A taxonomy for scientific models

the degree of accuracy with which it represents the target system. Admittedly, this working definition is a bit clumsy and does not answer many of the central philo-sophical questions about representation. However, it is useful insofar as it provides the necessary epistemic guarantees that the scientific model implemented as a com-puter simulation, and therefore the comcom-puter simulation itself, represents a target system. It is not within my interests to deepen the discussion of the relation be-tween scientific models and the world, but rather take it as relatively unproblematic and focus on the implementation of a scientific model into the computer simulation.

Allow me now to move to a brief discussion on sub-classes of scientific models that are of interest for this study.

In this vein, a phenomenological model is not completely independent of theory;

rather it is inspired by a theory of incorporating some principles and laws associated with such a theory.³⁰ For instance, the liquid drop model of the atomic nucleus represents the nucleus as a liquid drop having certain properties, such as surface tension and charge. Whereas surface tension can be found in hydrodynamic systems, charge is postulated by electrodynamics. The model, then, is a combination of certain aspects of these theories plus some observed behavior that determines the static and dynamical properties of the nucleus.

The distinctive mark of phenomenological models is that they do not postulate underlying structures or hidden mechanisms, but rather represent observable proper-ties of the target system. There is a principle ofmimickingguiding phenomenological models: either mimicking features of theories, or mimicking observable properties of target systems. The traditional example of a phenomenological model is the Lon-don and LonLon-don model of superconductivity, which was developed independently of theory in methods and aims. It is interesting to note that Fritz London himself insisted that a phenomenological model must be considered only atemporary model until a theoretical model could be elaborated.³¹

Models of data

Models of data share with phenomenological models the fact that they also lack theoretical underpinning, only capturing observable and measurable features of a phenomenon. Despite this similarity, there are also differences that make a model of data worth studying on its own. To begin with, a model of data is characterized by a collection of well-organized data, and therefore its construction is significantly different from a phenomenological model. In particular, they require more statistical and mathematical techniques since the collected data need to be filtered for noise, artifacts, and other sources of error.

An interesting philosophical problem is to decide which data need to be removed and under which criteria. A related problem is deciding which curve function rep-resents all the cleaned data. Is it going to be one curve or several curves? And what data points should be left out of consideration when no curve fits them all?

Roman Frigg and Stephan Hartmann explain that the problem of filtering data is usually dealt with within the context of the philosophy of experiment.³² On the other hand, the issue of fitting the data into a curve is a problem of its own, known as thecurve fitting problem. Briefly, the curve fitting problem consists in connecting a series of data points by means of a single function. In other words, provided a clean set of data, the question is, what curve fits them all together? The problem

is that the data themselves do not indicate what form the curve must have.³³ The curve fitting problem, then, raises a host of mathematical problems, especially in statistical inference and regression analysis.³⁴

Typical examples of data models come from astronomy, where it is common to find collections of large amounts of data obtained from observing and measuring astronomical events. Such data are classified by specific parameters, such as bright-ness, spectrum, celestial position, time, energy, and the like. The astronomer, then, wants to know what model lurks behind that pile of data. As an example, take the virtual observatory data model, a worldwide project where meta-data are used for classification of observatory data, construction of data models, and simulation of new data.³⁵

Theoretical models

The traditional exponent of this type of model is James Clerk Maxwell. Maxwell’s equations demonstrated that electricity, magnetism, and light are all manifesta-tions of the same phenomenon, namely, the electromagnetic field. Subsequently, all the classic laws and equations used in these disciplines became simplified cases of Maxwell’s equations. Models of the dynamics of fluids, such as the Navier-Stokes’

equations; statistical models of the distribution of population; logical models that represent the basic functioning of a vending machine system; or mental models of rational decision, are more examples of the forms that a theoretical model can take.

What is the underlying feature that ties all these examples together? On the one hand, they all stand for the underlying structures or mechanisms of their target sys-tems; on the other, they embody the knowledge that comes from a well-established theory. In this vein, a theoretical model significantly differs from a phenomenolog-ical model and a model of data in that it provides different ways of understanding the target system. To illustrate this point, consider a theoretical model of the dy-namics of fluids, such as Navier-Stokes, and a phenomenological model of the same system. The former model theoretically underpins the empirical system, providing better support for explaining the target system, predicting future states, and better evaluating evidence; a purely phenomenological model would only superficially rep-resent the empirical system, and its capacity for explaining and predicting could be undermined by its lack of epistemic reliability. To simplify matters, then, I use the term theoretical model as an umbrella term that covers models which stand for the deep mechanisms that underlie their target systems, and which are partially based (if not entirely) on well-established theories.

The precedent overview on the philosophy of models is not meant to be exhaus-tive, but to place each concept discussed here into the more general conceptual framework that is this first chapter. I now turn to a discussion on experiments, as they are equally important for our study on computer simulations.