Divergent convergent

Divergent-Convergent Cycling

The meta-pattern underlying most creative and analytical frameworks. Inspired by general divergent/convergent thinking research and design-process patterns. Use as a general-purpose exploration tool and default entry point for complex problems.

Skip check: If the solution space is already known and small (the user is picking between 2–3 named options), this is an evaluation problem, not an exploration problem — route to structured-evaluation or just answer.

Core principle

Two fundamentally different thinking modes. Never mix them.

Divergent — Expand. Generate options, possibilities, perspectives. Quantity over quality. No evaluation. No "but." Every idea gets written down.

Convergent — Contract. Evaluate, filter, rank, select. Quality over quantity. Critical judgment is welcome. Weak ideas get cut.

The power is in cycling: diverge → converge → diverge again from the focused point. Each cycle refines understanding.

Cognitive operations

Pattern recognition

"What kind of problem is this? What does it resemble?"

• Classify the problem type
• Identify analogies to known patterns

Memory retrieval

"What do we already know?"

• Gather existing knowledge, prior decisions, constraints
• This is where tool calls happen (search, lookups)

Divergent production

"What are all the possible approaches?"

• Generate multiple candidates without filtering
• Aim for 5-7+ options before any evaluation
• Suppress the inner critic during this phase

Convergent production

"What's the best approach given constraints?"

• Apply criteria: feasibility, cost, time, risk, alignment
• Rank options, identify top 2-3 for deeper evaluation

Evaluation

"How confident are we?"

• Test selected option against edge cases
• Identify remaining risks
• Decide: commit, iterate, or escalate

Two-cycle exploration pattern

Two cycles, each with a diverge and converge phase.

Cycle 1: Find the right problem

Diverge (Discover)

• What's the context? Who's affected? What are the symptoms?
• What adjacent problems exist? Are they connected?
• What do different stakeholders see as the problem?
• What's been tried before?

Converge (Define)

• What's the actual problem underneath the stated problem?
• Write a problem statement: "The core challenge is [X] because [Y], which matters because [Z]"
• Confirm with the user: "Is this the right problem?"

Cycle 2: Find the right solution

Diverge (Develop)

• Generate at least 5 substantially different approaches
• Include at least one unconventional or counterintuitive option
• For each, note what it optimizes for and what it sacrifices

Converge (Deliver)

• Evaluate against the problem statement from Cycle 1
• Apply constraints (time, resources, risk tolerance)
• Recommend with clear reasoning
• Identify next steps and open questions

Handoff to specialized skills

After Cycle 1 converges, the problem type may map to a more specialized skill:

• "This is an evaluation problem" → use structured-evaluation
• "This is a transformation problem" → use creative-transformation
• "This is a diagnostic problem" → use investigative-reasoning

If Cycle 2's divergent phase reveals contradictions → contradiction resolution If Cycle 2's convergent phase reveals hidden assumptions → Socratic questioning

Execution guidelines

• Announce phase transitions: "Switching to divergent mode" / "Converging now"
• In divergent phases, if you catch yourself writing "however" or "but" — stop. You're converging prematurely.
• In convergent phases, don't introduce new options. Work with what was generated.
• Each cycle should meaningfully advance understanding. If a cycle produces the same understanding you started with, the divergent phase wasn't broad enough.

Output format

Label phases clearly. In divergent phases, use numbered lists (countable). In convergent phases, state criteria and how options ranked. Final output: what was decided, why, and what's next.

For a complete worked example (both cycles end to end), read references/example.md. If unsure of the format, read it before starting.

Before finishing, verify

1. Every divergent phase produced a numbered list with at least 5 entries and contains no evaluative language ("however", "but", "the problem with this").
2. Every convergent phase stated its criteria and worked only with options already generated — no new options introduced.
3. Cycle 1 produced a problem statement in the form "The core challenge is [X] because [Y], which matters because [Z]".
4. At least one option in Cycle 2's divergent phase is unconventional or counterintuitive.
5. The final output names the decision, the reasoning, and the next step.

If any check fails, fix that phase before presenting the result.