Modelling complex systems, be they social, economic, terrorist-ic, environmental, ecological, whatever seems to be all the rage nowadays. Everyone (including myself!) seems to be so intrigued with the future that they cannot wait until it arrives.
But what is a model ? and how can/should it be used ? these are questions which are normally unanswered and can lead to disasters like the current financial circus. A systems model is, at its most abstract, a simplification of reality which can help us to answer questions about the future in a computationally tractable way (since everything at the end of the day gets reduced to number crunching, except maybe philosophy). It focusses on internal variables (state), inputs and outputs of a system that are considered important to understand its behavior. The contribution of a model is two-fold: to understand the underlying (simplified) structure, and to use this to answer questions that interest us.
We have to face that we cannot really understand even moderately complex systems properly, and we make certain idealizing assumptions (like there won’t erupt a World War), to make things simple. We then use an intuitive understanding (sometimes called pre-analytic vision) of the system structure to decide how to build the model. For example, economics models are built using the vision that man wants to maximize something (which makes it easy to use calculus of variations or mathematical programming), atmospheric models have to obey the laws of physics, and so on.
Once we identify a structure which can be represented using available mathematical tools, we put them in a computer and start crunching. If they can be represented using nice equations (called deterministic model), you would use differential equations or some cousin or mathematical programming. If it cannot, then you don’t give up, you simply say that it is random but with a structure and use stochastic models, using Monte Carlo methods or time series analysis or some such thing (Read this for a critique of the latter).
Before one gets immersed in fascinating mathematical literature, one must understand that each model comes with an ‘if’ clause: If such-and-such conditions are satisfied, then things might look like what we get here. Which is why I get irritated with both MBAs who talk about ‘market fundamentals being good’ and environmentalists who predict that I’m going to need a boat soon – neither qualifies results which come out a black box. Even worse, there are those who compare results which come out of different black boxes, which need not be comparable at all, just because they, like the modellers, have no idea what is going on. Atleast the modellers admit to this, but those who use these models for political purposes cannot dare to admit shades of gray.
Different models can take the same data and give you radically different answers – this is not due to programming errors, but the pre-analytic vision that the model is based upon. The reason why climate change remained a debate for so long is because of such issues, and vested interests, of course. Therefore, we see that the ‘goodness’ of a model depends critically on the assumed ontology and epistemology, even more than the sobriety of its programmer (well, maybe not).
Thus, as intelligent consumers of data that models spew out everyday, we should make sure that such ‘studies’ do not over-ride our common sense. But in the era of Kyunki Saas bhi, one cannot hope for too much.