4th World Congress of Social Simulation


Turing’s Economics

 

A Session Celebrating the Alan Turing Birth Centennial

 

Session Chair and Organizer:

K. Vela Velupillai, Department of Economics/Algorithmic Social Science Research Unit, University of Trento

 

Contributors:

K. Vela Velupillai, Algorithmic Social Science Research Unit, University of Trento

            Title: Turing’s Economics

 

It is little realised that what I call the Five Turing ClassicsOn Computable Numbers (Turing 1936-7), Systems of Logic (Turing, 1939), Computing Machinery and Intelligence (Turing, 1950), The Chemical Basis of Morphogenesis (1952) and  Solvable and Unsolvable Problems (1954) – should be read together to understand why there can be something called Turing’s Economics.  There is no record, known to this author, of Alan Turing’s engagement with formal problems in economics, despite the fact that he was intimately acquainted with serious – even famous – economists, almost throughout his adult life (particularly in Cambridge: Keynes, Pigou and Champernowne; but also A.G.D.Watson, a mathematician who introduced Turing to Wittgenstein, and who  had close connections to Sraffa). However, his last published article, Solvable and Unsolvable Problems can be considered the fountainhead for what became Classical Behavioural Economics, in Herbert Simon’s research program, underpinned by computability and computational complexity theory. In this paper an outline of the way the Five Turing Classics can be considered the basis for what I have called Turing’s Economics, since about 1983.

 

Keywords: Turing’s Economics, Solvable and Unsolvable Problems, Classical Behavioural Economics, Computability, Computational Complexity.

 

S. Barry Cooper, School of Mathematics, University of Leeds, UK 

            Title: Alan Turing: Computing in an Incomputable World

 

It is sometimes said that the more you understand, the more aware of the limitations of human understanding you become. One could see Alan Turing's simultaneous discovery of incomputability, along with his universal computer, as a formal counterpart of this very real experience of the world.  Another intuition is that the real world is persistently making a mockery of our efforts to compute it: but that our very survival in this dangerous world is an indication of some less digital but still practical form of engagement with reality. In this talk we explore routes to grounding this very contemporary intuition within the Turing conceptual legacy.

 

Keywords: Incomputability, Turing’s Universal Computer, Turing’s conceptual legacy, Limitations of human understanding, Non-digital engagement (with reality)

 

 

Stefano Zambelli, Algorithmic Social Science Research Unit, University of Trento

Title: The Relevance of the Halting Problem for Economics Technological  progress, R& D and Growth

 

The relevance of Turing Machine computations and of the halting problem for economics is well acknowledged by many economists, in particular by the computable economists. The notion of Universal Turing Machine, once the adherence to the Church-Turing Thesis is granted, is a very powerful concept that is of fundamental relevance for the understanding of economic processes. The Universal Turing Machine metaphor (computational universality) is an appropriate theoretical tool for modeling decision making and also for the understanding of discoveries, knowledge evolution, technological progress, innovations and growth. Here it is claimed that standard models are not Turing equivalents and hence are inadequate to deal with discoveries, knowledge evolution, technological progress, innovations and growth in a meaningful way. Two models are presented. The first is an application to knowledge evolution and growth: it is shown how investment in R&D is necessarily and intrinsically uncertain. The second is an application to the notion of process innovation, where different firms are competing for their survival: it is shown that it is not always the case that investment in R&D is economically convenient.

 

Keywords: Computable Economics, Turing Machine computations, Halting Problem, Church-Turing Thesis, technological change, R&D, discoveries, innovations, knowledge, Keynes-Simon-Velupillai rationality, classical behavioral economics.

 

Ying-Fang (Selda) Kao, Algorithmic Social Science Research Unit, University of Trento

            Title: Problem Solving: From Turing to Simon

 

We explore Alan Turing's approach to problem solving; relate this to Herbert Simon's approach to Human problem solving. A review of their approaches, models and theories concerning problem solving is presented. In particular, Turing's decisive influence on Simon's original research program is also briefly discussed. In doing so, the connection between Turing's Universal Computer and Simon's Information Processing System (IPS) is examined. In Simon's Classical Behavioural Economics, procedural decision making is central and decision makers adapt to the environment in which the decisions are taken. Problem solvers are, implicitly, characterised as dynamic entities in both their works. We make this connection explicit and place the notions of bounded rationality and near decomposability within this framework. Both Turing and Simon were interested in the game of GO (Wei-chi), unfortunately they did not proceed in exploring it in the context of human problem solving. One of the directions in which we hope to extend the theory of human problem solving is by placing this highly complex game as a paradigm for investigating the role of heuristics for decision making in complex environments.

 

Keywords: Human Problem Solving, Turing’s Universal Computer, Classical Behavioural Economics, Information Processing Systems, GO, Heuristics

 

V. Ragupathy, Algorithmic Social Science Research Unit, University of Trento

Title: Turing vs. Hopf Bifurcation - Applications in Endogenous Macrodynamics

           

Turing's seminal paper on Morphogenesis (1952) pioneered work on pattern formation resulting from diffusion-induced symmetry breaking. Economists are interested in explaining inhomogeneous patterns (concerning growth, distribution of wealth, sectoral structure, etc.) and endogenous instability (business cycles, structural change) in capitalistic economies. We attempt to explore the potential applications of Turing bifurcation in endogenous macrodynamics, both in linear and nonlinear models. By contrasting it with the Andronov-Hopf bifurcation, we point out the possibilities of using Turing bifurcation to explain endogenously generated instabilities and study the resulting patterns via simulations. In this context, we examine Goodwin's work on dynamically coupled markets and the spatio-temporal inhomogeneity of growth in predator-prey type models. We briefly discuss the methodological connection with the Fermi-Pasta-Ulam problem and address the algorithmic undecidabilities in characterizing these dynamic patterns (attractors), in general.

 

Keywords: Turing bifurcations, Endogenous Macrodynamics, Instability, Fermi-Pasta-Ulam Problem, Goodwin’s coupled markets Spatio-temporal inhomogeneity, Algorithmic undecidabilities