25 May 2017

Bruce's Modelling Gripes, No. 8: Unnecessary Mathematics

Before computational simulation developed, the only kind of formal model was mathematical [note 1]. Because it it important to write models formally for the scientific process [note 2] maths became associated with science. However, solving complicated mathematical models is very hard, so to push the envelope of these mathematical models tended to involve cutting edge maths.

These days when we have a choice of kinds of formal model, we can choose the most appropriate kind of model e.g.: analytic or computational [note 3]. Most complex models are not analytically solvable, so it is usually the computational route that is relevant.

Some researchers [note 4] feel it is necessary to dress up their models using mathematical formulas, or make the specification of the model more mathematical than it needs to be. This is annoying, not only does it make the specification harder to read, but it reduces one of the advantages of computational modelling -- that the rules can have a natural interpretation in terms of observable processes. [Note 5]

If this does involve maths, then use it, but do not just to look 'scientific' -- that is as silly as wearing a white lab coat to program a simulation!

Note 1: This is almost but not quite true, there were models in other formal systems, such as formal logic, but these were vanishingly rare and difficult to use.

Note 2: Edmonds, B. (2000) The Purpose and Place of Formal Systems in the Development of Science, CPM Report 00-75, MMU, UK. (http://cfpm.org/cpmrep75.html)

Note 3: It does not really matter if one uses maths or code to program, the only important difference is between solving analytically and calculating examples (which is simulating).

Note 4: All fields have their own 'machismo' how you prove you are a *real* member of the community, in some fields (e.g. economics) this has included showing one's skill at mathematics. Thus this problem is more common in some fields than others, but pretty widespread across many fields.

Note 5: My first degree was in Mathematics, so I am not afraid of maths, just can step back from the implicit status game of knowing and 'displaying' maths.

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