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135 lines
3.8 KiB
Markdown
135 lines
3.8 KiB
Markdown
---
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id: wiki-2026-0508-mental-operations-synthesized
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title: Mental Operations Synthesized
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [Cognitive Operations, Mental Tools]
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duplicate_of: none
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source_trust_level: B
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confidence_score: 0.85
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verification_status: applied
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tags: [cognition, problem-solving, learning]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: n/a
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framework: n/a
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---
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# Mental Operations Synthesized
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## 매 한 줄
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> **"매 think-about-thinking 의 toolkit"**. 매 Polya (1945 How to Solve It), Bloom's Taxonomy, Dual Process Theory (Kahneman), 매 lineage 의 synthesis — 매 generic mental moves 매 cross-domain transferable.
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## 매 핵심
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### 매 the operations
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1. **Decompose**: split problem into sub-problems.
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2. **Abstract**: drop irrelevant details, keep essence.
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3. **Generalize**: extend known to wider class.
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4. **Specialize**: take general → solve concrete instance.
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5. **Analogize**: structurally-similar known problem.
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6. **Invert**: solve the negation, the dual, the inverse.
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7. **Verify**: test boundary cases, sanity checks.
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8. **Iterate**: refine via cycles.
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### 매 modern frame
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- System 1 (Kahneman): pattern-match, intuitive.
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- System 2: deliberate, sequential, costly.
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- 매 expert 의 chunking 의 System 1 expansion.
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### 매 응용
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1. Algorithm design (CLRS-style).
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2. Debugging (binary search of state space).
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3. Strategy / business problems (MECE, issue trees).
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4. LLM prompting (Chain-of-Thought = explicit System 2).
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## 💻 패턴
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### Polya's 4-step (problem solving)
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```
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1. Understand: restate problem in own words.
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2. Plan: map to known technique (analogize).
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3. Execute: carry out plan, check each step.
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4. Look back: verify, generalize, simplify.
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```
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### Decompose: tree
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```
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Problem: Build chat app
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├── auth (sub: oauth flow, session, refresh)
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├── transport (sub: WS, fallback to SSE)
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├── persistence (sub: schema, migrations)
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└── UI (sub: list, composer, attachments)
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```
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### Inversion (Charlie Munger / Carl Jacobi)
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```
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Original: "How do I make this app fast?"
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Inverted: "How would I make it slow?"
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→ list 50 ways → avoid each
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```
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### Analogy mapping
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```
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Known: Dijkstra (shortest path on graph)
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New: "find cheapest API call sequence"
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Map: nodes=states, edges=API calls, weight=cost
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→ apply Dijkstra
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```
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### Specialize → Generalize bootstrap
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```
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1. Solve N=1 case by hand.
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2. Solve N=2.
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3. Spot pattern.
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4. Conjecture for N.
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5. Prove by induction.
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```
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### Verify: boundary tests (CS / engineering)
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```python
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def median(xs): ...
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assert median([5]) == 5 # single
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assert median([1, 2]) == 1.5 # even
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assert median([]) is None # empty
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assert median([1, 1, 1]) == 1 # duplicates
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```
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## 매 결정 기준
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| Stuck-state | Operation |
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|---|---|
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| Too big to grasp | Decompose |
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| Too messy / many details | Abstract |
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| No idea where to start | Analogize |
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| Direct attack failing | Invert |
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| Don't trust the answer | Verify |
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**기본값**: Polya 4-step + decompose-first. 매 invert when stuck.
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## 🔗 Graph
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- 부모: [[Problem_Solving|Problem-Solving]]
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- 변형: [[First-Principles]] · [[MECE]]
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- Adjacent: [[Chain-of-Thought]]
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## 🤖 LLM 활용
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**언제**: prompt-design (CoT = these operations made explicit), self-review of complex tasks.
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**언제 X**: routine pattern-match tasks (System 1 sufficient).
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## ❌ 안티패턴
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- **Always System 2**: 매 exhausting + slow.
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- **Always System 1 on hard problems**: 매 systematic errors.
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- **No verification step**: 매 plausible-but-wrong.
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## 🧪 검증 / 중복
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- Verified (Polya — How to Solve It; Kahneman — Thinking Fast and Slow; Bloom's Taxonomy).
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- 신뢰도 B+.
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## 🕓 Changelog
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| 날짜 | 변경 |
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|---|---|
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — Mental Operations FULL synthesis |
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