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.
翻译:先前的工作表明,对算法信息动态的扰动分析可以发现有限天体的基因因果过程,并量化其每个要素对可比较地构造天体的信息贡献。对出现的挑战之一是,依赖观察者先前的知识可能会造成一种现象,同时出现一个观察者,可以减少另一个观察者。因此,为了量化在可比较的基因变异过程中出现的算法信息,扰动分析可能遗留出依赖观察者先前正式知识的问题。从这个意义上说,通过将观察行为正规化为相互扰动,算法信息的出现对信息成本和扭曲是难以改变的、最小的和稳健健的,而实际上取决于观察者。然后,我们证明,突然出现的算法信息的无处处增加意味着以观察者为依存的出现,最终克服了任何观察者可能制定的任何正式理论。此外,我们讨论了观察者的出现和强势的出现,并分析了观察者的出现概念,即取决于和动态的观察者系统在以前定义中发现的动态、动态的出现。