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→Ambiguity
====Ambiguity====
====Ambiguity====
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 and irrationality <ref>Eberhardt, F., & Lee, L. L. (2022). Causal emergence: When distortions in a map obscure the territory. Philosophies, 7(2), 30.</ref>.
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 and irrationality <ref name="Eberhardt">Eberhardt, F., & Lee, L. L. (2022). Causal emergence: When distortions in a map obscure the territory. Philosophies, 7(2), 30.</ref>.
First, <ref name="Eberhardt"/> highlights that ambiguity can arise in coarse-graining the TPM if no constraints are imposed on the scheme. For example, when the two row vectors in the TPM corresponding to the two states to be merged are very dissimilar, forcibly merging them (for example, by taking the average) will cause ambiguity. This ambiguity arises in determining the meaning of intervention on the merged macroscopic state. Because the row vectors are dissimilar, the macroscopic state's intervention cannot directly correspond to microscopic state interventions. If the intervention on the macroscopic state is forcibly converted into the intervention on the microscopic states by taking the average, the differences between the microscopic states are ignored. At the same time, new contradictory problems of non-commutativity will also be triggered.
First, <ref name="Eberhardt"/> highlights that ambiguity can arise in coarse-graining the TPM if no constraints are imposed on the scheme. For example, when the two row vectors in the TPM corresponding to the two states to be merged are very dissimilar, forcibly merging them (for example, by taking the average) will cause ambiguity. This ambiguity arises in determining the meaning of intervention on the merged macroscopic state. Because the row vectors are dissimilar, the macroscopic state's intervention cannot directly correspond to microscopic state interventions. If the intervention on the macroscopic state is forcibly converted into the intervention on the microscopic states by taking the average, the differences between the microscopic states are ignored. At the same time, new contradictory problems of non-commutativity will also be triggered.
====Non-commutativity====
====Non-commutativity====