The present paper argues that ‘mature mathematical formalisms’ play a central role in achieving representation via scientific models. A close discussion of two contemporary accounts of how mathematical models apply—the DDI account (according to which representation depends on the successful interplay of denotation, demonstration and interpretation) and the ‘matching model’ account—reveals shortcomings of each, which, it is argued, suggests that scientific representation may be ineliminably heterogeneous in character. In order to achieve a degree of unification that is compatible with successful (...) representation, scientists often rely on the existence of a ‘mature mathematical formalism’, where the latter refers to a—mathematically formulated and physically interpreted—notational system of locally applicable rules that derive from (but need not be reducible to) fundamental theory. As mathematical formalisms undergo a process of elaboration, enrichment, and entrenchment, they come to embody theoretical, ontological, and methodological commitments and assumptions. Since these are enshrined in the formalism itself, they are no longer readily obvious to either the novice or the proficient user. At the same time as formalisms constrain what may be represented, they also function as inferential and interpretative resources. (shrink)

According to the "experimenter's regress", disputes about the validity of experimental results cannot be closed by objective facts because no conclusive criteria other than the outcome of the experiment itself exist for deciding whether the experimental apparatus was functioning properly or not. Given the frequent characterization of simulations as "computer experiments", one might worry that an analogous regress arises for computer simulations. The present paper analyzes the most likely scenarios where one might expect such a "simulationist's regress" to surface, and, (...) in doing so, discusses analogies and disanalogies between simulation and experimentation. I conclude that, on a properly broadened understanding of robustness, the practice of simulating mathematical models can be seen to have sufficient internal structure to avoid any special susceptibility to regress-like situations. (shrink)

The recent discussion on scientific representation has focused on models and their relationship to the real world. It has been assumed that models give us knowledge because they represent their supposed real target systems. However, here agreement among philosophers of science has tended to end as they have presented widely different views on how representation should be understood. I will argue that the traditional representational approach is too limiting as regards the epistemic value of modelling given the focus on the (...) relationship between a single model and its supposed target system, and the neglect of the actual representational means with which scientists construct models. I therefore suggest an alternative account of models as epistemic tools. This amounts to regarding them as concrete artefacts that are built by specific representational means and are constrained by their design in such a way that they facilitate the study of certain scientific questions, and learning from them by means of construction and manipulation. (shrink)

In the late 1990s, computational technology had advanced sufficiently that astrophysicists were able to construct reasonably high resolution computer simulations of the Local Group of galaxies. These simulations indicated there should be around 250 small satellite galaxies orbiting the Milky Way and Andromeda. In the real Local Group, however, only around 40 satellites had been observed, and only twenty or so more have been discovered since then. Despite this discrepancy in numbers, claims have been made in recent years that the (...) ‘missing satellites problem’ has been solved. Using the examples of the constructed luminosity curve, and hydrodynamic simulations, this paper explores how simulations are used in conjunction with observation to ‘solve’ the missing satellites problem. It is suggested that the simulated universes have sufficient complexity to be understood as worlds in their own right, ones that can be measured and observed. By demonstrating that these virtual worlds are sufficiently ‘realistic’ with respect to observations, astrophysicists are able to make a robust argument for the existence of ‘dark’, non-observable astrophysical objects. Observational and simulated data are combined to demonstrate the plausibility—a term that develops more ontologically meaningful connotations—of both the existence and the maintenance of dark satellites. It is thus through the conflation of the real and virtual worlds, the blending of simulation data with empirical data, that the missing satellites problem is ‘solved’. (shrink)

This paper contrasts and compares strategies of model-building in condensed matter physics and biology, with respect to their alleged unequal susceptibility to trade-offs between different theoretical desiderata. It challenges the view, often expressed in the philosophical literature on trade-offs in population biology, that the existence of systematic trade-offs is a feature that is specific to biological models, since unlike physics, biology studies evolved systems that exhibit considerable natural variability. By contrast, I argue that the development of ever more sophisticated experimental, (...) theoretical, and computational methods in physics is beginning to erode this contrast, since condensed matter physics is now in a position to measure, describe, model, and manipulate sample-specific features of individual systems – for example at the mesoscopic level – in a way that accounts for their contingency and heterogeneity. Model-building in certain areas of physics thus turns out to be more akin to modeling in biology than has been supposed and, indeed, has traditionally been the case. (shrink)

Building computational models of engineered exemplars, or prototypes, is a common practice in the bioengineering sciences. Computational models in this domain are often built in a patchwork fashion, drawing on data and bits of theory from many different domains, and in tandem with actual physical models, as the key objective is to engineer these prototypes of natural phenomena. Interestingly, such patchy model building, often combined with visualizations, whose format is open to a wide range of choice, leads to the discovery (...) of new concepts and control structures. Two key questions are raised by this practice: how could discoveries arise from building external representations for which there is wide latitude in choice of the components from which they are built, and thus can be considered significantly arbitrary, and how could such discoveries allow engineering a real-world prototype system. To examine these questions, we present two case studies of discoveries that emerged from the building of such computational models in the bioengineering sciences. We then develop a process model that accounts for the discovery and transfer problems raised by both these cases, focusing on the process of building the model. Specifically, to account for the discovery problem, we propose that the process of building such models gradually leads to a close coupling between the modeler’s internal processes and the external dynamic model. To account for the transfer problem, we propose that the process of building the model leads to the creation of an enactive model that is generic, which closely enacts, and thus reveals, the way the system-level behavior of the engineered prototype emerges in time through the interaction of its parts. This enactive replication process leads to the model and the prototype forming a new class, which allows concepts and control structures developed for the computational model to be transfered to the real-world prototype. We argue that this account requires rethinking correspondence in engineering sciences as a plastic and enactive relation. A closer focus on the process of building models is required to develop a general account of this emerging approach to discovery. (shrink)

Traditional frameworks for evaluating scientific models have tended to downplay their exploratory function; instead they emphasize how models are inherently intended for specific phenomena and are to be judged by their ability to predict, reproduce, or explain empirical observations. By contrast, this paper argues that exploration should stand alongside explanation, prediction, and representation as a core function of scientific models. Thus, models often serve as starting points for future inquiry, as proofs of principle, as sources of potential explanations, and as (...) a tool for reassessing the suitability of the target system. This is illustrated by a case study of the varied career of reaction-diffusion models in the study of biological pattern formation, which was initiated by Alan Turing in a classic 1952 paper. Initially regarded as mathematically elegant, but biologically irrelevant, demonstrations of how, in principle, spontaneous pattern formation could occur in an organism, such Turing models have only recently rebounded, thanks to advances in experimental techniques and computational methods. The long-delayed vindication of Turing’s initial model, it is argued, is best explained by recognizing it as an exploratory tool. (shrink)

Focusing on computational studies of pericyclic reactions from the late twentieth century into the twenty-first century, this paper argues that computational diagnostics is a key methodological development that characterize the management and coordination of plural approximation methods in computational organic chemistry. Predictive divergence between semi-empirical and ab initio approximation methods in the study of pericyclic reactions has issued in epistemic dissent. This has resulted in the use of diagnostics to unpack computational greyboxes in order to critically assess the effect of (...) specific misrepresentations on predictive accuracy given that approximations and idealizations must be made to render computational models tractable. Furthermore, benchmarking is used to determine the applicability of approximation methods depending on how accurate the results need to be in a given research context. The epistemology of benchmarking consists of the co-generation of data sets in a hybrid computational–experimental form used to standardize computational methods but does not determine a unique quantitative method to be used across computational organic chemistry. (shrink)