RBE I Workshop: Pietro Terna, "Complexity and Economics, Reading Notes for a Discussion"

A Historical Perspective

Collegio Carlo Alberto, Moncalieri (Torino, Italy)
April 16, 2010

Dipartimento di scienze economiche e finanziarie G. Prato, Università di Torino and ISI

Complexity and Economics, Reading Notes for a Discussion


1.      Basics
The complexity manifesto is mostly identified with Anderson (1972) paper “More is different”, where we read:
(p.393) The reductionist hypothesis may still be a topic for controversy among philosophers, but among the great majority of active scientists I think it is accepted without questions. The workings of our minds and bodies, and of all the animate or inanimate matter of which we have any detailed knowledge, are assumed to be controlled by the same set of fundamental laws, which except under certain extreme conditions we feel we know pretty well.

(…)The main fallacy in this kind of thinking is that the reductionist hypothesis does not by any means imply a "constructionist" one: The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. In fact, the more the elementary particle physicists tell us about the nature of the fundamental laws, the less relevance they seem to have to the very real problems of the rest of science, much less to those of society.
The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity. The behavior of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles. Instead, at each level of complexity entirely new properties appear, and the understanding of the new behaviors requires research which I think is as fundamental in its nature as any other.

(p.396) In closing, I offer two examples from economics of what I hope to have said. Marx said that quantitative differences become qualitative ones, but a dialogue in Paris in the 1920's sums it up even more clearly:
FITZGERALD: The rich are different from us.
HEMINGWAY: Yes, they have more money.

… and the dialog is only apparently a joke.
From the wonderful list of foundational paper about complexity that we can find at this page, let’s have a second basic reference related to the model building perspective. In Rosenblueth and Wiener (1945), the founders of cybernetics, we read:
(p. 317) A distinction has already been made between material and formal or intellectual models. A material model is the representation of a complex system by a system which is assumed simpler and which is also assumed to have some properties similar to those selected for study in the original complex system. A formal model is a symbolic assertion in logical terms of an idealized relatively simple situation sharing the structural properties of the original factual system.
Material models are useful in the following cases. a) They may assist the scientist in replacing a phenomenon in an unfamiliar field by one in a field in which he is more at home.
(…) b) A material model may enable the carrying out of experiments under more favorable conditions than would be available in the original system. This translation presumes that there are reasonable grounds for supposing a similarity between the two situations; it thus presupposes the possession of an adequate formal model, with a structure similar to that of the two material systems. The formal model need not be thoroughly comprehended; the material model then serves to supplement the formal one.
(p. 319) It is obvious, therefore, that the difference between open-box and closed-box problems, although significant, is one of degree rather than of kind. All scientific problems begin as closed-box problems, i.e., only a few of the significant variables are recognized. Scientific progress consists in a progressive opening of those boxes. The successive addition of terminals or variables, leads to gradually more elaborate theoretical models: hence to a hierarchy in these models, from relatively simple, highly abstract ones, to more complex, more concrete theoretical structures. The setting up of a simple model for a closed-box assumes that a number of variables are only loosely coupled with the rest of those belonging to the system. The success of the initial experiments depends on the validity of that assumption. As the successive models become progressively more sophisticated the number of closed regions may actually and does usually increase, because the process may be compared with the subdivision of an original single box into several smaller shut compartments. Many of these small compartments may be deliberately left closed, because they are considered only functionally, but not structurally important. At an intermediate stage in the course of a scientific inquiry the formal model may thus be a heterogeneous assembly of elements, some treated in detail, that is specifically or structurally, and some treated merely with respect to their overall performance, that is, generically or functionally.

Being cybernetics a root of all our contemporary work in complexity and agent based simulation, it is important to underline the analogy between the ‘material model’ above, which is now the artifact we can construct into a computational system, with more or less open-boxes, to see in a closest way the problem while we are also studying it in a theoretical way.
Why this is more and more important in social science and economics?

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