Measurement Algebra

The formalism named for the perspectival view, and the one entry in the atlas that names a formalism which does not yet exist.

What it would be

Treat each interpretability method as an operation applied to the model rather than a passive readout. An algebra over those operations would say how they compose: whether activation patching and sparse-autoencoder decomposition commute, whether two methods’ results are algebraically compatible, what can and cannot be measured jointly. The idea is borrowed from quantum mechanics, where observables are operators and two that fail to commute cannot be jointly measured to arbitrary precision. The application here is structural, not quantum-mechanical.

See Operator algebra and Measurement in quantum mechanics on Wikipedia for the origin.

Why the view wants one, and what it uses instead

Perspectival identity is cross-method coherence: two descriptions pick out the same mechanism when what they report survives changing the method. Stating that precisely needs a composition law — some formal answer to when two method-outputs are compatible. An algebra would supply it, and a coherence claim would become checkable rather than assessed.

No such algebra has been constructed, and constructing one is open. In its absence the view operates on multi-method robustness: run several methods, see whether a structure survives all of them. That is a weaker test, since agreement among methods that share a blind spot is not evidence, and it is the reason no widely adopted method sits in the perspectival view — the view describes a research direction rather than current practice.