Just Playing? Toy Models in the Sciences

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May, 8th

09.30 - 09:45 Welcome
09:45 - 11:00 Erwin Frey: Bacterial Games
11:00 - 11:30 Coffee Break
11:30 - 12:45 Claus Beisbart: Just Playing With Computers? Toy Models and Computer Simulations
12:45 - 14:15 Lunch Break
14:15 - 15:30 Sabina Leonelli: Just a Game? Data Models in Plant Science
15:30 - 16:45 Ulrich Schollwöck: What Do Quantum Simulators Simulate?
16:45 - 17:15 Coffee Break
17:15 - 18:30 Margaret Morrison: Toy Models – More Than Playing Around

May, 9th

09:30 - 10:45 Till Grüne-Yanoff: Toy Models as Possibility-Identifying Devices
10:45 - 11:15 Coffee Break
11:15 - 12:30 Dominik Hangleiter, Stephan Hartmann and Alexander Reutlinger: Do Toy Models Yield Understanding?
12:30 - 14:00 Lunch Break
14:00 - 15:15 Ulrike HahnWhy Toy Models Are Best
15:15 - 16:30 Rainer Hegselmann: The Bounded Confidence Model – Complexity By One Parameter
16:30 - 17:00 Coffee Break
17:00 - 18:15 Robert Sugden: Economic Models Are Not Toys – Just Fictions
18:15 - 19:00 Round Table: Conclusions and Open Discussion


Claus Beisbart (University of Bern, Department of Philosophy)
Just playing with Computers? Toy Models and Computer Simulations

A number of well-known computer simulations trace the behaviour of toy models, e.g. of cellular automata. This may seem puzzling because computers have the power to follow the dynamics of much more complicated models. What then is the reason why scientists run computer simulations based upon toy models instead of doing more complicated simulations? The aim of the talk is to answer this question. A couple of possible answers are discussed: a. Simulations of toy models are only transient phases in developing more complicated models. b. Simulated toy models sacrifice accuracy in representation for a broader range of applications. c. Simulated toy models serve to isolate important mechanisms (cf. U. Mäki's account of modeling). d. Simulated toy models provide qualitative understanding of systems. I discuss each of these claims by drawing on the recent literature about computer simulations.top

Erwin Frey (LMU Munich, Department of Statistical and Biological Physics)
Bacterial Games

Microbial laboratory communities have become model systems for studying the complex interplay between evolutionary selection forces, stochastic fluctuations, and spatial organization. Two fundamental questions that challenge our understanding of evolution and ecology are the origin of cooperation and biodiversity. Both are ubiquitous phenomena yet conspicuously difficult to explain since the fitness of an individual or the whole community depends in an intricate way on a plethora of factors, such as spatial distribution and mobility of individuals, secretion and detection of signaling molecules, toxin secretion leading to inter-strain competition and changes in environmental conditions. We discuss two possible solutions to these questions employing concepts from evolutionary game theory, nonlinear dynamics, and the theory of stochastic processes. Our work provides insights into some minimal requirements for the evolution of cooperation and biodiversity in simple microbial communities. It further makes predictions to be tested by new microbial experiments.top

Till Grüne-Yanoff (Royal Institute of Technology, Stockholm)
Toy Models as Possibility-Identifying Devices

In science, models are often used to identify and analyze possibilities. For example, climate scientists use models to derive possible future climate developments; anthropologists employ models to identify possible evolutionary histories of human traits; economists devise models to describe possible causes of social phenomena. I call such models possibility-identifying models, and in my talk I address two issues related to them. First, it seems obvious that one cannot simply use any model to identify possibilities relevant for one’s questions. Instead, for a given research question, only some models will yield serious possibilities that one might want to take into considerations, while other models will identify mere nonsense possibilities that one will not want to take into account. So the first issue that needs to be addressed is how one selects the serious-possibility-identifying models from the nonsense-producing ones. My answer here will be a modified version of Sugden’s credible worlds account. The second issue concerns how to fit the assessment of possibility-identifying models with mainstream philosophy of science accounts of scientific models. The still-dominant view of scientific models is that they are representations, and that they must be evaluated according to their representational properties. Yet what, if anything, do possibility-producing models represent? And if that question can be answered positively, does it give us a way to pick out serious-possibilities-producing models? My answer here is that while one might be capable (in some rather contorted way) to give a representational account of possibility-identifying models, such an account will not be helpful for the evaluation of such models. To conclude, while the mainstream account often dismisses such models as toy models, some of them are not for toying around. Rather, they facilitate investigating serious possibilities.top

Ulrike Hahn (Birkbeck University of London, Department of Psychological Sciences)
Why Toy Models Are Best 

Using examples drawn from cognitive science and psychology, the talk examines the types of inferences drawn from and supported by models. On the basis of this it is demonstrated how and why the most restrictive models often provide the greatest explanatory purchase.top

Dominik Hangleiter, Stephan Hartmann, Alexander Reutlinger (LMU Munich, MCMP)
Do Toy Models Yield Scientific Understanding?

While practicing scientists - in their philosophical moments - unanimously regard toy models as providing understanding of their target system (e.g. Ziman 1965, Fisher 1983), this claim is contentious among philosophers of science (e.g. Grüne-Yanoff 2007, Batterman and Rice 2014). This is because toy models typically include false assumptions, are not empirically adequate, or even inconsistent with an empirically well-confirmed underlying theory. Here we argue that at least in some cases are justified to regard toy models as vehicles of scientific understanding. When is this the case? According to an influential view of scientific understanding, a scientist can understand a phenomenon P by applying a model M to P if M is (1) intelligible, and (2) meets “the usual methodological and empirical requirements” (De Regt and Dieks, 2005, p. 151). In order to argue for our main claim, we draw a distinction between two types of toy models: embedded toy models, that is toy models that are “embedded” into an underlying scientific theory such as the Ising model in quantum statistical physics, and autonomous toy models, ones that are not embedded, such as Schelling's model of residential segregation. We argue that while autonomous models are merely intelligible (but still valuable for certain purposes), embedded models provide scientific understanding via the virtues of the embedding theory.top

Rainer Hegselmann (University of Bayreuth, Department of Philosophy and Economics)
The Bounded Confidence Model – Complexity By One Parameter

The bounded confidence model (BC model) of opinion dynamics tries to answer the question: What happens if individuals take seriously only those others whose opinions are not too far away from their own opinion? The few assumptions of the BC model are:

  • There is a set of n individuals; i, j ∈ I.
  • Time is discrete; t = 0, 1, 2, ... .
  • Each individual starts with a certain opinion, given by a real number xi(t0) [0,1] . The profile of all opinions at time t is X(t)= x1(t), ..., xi(t), xj(t), ..., xn(t).
  • The individuals update their opinions. The next period's opinion of individual i is the average opinion of all for which |xi(t) - xj(t)| ≤ ε (confidence level). The set of all others that i takes into account at time t is: I(i,X(t)) = {j | |xi(t) - xj(t)| ≤ ε}.

The updated opinion then is xi(t + 1) =1/|I(i,X(t))| Σj I(i,X(t)) xj(t).
The model is basically driven by just one parameter: the confidence level ε. Depending upon the confidence level ε the model generates complicated phase transitions as to the number of emerging clusters. Up to now the stabilisation behaviour is only partially understood. Several non-monotonicities are surprising. The BC-model was the starting point for extensions of all sorts. In my talk the BC model will be used for a case study on what one can get from a toy model as the BC model undoubtedly is.


Sabina Leonelli (University of Exeter, Department of Sociology, Philosophy and Anthropology)
Just a Game? Data Models in Plant Science

This talk discusses the notion of ‘data model’, its current role in philosophy of science and what focusing on these objects can teach philosophers about the complex relationship between data and models. My discussion is grounded on an empirical approach to philosophical analysis, in which the discussion of the epistemic role of data and models is grounded on a study of how contemporary scientists are using these research components to explore the world and reason about it. I start by arguing that data models have often been seen as ‘toy models’, i.e. as oversimplified/idealised version of actual dataset whose main function is to make data useful as evidence for theoretical claims (for instance, in a 2006 review paper Roman Frigg defines them as a “corrected, rectified, regimented and in many instances idealized version of the data we gain from immediate observation, the so-called raw data”); and that capturing the relation between data and models in this way has inhibited a close philosophical investigation of the status of data in scientific research and its relation to modeling. Building on ongoing empirical work of how data are circulated and modelled in contemporary plant science, I then reflect on the status of data models, the extent to which they can be viewed as ‘representations’ of a target system, the possible differences between data models and ‘simple’ datasets (and their respective roles as communication and exploration tools within and across scientific communities), and the crucial importance of these tools towards the achievement of scientific understanding.top

Margaret Morrison (University of Toronto, Department of Philosophy)
Toy Models – More than Playing Around

Toy models are often characterized in terms of the level of simplification with which they represent some particular mechanism or system. The virtue of toy models is that they allegedly illustrate a mechanism or behaviour in a way that is unencumbered by theoretical details, thereby making the process easier to understand (e.g. the Ising model as an illustration of ferromagnetism). The mechanical models of nineteenth century British field theorists are an interesting example of the use of toy models that extends well beyond illustration. Their use included modification of Maxwell’s field equations to “experimenting” on the aether. I discuss these and some other examples of toy models in an attempt to uncover what makes them such valuable aids for model and theory construction more generally.top

Ulrich Schollwöck (LMU Munich, Department of Theoretical Nanophysics)
What Do Quantum Simulators Simulate?

Quantum many-body physics faces the challenge that, while the mathematical problems to be solved can be formulated precisely, their solution is beyond the means of humans and (at least) classical computers. This has led to the introduction of a plethora of simplified toy models, some of which I will discuss, but which are still impossible to solve exactly, and approximate numerical techniques have to be resorted to. In recent years, experimental progress has made it possible to build so-called quantum simulators, which act essentially like an analog computer. I want to present how such quantum simulators are built, how they are certified by theoretical calculations, and critically assess what the expected progress in terms of understanding real-world phenomena of many-body physics could be.top

Robert Sugden (University of East Anglia, School of Economics)
Economic Models Are Not Toys – Just Fictions

It has become fashionable for economists to refer to simple theoretical models (such as Akerlof’s ‘market for lemons’ or Bikhchandani et al.’s model of information cascades) as ‘toy models’. My paper registers a protest against this term. I suggest that the language of ‘just playing’ is one of the disingenuous ways in which theorists avoid claiming that their models are intended as explanations of real phenomena, while expecting their fellow-scientists to treat these models in ways that would not make sense if the disclaimers were taken at face value. Many methodologists are complicit in this practice, describing the practice of modelling in ways which do not attribute explanatory power to models. One of the merits of my ‘credible worlds’ account is that it shows how models can be fictions and yet provide genuine explanations of real phenomena.