Causal Geometry

Area of Science:

• Theoretical Physics
• Causal Inference
• Information Geometry

Background:

• Information geometry quantifies model parameter impact on predicted effects.
• Causation lacks formal investigation within existing information geometry frameworks.
• Causal models are fundamental to scientific explanation.

Purpose of the Study:

• Introduce causal geometry to formalize causation in scientific models.
• Develop a geometric measure of effective information for causal relationships.
• Investigate the relationship between intervention capability and model effectiveness.

Main Methods:

• Formalized intervention on model parameters within a geometric framework.
• Introduced a geometric version of effective information.
• Analyzed geometric congruence between the space of effects and interventions.

Main Results:

• Effective information is determined by the geometric congruence between effects and interventions.
• An effective causal model is well-matched to its intervention capabilities.
• Causal emergence demonstrates that macroscopic causal relationships can be more informative than microscopic ones.

Conclusions:

• Causal geometry provides a formal framework for studying causation and intervention.
• Model effectiveness is linked to the alignment between its structure and intervention possibilities.
• Coarse-grained models can be more informative than microscopic ones if they better match accessible interventions.