decisions for the good of the company as a whole (Eisenhardt and Piezunka, 2011). Besides, many large companies have a business-unit (BU) structure, whereby BU-executives have information limited to their own BU

and make choices accordingly (Hill, Hitt, and Hoskisson, 1992). This defi-nition reflects an approach to business management as a complicated issue, as opposed to a complex one, whereby an optimal strategy of local units is expected to lead to optimality for the company as a whole. Concerning com-plex strategies in multinational corporations, Eisenhardt and Piezunka (2011) (quoting Chandler 1962) propose the telling example of the large chemi-cal company DuPont, which turned from a single-business firm into a large multinational company operating in several markets in the post-War period.

Initially, the company retained its strongly centralized organisation, which led to poor performance. As a reaction, executives restructured the company into several loosely-linked units, which resulted in a significant performance boost. As another example, they also mention the case of General Motors, which was initially a group of several independent producers. Only when the company started organising these units in such a way as to create links among them did the company reach high levels of performance.

Multinational companies (or, better, companies dealing with people from different cultural backgrounds, which are not necessarily multinational)25 of-ten find themselves in the situation of having to decide on language issues for internal and external purposes. As is discussed more at length in Chapter 2, a constantly recurring issue is the trade-off between prioritizing the use of a single language and continuously adapting to the local context, especially when managing the aftermath of a merger or acquisition. On the one side, unrestricted multilingualism can cause severe inefficiencies. On the other side, though a common language could boost cross-border collaboration, it can come at a very high price, such as, shadowing talented workers who are not proficient in it. Besides, it can (quite paradoxically) generate misun-derstandings due to non-proficient use. Neeley and Kaplan (2014) mention the detrimental promotion of a Japanese worker in a US company’s Japanese subsidiary exclusively based on his fluency in English. Only later did it ap-pear clear that he was not the best performer and most deserving employee, and that his promotion, based on a severely biased view, had generated dis-content among his peers. Besides, a common language does not amount to a common culture and definitely not to a common set of values and underly-ing assumptions when it comes to handlunderly-ing interpersonal relationships. Re-searchers call “cultural clash” the phenomenon of disruptive tension expe-rienced by individuals when they have to interact in a second language and

25This is the case of many national companies working in multilingual countries, though the “one-nation-one-state-one-language” ideology is still somewhat resistant.

adopt the ways of another culture (Berry,1983). Many scholars found that in-tercultural interactions are very likely to generate misunderstandings, in that individuals are used to (sometimes radically) different social customs and rules (Calori, Lubatkin, and Very, 1994; Weber, Shenkar, and Raveh, 1996;

Vaara,2000).

Besides, language issues develop in different ways at different levels. In fact, micro-linguistic behaviours can differ significantly from those at the macro level. Even if we conceived language choices and behaviours sim-ply as the strategy that guarantees optimality of communication overall, it is easy to see that accommodating one’s own individual needs is very different from meeting the need of a large (and possibly linguistically and culturally diverse) community. Besides, discussing the scale of complex phenomena, some authors found it suitable to mention also a meso-level (as defined in the previous pages), recognizing that the micro-macro dichotomy is better described as a continuum rather than two separate points (see, for example, Kaplan and Baldauf1997).

### 1.5.2Complexity in public policy

Most policy decisions more and more frequently concern complex systems.

Their effects spread all over the system concerned through multiple actions and reactions (Bankes,2011). For example, environmental policies are never strictly environmental, in that they are introduced in a system that has sev-eral other characteristics (political, cultural, demographic, economic. . . ). This is a rising trend. Government officials and policy makers deal with very di-verse systems involving a large number of interacting parts (OECD, 2009).

Therefore, complexity science constitutes a valuable approach to policy mak-ing and policy evaluation, especially once we recognize that the questions

Therefore, complexity science constitutes a valuable approach to policy mak-ing and policy evaluation, especially once we recognize that the questions

Dans le document Complexity Theory: Applications to Language Policy and Planning (Page 56-0)