This ambitious work puts forward a new account of mathematics-as-language that challenges the coherence of the accepted idea of infinity and suggests a startlingly new conception of counting. The author questions the familiar, classical, interpretation of whole numbers held by mathematicians and scientists, and replaces it with an original and radical alternative--what the author calls non-Euclidean arithmetic. The author's entry point is an attack on the notion of the mathematical infinite in both its potential and actual forms, an attack organized (...) around his claim that any interpretation of "endless" or "unlimited" iteration is ineradicably theological. Going further than critique of the overt metaphysics enshrined in the prevailing Platonist description of mathematics, he uncovers a covert theism, an appeal to a disembodied ghost, deep inside the mathematical community's understanding of counting. (shrink)

The ArgumentThe societal context within which science is pursued generally acts as a productive force in the generation of knowledge. To analyze this action it is helpful to consider particular modes of mediation through which societal concerns are projected into the very local and esoteric concerns of a particular domain of research. One such mode of mediation occurs through material systems. Here I treat two such systems – the steam engine and the electric telegraph – in the natural philosophy of (...) William Thomson (Lord Kelvin).The steam engine illustratesconceptualmediation. It simultaneously instantiates “labor value” in political economy and “work” in engineering mechanics, thereby identifying the two concepts in the region of their common reference. The partial identification carries with it a structural analogy between a network of concepts from political economy and a similar network in natural philosophy, providing a potent heuristic for the reformulation and further development of dynamics.The electric telegraph illustratesmethodologicalmediation. It projects the interests of engineering and industry into the interests of electromagnetic theory and vice versa, thereby establishing, in Thomson's view, a Baconian unity of truth and utility. As the common reference of theory and practice, the telegraph locates the truth of theoretical knowledge in its utility and the utility of practical knowledge in its truth.These particular cases of conceptual and methodological mediation indicate how the local practices, concepts, and interests of a research specialty, or subculture, draw on and are adapted to those of the larger culture within which they develop. Thus the analysis of mediation leads to an ecological model of the social construction of scientific knowledge. (shrink)

In the 1990s, Building Information Modeling (BIM) software significantly altered architectural approaches to planning and building. Based on parametric methods, BIM technologies sought to simulate the construction process prior to a building’s realisation. These computer simulations challenged the existing practice of representing a building through plan, section and elevation, proposing that one computational model could create a more efficient way of building. The history of BIM explorations and applications, while hardly linear, can be traced back to developments in computing since (...) the post-war period. This article maps some of these histories by examining how the computational model became an organisational infrastructure, collecting data about design and building parameters, and facilitating knowledge transfer across industries. Special attention will be given to the foundational role of Charles Eastman’s work on a Building Description System (BDS) in the 1970s, as well as Robert Aish’s contribution to RUCAPS, one of the earliest applications of Building Modeling for the design of parametric structures. I will further address research on interface technologies and computational curve modelling as well as the popularisation of Building Information systems through the office of Gehry Partners. By highlighting the interrelated nature of technology and cultural shifts in the making of BIM, this contribution sheds light on the epistemic status of computer simulations in architecture, and the dynamics of the design and building processes in which they are used. (shrink)

What is the significance of high-speed computation for the sciences? How far does it result in a practice of simulation which affects the sciences on a very basic level? To offer more historical context to these recurring questions, this paper revisits the roots of computer simulation in the development of the ENIAC computer and the Monte Carlo method.With the aim of identifying more clearly what really changed (or not) in the history of science in the 1940s and 1950s due to (...) the computer, I will emphasize the continuities with older practices and develop a two-fold argument. Firstly, one can find a diversity of practices around ENIAC which tends to be ignored if one focuses only on the ENIAC itself as the originator of Monte Carlo simulation. Following from this, I claim, secondly, that there was no simulation around ENIAC. Not only is the term ‘simulation’ not used within that context, but the analysis also shows how ‘simulation’ is an effect of three interrelated sets of different practices around the machine: (1) the mathematics which the ENIAC users employed and developed, (2) the programs, (3) the physicality of the machine. I conclude that, in the context discussed, the most important shifts in practice are about rethinking existing computational methods. This was done in view of adapting them to the high-speed and programmability of the new machine. Simulation then is but one facet of this process of adaptation, singled out by posterity to be viewed as its principal aspect. (shrink)

What is the significance of high-speed computation for the sciences? How far does it result in a practice of simulation which affects the sciences on a very basic level? To offer more historical context to these recurring questions, this paper revisits the roots of computer simulation in the development of the ENIAC computer and the Monte Carlo method. With the aim of identifying more clearly what really changed (or not) in the history of science in the 1940s and 1950s due (...) to the computer, I will emphasize the continuities with older practices and develop a two-fold argument. Firstly, one can find a diversity of practices around ENIAC which tends to be ignored if one focuses only on the ENIAC itself as the originator of Monte Carlo simulation. Following from this, I claim, secondly, that there was no simulation around ENIAC. Not only is the term ‘simulation’ not used within that context, but the analysis also shows how ‘simulation’ is an effect of three interrelated sets of different practices around the machine: (1) the mathematics which the ENIAC users employed and developed, (2) the programs, (3) the physicality of the machine. I conclude that, in the context discussed, the most important shifts in practice are about rethinking existing computational methods. This was done in view of adapting them to the high-speed and programmability of the new machine. Simulation then is but one facet of this process of adaptation, singled out by posterity to be viewed as its principal aspect. (shrink)

This paper explores the epistemic status of models and simulations between theory, on the one hand, and observations, on the other. In particular, I will argue that the interpretation of an essentially invariant astrophysical model structure can change substantially over time. I will illustrate this claim using as an example the first 20 years (1985–2004) of development of the Paris-Durham shock code—a numerical model of slow interstellar shock waves (i.e. a disturbance of the medium that travel faster than the local (...) speed of sound). I will show that the model’s interpretation and, in particular, its underlying representational ideal—the modeler’s (often implicit) goal governing the development and the use of the model—changed notably during this period. Whereas the code was originally used in a purely exploratory fashion, it was later taken to represent and encompass the target phenomenon as completely as possible. It is noteworthy that during this transition the model’s change of epistemic status was never explicitly acknowledged or in any way articulated. However, the impetus for the change can, I claim, be found in the role that observational data came to play in the later publications. (shrink)

In the 1990s, Building Information Modeling (BIM) software significantly altered architectural approaches to planning and building. Based on parametric methods, BIM technologies sought to simulate the construction process prior to a building’s realisation. These computer simulations challenged the existing practice of representing a building through plan, section and elevation, proposing that one computational model could create a more efficient way of building. The history of BIM explorations and applications, while hardly linear, can be traced back to developments in computing since (...) the post-war period. This article maps some of these histories by examining how the computational model became an organisational infrastructure, collecting data about design and building parameters, and facilitating knowledge transfer across industries. Special attention will be given to the foundational role of Charles Eastman’s work on a Building Description System (BDS) in the 1970s, as well as Robert Aish’s contribution to RUCAPS, one of the earliest applications of Building Modeling for the design of parametric structures. I will further address research on interface technologies and computational curve modelling as well as the popularisation of Building Information systems through the office of Gehry Partners. By highlighting the interrelated nature of technology and cultural shifts in the making of BIM, this contribution sheds light on the epistemic status of computer simulations in architecture, and the dynamics of the design and building processes in which they are used. (shrink)