THE EPISTEMOLOGY OF SIMULATION,
COMPUTATION AND DYNAMICS IN ECONOMICS
K. VELA VELUPILLAI
ALGORITHMIC SOCIAL SCIENCES RESEARCH UNIT
DEPARTMENT OF ECONOMICS
U N I V E R S I T Y O F T R E N T O
P R E P A R E D F O R A K E Y N O T E A D D R E S S A T T H E
4TH WORLD CONGRESS OF THE SOCIETY OF SOCIAL
NATIONAL CHENGCHI UNIVERSITY, TAIPEI, TAIWAN
4 – 7, SEPTEMBER, 2012
We identify and characterise five frontier research fields, encompassing
both micro and macro aspects of economic theory, where machine
computation, in its digital mode, play crucial roles in formal modelling
exercises: computable general equilibrium theory (CGE) (and its
‘extensions’: Recursive Competitive Equilibrium (RCE) & Dynamic
Stochastic General Equilibrium (DSGE) theories), agent based
computational economics, computational economics, classical behavioural
economics (CBE, as distinct from MBE: Modern Behavioural Economics)
and computable economics. These five research frontiers broach, without
resolving, many interesting methodological and epistemological issues in
economic theorising in (alternative) mathematical modes. The main claim in
the paper is that there is a serious epistemological deficit in all of the
approaches, but can be ‘discovered’ only in the last two, precisely because
the latter are underpinned by computability and constructivity theories, in
their strict mathematical senses, and the former are not. However, this
claim does not imply that classical behavioural economics and computable
economics are ‘complete’ from an epistemological perspective, especially
from the point of view of natural or intrinsic dynamics of formal models. The
epistemological deficit and the epistemological incompleteness, it is
suggested, can be resolved by a theory of simulation, itself based on
recognising the ‘duality’ between dynamical systems and numerical
analysis, interpreted computably. Hence paying heed to Turing’s Precept:
“the inadequacy of ‘reason’ unsupported by common sense.”
FOUR SCENES FROM THE THEATRE OF THE ABSURD [PACE: MARTIN ESSLIN]
"Agent-based computational methods provide the only way
in which the self-regulatory capabilities of complex dynamic
models can be explored so as to advance our understanding
of the adaptive dynamics of actual economies."
“If you didn’t grow it [the social phenomenon], you didn’t explain
“We use the term “emergent” to denote stable macroscopic patterns arising
from the local interaction of agents.”
“The weakness of applying GE models to policy issues is twofold: First,
they provide non-constructive rather than constructive proofs of the
existence of equilibrium; that is, they show that equilibria exist but do
not provide techniques by which equilibria can actually be determined.
Second, existence per se has no policy significance. .. They can only be
employed in this way if they can be made constructive (i.e., be used to
find actual equilibria). The extension of the Brouwer and Kakutani
fixed point theorems in this direction is what underlies the work of
Scarf.... on fixed point algorithms ..."
EPISTEMOLOGY, COMPUTATION, DYNAMICS - ECONOMICS
What is a Computation?
Kant: What is Man?
What can I know?
What must I do?
What may I hope?
Every simulation is a computation;
Every computation is a dynamic process
What is the epistemological status of a dynamic process?
What can be computed? What can be simulated? [Philosophy]
What must be done [to compute, to simulate]? [Methodology]
What may we expect [from a computation, from a simulation]?
FIVE KINDS OF ECONOMICS UNDERPINNED – OSTENSIBLY -
BY ‘THEORIES’ OF COMPUTATION
I. Classical Behavioural Economics (CBE)
II. Computable General Equilibrium Theory (CGE)
III. Computational Economics (CE)
IV. Computable & Constructive Economics (CCE)
V. Agent-Based Computational Economics & Finance (ABCEF)
Remark 1: I divide behavioural economics into a ‘Modern’ and a ‘Classical’ version – MBE &
CBE, respectively. CBE is computably underpinned (see Velupillai-Kao).
Remark 2: CGE forms the ‘CORE’ of RCE which, in turn, is the basis for DSGE
Remark 3: Endogenous Macrodynamics is, from the point of view of my current research, part
Remark 4: See the following references for detailed discussions, critical comparisons and
‘precise’ definitions of the above:
• Vela Velupillai & Stefano Zambelli, Computing in Economics, Ch.12, in: The Elgar
Companion to Recent Economic Methodology, ed.by John B. Davis and Wade D. Hands, Edward
Elgar, Cheltenham, Glos., 2011.
• Vela Velupillai & Ying-Fang Kao, Origins and Pioneers of Behavioural Economics,
Interdisciplinary Journal of Economics & Business Law, Vol. 1, #. 3, 2012.
• Vela Velupillai, Stefano Zambelli & Stephen Kinsella (eds.), Computable Economics
Edward Elgar International Library of Critical Writings, # 259, Edward Elgar, Cheltenham,
FIVE KINDS OF COMPUTATION THEORIES
Varieties of Constructive Mathematics
and Constructive Analysis (CMCA)
Computability Theory and Varieties of
Computable Analysis (CTCA)
Interval Analysis (IA)
Real Computation (RC)
Numerical Analysis (NA)
K. Vela Velupillai, A Computable Economist’s Perspective on Computational Complexity, ch.
4, in: Handbook of Research on Complexity, ed. by, J. Barkley Rosser, Jr., Edward Elgar,
Cheltenham, Glos., 2009.
Vela Velupillai & Stefano Zambelli, Computing in Economics, Ch.12, in: The Elgar
Companion to Recent Economic Methodology, ed.by John B. Davis and Wade D. Hands,
Edward Elgar, Cheltenham, Glos., 2011.
EPISTEMOLOGICAL DEFICITS & INCOMPLETENESS
MODES OF COMPUTATION
Every simulation is a computation
Every mode of computation is a dynamic process
What is the dynamical system status of Numerical Analysis?
TOWARDS AN EPISTEMOLOGY OF COMPUTATION –
HENCE OF SIMULATION AND DYNAMICS
• “Computer science ... is not actually a science. It does
not study natural objects. Neither is it, as you might
think, mathematics; although it does use
mathematical reasoning pretty extensively. Rather,
computer science is like engineering - it is all about
getting something to do something, rather than just
dealing with abstractions ... . ...But this is not to say
that computer science is all practical, down to earth
bridge-building. Far from it. Computer science
touches on a variety of deep issues. ... . It naturally
encourages us to ask questions about the limits of
computability, about what we can and cannot know
about the world around us.”
Richard Feynman: Feynman Lectures on Computation, Addison-Wesley Publishing Company, Inc., Reading,
Mass., p. xiii
UNDECIDABILITY OF ALGORITHMIC KNOWLEDGE-
INCOMPLETENESS OF TACIT KNKOWLEDGE
“I shall reconsider human knowledge by starting from the fact that we can
know more than we can tell.”
[Michael Polanyi, Tacit Knowledge, p. 4; italics in the original]
“The principle here is that you can know a lot more than you can prove!
Unfortunately, it is also possible to think you know a lot more than you
actually know. Hence the frequent need for proof.”
[Richard Feynman, op.cit., p. 90; italics added]
Michael Polanyi’s caveat (ibid, p.7):
“We have here examples of knowing, both of a more intellectual and more practical kind; both
the ‘wissen’ and ‘können’ of the Germans, or the ‘knowing what’ and the ‘knowing how’
of Gilbert Ryle. These two aspects of knowing have a similar structure and
neither is ever present without the other.”
Algorithmic Knowledge and Tacit Knowledge are capable of being encapsulated in the
formalisms of CBE & CCE – but not in CGE, CE or ABCEF. Hence: the impossibility of
discussing epistemological deficits or incompleteness in CGE,CE or ABCEF.
This is because CGE, CE & ABCEF are not subject to Turing’s Precept 1: ‘[O]f the
inadequacy of ‘reason’ unsupported by common sense.’
FIVE KINDS OF DYNAMICAL SYSTEMS IN
Ordinary Differential Equations (Linear & Nonlinear): ODEs – Standard
Partial Differential Equations (Linear & Nonlinear): PDEs.
Stochastic Differential Equations (Linear, Nonlinear and Partial) SDEs.
Mixed Dynamic Difference-Differential Equations.
Difference Equations (Linear & Nonlinear).
Remark 1:The above is a ‘descriptive’ delineation. I am able to ‘reduce’ them to two classes –
perhaps even one – s.t. all the other forms can be dealt with as ‘special cases’. But this makes
the discussion somewhat un-illuminating!
• K. Vela Velupillai, Non-Linear Dynamics, Complexity and Randomness: Algorithmic