It is easy to identify complex systems in the natural world for which simulation fails. We only have to mention turbulent fluid flow, long range weather forecasting, crashes and fluctuations on the world stock markets, and the behaviour of human adversaries in conflict situations. To what extent is it possible to use simulation to design engineered complex systems?
For, complexity in engineered systems is increasing rapidly, together with penetration of computing and IT systems into the "combined complex systems", that makes this process of increasing complexity possible. Of course, the computers themselves may be regarded as complex systems. However, we think we have a reasonable grasp of the various kinds of behaviour of digital computer, but even here, catastrophic failures and behaviour that is not qualitatively understood are endemic and frequent.
However, in a "combined complex system", there are often many different kinds of subordinate complex system besides any possible embedded deterministic digital computers.
The subordinate systems may be human, or traffic-based; they may be populations, or electrical distribution networks; they may be military units, or health provision systems, and they may be described by continuous variables, or by discrete logical models. Economic systems subject to automatic control by digital computer are especially important; for example, we have adjustable economic regulators based on the collection of indicators across the economy being regulated. Many of these complex systems contain human (or other biological) elements as subsystems.
The design of such a ``combined complex system" presents problems; the only design tools available which are available are the variety of computers that may be a component part of the combined complex system. These may be inappropriate to the task. There is a theorem {Casti} that a complex simulator can not in principle simulate a system that is intrinsically of a greater level of complexity. There is belief in the community that Turing-machine-like computers are intrinsically limited in their ability to predict truly emergent phenomena. Biologists believe that computer simulation has not progressed to the point where it can capture the essential flexibility and adaptiveness of life.
The design process is becoming increasingly reliant on direct computer simulation. To a large degree, this is for the two reasons that
There is division into ``syntax" and ``semantics" ...the computer works by manipulations with bit patterns, which is called the syntax of the rules, but much of the utility of the simulation is based on the interpretation of such patterns, which can be observer-dependent. The interpretation is called the semantics. The results of the simulation depend on the semantics of interpretation at least as much as on the syntax, or details of the bit-pattern manipulations.
Such simulation provides raw data for making design decisions, in the absence of data from the real system, or comprehension on the part of the designer(s).
Whilst it is known and accepted (for example in the fields of digital signal processing and image processing) that in the design of complex digital electronic software systems, simulation on a machine identical to, or similar to, the processor on which the resultant software is to run is perfectly sound and acceptable, the application of direct simulation to other component complex systems is more questionable.
As is now well-understood from the disciplines of chaotic dynamics{Ott}, {Jefferies} and complex adaptive systems {NECSI}, digital computers may be ill-adapted to simulate some classes of continuous-variable deterministic electronic mechanical or chemical complex system. There is ongoing discussion {NECSI} as to whether this is a fundamental limitation in principle, or just a limitation of scale.
It is not only continuous-variable systems for which there are problems. It is also known {Kirkby} that the mathematical description of discrete processes (for example population problems) by continuous variables can also give rise to gross errors; for example, a population of less than a single unit cannot recover in the real world, yet a chaotically fluctuating continuous variable may recover from a tiny fraction of a single unit and provide a mechanism for the continuation of the process. Thus it is important to choose the resolution of the simulator to match that of the component complex system being simulated.
So there are now concerns that the digital computer simulations which underpin the building of large complex systems may not be robust. Even if this is suspected to be the case, attempts to patch up the problem by parameter and input variable variations, and even simulator structural variations, may not pick up the way the real world works. Digital computer simulations may give erroneous indications of not just the system state variables, but more importantly, of the gross behaviour and the functionality of the system (for example under extreme operating conditions,) and they may obscure some reasonably obvious factors that a human-designed system would easily pick up. We may illustrate these problems by reference to the validation of air traffic control system software on both sides of the Atlantic; our thesis here (to be investigated) it that it is impossible in principle to ensure the safety (to an existing level provided by humans) of such systems. Of course, the system designer will claim otherwise, based on his best understanding (from simulation) of the failure modes.
Errors in the simulation of individual subsystems may propagate catastrophically throughout the whole system; the functionality or otherwise of the simulation result may give little idea as to the practical hazards in the real world. This is a serious problem for complex system engineers, who are required to take responsibility in advance of implementation for their systems.
Domains of applicability of complex systems design include (but are not limited to) telecoms networks, transport and distribution systems including air traffic control and power supply, and systems which involve humans in the command and control chain. Biological systems are increasingly handled by computer simulation, as are ecological and environmental scenarios.
There is a well-understood distinction (which is often overlooked) to be made between what the engineer or simulator wants to do, and that which is possible in principle to do. One can address the issue as to which classes of complex system it is reasonable to model by computer, and which classes of system one can show that it is unwise to attempt to simulate.
John Casti ``Reality Rules II" Wiley-Interscience 0-471-57798-7 pages 349--355 (1992)
Edward Ott, ``Chaos in Dynamical systems", CUP 0-521-43799-7 1993.
D J Jefferies and J H B Deane, ``Emergent approximate fractal structures in cyclic iterated image transformations", Complexity International to be published 2001. http://www.csu.edu.au/ci/
NECSI (New England Complex Systems Institute) list http://www.necsi.org/
N Kirkby, Biological simulations. Private communication.
D J Jefferies ``Noise traps and snags in electronic systems" 1997 ECCTD97 Budapest pp1014-1019
J H B Deane and D J Jefferies ``Chaotic dynamics and forbidden words." Complexity International to be published 2001. http://www.csu.edu.au/ci/
Dominique Gross and David Jefferies, ``Complexity beyond agent-based models'' Complexity International to be published 2001. http://www.csu.edu.au/ci/
D J Jefferies and J H B Deane NOLTA2000, Dresden, Germany, September 2000 ``Chaotic itinerancy in a 1-d lattice of harmonic potential wells" NOLTA2000, Dresden, Germany, September 2000 pages 315--318
D.J.Jefferies and M.J.Underhill ``Reliability in parallel machines" Complexity International volume 3 http://www.csu.edu.au/ci/
D J Jefferies ``The variable structure system: Intermittency chaos and trapping in electronic experiments and simulations" D.Jefferies http://www.csu.edu.au/ci/vol06/jefferies/jefferies.html
Copyright © D Jefferies, 2003.