A First Note on Complexity theory
« L’organisation, la chose organisée, le produit de cette organisation et l’organisant sont inséparables ».
Paul Valéry (1920).
According to Robert Delorme, “complexity is a word connoting nowadays what may be simplified into two broad strands of research in economics, a computer-based complexity and an observation-based complexity, which differ in their tools but not in the central features they highlight, their method and their status in economic science. The difference in tools appears as follows. One strand is based mainly on computer simulation and on formal modelling in search of a substitute for the analytic limits of conventional mathematics. The Santa Fe Institute programme is representative of this perspective. The other one is based on observation, on empirical enquiry and on theorising from it, and is represented by the evolutionary, institutionalist and behavioural perspectives in political economy” (Delorme 2001).
Let me add another view of complexity that comes from law studies and is quite relevant for the economy of the 21st century and some quarters of the current research in economics referred above:
“There is no doubt that the law has always been complicated. It is a frequently heard complaint these days that we suffer from legislative inflation and that legal procedures are interminable and uncertain. But Leibniz wrote as early as 1678 that « it is not possible to know the law without a very large library », while Bentham in an open letter to the American citizens said, « Everywhere the common law has set foot, security has disappeared. »
At that time, we may say that the law was only complicated, while today we are obliged to talk about its complexity. Complication arises from the accumulation of simple sequences; it is the repetition of the same code or the same logic that produces the effect known as complication, in the sense that clockwork or 18th-century automata were complicated, while relying simply on a limited number of mechanical gears.
However, the law has indeed become complex and we are therefore obliged to think in terms of this complexity. In her most recent work, Pour un droit commun, Mireille Delmas-Marty makes the following observation, « Whether concerned to prescribe a norm, to interpret it or to justify it by reference to meta-judicial values, our patterns of thinking are still strongly influenced by the age of enlightenment. Precise rules, syllogistic reasoning and homogeneous values – in short, a « monological » order – are vastly preferred by the legal profession.”(Ost and van de Kerchove 2002) 
This definition is not complete. I must add some remarks. First, « two fundamental meanings of complexity must be distinguished : complexity as reality and complexity as method » (Caetano and Jacquinet 2003, forthcoming) as stated in the aforementioned definition of Delorme.
For Bruce Edmonds, “complexity is that property of a language expression which makes it difficult to formulate its overall behaviour even when given almost complete information about its atomic components and their inter-relations” (Edmonds 1999). Behind the notion of complexity there is the concept of emergence that turns the traditional methods of analysis ill-suited for radical novelty and radical uncertainty.
 Ost, François and Michel van de Kerchove (2002) « Constructing the complexity in the law: towards a dialectic theory », Réseau Européen Droit et Société (RED&S), / G.W. LEIBNIZ, Trois textes sur le droit et la codification, in Archives de philosophie du droit, 1986, p. 361. BENTHAM, Lettre de J. Bentham, un Anglais, aux citoyens des divers États des États-Unis d’Amérique, in Papers relative to codification, The works of J. Bentham, ed. Bowring, Edinburgh, 1838-1843, v. IV, p. 479. DELMAS-MARTY, Pour un droit commun, Paris, 1994, p. 193-194.
 I must thank the editor and my co-author for permitting me to use some of the material written on complexity.