Previous work has shown that perturbation analysis in software space can produce candidate computable generative models and uncover possible causal properties from the finite description of an object or system quantifying the algorithmic contribution of each of its elements relative to the whole. One of the challenges for defining emergence is that one observer's prior knowledge may cause a phenomenon to present itself to such observer as emergent while for another as reducible. When attempting to quantify emergence, we demonstrate that the methods of Algorithmic Information Dynamics can deal with the richness of such observer-object dependencies both in theory and practice. By formalising the act of observing as mutual algorithmic perturbation, the emergence of algorithmic information is rendered invariant, minimal, and robust in the face of information cost and distortion, while still observer-dependent. We demonstrate that the unbounded increase of emergent algorithmic information implies asymptotically observer-independent emergence, which eventually overcomes any formal theory that an observer might devise to finitely characterise a phenomenon. We discuss observer-dependent emergence and asymptotically observer-independent emergence solving some previous suggestions indicating a hard distinction between strong and weak emergence.

翻译：先前的工作表明,软件空间的扰动分析可以产生候选可比较的遗传模型,并发现从一个物体或系统的有限描述中可能存在的因果特性,量化其每个要素相对于整体的算法贡献。 确定出现时遇到的挑战之一是,一位观察员先前的知识可能导致一种现象向作为新兴观察者展示,而另一个则可以减少。在试图量化出现时,我们表明,变异信息动态系统的方法可以处理这种观察者-对象依赖在理论和实践上的丰富性。通过将观察行为正规化为相互算法干扰,在信息成本和扭曲面前,算法信息的出现是变化性的、最小的和稳健健的,同时仍然依赖观察者。我们证明,突然出现的算法信息的增加无处不在,意味着观察员依赖的出现,最终克服了观察员可能试图使一种现象具有一定特性的任何正式理论。我们讨论了观察者独立出现和观察者独立出现时出现的一些建议之间很难区分。