Liu Yu, Di Zengru, Gerlee Philip
International Academic Center of Complex Systems, Beijing Normal University, Zhuhai 519087, China.
Department of Mathematical Sciences, Chalmers University of Technology, 405 30 Gothenburg, Sweden.
Entropy (Basel). 2022 Aug 5;24(8):1082. doi: 10.3390/e24081082.
The notion of information and complexity are important concepts in many scientific fields such as molecular biology, evolutionary theory and exobiology. Many measures of these quantities are either difficult to compute, rely on the statistical notion of information, or can only be applied to strings. Based on assembly theory, we propose the notion of a , which describes how an object can be decomposed into hierarchical structures using repetitive elements. From the ladderpath, two measures naturally emerge: the ladderpath-index and the order-index, which represent two axes of complexity. We show how the ladderpath approach can be applied to both strings and spatial patterns and argue that all systems that undergo evolution can be described as ladderpaths. Further, we discuss possible applications to human language and the origin of life. The ladderpath approach provides an alternative characterization of the information that is contained in a single object (or a system) and could aid in our understanding of evolving systems and the origin of life in particular.
信息和复杂性的概念是分子生物学、进化理论和外生物学等许多科学领域中的重要概念。这些量的许多度量要么难以计算，依赖于信息的统计概念，要么只能应用于字符串。基于组装理论，我们提出了阶梯路径的概念，它描述了一个对象如何使用重复元素分解为层次结构。从阶梯路径中，自然出现了两种度量：阶梯路径指数和秩序指数，它们代表了复杂性的两个轴。我们展示了阶梯路径方法如何应用于字符串和空间模式，并认为所有经历进化的系统都可以描述为阶梯路径。此外，我们讨论了其在人类语言和生命起源方面的可能应用。阶梯路径方法为单个对象（或系统）中包含的信息提供了一种替代表征，尤其有助于我们理解进化系统和生命起源。
