Emergence 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 0^◦Cbetween 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:

ME_j =

∑

MI_i (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).