The Causal Measure

We introduce the Causal Measure, a normalized scalar weighting scheme over finite directed acyclic graphs. Causal substance is modeled as a non-negative scalar for purposes of the measure. Given the premise that causes precede effects, the measure assigns to each node a value D(i) = W(i)/W_T · P, where W(i) denotes the causal weight of a node’s territory and P is the total causal pool. By construction, the measure satisfies the normalization identity Σ D(i) = P. The measure and the Incompatibility Theorem for Positive Inputs and Predecessor Closure are formally independent.

Independently of the measure, we establish the Incompatibility Theorem for Positive Inputs and Predecessor Closure: no finite, well-founded DAG satisfying five structural conditions can contain a node with positive causal input without requiring at least one predecessor outside the modeled system. The proof proceeds via three lemmas — root zero-input, walk termination, and positivity propagation. Hence any exogenous positive source demanded by the theorem lies strictly outside the modeled set A and cannot be internalized as a node while preserving the axioms.

Together, the normalization identity and the impossibility theorem identify a structural boundary condition: under the stated axioms, such a causal system cannot be self-originating within its own formal domain.

Read The Causal Measure full paper (PDF)

Contact: kevin.rich@maskilon.com

We bridge ancient wisdom traditions with frontier AI research, building systems that don't just process information — they develop understanding.