Hangleiter, Dominik
(2014)
When scientists play: how toy models in science help us
understand the world.
UNSPECIFIED.
Abstract
In science toy models are developed and explored ubiquitously. Their study aims either at making a puzzling phenomenon comprehensible or at learning about the core mechanisms behind more complex models. Model building is a core skill of the theoretician. Not any model is a good tool, it is only those models that meet certain standards. Models should contain the essence of a physical problem, and be mathematically tractable. Toy models meet these standards. In this thesis I argue that with a toy model at hand a theorist may set out to understand the phenomenon under study. But how do toy models function in order to help theorists gain understanding?
To answer this question I take three steps. The first one is an illustrative one: I analyse three case studies, the Lotka-Volterra model of predator-prey dynamics, Schelling’s chequerboard model of residential segregation and the Ising model of second-order phase transitions. From these case studies I extract four functions that toy models can perform, namely representation of a type of phenomenon, theoretical exploration, pedagogical usage, and substantiating arguments that effect hypothesis revision. Second, as a preliminary argument I analyse in virtue of what toy models are particularly apt to perform these functions. I argue that the core properties in furnishing the representative functions are their high level of idealisation and their mathematical structure. The exploratory and pedagogical functions require the mathematical tractability (exact solvability) and the open domain of application that are characteristic of toy models. Thus the properties and functions of toy models are linked.
The functions toy models and my analysis of how their properties afford these functions form the basis of my main thesis: by studying a toy model a scientist can understand the type of phenomenon it represents. Thus she gains partial un derstanding of the elements of the type. Prior to the argument I need to clarify the notions of explanation, understanding and intuition. With the notion of understanding as qualitative knowledge at hand the thesis follows. In order to make sense of how the sharable representation of a toy model results in understanding as a private cognitive category I draw on cognitive science. In particular, I show how the model of mental models for toy modelling as a cognitive process suits the problem perfectly and is able to connect the core aspects of understanding: recognition of a pattern, and association of a model with other concepts. With the distinction between the sharable external and the private internal representation of a toy model can we make sense of how toy models function as guides for scientific progress.
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