Ramblemuse Touch Points

In reading through Ian Stewart’s The Mathematics of Life, I came across an interesting statement on models and modeling (pp. 273-274). It speaks both to the approximate nature of models and to the observation that exactness is neither the prerequisite for usefulness nor even always desirable.

These three models of the foot-and-mouth epidemic show how mathematics can help to answer biological questions. Each model was much simpler than any truly ‘realistic’ scenario. The models did not always agree with one another, and each did better than the others in appropriate circumstances, so a simple-minded verdict on their performance would be that all of them were wrong.

However, the more realistic the model was, the longer it took to extract anything useful from real-world data. Since time was of the essence, crude models that gave useful information quickly were of greater practical utility than more refined models. Even in the physical sciences, models mimic reality; they never represent it exactly. Neither relativity nor quantum mechanics captures the universe precisely, even though these are the two most successful physical theories ever. It is pointless to expect a model of a biological system to do better. What matters is whether the model provides useful insight and information, and if so, in which circumstances. Several different models, each with its own strengths and weaknesses, each performing better in its own particular context, each providing a significant part of an overall picture, can be superior to a more exact representation of reality that is so complicated to analyse that the results aren’t available when they’re needed.

The complexity of biological systems, often presented as an insuperable obstacle to any mathematical analysis, actually represents a major opportunity. Mathematics, properly used, can make complex problems simpler. But it does so by focusing on essentials, not by faithfully reproducing every facet of the real world.