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→Chinese classical philosophy
For example, taking the concept of five elements in Eastern philosophy, we can completely understand the five elements as five macroscopic states of everything, and the relationship of mutual generation and restraint of the five elements can be understood as a macroscopic causal mechanism between these five macroscopic states. Then, the cognitive process of extracting these five states of the five elements from everything is a coarse-graining process, which depends on the observer's ability to analogize. Therefore, the theory of five elements can be regarded as an abstract causal emergence theory for everything. Similarly, we can also apply the concept of causal emergence to more fields, including traditional Chinese medicine, divination, feng shui, etc. The common point of these applications will be that its causal mechanism is simpler and possibly has stronger causality compared to Western science, but the process of obtaining such an abstract coarse-graining is more complex and more dependent on experienced abstractors. This explains why Eastern philosophies all emphasize the self-cultivation of practitioners. This is because these Eastern philosophical theories put huge complexity and computational burden on '''analogical thinking'''.
For example, taking the concept of five elements in Eastern philosophy, we can completely understand the five elements as five macroscopic states of everything, and the relationship of mutual generation and restraint of the five elements can be understood as a macroscopic causal mechanism between these five macroscopic states. Then, the cognitive process of extracting these five states of the five elements from everything is a coarse-graining process, which depends on the observer's ability to analogize. Therefore, the theory of five elements can be regarded as an abstract causal emergence theory for everything. Similarly, we can also apply the concept of causal emergence to more fields, including traditional Chinese medicine, divination, feng shui, etc. The common point of these applications will be that its causal mechanism is simpler and possibly has stronger causality compared to Western science, but the process of obtaining such an abstract coarse-graining is more complex and more dependent on experienced abstractors. This explains why Eastern philosophies all emphasize the self-cultivation of practitioners. This is because these Eastern philosophical theories put huge complexity and computational burden on '''analogical thinking'''.
==Critique==
Throughout history, there has been a long-standing debate on the ontological and epistemological aspects of causality and emergence.
For example, Yurchenko pointed out in the literature <ref>Yurchenko, S. B. (2023). Can there be a synergistic core emerging in the brain hierarchy to control neural activity by downward causation?. Authorea Preprints.</ref> that the concept of "causation" is often ambiguous and should be distinguished into two different concepts of "cause" and "reason", which respectively conform to ontological and epistemological causality. Among them, cause refers to the real cause that fully leads to the result, while reason is only the observer's explanation of the result. Reason may not be as strict as a real cause, but it does provide a certain degree of predictability. Similarly, there is also a debate about the nature of causal emergence.
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. However, when the solution that maximizes <math>EI</math> is not unique, that is, there are multiple coarse-graining schemes that can maximize <math>EI</math>, it will lead to difficulties in this theory and a certain degree of subjectivity cannot be avoided.
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.
In addition, Hoel's <math>EI</math> calculation and the quantification of causal emergence depend on two known prerequisite factors: (1) known microscopic dynamics; (2) known coarse-graining scheme. However, in practice, people rarely can obtain both of these factors at the same time, especially in observational studies, these two factors may be unknown. Therefore, this limitation hinders the practical applicability of Hoel's theory.
At the same time, it is pointed out that Hoel's theory ignores the constraints on the coarse-graining method, and some coarse-graining methods may lead to ambiguity <ref>Eberhardt, F., & Lee, L. L. (2022). Causal emergence: When distortions in a map obscure the territory. Philosophies, 7(2), 30.</ref>. In addition, some combinations of state coarse-graining operations and time coarse-graining operations do not exhibit commutativity. For example, assume that <math>A_{m\times n}</math> is a state coarse-graining operation (combining n states into m states). Here, the coarse-graining strategy is the strategy that maximizes the effective information of the macroscopic state transition matrix. <math>(\cdot) \times (\cdot)</math> is a time coarse-graining operation (combining two time steps into one). In this way, [math]A_{m\times n}(TPM_{n\times n})[/math] is to perform coarse-graining on a [math]n\times n[/math] TPM, and the coarse-graining process is simplified as the product of matrix [math]A[/math] and matrix [math]TPM[/math].
Then, the commutativity condition of spatial coarse-graining and temporal coarse-graining is the following equation:
{{NumBlk|:|
<math>
A_{m\times n}(TPM_{n\times n}) \times A_{m\times n}(TPM_{n\times n}) = A_{m\times n}(TPM_{n\times n} \times TPM_{n\times n})
</math>
|{{EquationRef|3}}}}
The left side represents first performing coarse-graining on the states of two consecutive time steps, and then multiplying the dynamics TPM of the two time steps together to obtain a transfer matrix for two-step evolution; the right side of the equation represents first multiplying the TPMs of two time steps together to obtain the two-step evolution of the microscopic state, and then using A for coarse-graining to obtain the macroscopic TPM. The non-satisfaction of this equation indicates that some coarse-graining operations will cause differences between the evolution of macroscopic states and the coarse-grained states of the microscopic system after evolution. This means that some kind of consistency constraint needs to be added to the coarse-graining strategy.
However, as pointed out in the literature <ref name=":6" />, the above problem can be alleviated by considering the error factor of the model while maximizing EI in the continuous variable space. However, although machine learning techniques facilitate the learning of causal relationships and causal mechanisms and the identification of emergent properties, it is important whether the results obtained through machine learning reflect ontological causality and emergence, or are they just an epistemological phenomenon? This is still undecided. Although the introduction of machine learning does not necessarily solve the debate around ontological and epistemological causality and emergence, it can provide a dependence that helps reduce subjectivity. This is because the machine learning agent can be regarded as an "objective" observer who makes judgments about causality and emergence that are independent of human observers. However, the problem of a unique solution still exists in this method. Is the result of machine learning ontological or epistemological? The answer is that the result is epistemological, where the epistemic subject is the machine learning algorithm. However, this does not mean that all results of machine learning are meaningless, because if the learning subject is well trained and the defined mathematical objective is effectively optimized, then the result can also be considered objective because the algorithm itself is objective and transparent. Combining machine learning methods can help us establish a theoretical framework for observers and study the interaction between observers and the corresponding observed complex systems.