Applications

Ways of putting the encyclopedia to work — including Abstractopia, an interactive prototype that turns the catalog from something you read into a skill you practise, plus position papers and companion documents: direct teaching of abstract reasoning, the catalog-augmented reasoning pipeline, the pilot study testing it against bare chain-of-thought, and the substrate-independence framework that scopes the catalog's claim.

• Abstractopia — a hands-on companion for training abstract reasoning

  Abstractopia is an early, experimental web app that turns the Encyclopedia's catalog from something you read into a skill you practise. Where the other entries here are papers, this one is a thing you use: a spaced-repetition trainer that teaches you to recognise the catalog's patterns in situations that look nothing alike — and to tell them apart from their convincing look-alikes. Its design is disciplined by the few learning-science findings that have actually replicated — comparison-first, induce-then-name, a spaced spiral over weeks, and crediting recognition only far from where you learned it — and it is honest that whether this produces durable cross-domain transfer is an open question the project exists to test. A research-preview prototype, not a finished product.

• Teaching Abstract Reasoning Directly: An Exploratory Proposal

  We teach formal logic. We teach mathematics. We teach the methods of historical inquiry, the conventions of literary analysis, the experimental protocols of the natural sciences. Across the K–12 curriculum and into university, we devote substantial time to teaching reasoning within domains — the way a chemist reasons about reactions, the way a historian reasons about evidence, the way a programmer reasons about computation.

• Substrate Independence Framework

  This document describes the substrate-independence framework — what it is, why it matters for the Encyclopedia of Abstractions' central claim, and the method used to score the catalog's 1,402 primes on it. The methodology is reproducible: it can be re-run as the catalog grows, or if the rubric needs to be re-tuned.

• Augmented Abstract Reasoning: A Pipeline Complement to Chain-of-Thought

  Chain-of-thought (CoT) prompting has well-documented failure modes: brittleness on compositional reasoning, surface-feature reliance under perturbation, and unfaithful chains that rationalize predetermined answers. Many of these stem from a structural absence — CoT does not surface the abstract patterns that govern cross-domain transfer, so the technique succeeds only when the training distribution has already paired similar patterns. We propose Augmented Abstract Reasoning (AAR), a pipeline that complements rather than replaces CoT. AAR factors cross-domain reasoning into nine explicit steps — prime-abstraction identification, salience ranking, pruning, context-specific model construction, meta-model abstraction, archetype query, dual-pass reasoning, and evaluation — drawing on the Encyclopedia of Abstractions catalog (1,402 primes and 1,108 archetypes). A worked example on fishery stock governance demonstrates the pipeline; the paper positions it relative to CoT, RAG, and agentic frameworks, and identifies open empirical questions.

• Augmented Abstract Reasoning Pilot Comparison

  Headline. On a single canonical common-pool-resource problem, a blinded grader scored a catalog-augmented recommendation 50/60 against a bare chain-of-thought recommendation at 45/60. Treated as a pilot, the directional signal is consistent with the hypothesis that the catalog complements CoT. Treated as evidence for that hypothesis, the result is insufficient: N=1, mature-domain problem, same-model agents, same-class grader, non-pre-registered, conducted by the prototype's implementer. The pilot's purpose is to determine whether a properly designed study is worth running. The conclusion is that it is.