Rethinking Statistics and Causality: Why Mechanisms Cannot Be Inferred from Projected Data Distributions

Statistical and causal inference have become universal currencies of explanation across the sciences, especially where underlying mechanisms remain opaque. Their authority rests on the assumption that patterns in observed data can reveal the processes that generated them. Yet persistent mismatches between empirical findings and real-world behavior point to a deeper limitation: observed data are projections of an original system, not the system itself. Such projections need not preserve the structural or semantic properties of what they represent. As a result, operations on projected data cannot be assumed to correspond to operations on the original system. Statistical and causal inference often deepen this substitution by treating mathematical decomposition in the observed space as mechanistic decomposition of the original system. Yet decompositions of projected data remain confined to the projected representation and are generally non-unique; they do not establish correspondence with the mechanism of the original system. This reframes a central limit of modern inference: precision, fit, and decomposition within observed data are not evidence of mechanistic correspondence with the original system. Mechanistic understanding therefore requires either 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.