4^{th} 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 Classics
– On 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