Complexity and emergence

An interview with Chris Langton from the Santa Fe Institute

Interview and editing:

Yoav Ben-Dov

Cohn Institute for the History of Science
Tel-Aviv University

Made during the conference "Einstein Meets Magritte", Brussels, June 1995.
Published in Hebrew: Galileo 12, Sept-Oct 1995.

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Yoav ben-Dov: What is complexity research?

Chris Langton: Complexity is a field of research in which we try to study systems that are scientifically very interesting, but which do not yield to the usual tools of mathematical analysis. Such systems contain many autonomous participants which interact with each other, for example: human society and economy, insect colonies, cellular automata on computers, some chemical systems, and other systems in various domains. In all these systems, a global behaviour emerges from the local interactions between the participants. We are trying to study this behaviour, and our working hypothesis is that it exhibits some common structural features, which are more relevant than the specific details of each system.

YB: What kind of common features?

CL: Let me illustrate this with a simple image:

a great number of systems seem to share this kind of architecture. They contain many individual agents, each one of which interacting with its neighbors. From the network of these local interactions, there are global features which emerge (up-going arrows): market forces, cultural and social trends, features of insect colonies like a well-defined ant trail, etc. These global features, in their turn, define an environment which influences the rules of interaction of every single participant with its neighbors (the down-going fat arrows). Traditional scientific research was concerned only with the up-going arrows - to understand a system, you try to go to a more fundamental level. But in complex system, sometimes you have to go to the higher level of emergent collective behaviour.

YB: You seem to imply that the understanding of a complex system involves something more than the understanding of its individual parts. Why is that so?

CL: The problem with this kind of systems is that you cannot predict in advance how changing the detailed rules of the individual interactions will affect the global behaviour. For example, a new juridicial law that will affect the conduct of individual participants in a social system may give rise to global side-effects, which will finally yield a collective behaviour that is just the opposite of what was originally intended. Thus, to act effectively in such domains, it is important to understand the ways in which a global behaviour emerges from the collection of many local interactions. There are many open questions here, and one of the most important is: which exactly are the systems that exhibit this kind of behaviour?

YB: How do these global features emerge?

CL: Let me give you an example of the way an ant-trail is formed. When ants are looking for food, they walk to a certain distance from their nest, and than they go about randomly. When one of them finds food, it goes back to the nest, dispersing pheromones on its way. These pheromones attract other ants, which disperse more pheromones, and so on. In this manner, an organized ant-trail is formed, although no-one planned it in advance. it emerges from the collective behaviour of the individual ants. A significant point is that pheromones evaporate quickly, so that once the food is finished, the trail dissapears. Perhaps we should learn from this how to let go of accepted institutions and modes of thinking once they have stopped serving their original purpose.

YB: There are some who doubt that complexity studies can qualify as "real science". What is your opinion?

CL: There are different kinds of science. There are theories which rely on analytical mathematics, like Newton's mechanics. Other theories allow only computational mathematical methods, like simulations on a computer which allow quantitative prediction, for example weather prediction. Still others, like the theory of evolution in biology, are explanatory - the theory of evolution explains the diversity of living being, but it is not mathematical, and does not give quantitative predictions. It is always good to have an analytic solution, but much of the world cannot be described with such methods. So, in complexity studies, we do computer simulations, which are like an empirical scientific experiment - you devise a simulation, change the parameters and observe what comes out.

YB: Do you believe that you can come up one day with a fundamental theory of complex systems?

CL: I believe that there are mathematical laws underlying complexity, but I also believe that in order to formulate them, we shall have to expand our mathematical tools. After all, the calculus, on which Newtonian mechanics is based, exists only for 300 years, and we may expect new mathematical developments in the future, which might enable us to account for the behaviour of complex systems.

YB: What is the present state of research in this direction?

CL: We seem to have found some common mathematical features of complex systems, for example the power law, which indicates to what extent big events are more rare than small events. But for the moment, we are not even sure that we are asking the right questions. One can compare this to the evolution of thermodynamics in the 19th century, in which the fundamental concepts - energy and entropy - appeared only after much research was done, and only then one could formulate the right kind of questions.

YB: If complex systems are so abundant, why is it only now that research on them has started seriously?

CL: Scientists ask questions to which they can reasonably expect to find answers. The usual tools of mathematical analysis could give results only for simple, linear systems, like the motion of a planet around the sun. Many systems in nature are not linear, but we have been using a spotlight, which could only reveal the orderly behaviour of linear systems. All of the successes of traditional scientific methods were in problems of a certain kind, but this does not mean that other problems cannot be solved, perhaps with the aid of new methods. In other words, what we are trying to do is to broaden the spotlight.