Dynamic vs. Static Models - Philosophical Concept | Alexandria
Dynamic vs. Static Models: Mathematical modeling offers powerful tools to understand and predict real-world phenomena. At the heart of this field lies a fundamental distinction: the contrast between dynamic and static models. Static models, in their essence, offer a snapshot, a timeless view of a system frozen at a particular moment. Dynamic models, in contrast, embrace the flow of time, revealing how systems evolve, adapt, and transform across different periods. But is this static/dynamic divide truly fixed, or does it conceal a deeper spectrum of possibilities?
Although the explicit terminology of "dynamic" and "static modeling" may have emerged later, the conceptual roots extend back to the earliest attempts to quantify natural phenomena. Isaac Newton's laws of motion (late 17th century), for example, arguably laid the groundwork. When dealing with systems in equilibrium, one could say he used a static model, whereas using differential equations to describe how velocity changes over time implied a dynamic model. Interestingly, this period also saw heated debates about infinitesimals and the nature of calculus, reflecting the challenges inherent in representing continuous change mathematically.
The interpretation and application of dynamic and static models have evolved significantly. The rise of computer simulations in the 20th century allowed for the creation of complex, dynamic models previously impossible to analyze. Consider, for example, the pioneering Forrester's World Dynamics (1971). Its global-scale dynamic model, though controversial, sparked intense discussion about resource depletion and environmental sustainability. Less well-known is the criticism that such models, while seemingly objective, are intrinsically limited by the assumptions and biases embedded in their design. And are all models truly one or the other, or is there a middle ground?
Today, dynamic and static models are integral to fields ranging from finance to epidemiology. The static CGE (computable general equilibrium) models used by economists provide an "instantaneous" view of economies, while dynamic models track long-term growth. As society grapples with increasingly complex challenges, the choice between static and dynamic approaches reflects, in essence, the broader philosophical question of how we perceive and engage with a world in constant flux. But how much of the future can we really predict, and at what cost to our understanding of the present?