Closer To The Ideal

I am planning to write something about evolutionary psychiatry, which has become the secular fundamentalism of our time. The evolutionary psychiatrists offer a simple model of human behavior, which some writers then insist is the truth. The assumptions of game theory, which allow the model to exist, are forgotten, and the relevance of the simplifications is ignored. That is the mark of fundamentalism – to insist that a simple model represents the truth.

Of course, the progress of science is the progress of simple models. But most of the time, researchers are careful to state what the limits are. I’m currently looking for some quotes that I can use in this context, on the importance of simple models, and the importance of clearly stating the limits of the model. I ran into a bit about math modeling that I think I’ll use later, when I have time to write more. Good math modeling involves making assumptions that simplify the problem:

The skills required in mathematical modelling include many general problem-solving skills. To be able to deal with mathematical modelling problems is more generally useful, and more difficult, than (say) being able to solve first-order differential equations by the integrating factor method. It calls upon skills of creativity, analysis and interpretation which apply to all sorts of problems, not just mathematical ones.

Here is a list of skills that may be required in the solution of a modelling problem, placed in the order of the modelling framework introduced earlier. You need to be able to do the following.

Specify the purpose of the model, by defining or interpreting the problem you are investigating.

Create the model by
– simplifying the problem (by means of appropriate assumptions),
– choosing appropriate variables and parameters,
– formulating relationships between the variables.

Use mathematics to find a solution from the relationships.

Interpret the results by describing them in words (or otherwise) so that they can be understood by a possible user.

Evaluate the model by
– checking that the mathematical relationships and the solution make sense,
– comparing the results with reality,
– checking their sensitivity to changes in the data.

Later, the same article says:

Simplify the problem by stating assumptions

The skid marks model depended on the results that the deceleration of a skidding car is constant and that, for given conditions, different cars have the same deceleration while skidding. These follow from assumptions that underpin a well-established theory of sliding friction, but hold only if (for example) air resistance is ignored. To ignore air resistance is justified on two counts: firstly, its effects are probably small compared with those of sliding friction; secondly, the resulting model is relatively easy to analyse, and may provide some insight into the problem. In modelling you should always look for as simple a model as possible, consistent with the principal features of the problem. (To have ignored the effects of friction would obviously have been counter-productive.) It is important to be clear about the simplifying assumptions that have been made in order to arrive at the model. Recording an explicit list of the assumptions makes it easier for the reader to follow the development of the model, and should you need to improve your model, you then have an obvious place to start: review the assumptions, and ask which should be modified or relaxed.

Simple models give us tools for important analysis. Simple models give us insight into how the world works. Simple models allow engineers to build things, without having to take into account “the falling of a leaf on a distant planet” (from Gleick’s book). But simple models are not the truth. Reasonable people use simple models, while recalling how many simplifying assumptions have been made.

The folks who rely on evolutionary psychiatry in their writing tend to rely on some fairly extreme simplifications (men are hunters and women are gatherers). So I plan to write something soon, making fun of their technique. When you rely on a simplifying theory, and you act like the theory is the truth, rather than an extreme simplification of the truth, then you are engaging in a kind of fundamentalism. But I’ll save all that for another post.

This entry was posted on Saturday, August 1st, 2009 at 11:23 pm and is filed under evolutionary psychiatry, fundamentalism, science, simple models. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.