Useless arithmetic

Linda Pilkey-Jarvis and Orrin H. Pilkey have written an article in Public Administration Review about the use of mathematical models in environmental decision making. Mathematical models are used extensively in the context of environmental issues and natural resources, and when these methods were first used, they were thought to represent a bridge to a better and more foreseeable future. There has also been much controversy in this respect, and the authors pose the question whether the optimism about the use of these models were ever realistic. In this article, they review the two main types of such models: quantitative and qualitative.

Although both present us with a generalized perspective on a natural problem, they are not equal in terms of predictive power. The first type—quantitative models—can be used as a surrogate for nature, whereas the second—qualitative models—do the same but with less accuracy.

After a review of these types of models, they provide a list of ten lessons that policy makers should learn when it comes to quantitative mathematical modeling:

1. The outcome of natural processes on the earth’s surface cannot be absolutely predicted.
2. Examine the excuses for predictive model failures with great care and skepticism.
3. Did the model really work? Examine claims of past "successes" with the same level of care and skepticism that "excuses" are given.
4. Calibration of models doesn’t work either.
5. Constants in the equations may be coefficients or fudge factors.
6. Describing nature mathematically is linking a natural flexible, dynamic system with a wooden, inflexible one.
7. Models may be used as "fig leaves" for politicians, refuges for scoundrels, and ways for consultants to find the truth according to their clients’ needs.
8. The only show in town may not be a good one.
9. The mathematically challenged need not fear models and can learn how to talk with a modeler.
10. When humans interact with the natural system, accurate predictive mathematical modeling is even more impossible.

These points are directed at policy makers, but I think several of them are also relevant for students at university level (and perhaps also upper secondary). In a simplified form, I think some of these points might even be relevant for younger pupils.
In the wrapping up of the article, they clarify their main argument:

Our argument in this article has been that mathematical models are wooden and inflexible next to the beautifully complex and dynamic nature of our earth. Quantitative models can condense large amounts of difficult data into simple representations, but they cannot give an accurate answer, predict correct scenario consequences, or accommodate all possible confounding variables, especially human behavior.

Reference:
Pilkey-Jarvis, L. & Pilkey, O.H. (2008). Useless Arithmetic: Ten Points to Ponder When Using Mathematical Models in Environmental Decision Making. Public Administration Review 68 (3) , 470–479 doi:10.1111/j.1540-6210.2008.00883_2.x