更改

Is causal emergence a real phenomenon that exists independently of a specific observer? Here it should be emphasized that for Hoel's theory, different coarse-graining strategies can lead to different macroscopic dynamical mechanisms and different causal effect measurement results (<math>EI</math>). Essentially, different coarse-graining strategies can represent different observers. Hoel's theory links emergence with causality through intervention and introduces the concept of causal emergence in a quantitative way. Hoel's theory proposes a scheme to eliminate the influence of different coarse-graining methods, that is, maximizing <math>EI</math>. The coarse-graining scheme that maximizes EI is the only objective scheme. Therefore, for a given set of [[Markov dynamics]], only the coarse-graining strategy and corresponding macroscopic dynamics that maximize <math>EI</math> can be considered objective results. If multiple coarse-graining schemes maximize <math>EI</math> is not unique, that is, there are multiple coarse-graining schemes that can maximize <math>EI</math>, it introduces theoretical difficulties and unavoidable subjectivity.

Is causal emergence a real phenomenon that exists independently of a specific observer? Here it should be emphasized that for Hoel's theory, different coarse-graining strategies can lead to different macroscopic dynamical mechanisms and different measures of causal effects' results (<math>EI</math>). Essentially, different coarse-graining strategies can represent different observers. Hoel's theory links emergence with causality through intervention and introduces the concept of causal emergence in a quantitative way. Hoel's theory proposes a scheme to eliminate the influence of different coarse-graining methods, that is, maximizing <math>EI</math>. The coarse-graining scheme that maximizes EI is the only objective scheme. Therefore, for a given set of [[Markov dynamics]], only the coarse-graining strategy and corresponding macroscopic dynamics that maximize <math>EI</math> can be considered objective results. If multiple coarse-graining schemes maximize <math>EI</math> is not unique, that is, there are multiple coarse-graining schemes that can maximize <math>EI</math>, it introduces theoretical difficulties and unavoidable subjectivity.

Dewhurst <ref>Dewhurst, J. (2021). Causal emergence from effective information: Neither causal nor emergent?. Thought: A Journal of Philosophy, 10(3), 158-168.</ref> provides a philosophical clarification of Hoel's theory, arguing that it is epistemological rather than ontological. This indicates that Hoel's macroscopic causality is only a causal explanation based on information theory and does not involve "true causality". This also raises questions about the assumption of [[uniform distribution]] (see the entry for [[effective information]]), as there is no evidence that it should be superior to other distributions.

Dewhurst <ref>Dewhurst, J. (2021). Causal emergence from effective information: Neither causal nor emergent?. Thought: A Journal of Philosophy, 10(3), 158-168.</ref> provides a philosophical clarification of Hoel's theory, arguing that it is epistemological rather than ontological. This indicates that Hoel's macroscopic causality is only a causal explanation based on information theory and does not involve "true causality". This also raises questions about the assumption of [[uniform distribution]] (see the entry for [[effective information]]), as there is no evidence that it should be superior to other distributions.

===From the technical aspect===

===From the technical aspect===