Going forward I hope to summarize the advice on model derivation provided in some of the popular mathematical modelling textbooks. I knew Fred Adler had a Calculus textbook for biologists and so I visited his website to figure out the exact title of the book. And I found this quote:
The Adler lab group brings together empirical and mathematical approaches to study a wide variety of problems. We neither fear complexity nor embrace it for its own sake, but rather face it with the faith that simplicity and understanding are within reach.
This is another brilliant quote. I like that they don’t fear complexity. Adler concedes that biological problems are complex, that this is the reality, and that it’s a reality to embrace. The end part is inspirational: understanding is within reach – how can you not love mathematical biology after that?
Figure 1. A grad student quantitatively expresses some practical concerns and is hesitant to embrace additional complexity.
This morning’s reading has lead me to a nice quote:
Model building is the art of selecting those aspects of a process that are relevant to the question being asked – J.H Holland*
What I like about the quote, is that it not only highlights the principle of parsimony (as the Einstein quote did), but it highlights that the question being asked is the element of the scientific problem that should be referenced to determine if an aspect of the model should be kept in or kicked out.
In a world where we might identify ourselves as a landscape ecologist, a toxicologist, or even an expert in neural networks – consider this: there are unlikely to be any discipline specific guides to parsimonious model building. And my reason for wanting to catalog the different types of questions was that this could, possibly, serve as a useful framework; where the same types of questions share the same types of guiding principles regarding how best to achieve parsimony.
Holland, JH (1995) Hidden Order. Addison-Wesley, New York, USA.