1. The Theory and Computation of
Anticipatory Systems
Loet Leydesdorff
University of Amsterdam,
Amsterdam School of Communication Research (ASCoR)

2. Robert Rosen (1985): “An anticipatory system can be defined as a system which entertains a model of itself.”  Computing Anticipatory Systems (CASYS; Daniel Dubois)
Talcott Parsons’s (1951) “double contingency”:
Ego expects Alter to entertain expectations about Ego like herself.
Ego (xt) operates on the basis of an expectation of its own next state (axt+1) and the next state of an Alter (1 – xt+1).
xt = axt+1 (1 – xt+1)
The relation between Ego and Alter is reciprocal, but not symmetrical;
The operation is future-oriented; intentional meaning is communicated
Expectations are transitive and can cycle among more than two persons → a non-linear dynamics of expectations (Niklas Luhmann).

3. Historical patterns of communication along trajectories
Horizon of meanings
time
Historical patterns of communication along trajectories
Meaning is communicated from the perspective of hindsight, that is, using the backward arrow
 In a knowledge-based system, the intersubjective layer of codified expectations feeds back as a regime on and reconstructs the carrying agents

4. The Computation of Anticipatory Systems (Dubois, 1992, 1998, 2003)
recursive: x(t) = a x(t-1) {1 – x(t-1)}
incursive: x(t) = a x(t-1) {1 – x(t)}
hyper-incursive: x(t) = a x(t+1) {1 – x(t+1)}
Examples:
Incursive: Technologies develop historically, but are selected on the market in the present (trajectory);
Hyper-incursive: The Rule of Law is an order of expectations (regime).

5. Recursive; historical
Hyper-incursive order of expectations
This equation has two solutions:

6. xt+1 = ½ ± ½ √[1 – (4/a) xt]
Nature
Culture

7. xt+1 = ½ ± ½ √[1 – (4/a) xt]
NetSci07

8. weak anticipation; prediction
Horizons of meaning
weak anticipation; prediction
Strong anticipation;
Knowledge-based reconstructions and innovations

9. Political Power
Scientific Truths
Economic Transactions

10. Luhmann (1975, p. 76): “No matter how abstractly formulated are a general theory of systems, a general theory of evolution and a general theory of communication, all three theoretical components are necessary for the specifically sociological theory of society. They are mutually interdependent. (...)
The decisive questions now become: How are these various theories related to one another? What unifies them? How must a theory that integrates them be constructed?”
Communication theory: What is communicated? Meaning cannot be transferred  nonlinear dynamics of meaning;
Evolution theory: What is evolving? Codification of Meaning  Global versus local; horizons of meaning
Systems theory: The mechanism: Functional differentiation among the symbolically generalized codes of communication.

11. Summary and Conclusions
At the level of social systems, we don’t only entertain models, but also communicate them. The interaction among expectations generates a non-linear dynamics of meaning;
Luhmann: Interaction, organization, and self-organization of meaning-processing at the level of the social system;
Incursive organization and hyper-incursive self- organization of fluxes: the one cannot proceed without the other;
Reflexivity couples the strongly anticipatory system to weakly anticipatory (human) minds
The system is constructed bottom-up, but control tends to be top-down