Thinking Frameworks & Mental Models

A collection of proven mental models for problem-solving, decision-making, and analysis.

Quick Reference

Detailed Frameworks

First Principles Thinking

Strip away assumptions to fundamental truths, then rebuild.

Process:

1. State the problem
2. List ALL assumptions (even obvious ones)
3. Challenge each: "Is this actually true?"
4. Identify irreducible truths
5. Rebuild from fundamentals only

Example:

Problem: Need better pitch detection
Assumptions:
  - Must use time-domain autocorrelation (FALSE - frequency domain works)
  - Need complex algorithm (FALSE - HPS is simple and effective)
  - Accuracy requires YIN (FALSE - HPS achieves ±2 cents)
Fundamental truths:
  - Need to identify fundamental frequency
  - Must work in real-time (<50ms)
  - Target ±2 cent accuracy
Rebuilt solution: Use HPS - simple, fast, accurate enough

5 Whys

Drill to root cause by asking "why" repeatedly.

Example:

• Problem: Tests failing on CI
• Why? Sample rate mismatch
• Why? Test uses 44100, app uses 48000
• Why? Test has hardcoded value
• Why? Copied from old codebase
• Why? Didn't check iOS defaults
• Root: Assumption about audio defaults

SWOT Analysis

Systematic evaluation of internal/external factors.

Algorithm Choice: HPS vs YIN

HPS:
  Strengths: Simple (100 lines), proven, fast O(N log N)
  Weaknesses: Octave errors possible (±20% cases)
  Opportunities: Easy to optimize, well-understood
  Threats: Less effective below 50Hz

YIN:
  Strengths: Academic gold standard
  Weaknesses: Complex FFT (300+ lines), many gotchas
  Opportunities: Potentially higher accuracy
  Threats: Hard to implement correctly

Decision: HPS for v1, consider YIN if accuracy insufficient

Occam's Razor

Simplest explanation is usually correct.

Debugging Application:

Bug: Constant 3-cent sharp error
Complex theory: FFT circular correlation bias, needs windowing correction
Simple theory: Sample rate is wrong
Occam says: Check sample rate first ✓

Result: Using 44100 instead of 48000 → Fix in 1 line

Second-Order Thinking

Consider ripple effects beyond immediate consequences.

Example - Caching Algorithm:

• 1st order: Faster performance ✓
• 2nd order: Memory usage increases, stale data if settings change
• 3rd order: Need cache invalidation, increased code complexity
• Decision: Only cache if performance actually matters

Inversion

Define how to fail, then avoid those paths.

Pitch Detection Reliability:

Goal: Accurate detection
Inversion: How to guarantee failure?
  1. Wrong sample rate ✗
  2. No window function ✗
  3. Skip interpolation ✗  
  4. Ignore amplitude ✗
  5. Don't test octaves ✗

Production Checklist:
  ✓ Capture sample rate from AVAudioSession
  ✓ Apply Hann window before FFT
  ✓ Use parabolic interpolation
  ✓ Check amplitude threshold
  ✓ Test A1-A6 (55Hz-1760Hz)

Pareto Principle (80/20)

Focus on the vital few, not trivial many.

Application:

• 80% of bugs come from 20% of code → Focus testing there
• 80% of CPU time in 20% of functions → Optimize those first
• 80% of accuracy from 20% of implementation:
  • Correct sample rate
  • Proper windowing
  • Parabolic interpolation

Anti-pattern: Spending 80% time on features giving 20% value

Opportunity Cost

Every choice means giving up alternatives.

Example:

Option A: Implement YIN (3 days)
Opportunity cost:
  - HPS (1 day) + UI polish (2 days)
  - Transposition feature (2 days) + tests (1 day)
  - Documentation (3 days)

Question: Is YIN worth more than alternatives?
Answer: Not unless HPS proves insufficient

One Thing Focus

What ONE thing makes everything else easier or unnecessary?

Questions:

• Feature work: What's the ONE feature users actually need?
• Bug fixing: What's the ONE root cause of multiple symptoms?
• Optimization: What's the ONE bottleneck?

Example:

• Don't optimize 10 minor functions
• Find the ONE hotpath (FFT) and optimize that
• Result: 10x speedup from 1 optimization vs 2x from 10 optimizations

10-10-10 Rule

Evaluate decisions across time horizons.

Example - Hardcode vs Config:

Decision: A4 frequency (440 Hz default)

10 minutes: Hardcoding is faster
10 months: Users want customization → Refactor needed
10 years: Standard feature expectation

Decision: Make configurable now (saves 10-month refactor pain)

Via Negativa

Improve by removing, not adding.

Application:

Problem: Complex, buggy YIN implementation

Addition approach:
  + Add more tests
  + Add error handling
  + Add comments
  + Add validation

Subtraction approach:
  - Remove YIN entirely
  - Use simpler HPS
  Result: Fewer bugs, less code, same accuracy

Question always: "What can I remove to make this simpler?"

Usage Patterns

Debugging Workflow

1. 5 Whys → Root cause
2. Occam's Razor → Simplest explanation first
3. Inversion → How would this bug happen?

Architecture Decisions

1. First Principles → What do we actually need?
2. SWOT → Compare options
3. Second-Order → Long-term consequences?
4. 10-10-10 → How will this age?

Feature Prioritization

1. Pareto → Which features give 80% of value?
2. One Thing → What's the most important feature?
3. Opportunity Cost → What are we giving up?

Code Review

1. Via Negativa → What can we remove?
2. Occam's Razor → Is this the simplest solution?
3. Inversion → How could this fail?

Combining Frameworks

Complex decisions benefit from multiple frameworks:

Example - Algorithm Choice:

1. First Principles: Need frequency (Hz) from audio in <50ms
2. SWOT: Compare HPS vs YIN
3. Occam's Razor: HPS is simpler
4. Pareto: HPS gives 80% accuracy with 20% complexity
5. Opportunity Cost: YIN costs 2 extra days
6. 10-10-10: HPS sufficient for v1, can upgrade later

Decision: HPS
Confidence: High (multiple frameworks agree)

Anti-Patterns

Don't use frameworks to:

• ❌ Justify pre-made decisions (confirmation bias)
• ❌ Avoid deciding (analysis paralysis)
• ❌ Sound smart (intellectual peacocking)
• ❌ Over-analyze simple choices

Do use frameworks to:

• ✓ Think clearly about complex problems
• ✓ Challenge your assumptions
• ✓ Communicate reasoning
• ✓ Make better decisions faster

When to Use Which Framework

Quick decisions → Occam's Razor, One Thing Complex decisions → First Principles, SWOT, Second-Order Prioritization → Pareto, Opportunity Cost, Eisenhower Matrix Risk mitigation → Inversion, Second-Order Simplification → Via Negativa, Occam's Razor Root causes → 5 Whys, First Principles