Claude-skill-registry decomposing-complex-problems
Deconstructs complex problems using the 'Polymath Investor' framework with a 5-step cognitive chain (First Principles → Modular Isolation → Pareto Filtering → Cross-Domain Mapping → Dynamic Zooming). Use when analyzing systems, architectures, businesses, or learning challenges; when seeking high-leverage insights or 'Alpha'; when applying first principles thinking; or when needing cross-disciplinary perspectives to reveal blind spots. Transforms overwhelming complexity into actionable levers.
git clone https://github.com/majiayu000/claude-skill-registry
T=$(mktemp -d) && git clone --depth=1 https://github.com/majiayu000/claude-skill-registry "$T" && mkdir -p ~/.claude/skills && cp -r "$T/skills/data/decomposing-complex-problems" ~/.claude/skills/majiayu000-claude-skill-registry-decomposing-complex-problems && rm -rf "$T"
skills/data/decomposing-complex-problems/SKILL.mdPolymath Decomposition Protocol
Overview
A high-fidelity cognitive tool for breaking down complexity. It rejects linear "specialist" thinking in favor of a "lattice of mental models."
Goal: Transform "Overwhelming Complexity" into "Actionable Levers."
Critical Rules
- NO ANALOGY (Initially) - Phase 1 must be pure fact/physics. Analogies are forbidden until Phase 4.
- RUTHLESS REDUCTION - If it doesn't drive the outcome, it is noise. Ignore it.
- FORCED ISOMORPHISM - Find a structural match in a non-related field (Biology/Physics/History).
The 5-Phase Process
PHASE 1: THE LEGO DEMOLITION (First Principles)
"Decompose to the basic truths."
- Action: Smash the problem/system into its smallest indivisible units ("The LEGO Bricks").
- Constraint: Ignore "Best Practices" or "Industry Standards".
- Question: What are the physical, mathematical, or economic limits that cannot be violated?
- Output: A list of 3-5 "Atomic Facts" (e.g., "Data travels at speed of light," "Users have finite attention").
PHASE 2: ISOLATION & DECOUPLING (Divide & Conquer)
"Make it digestible."
- Action: Group atomic units into independent "Black Boxes" (Modules).
- Constraint: Modules must be Decoupled. Analyzing Module A should not require holding Module B in memory.
- Question: What are the clear "Interfaces" between these boxes? Where do they touch?
- Output: A defined list of Sub-systems and their Inputs/Outputs.
PHASE 3: THE PARETO FILTER (Key Drivers)
"Ignore the noise."
- Action: Identify the "High Convexity" modules.
- Constraint: 80% of the modules are "Maintenance/Noise". Ignore them. Focus on the 20% that generate value or risk.
- Question: If this module is deleted, does the system die? If this module improves by 1%, does the outcome improve by 10%?
- Output: Identification of the single "Bottleneck" or "Growth Engine."
PHASE 4: STRUCTURAL MAPPING (The Polymath Lens)
"Find the isomorphism."
- Action: Force a metaphor from a completely alien domain onto the "Key Driver" identified in Phase 3.
- Domains to Scan:
- Physics/Thermodynamics: (Entropy, Friction, Leverage, Potential Energy)
- Evolutionary Biology: (Adaptation, Parasitism, Symbiosis, Immune Response)
- History/Warfare: (Empires, Supply Lines, Guerilla Tactics)
- Question: "What is this system's equivalent in Nature?" (e.g., "This microservice architecture looks like a hive mind," or "This marketing funnel has high 'kinetic friction'.")
- Output: A "Cross-Domain Insight" that reveals a blind spot.
PHASE 5: DYNAMIC ZOOM (Zoom In & Out)
"See the forest and the bark."
- Action: Oscillate between the texture and the landscape.
- Zoom In: Look at the "Code/Texture" of the Key Driver. (The implementation detail).
- Zoom Out: Look at the "Time/Cycle" of the system. (Where is this in the historical lifecycle?).
- Output: A synthesis of how the micro-detail affects the macro-destiny.
Output Format
Present the analysis using this structure:
### 1. 乐高拆解 (First Principles) * **原子事实**: [不可再分的物理/逻辑真相] * **原子事实**: ... ### 2. 模块隔离 (Decoupling) * [模块A] -> (接口) -> [模块B] * **解耦说明**: [为何这两个模块可以独立看待] ### 3. 帕累托杠杆 (The 20%) * **关键驱动因子**: [系统生死的决定性模块] * **被忽略的噪音**: [可以暂时无视的80%细节] ### 4. 跨学科映射 (Structural Mapping) * **映射领域**: [例如:生物免疫系统] * **同构性分析**: [系统的Bug处理机制就像...因此它缺少...] * **盲点揭示**: [基于这个比喻,我们要警惕...] ### 5. 变焦综合 (Zoom In/Out) * **微观纹理**: [代码/执行层面的具体观察] * **宏观定位**: [该系统处于历史周期的哪个阶段] * **下一步行动**: [基于上述所有分析的一个高杠杆动作]