Setting Up for Success with Modeling

Mathematics is a beautiful and elegant field of science, and many of the theorems that have developed over the centuries have involved years and years of deep thought and intense exploration in their construction. However for most people mathematics is a tool meant to be applied to other fields of study, and for these individuals the beauty and elegance of a mathematical equations isnít nearly as important as how well it answers the question at hand.

One of the main problems in this situation is that the language of mathematics is often very different from that of the scientists, policy-makers, planners and developers who need to utilize modeling and simulation in their everyday duties. This failure to communicate is most obvious when the latter group chooses to hire a mathematician from outside the organization in order to develop said models - frequently the model the mathematician thinks he or she is being hired to develop is completely different from what the customer actually needs. With this potentially catastrophic stumbling-block to what could be a beneficial collaboration, what is necessary is a translator - or at least a common language that both parties understand.

The best place to start for this is with the end-user or target audience for the results of the modeling and simulation effort. What is their main, pressing question that needs to be answered in the study? Can it be focused down to a single question, or are there multiple issues to explore? From the modeling perspective, the best way to present this is as a hypothesis, a very specific and detailed statement that can be tested and either proved or disproved. The development of a clear hypothesis prior to starting the model is beneficial to all parties involved:

  • For the end-user, it is an affirmation that their specific question is understood as it is intended;
  • For the scientist / policy-maker / planner / developer, it is a reduction of the sometimes innumerable minor issues floating around the main problem, confusing the matter or causing distraction, down to the central question at-hand, allowing these individuals to focus their data-gathering and communication efforts to minimize project-creep and maximize the potential for success;
  • And for the mathematician, a clear hypothesis provides the super-structure and scaffolding around which the model can be built and provides guidance for the types of simulations that must be run in order to answer the right question.

    In so many modeling collaborations time, money, effort and patience have been wasted simply because the problem the mathematician was working to solve didnít address the question the end-user needed answered - a simple failure to communicate.

    If done well, and if all parties involved are on the same page regarding the purpose of the project, the results of the modeling and simulation effort can be analyzed and interpreted to then either prove or disprove the original hypothesis. Keep in mind, however, that occasionally the latter can be more informative than the former - disproving a theory leads to additional questioning and exploration, and sometimes can provide new guidance into underlying causes and effects that would never have been observed otherwise.

    But whether it is proven or disproven, the development and implementation of a sound, testable hypothesis ensures that the mathematician, the target audience, and all parties in between are on the same page, and when the final results of the modeling effort are communicated, that the correct questions have been answered with minimal distraction, creep, and wastage of resources. And in the end, isnít that the whole point of mathematical modeling in the first place?

    If your organization has a hypothesis that needs testing via modeling and simulation, or if you need help in developing that hypothesis, contact MathEcology - weíd be happy to help out!

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