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 underlying systems, not the systems themselves. 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 structure. Statistical and causal inference often deepen this substitution by treating mathematical decomposition in the observed space as mechanistic decomposition of the system that produced it. But decompositions of projected data remain confined to the projected representation and are generally non-unique; they do not establish correspondence with the underlying mechanism. This reframes a central limit of modern inference: precision, fit, and decomposition within observed data are not evidence of mechanistic correspondence with the original structure. Mechanistic understanding therefore requires either direct operation on the underlying structure, or operation through a representation whose mapping has been shown to preserve the relevant properties of the original system, such as a validated simulation.