jurgendn Cross-Domain Analogy Finder
Two problems can be the same problem speaking different languages.
The job is to find a concept's structural twin in another field — then decide, honestly, which of four things you are actually holding. The entire value of this skill is the verification gate. Without it, this is an analogy fountain with good production values.
This skill is supposed to disappoint you most of the time. A run that returns three exciting transferable analogies is lying. Real structural transfer across distant domains is rare; that rarity is what makes the hits worth anything.
When NOT to use this
- As a way to feel productive while avoiding a hard problem. This has the texture of deep work while deferring the grind. Deploy it when genuinely stuck or vetting novelty — not as a default.
- For precedent inside or near your own field →
literature-triangulation. - To survey a research area →
literature-triangulation. - To vet one already-chosen idea →
research-idea-stress-test.
If you cannot name the problem you are stuck on or the idea you are vetting, stop and get that first. This skill needs a concrete seed.
The two modes
Pick one before starting. They differ on distance, on spirit, and on what counts as success. The postures are not symmetric.
| OFFENSE (borrow a solution) | DEFENSE (check novelty) | |
|---|---|---|
| Goal | import a tool from elsewhere | confirm your idea is (not) already solved |
| Where to walk | distant domains — distance is a reward | adjacent first, then distance-complete |
| Retrieval net | loose (chase any promising lead) | loose (alien vocabulary hides the twin) |
| Acceptance | structural: "can I take something from this?" | skeptical: "am I caught by this?" |
| One win is | one portable tool | one tight identity match |
| Stop when | a result transfers and passes the import test | the skeleton's instances are cleared, near AND far |
Both modes retrieve loosely and judge structurally. What differs is the question the structural judge asks. Offense is expansive (one carry-able result is a win). Defense is contractive and distrusts your own originality (one twin is a verdict).
Offense → distant nodes. Near neighbors already talk to each other; an analogy you find there is probably in a textbook. The gold is far: the source domain's people never noticed the shared structure, so the transfer is both novel and likely to carry a genuinely different technique. Bias the walk toward distance.
Defense → adjacent-first but distance-complete. Start near (cheapest place the twin usually lives), but adjacency is a search order, not a stopping rule. A novelty claim is only valid once the distant instances sharing your skeleton are also cleared. Stopping at adjacency is how you fabricate false confidence in your own originality — and how a reviewer finds the 1987 paper you missed.
Procedure
1. Abstract — strip the vocabulary
The hardest step, and the one that fails quietly. Reduce the concept to its skeleton:
- objects — what are the things?
- operator — what acts on them?
- invariant — what quantity/property is controlled?
- dynamics — how does it evolve / what is optimized?
Calibration: abstract until the invariant survives but the vocabulary dies.
- Too shallow → you search the name and match the name. Useless.
- Too deep → everything is "a dynamical system on a state space" and the search goes vacuous.
Diagnostic from the store (§5): if your skeleton already has dozens of instances across unrelated domains, you abstracted too shallow — it has become a useless hub. If it has exactly one, you went too deep, or it is genuinely new. The sweet spot is a handful of instances from distant domains.
2. Search the abstraction, not the name
Search the skeleton's signature, not its label. "Spectral gap" returns spectral gap; "the scalar governing exponential relaxation to a dominant eigenmode" returns Kuramoto thresholds, Cheeger constants, adiabatic gaps, stat-mech relaxation time — none of which say "spectral gap," all of which are it.
- OFFENSE: walk toward far domains and unfamiliar vocabulary.
- DEFENSE: enumerate the skeleton's instances near→far; the set is finite once the abstraction is right, which is what makes "distance-complete" achievable rather than "search all of science."
Use the skeleton store (§5) as a retrieval prior. The store proposes; it never verifies. The moment a stored edge stands in for evidence, you launder a surface-match as real.
For methodology inspiration retrieval (MIR-style search), treat prior methods as candidate solution patterns, not citations to paste. Prefer papers connected by methodological lineage or reusable operators over papers that merely share topical keywords. Then still run the four-way gate below: inspiration is a lead until a specific theorem, algorithm, bound, or proof technique transfers.
3. Classify each hit — the four-way gate
Every candidate is exactly one of these. They all feel identical at first glance ("huh, that looks related"). Telling them apart is the whole job, because acting on a surface-match as portable wastes a month, and dismissing a twin-with-a-delta as "already exists" wastes a paper.
- Identical → the same problem, already solved. STOP. Read their literature, inherit their toolbox, their failure modes, their counterexamples. (Defense win — a gift, not a death sentence.)
- Portable → the solution transfers. State the precondition it smuggles in (a metric? a symmetry? a conservation law?) and check it holds in your setting. (Offense win.)
- Twin-with-a-delta → matches everywhere except one structural place. The
mismatch is your open problem, pre-located. (The jackpot → hand to
gap-finder.) - Surface-only → resemblance with nothing carry-able. DISCARD. This is the bucket the gate exists to fill; most honest runs should land here.
4. The import-a-result test — the teeth
For every candidate that is not Surface-only, name the specific thing that crosses over: a theorem, a bound, an algorithm, or a proof technique — and check it says something nontrivial back home.
If you cannot name the carry-able result, it is Surface-only. No exceptions.
"They're both kinda about flow" fails. An analogy is a partial functor between two domains; keep it only if it preserves the load-bearing morphisms.
5. Provenance — non-negotiable for a research skill
The catastrophic failure is not a missed analogy. It is a confabulated one: "stat-mech solved this in 1987" with a hallucinated paper that makes you abandon a real contribution out of false humility.
- Every DEFENSE claim ("field X already solved this") needs a real, checkable source
or it is stamped
unverified. - Treat all retrievals as leads, never facts, until a source is in hand.
- Ground prior-art through
literature-triangulation— do not assert citations from memory. This skill proposes the analogy; that skill confirms the prior art.
6. Accrete
Append what you found to the skeleton store (§ store file): the skeleton, the concrete instances, their carry-able results with provenance, and any delta. The store compounds — over months it becomes a concept-graph centered on your research neighborhoods. Build it emergent, never global. Do not try to pre-map all of science; that is the years-long, dangerously-fun version that eats your timeline.
Output contract
For each surfaced hit:
- Skeleton — objects / operator / invariant / dynamics.
- The hit — concept, domain, distance from source.
- Verdict — Identical / Portable / Twin-with-a-delta / Surface-only.
- Carry-able result — the named theorem/bound/algorithm/technique, or "none → discard."
- Provenance — source, or
unverified. - Delta (if twin) — the single structural mismatch →
gap-finder. - Precondition (if portable) — the smuggled assumption to check.
End with an honest tally. If everything came back Surface-only, say so plainly — that is a successful run, not a failed one.
Companion files
skeleton-store.yaml— the accreting concept↔skeleton index (retrieval prior + schema).calibration-set.md— graded worked examples; the skill's ground truth.
Hand-offs
- Prior-art grounding →
literature-triangulation - The delta from a twin →
gap-finder - A chosen borrowed idea, to vet →
research-idea-stress-test