cmplx-complex-analysis

name	cmplx - Complex Analysis
description	Framework for genuinely complex problems that resist simple answers. Identify sources of complexity, choose appropriate tools, decompose without oversimplifying, and synthesize.
output	{"format":"prose"}

CMPLX - Complex Analysis

Input: $ARGUMENTS

---

Step 1: Identify Why This Is Complex

PROBLEM: [statement of the problem]

COMPLEXITY SOURCES (check all that apply):
  [ ] MANY VARIABLES: [list the key variables]
  [ ] FEEDBACK LOOPS: [describe circular causation]
  [ ] UNCERTAINTY: [what's unknown and how much it matters]
  [ ] CONFLICTING STAKEHOLDERS: [who wants what, and how do they clash]
  [ ] EMERGENT BEHAVIOR: [outcomes that can't be predicted from parts]
  [ ] NONLINEARITY: [small changes produce disproportionate effects]
  [ ] TIME DYNAMICS: [behavior changes depending on timescale]
  [ ] MEASUREMENT DIFFICULTY: [key factors are hard to observe]

PRIMARY COMPLEXITY: [the dominant source of complexity]

Name the complexity. "It's complicated" is not analysis. Identifying WHICH KIND of complicated determines which tools to use.

---

Step 2: Choose Complexity-Handling Tools

Based on the complexity sources identified:

SELECTED APPROACHES:
  FOR [complexity source]: USE [approach]
    - Many variables → decomposition, sensitivity analysis
    - Feedback loops → systems mapping (/sysk), causal loop diagrams
    - Uncertainty → scenario planning, probabilistic reasoning
    - Conflicting stakeholders → multi-perspective analysis, trade-off mapping
    - Emergent behavior → simulation thinking, agent-based reasoning
    - Nonlinearity → threshold identification, regime analysis
    - Time dynamics → temporal decomposition, phase analysis
    - Measurement difficulty → proxy identification, triangulation

PRIMARY TOOL: [the main analytical approach]
SUPPORTING TOOLS: [secondary approaches]

---

Step 3: Decompose Without Oversimplifying

DECOMPOSITION:
  PART 1: [sub-problem]
    SELF-CONTAINED: [yes | no — does it interact with other parts?]
    INTERACTIONS: [which other parts it affects and how]
  PART 2: [sub-problem]
    SELF-CONTAINED: [yes | no]
    INTERACTIONS: [cross-part effects]
  PART 3: [sub-problem]
    SELF-CONTAINED: [yes | no]
    INTERACTIONS: [cross-part effects]

INTERACTIONS MAP:
  [Part 1] ←→ [Part 2]: [how they influence each other]
  [Part 2] ←→ [Part 3]: [interaction]
  [Part 1] ←→ [Part 3]: [interaction]

DECOMPOSITION RISK: [what do you lose by analyzing parts separately?]

The risk of decomposition is losing interactions. Always map the interactions explicitly, and check whether analyzing parts separately would miss something critical.

---

Step 4: Maintain Awareness of Interactions

CROSS-CUTTING CONCERNS:
  1. [factor that affects multiple parts]
     PARTS AFFECTED: [list]
     MECHANISM: [how it crosses boundaries]
  2. [factor]
     PARTS AFFECTED: [list]
     MECHANISM: [how]

SECOND-ORDER EFFECTS:
  IF [action on Part 1] THEN [effect on Part 2] THEN [effect on Part 3]
  IF [action on Part 2] THEN [effect on Part 1] THEN [cascade]

This is where complexity analysis earns its keep. Simple analysis misses these interactions. Complex analysis tracks them.

---

Step 5: Synthesize

SYNTHESIS
=========
PROBLEM: [restate]
COMPLEXITY TYPE: [primary source]

ANALYSIS:
  1. [key finding from Part 1]
  2. [key finding from Part 2]
  3. [key finding from Part 3]

INTERACTIONS THAT MATTER:
  1. [critical interaction between parts]
  2. [critical interaction]

WHAT SIMPLE ANALYSIS WOULD MISS:
  [the specific insight that only emerges from tracking complexity]

RECOMMENDATIONS:
  1. [action] — ACCOUNTS FOR: [which complexity source]
  2. [action] — ACCOUNTS FOR: [which complexity source]

REMAINING UNCERTAINTY:
  [what's still unclear and how to make progress on it]

CONFIDENCE: [high | medium | low]
  WHY: [what drives the confidence level]

---

Failure Modes

Failure	Signal	Fix
Fake complexity	Problem is actually simple	Use /smpl — not everything deserves this framework
Decompose and forget	Parts analyzed in isolation, interactions ignored	Step 4 exists specifically to prevent this
Complexity paralysis	Analysis never reaches conclusions	Set a stopping point — perfect analysis of complex systems is impossible
Tool mismatch	Using simple tools on complex problems	Match the tool to the complexity type from Step 2
Missing the dominant source	All complexity sources treated equally	One source is usually primary — focus there

---

Integration

• Opposite of: /smpl (use smpl when cmplx is overkill)
• Use with: /sysk when feedback loops are the primary complexity source
• Use with: /dtsk when uncertainty can be reduced with data
• Use from: /analyze when the router detects genuine complexity
• Escalate to: /certainty when maximum rigor is required