Chaitin’s Thin Line in the Sand: Information, Algorithms, and the Role of Ignorance in Social Complex Networks

Ugo Pagallo

University of Turin


Chaitin’s algorithmic theory on information sheds light on Hilbert’s famous phrase “We must know. We will know.” in a twofold way. On the one hand, what Chaitin demonstrates, after Gödel’s theorems on incompleteness and Turing’s halting problem, is something--namely the halting probability Ù--strikingly unknowable, maximally uncomputable. On the other hand, according to Chaitin, human knowledge requires something beyond simple mechanical rules, which is creativity. Hence, we have got a sound perspective in order to grasp the peculiarity of contemporary research on social complex networks. In fact, social complex networks are defined by an amount of information that goes beyond any human capability of complete rationalization as shown by the emergence of spontaneous orders, by the unpredictable evolution of social networks, and also by the fact that even in the realm of human interaction some things are without reason. The constitutive role of ignorance in social sciences, however, does not mean that we cannot understand how those orders spontaneously emerge or how social networks do evolve. On the contrary, in recent years we have grasped many of these very laws, as in the case of small world-networks, adaptive complex systems, etc. As is the case with Ù, the algorithmic theory of social information as an evolutionary theory of both legal and political institutions represents a sort of border between what we can deal with and what transcends our theoretical possibilities as social scientists.  As Chaitin said, "it draws a...thin line in the sand that we dare not cross, that we cannot cross!”