Rethinking Statistics and Causality: Why Cause and Effect Cannot Be Inferred from Projected Observations

Statistical and causal inference have long lacked clear and stable definitions of cause and effect, leading to assumptions and representations that assign them without establishing why those assignments should hold. This has contributed directly to persistent replication failures and broader empirical crises, where statistical results fail to correspond to empirical reality. The underlying problem is the same as a standard problem in 3D computer vision: a 3D object is projected by a camera onto an image plane, while the goal is to understand the original object from its projection. Statistical inference has the same setting: a high-dimensional original system is observed through low-dimensional projections, often represented as 1D variables, while the goal is to determine its properties and responses to different inputs. Cause and effect concern these responses, yet statistical and causal inference operate only on projected observations through regression, conditioning, factorization, and related operations. These operations do not access the original system and therefore provide no information about its responses to different inputs or about cause and effect. Adding assumptions does not resolve the original problem; it replaces the problem of understanding an unknown high-dimensional system with a different problem posed under a prespecified mathematical structure. Accordingly, determining cause and effect requires direct intervention on the original system, or intervention through a representation whose mapping has been shown to preserve the relevant properties of that system, such as a validated simulation.