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Defending chaos: An examination and defense of the models used in chaos theory.

机译：捍卫混沌：对混沌理论中使用的模型的检验和辩护。

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摘要

The indispensable role of models in science has long been recognized by philosophers. In contemporary dynamics, the models are often simply sets of equations. Bridging the gap between pure mathematics and real-world phenomenon is especially difficult when the model is chaotic. I address the charge that this bridge has not, in fact, been built and that chaos remains "just math." Although the problems discussed have become acute with the rise of modern chaos theory, their roots were recognized nearly a century ago by Pierre Duhem. The skeptical attacks are both foundational and epistemic.; Targeting the foundations of chaos theory, the skeptic claims that the (fractal) geometry instantiated by some chaotic models cannot be representative of real-world processes. Specifically, mathematical fractals are said to have more complexity than can be captured in a material world of discrete atoms. Furthermore, there is what physicists call "the problem of quantum chaos:" quantum mechanics appears to forbid full-blown chaotic evolutions. I argue that the counterfactual nature of chaotic models can be used to resolve these tensions. Moreover, I show that the skeptic cannot attack the foundations of chaos theory without calling into question unproblematic areas of mathematical science.; The epistemological problems are driven by an essential property of chaotic dynamics, viz., sensitive dependence on initial conditions. This sensitivity confounds the confirmation schemes familiar to philosophers by precluding future predictions of the state of a system. The skeptic argues that without such predictions, the models cannot be tested. I show how researchers in chaos theory can overcome these skeptical objections via a recently developed method of model construction. This new method not only yields a decisive answer to the skeptic, but reveals a lacuna in the philosophical literature on models in science. I present a new taxonomy of models that incorporates these recent discoveries and conforms more closely to contemporary scientific practice than do previous classifications.
机译：模型在科学中不可或缺的作用早已为哲学家所认识。在当代动力学中，模型通常只是方程组。当模型混乱时，弥合纯数学和现实世界现象之间的差距特别困难。我要指出的是，实际上并没有建造这座桥，而且混乱仍然是“只是数学上的问题”。尽管所讨论的问题随着现代混沌理论的兴起而变得尖锐，但其根源已在近一个世纪前被Pierre Duhem所认可。怀疑性攻击既是基础性的也是认知性的。怀疑论者针对混沌理论的基础，声称由某些混沌模型实例化的（分形）几何不能代表现实世界的过程。具体而言，据说数学分形比在离散原子的材料世界中所能捕获的复杂得多。此外，物理学家称之为“量子混沌问题”：量子力学似乎禁止全面的混沌演化。我认为混沌模型的反事实性质可以用来解决这些紧张关系。而且，我证明了怀疑者不能在不质疑数学科学的无问题领域的情况下攻击混沌理论的基础。认识论问题是由混沌动力学的基本性质所驱动的，即对初始条件的敏感依赖性。这种敏感性通过排除系统状态的未来预测而混淆了哲学家熟悉的确认方案。怀疑论者认为，没有这种预测，就无法对模型进行检验。我展示了混沌理论的研究人员如何通过最近开发的模型构建方法克服这些怀疑的反对意见。这种新方法不仅对怀疑论者给出了决定性的答案，而且揭示了关于科学模型的哲学文献中的空白。我提出了一种新的模型分类法，该分类法结合了这些最新发现，并且比以前的分类更符合当代科学实践。

著录项

  • 作者

    Koperski, Jeffrey David.;

  • 作者单位

    The Ohio State University.;

  • 授予单位 The Ohio State University.;
  • 学科 Mathematics.; Philosophy.
  • 学位 Ph.D.
  • 年度 1997
  • 页码 165 p.
  • 总页数 165
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 数学;哲学理论;
  • 关键词

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