Karl Aubert on mathematical modelling
In his paper 'Spurious Mathematical Modelling', The Mathematical Intelligencer 6 (3) (1984), 54-60, Karl Egil Aubert presents an interesting discussion on mathematical modelling in the social sciences. We present here the introduction to that paper. We recommend the reader to look at the whole paper:
Mathematical modelling has become an industry of great proportions. As in the wake of every big industry, there is some need for ecological concern. One reason why mathematical modelling is so popular, and is spreading to every comer of science, is the great prestige which is attached to mathematics in almost every academic community. This prestige has its roots in the overwhelmingly successful application of mathematics in physics. Scientists know of this success and many of them look at it with deep admiration and respect, considering it a worthy ideal to strive towards in practically all scientific endeavour.
Modern physics possesses a rare combination of a very high degree of sophistication both on the theoretical and on the experimental side. On the one hand the theory builds on a highly advanced experimental basis. On the other hand, the experiments may in their turn stand on the shoulders of an impressive mathematical theory - a theory that not only makes use of plain calculus and differential equations, but also of a host of other and more modern mathematical tools. It is not surprising that some social scientists might develop an inferiority complex. In comparison, most of the papers that are written within the social sciences took like child's play.
For instance, as compared to physics, papers in sociology often take on a conversational and literary form, using predominantly everyday language and common sense. Somehow, we tend to be less impressed by the kind of science which appears to be within the reach of the well-educated layman in contrast to a science which requires years of study to merely understand its language. It is understandable that social scientists might be tempted to imitate physics by using more sophisticated mathematical models. The hope is that this will bring about scientific success. But it should also be pointed out that in many academic quarters there is no better way to impress or silence a colleague than to refer to some deep mathematical theorem.
Enthusiasm (if not craze) for mathematical modelling is perhaps farthest developed within modern economics. In a letter to Science (1983), the distinguished economics scholar Wassily Leontief recently launched a fierce attack on mathematical modelling in academic economics: "Not having been subjected from the outset to the harsh discipline of systematic fact-finding, traditionally imposed on and accepted by their colleagues in the natural and historical sciences, economists developed a nearly irresistible predilection for deductive reasoning. As a matter of fact, many entered the field after specializing in pure or applied mathematics.
Page after page of professional economic journals are filled with mathematical formulas leading the reader from sets of more or less plausible but entirely arbitrary assumptions to precisely stated but irrelevant theoretical conclusions. ... Year after year economic theorists continue to produce scores of mathematical models and to explore in great detail their formal properties; and the econometricians fit algebraic functions of all possible shapes to essentially the same sets of data without being able to advance, in any perceptible way, a systematic understanding of the structure and the operations of a real economic system."