Mathematic v. conceptual modeling
Limitations of Models
Mathematical models are often the most straightforward and simple forecasters of future outcomes, but they have severe limitations as well. Not only do most mathematical models contain a certain degree of uncertainty or risk, but there is also the risk of the model itself failing (Kay 2006). Mathematical models are unable to cope with non-quantifiable input, and thus are limited both in their use and by the increased risk that a key factor has been overlooked within the model itself (Kay 2006). Conceptual models are inherently adaptable, more able to account for the complexities of the real world and less fixed in their operations (Aspinall 2007). Conceptual models can often be used as a starting point for interactive with the model's user and the available information, allowing the model to be adjusted and still effective when situations change, as opposed to mathematical models which often have to be scrapped in their entirety when information or situations change (Aspinall 2007).
It has been said that "all models are wrong; some models are useful." This reflects the gap that exists between the complexities of the real world and the abilities of abstract models. Models are by definition simplified ways of understanding complex phenomenon; they are necessarily incomplete in their estimations and valuations of real world figures and occurrences. This is why "all models are wrong." "Some models are useful," however, because they are able to approximate to a high degree the outcomes of real world events despite the incomplete nature of the information processed by the model. To make a model useful, bias must be removed. This is not an issue with the certainty of mathematical models, but conceptual models are necessarily subjective, built on the modeler's understanding of an issue. Reducing bias is key to the model's performance.
References
Aspinall, D. (2007). "Designing interaction." University of Edinburgh. Accessed 30 July 2009. http://www.inf.ed.ac.uk/teaching/courses/hci/0708/lecs/intdesign-6up.pdf
Kay, J. (2006). "Amaranth and the limits of mathematical modeling." Financial times, 10 October. Accessed 30 July 2009. http://www.johnkay.com/decisions/464
