---
id: wiki-2026-0508-mental-operations-synthesized
title: Mental Operations Synthesized
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Cognitive Operations, Mental Tools]
duplicate_of: none
source_trust_level: B
confidence_score: 0.85
verification_status: applied
tags: [cognition, problem-solving, learning]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: n/a
  framework: n/a
---

# Mental Operations Synthesized

## 매 한 줄
> **"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.

## 매 핵심

### 매 the operations
1. **Decompose**: split problem into sub-problems.
2. **Abstract**: drop irrelevant details, keep essence.
3. **Generalize**: extend known to wider class.
4. **Specialize**: take general → solve concrete instance.
5. **Analogize**: structurally-similar known problem.
6. **Invert**: solve the negation, the dual, the inverse.
7. **Verify**: test boundary cases, sanity checks.
8. **Iterate**: refine via cycles.

### 매 modern frame
- System 1 (Kahneman): pattern-match, intuitive.
- System 2: deliberate, sequential, costly.
- 매 expert 의 chunking 의 System 1 expansion.

### 매 응용
1. Algorithm design (CLRS-style).
2. Debugging (binary search of state space).
3. Strategy / business problems (MECE, issue trees).
4. LLM prompting (Chain-of-Thought = explicit System 2).

## 💻 패턴

### Polya's 4-step (problem solving)
```
1. Understand: restate problem in own words.
2. Plan:       map to known technique (analogize).
3. Execute:    carry out plan, check each step.
4. Look back:  verify, generalize, simplify.
```

### Decompose: tree
```
Problem: Build chat app
├── auth (sub: oauth flow, session, refresh)
├── transport (sub: WS, fallback to SSE)
├── persistence (sub: schema, migrations)
└── UI (sub: list, composer, attachments)
```

### Inversion (Charlie Munger / Carl Jacobi)
```
Original: "How do I make this app fast?"
Inverted: "How would I make it slow?"
  → list 50 ways → avoid each
```

### Analogy mapping
```
Known: Dijkstra (shortest path on graph)
New:   "find cheapest API call sequence"
Map:   nodes=states, edges=API calls, weight=cost
→ apply Dijkstra
```

### Specialize → Generalize bootstrap
```
1. Solve N=1 case by hand.
2. Solve N=2.
3. Spot pattern.
4. Conjecture for N.
5. Prove by induction.
```

### Verify: boundary tests (CS / engineering)
```python
def median(xs): ...
assert median([5]) == 5                       # single
assert median([1, 2]) == 1.5                  # even
assert median([]) is None                     # empty
assert median([1, 1, 1]) == 1                 # duplicates
```

## 매 결정 기준
| Stuck-state | Operation |
|---|---|
| Too big to grasp | Decompose |
| Too messy / many details | Abstract |
| No idea where to start | Analogize |
| Direct attack failing | Invert |
| Don't trust the answer | Verify |

**기본값**: Polya 4-step + decompose-first. 매 invert when stuck.

## 🔗 Graph
- 부모: [[Problem_Solving|Problem-Solving]]
- 변형: [[First-Principles]] · [[MECE]]
- Adjacent: [[Chain-of-Thought]]

## 🤖 LLM 활용
**언제**: prompt-design (CoT = these operations made explicit), self-review of complex tasks.
**언제 X**: routine pattern-match tasks (System 1 sufficient).

## ❌ 안티패턴
- **Always System 2**: 매 exhausting + slow.
- **Always System 1 on hard problems**: 매 systematic errors.
- **No verification step**: 매 plausible-but-wrong.

## 🧪 검증 / 중복
- Verified (Polya — How to Solve It; Kahneman — Thinking Fast and Slow; Bloom's Taxonomy).
- 신뢰도 B+.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — Mental Operations FULL synthesis |