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Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

2026-05-20 23:52:15 +09:00

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title

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

Decompose: split problem into sub-problems.
Abstract: drop irrelevant details, keep essence.
Generalize: extend known to wider class.
Specialize: take general → solve concrete instance.
Analogize: structurally-similar known problem.
Invert: solve the negation, the dual, the inverse.
Verify: test boundary cases, sanity checks.
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

Algorithm design (CLRS-style).
Debugging (binary search of state space).
Strategy / business problems (MECE, issue trees).
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)

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
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

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