Lesson 3.3: Self-Refinement & Iteration

Problem: A store offers 20% off, then an additional 10% off the discounted price. 
What's the total discount on a $100 item?

Generate 3 independent solutions:

Solution 1:
- First discount: $100 × 0.20 = $20
- Price after first discount: $100 - $20 = $80
- Second discount: $80 × 0.10 = $8
- Final price: $80 - $8 = $72
- Total discount: $100 - $72 = $28 (28%)

Solution 2:
- Combined discount: 1 - (0.80 × 0.90) = 1 - 0.72 = 0.28
- Total discount: 28%
- Final price: $100 × 0.72 = $72

Solution 3:
- First discount: 20% off = $80
- Second discount: 10% off $80 = $8 off
- Total saved: $20 + $8 = $28
- Total discount: 28%

Consensus: All three solutions agree on 28% total discount and $72 final price.
Answer: 28% total discount, final price $72

Problem: If 5 machines make 5 widgets in 5 minutes, how long does it take 100 machines 
to make 100 widgets?

Solution 1:
- 5 machines make 5 widgets in 5 minutes
- So 100 machines make 100 widgets in 5 minutes
Answer: 5 minutes

Solution 2:
- 5 machines make 5 widgets in 5 minutes
- Rate: 1 widget per machine per 5 minutes
- 100 machines × 1 widget each = 100 widgets in 5 minutes
Answer: 5 minutes

Solution 3:
- 5 machines make 5 widgets in 5 minutes
- 100 machines make 20× more = 100 widgets
- Time needed: 5 minutes × (100/5) = 100 minutes
Answer: 100 minutes ❌

Analysis: Solutions 1 and 2 agree (5 minutes). Solution 3 made an error in reasoning.
The correct answer is 5 minutes (majority vote).

Verification: Each machine makes 1 widget in 5 minutes, so 100 machines make 100 widgets 
in 5 minutes simultaneously.

Step 1: Generate Initial Response
[Create first draft]

Step 2: Critique the Response
Identify weaknesses:
- What's missing?
- What could be clearer?
- What's incorrect?
- What could be improved?

Step 3: Generate Improved Version
[Create refined version addressing critiques]

Task: Write a professional email declining a job offer.

STEP 1: Initial Draft

Subject: Job Offer

Hi,

Thanks for the offer but I've decided to go with another company. 

Best,
John

STEP 2: Critique

Issues identified:
- Subject line too vague
- Lacks gratitude and professionalism
- Too brief and abrupt
- Doesn't maintain relationship
- No specific reason given
- Missing proper closing

STEP 3: Refined Version

Subject: Re: Software Engineer Position - Decision

Dear [Hiring Manager Name],

Thank you so much for offering me the Software Engineer position at [Company Name]. 
I truly appreciate the time you and your team invested in the interview process and 
the opportunity to learn more about your innovative work.

After careful consideration, I have decided to accept a position with another organization 
that aligns more closely with my current career goals. This was a difficult decision, as 
I was impressed by [Company Name]'s mission and the talented team I met.

I hope we can stay in touch, and I wish you and the team continued success.

Warm regards,
John Smith

Task: Explain quantum computing to a 10-year-old.

ITERATION 1:
Quantum computers use quantum mechanics to process information using qubits instead of bits, 
leveraging superposition and entanglement for parallel computation.

Critique 1:
- Too technical (quantum mechanics, qubits, superposition, entanglement)
- No relatable examples
- Assumes too much prior knowledge

ITERATION 2:
Quantum computers are super powerful computers that work differently from regular computers. 
They can solve really hard problems much faster.

Critique 2:
- Better but still vague
- Doesn't explain HOW they're different
- Needs concrete example
- Could use analogy

ITERATION 3:
Imagine you're in a maze trying to find the exit. A regular computer would try one path at 
a time until it finds the way out. A quantum computer is like having a magical ability to 
try ALL paths at the same time! That's why it can solve really tricky puzzles much faster 
than regular computers. Scientists use them for things like creating new medicines and 
understanding space.

Critique 3:
- Clear analogy (maze)
- Age-appropriate language
- Concrete examples (medicines, space)
- Explains the key difference (parallel vs sequential)
- Good! Minor improvement: could add one more relatable example

FINAL VERSION:
Imagine you're in a maze trying to find the exit. A regular computer would try one path at 
a time until it finds the way out. A quantum computer is like having a magical ability to 
try ALL paths at the same time! That's why it can solve really tricky puzzles much faster.

Scientists use quantum computers for amazing things like:
- Creating new medicines to help sick people
- Understanding how stars and planets work
- Making super-secure passwords that no one can crack

It's like having a super-brain that can think about many things at once!

Task: [TASK DESCRIPTION]

Step 1: Generate initial response
[RESPONSE]

Step 2: Critique your response
Evaluate based on:
- Accuracy: Is the information correct?
- Completeness: Is anything missing?
- Clarity: Is it easy to understand?
- Relevance: Does it address the task?

Identified issues:
[LIST ISSUES]

Step 3: Generate improved response
[IMPROVED RESPONSE]

Task: Write a Python function to check if a string is a valid email address.

STEP 1: Initial Code

def is_valid_email(email):
    return '@' in email and '.' in email

STEP 2: Self-Critique

Accuracy Issues:
- Too simplistic - "a@b.c" would pass but isn't valid
- Doesn't check for proper format
- Doesn't validate domain
- Allows multiple @ symbols

Completeness Issues:
- No input validation (None, empty string)
- No docstring
- No error handling
- Missing edge cases

Clarity Issues:
- Function name is good
- But logic is too simple to be clear about what it actually validates

STEP 3: Improved Code

import re

def is_valid_email(email):
    """
    Validate email address format.
    
    Args:
        email (str): Email address to validate
        
    Returns:
        bool: True if valid email format, False otherwise
        
    Examples:
        >>> is_valid_email("user@example.com")
        True
        >>> is_valid_email("invalid.email")
        False
    """
    if not email or not isinstance(email, str):
        return False
    
    # RFC 5322 simplified pattern
    pattern = r'^[a-zA-Z0-9._%+-]+@[a-zA-Z0-9.-]+\.[a-zA-Z]{2,}$'
    
    return bool(re.match(pattern, email))

Statement: [CLAIM TO VERIFY]

Step 1: Identify verifiable facts
[LIST FACTS]

Step 2: Check each fact
Fact 1: [FACT]
Verification: [TRUE/FALSE/UNCERTAIN]
Source/Reasoning: [EXPLANATION]

Step 3: Overall assessment
[VERIFIED/PARTIALLY VERIFIED/UNVERIFIED]

Statement: "The Great Wall of China is visible from space and is over 13,000 miles long."

Step 1: Identify verifiable facts
Fact A: The Great Wall is visible from space
Fact B: The Great Wall is over 13,000 miles long

Step 2: Check each fact

Fact A: Visible from space
Verification: FALSE
Reasoning: This is a common myth. The Great Wall is not visible from space with the naked eye. 
NASA astronauts have confirmed this. While it's visible from low Earth orbit with aid, it's 
not visible from the Moon or deep space.

Fact B: Over 13,000 miles long
Verification: TRUE
Reasoning: According to archaeological surveys, the Great Wall (including all branches) 
measures approximately 13,171 miles (21,196 km). This was confirmed by Chinese surveys 
in 2012.

Step 3: Overall assessment
PARTIALLY VERIFIED: The length claim is accurate, but the visibility from space claim is false.

Corrected statement: "The Great Wall of China is over 13,000 miles long, making it one of 
the longest structures ever built, though contrary to popular belief, it is not visible 
from space with the naked eye."

Argument: [LOGICAL ARGUMENT]

Step 1: Identify premises and conclusion
Premises:
1. [PREMISE 1]
2. [PREMISE 2]
Conclusion: [CONCLUSION]

Step 2: Check logical validity
Does the conclusion follow from the premises?
[ANALYSIS]

Step 3: Check soundness
Are the premises true?
[VERIFICATION]

Step 4: Final assessment
[VALID/INVALID, SOUND/UNSOUND]

Initial Output: [CONTENT]

Refinement Focus: [SPECIFIC ASPECT]

Critique focused on [ASPECT]:
[TARGETED CRITIQUE]

Refined version (improving [ASPECT]):
[IMPROVED CONTENT]

Initial: "Our product is good and customers like it."

Refinement Focus: Specificity and evidence

Critique: Too vague. "Good" is subjective. "Customers like it" needs evidence.

Refined: "Our product has a 4.8/5 star rating from over 10,000 customers, with 94% 
reporting they would recommend it to others."

Task: [TASK]

Version A: [APPROACH 1]
Version B: [APPROACH 2]
Version C: [APPROACH 3]

Comparison:
- Version A: [STRENGTHS/WEAKNESSES]
- Version B: [STRENGTHS/WEAKNESSES]
- Version C: [STRENGTHS/WEAKNESSES]

Best version: [SELECTION]
Reasoning: [WHY]

Final output (combining best elements):
[OPTIMIZED VERSION]

Initial Output: [CONTENT]

Perspective 1: [STAKEHOLDER TYPE]
Concerns: [ISSUES FROM THIS PERSPECTIVE]
Refinement: [ADJUSTMENTS]

Perspective 2: [STAKEHOLDER TYPE]
Concerns: [ISSUES FROM THIS PERSPECTIVE]
Refinement: [ADJUSTMENTS]

Balanced Final Version:
[CONTENT ADDRESSING ALL PERSPECTIVES]

def calculate(a, b, op):
    if op == '+':
        return a + b
    elif op == '-':
        return a - b
    elif op == '*':
        return a * b
    elif op == '/':
        return a / b

You are a content quality assistant. Help refine content through systematic critique.

Content: [INPUT CONTENT]
Purpose: [INTENDED USE]
Audience: [TARGET AUDIENCE]

STEP 1: Initial Assessment
Rate the content (1-10) on:
- Clarity: [SCORE] - [REASONING]
- Accuracy: [SCORE] - [REASONING]
- Completeness: [SCORE] - [REASONING]
- Engagement: [SCORE] - [REASONING]
- Appropriateness: [SCORE] - [REASONING]

STEP 2: Detailed Critique
Identify specific issues:
- Clarity issues: [LIST]
- Factual concerns: [LIST]
- Missing elements: [LIST]
- Tone/style issues: [LIST]
- Structural problems: [LIST]

STEP 3: Prioritized Improvements
High priority (must fix):
1. [ISSUE] - [WHY CRITICAL]

Medium priority (should fix):
1. [ISSUE] - [WHY IMPORTANT]

Low priority (nice to have):
1. [ISSUE] - [WHY BENEFICIAL]

STEP 4: Refined Version
[IMPROVED CONTENT]

STEP 5: Verification
Confirm improvements address all high-priority issues:
✓ [ISSUE] - [HOW ADDRESSED]