This book addresses key conceptual issues relating to the modern scientific and engineering use of computer simulations. It analyses a broad set of questions, from the nature of computer simulations to their epistemological power, including the many scientific, social and ethics implications of using computer simulations. The book is written in an easily accessible narrative, one that weaves together philosophical questions and scientific technicalities. It will thus appeal equally to all academic scientists, engineers, and researchers in industry interested in questions (...) related to the general practice of computer simulations. (shrink)

In this paper I study the activity of mathematical problem-solving in scientific practice, focussing on enquiries in mathematical social science. I identify three salient phases of mathematical problem-solving and adopt them as a reference frame to investigate aspects of applications that have not yet received extensive attention in the philosophical literature.

In this paper, I will argue that with the emergence of digital virtual worlds (in video games, animation movies, etc.) by the animation industry, we need to rethink the role and authority of mathematics, also from an ontological point of view. First I will demonstrate that the application of mathematics to the creation and description of the digital, virtual worlds behaves in many respects analogously to the application of mathematics to the description of real-world phenomena from the viewpoint of the (...) history of science. However, from other aspects, the application of mathematics significantly differs in this virtual world from the application to real-world fields. The main thesis of my paper is that the role of mathematics in the digital animation industry can be ontologically different from its usual role. In the application of mathematics to digital virtual worlds, mathematical concepts are no longer just modelling tools, forming a subordinated, computational basis, but they can direct and organise, and even create non-mathematical theory, something that we can call, for example, digital physics and biology. I will study this new, creative role of mathematics through some concrete phenomena, specifically through gravity. Our conclusion is that the animation industry opens an entirely new chapter in the relationship between (digital) sciences and mathematics. (shrink)

Despite being one of the most dependable methods used by applied mathematicians and engineers in handling complex systems, the finite element method commits variational crimes. This paper contextualizes the concept of variational crime within a broader account of mathematical practice by explaining the tradeoff between complexity and accuracy involved in the construction of numerical methods. We articulate two standards of accuracy used to determine whether inexact solutions are good enough and show that, despite violating the justificatory principles of one, the (...) finite element method nevertheless succeeds in obtaining its legitimacy from the other. (shrink)

A chronicled approach to the notion of computer simulations shows that there are two predominant interpretations in the specialized literature. According to the first interpretation, computer simulations are techniques for finding the set of solutions to a mathematical model. I call this first interpretation the problem-solving technique viewpoint. In its second interpretation, computer simulations are considered to describe patterns of behavior of a target system. I call this second interpretation the description of patterns of behavior viewpoint of computer simulations. This (...) article explores these two interpretations of computer simulations from three different angles. First, I collect a series of definitions of computer simulation from the historical record. I track back definitions to the early 1960s and show how each viewpoint shares similar interpretations of computer simulations—ultimately clustering into the two viewpoints aforementioned. This reconstruction also includes the most recent literature. Second, I unpack the philosophical assumptions behind each viewpoint, with a special emphasis on their differences. Third, I discuss the philosophical implications of each viewpoint in the context of the recent discussion on the logic of scientific explanation for computer simulations. (shrink)

A chronicled approach to the notion of computer simulations shows that there are two predominant interpretations in the specialized literature. According to the first interpretation, computer simulations are techniques for finding the set of solutions to a mathematical model. I call this first interpretation the problem-solving technique viewpoint. In its second interpretation, computer simulations are considered to describe patterns of behavior of a target system. I call this second interpretation the description of patterns of behavior viewpoint of computer simulations. This (...) article explores these two interpretations of computer simulations from three different angles. First, I collect a series of definitions of computer simulation from the historical record. I track back definitions to the early 1960s and show how each viewpoint shares similar interpretations of computer simulations—ultimately clustering into the two viewpoints aforementioned. This reconstruction also includes the most recent literature. Second, I unpack the philosophical assumptions behind each viewpoint, with a special emphasis on their differences. Third, I discuss the philosophical implications of each viewpoint in the context of the recent discussion on the logic of scientific explanation for computer simulations. (shrink)

In philosophical studies regarding mathematical models of dynamical systems, instability due to sensitive dependence on initial conditions, on the one side, and instability due to sensitive dependence on model structure, on the other, have by now been extensively discussed. Yet there is a third kind of instability, which by contrast has thus far been rather overlooked, that is also a challenge for model predictions about dynamical systems. This is the numerical instability due to the employment of numerical methods involving a (...) discretization process, where discretization is required to solve the differential equations of dynamical systems on a computer. We argue that the criteria for numerical stability, as usually provided by numerical analysis textbooks, are insufficient, and, after mentioning the promising development of backward analysis, we discuss to what extent, in practice, numerical instability can be controlled or avoided. (shrink)