In 1959, mathematician Mark Kac introduced a model, called the Kac ring, in order to elucidate the classical solution of Boltzmann to the problem of macroscopic irreversibility. However, the model is far from being a realistic representation of something. How can it be of any help here? In philosophy of science, it is often argued that models can provide explanations of the phenomenon they are said to approximate, in virtue of the truth they contain, and in spite of the idealisations they are made of. On this view, idealisations are not supposed to contribute to any explaining, and should not affect the global representational function of the model. But the Kac ring is a toy model that is only made of idealisations, and is still used trustworthily to understand the treatment of irreversible phenomena in statistical mechanics. In the paper, my aim is to argue that each idealisation ingeniously designed by the mathematician maintains the representational function of the Kac ring with the general properties of macroscopic irreversibility under scrutiny. Such an active role of idealisations in the representing has so far been overlooked and reflects the art of modelling.

中文翻译：

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Kac 戒指或理想化的艺术

1959 年，数学家 Mark Kac 引入了一个模型，称为 Kac 环，以阐明玻尔兹曼对宏观不可逆问题的经典解。然而，该模型远非某种事物的真实表现。怎么能在这里有任何帮助？在科学哲学中，经常有人争辩说，模型可以提供对它们所说的近似现象的解释，凭借它们包含的真理，尽管它们是由理想化构成的。根据这种观点，理想化不应有助于任何解释，也不应影响模型的全局表征功能。但是 Kac 环是一个仅由理想化组成的玩具模型，并且仍然值得信赖地用于理解统计力学中不可逆现象的处理。在论文中，我的目的是论证数学家巧妙设计的每个理想化都保持了 Kac 环的表征功能，并在仔细审查下具有宏观不可逆性的一般特性。理想化在表现中的这种积极作用迄今为止被忽视，反映了建模的艺术。