Self-Reference Map

Recursion, paradox, and alignment analogies compared by selected features.

Conceptual map The feature choices and solid relations are hand-authored. Computed proximity indicates similarity under those choices, not mathematical equivalence or a causal relationship.

Self-reference appears in constructions with very different outcomes: recursion and quines put it to work, while the Liar and Gödel expose precisely scoped limits. Goodhart, ELK, and probe contamination are included as proposed machine-learning analogies, not direct instances of the same theorem. Each node is scored on five features (mechanism, productivity, what breaks, locus, domain). Solid lines are hand-labeled relations; dashed lines are computed affinities, pairs whose feature distance is small. Click a node for its story; drag to untangle.

show computed affinities (dashed)

The productive→collapse spectrum offers one way to compare material from the limits-of-formalization post and the limits/ interactive. The logic results, alignment questions, and productive constructions occupy nearby regions under the selected features; proximity does not show that alignment systems inherit the theorems' conclusions. Distances are weighted Jaccard over the feature sets; weights and data in self_reference.json.