Simulations: how simple is too simple

One of the quotes that is attributed to Einstein is the following:

Make everything as simple as possible, but not simpler.

That brings us to the question, how simple is too simple?

Tomslee at Whimsley talks about this question, albeit only obliquely while discussing the need for (and uses of) simplified simulations:

The goal of simulations is not always to reproduce reality as closely as possible. In fact, building a finely-tuned, elaborate model of a particular phenomenon actually gets in the way of finding generalizations, commonalities, and trends, because with an accurate model you cannot find commonalities.

For example (and I’m not comparing my little blog post to any of these people’s work), in chemistry, Roald Hoffmann got a Nobel Prize and may be the most influential theorist of his generation because he chose to use a highly simplified model of electronic structure (the extended Huckel model). It is well known that the extended Huckel model fails to include the most elementary features needed to reproduce a chemical bond. Yet Hoffman was able to use this simple model to identify and explain huge numbers of trends among chemical structures precisely because it leaves out so many complicating factors. Later work using more sophisticated models like ab initio computations and density functional methods let you do much more accurate studies of individual molecules, but it’s a lot harder to extract a comprehensible model of the broad factors at work.

Or in economics, think of Paul Krugman’s description of an economy with two products (hot dogs and buns). Silly, but justifiably so. In fact, read that piece for a lovely explanation of why such a thought experiment is worthwhile.

Or elsewhere in social sciences, think of Thomas Schelling’s explorations of selection and sorting in Micromotives and Macrobehaviour, or of Robert Axelrod’s brilliantly overreaching The Evolution of Cooperation, which built a whole set of theories on a single two-choice game and influenced a generation of political scientists in the process. All these efforts work precisely because they look at simple and even unrealistic models. That’s the only way you can capture mechanisms: general causes that lead to particular outcomes. More precise models would not improve these works – they would just obscure the insights.

A good one!

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