Modeling is not quite as simple in practice as it is in theory. What are the issues that must be addressed and solved to make the technique of building simulations workable? Use the example of Galileo's 16th-century experiment dropping balls from the Tower of Pisa within your answer.

Fill in the blank(s) with the appropriate word(s).

The first issue is achieving the proper balance between accuracy and complexity. Our model must be an accurate representation of the physical system, but at the same time, it must be simple enough to implement as a program or set of equations and solve on a computer in a reasonable amount of time. Often this balance is not easy to achieve, as most real-world systems are acted upon by a large number of external factors. We need to decide which of those factors are important enough to be included in our model and which can safely be omitted without jeopardizing the validity of our conclusions.For example, the model of a falling body given earlier is inaccurate because it does not account for the effects of air resistance. (It is only an appropriate model if the object is falling in a vacuum.) Whereas the effect of air resistance on a cannonball is minimal, imagine dropping a feather! The model would produce totally inaccurate results, and our conclusions about how the system behaves would be wrong. It is obvious that we need to incorporate the effects of air resistance into our model if we have any hope of producing worthwhile and useful results.Our model also assumes that the Earth is a perfect sphere and that the acceleration due to gravity is constant everywhere along its surface. That assumption is not quite true. The Earth is a "slightly squashed" sphere with a radius of 6,378 km at the equator and 6,357 km at the poles. This means that the acceleration due to gravity is a tiny bit greater at the North and South Poles than at the equator, because the poles are 21 km closer to the center of the Earth. Is this something for which we should account? Is this effect important when constructing a model of a freely falling body? In this case, probably not—because the miniscule error resulting from this approximation will almost certainly not affect our conclusions.This is how computational models are built. We include the truly important factors that act upon our system so that our model is an accurate representation but omit the unimportant factors that would only make the model harder to build, understand, and solve. As you might imagine, identifying these factors and distinguishing the important from the unimportant can be a daunting task.Another problem with building simulations is that we may not know, in a mathematical sense, exactly how to describe certain types of systems and behaviors. The gravitational model given earlier is an example of a continuous model. In a continuous model, we write out a set of explicit mathematical equations that describes the behavior of a system as a continuous function of time t. These equations are then solved on a computer system to produce the desired results. Unfortunately, there are many systems that cannot be modeled using precise mathematical equations because researchers have not discovered exactly what those equations should be. Simply put, science is not yet sufficiently knowledgeable about how some systems function to characterize their behavior using explicit mathematical formulae.In some cases, what makes these systems difficult to model is that they contain stochastic components. This means there are parts of the system that display random behavior, much like the throw of the dice or the drawing of a playing card. In these cases, we cannot say with certainty what will happen to our system because it is the very essence of randomness that we can never know exactly which event will occur next. An example of this is a model of a business in which customers walk into the store at random times. In these cases, we need to build models that use statistical approximations rather than precise and exact equations.