Understanding and Misunderstanding Models (and everything else)

Richard Shiffrin, Indiana University, Bloomington
Models for complex systems can be enormously complex and as a result difficult to understand even for the author, and difficult to explain to others. Examination of such models reveals many levels of both understanding and explanation, from the superficial to the very deep, each of which can be useful (and harmful) for different purposes, such as scientific progress, real world applications, teaching, public education, convincing others of a position, and more. This is unsurprising when modeling aspects of what are likely infinitely complex systems. However, there is a related but deeper issue arising in all scientific models, not just complex ones: Induction and abduction, the basis for understanding and explanation, always raises questions of understanding. I illustrate in today's lecture with something very simple every scientist thinks they understand: linear regression. Some scientists may understand its use for description, prediction, and correlation, but that is not where the difficulties lie. We shall see that what the data mean when described with a linear regression is an extremely difficult and deep matter. The talk allows me to explore the many levels of explanation and understanding that arise in what are even the simplest of situations, ones in which we have the illusion of understanding. It also allows me to discuss ways to communicate and explain, not only to others, but to oneself.
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