Previous work has shown that perturbation analysis in algorithmic information dynamics can uncover generative causal processes of finite objects and quantify each of its element's information contribution to computably constructing the objects. One of the challenges for defining emergence is that the dependency on the observer's previous knowledge may cause a phenomenon to present itself as emergent for one observer at the same time that reducible for another observer. Thus, in order to quantify emergence of algorithmic information in computable generative processes, perturbation analyses may inherit such a problem of the dependency on the observer's previous formal knowledge. In this sense, by formalizing the act of observing as mutual perturbations, the emergence of algorithmic information becomes invariant, minimal, and robust to information costs and distortions, while it indeed depends on the observer. Then, we demonstrate that the unbounded increase of emergent algorithmic information implies asymptotically observer-independent emergence, which eventually overcomes any formal theory that any observer might devise. In addition, we discuss weak and strong emergence and analyze the concepts of observer-dependent emergence and asymptotically observer-independent emergence found in previous definitions and models in the literature of deterministic dynamical and computable systems.

中文翻译：

---

系统和观察者的涌现和算法信息动力学

先前的工作表明，算法信息动力学中的扰动分析可以揭示有限对象的生成因果过程，并量化其每个元素对可计算构造对象的信息贡献。定义涌现的挑战之一是，对观察者先前知识的依赖可能导致一种现象在一个观察者看来是涌现的，同时对另一个观察者来说却是可还原的。因此，为了量化可计算生成过程中算法信息的出现，扰动分析可能会继承依赖观察者先前形式知识的问题。从这个意义上说，通过将观察行为形式化为相互扰动，算法信息的出现变得不变、最小、并且对信息成本和扭曲具有鲁棒性，而它确实取决于观察者。然后，我们证明了涌现算法信息的无限增加意味着渐近独立于观察者的涌现，这最终克服了任何观察者可能设计的任何形式理论。此外，我们讨论了弱涌现和强涌现，并分析了在确定性动态和可计算系统文献中的先前定义和模型中发现的依赖于观察者的涌现和渐近独立于观察者的涌现的概念。它最终克服了任何观察者可能设计的任何形式理论。此外，我们讨论了弱涌现和强涌现，并分析了在确定性动态和可计算系统文献中的先前定义和模型中发现的依赖于观察者的涌现和渐近独立于观察者的涌现的概念。它最终克服了任何观察者可能设计的任何形式理论。此外，我们讨论了弱涌现和强涌现，并分析了在确定性动态和可计算系统文献中的先前定义和模型中发现的依赖于观察者的涌现和渐近独立于观察者的涌现的概念。