07 Problem Inversion

This skill provides three concrete strategies for navigating around obstacles by reframing problems. When stuck, instead of pushing harder on the current approach, try inverting the problem.

Core Principle

“Turn a problem on its head”

Three powerful strategies:

1. Unfix parameters (covered in Skill 4, applied here in crisis)
2. Don’t achieve goal A? Achieve comparable goal B
3. “I have the answer; what is the question?”

Strategy 1: Unfix Parameters (In Crisis Mode)

When to Use: Run-of-the-mill issues in project execution

Approach: Let a “sacred” fixed parameter float

Example from Lecture:

• Stuck: Spatial transcriptomics of APC-T cell interactions in tumor microenvironment
• All fixed: Technique, cell types, context
• Inversion:
  • Unfix technique → What else could measure these interactions?
  • Unfix cell types → What other interactions matter in tumors?
  • Unfix context → Where else do APC-T interactions matter?

Your Application: For each fixed parameter in your project:

• What if this floated?
• What alternatives exist?
• Which would be easier/faster/more informative?

Strategy 2: Comparable Goal Substitution

When to Use: Existential threats to project (can’t achieve original goal)

Approach: Achieve a different but equally valuable goal

Mindset Shift:

• Wrong: “I failed to do X”
• Right: “The world needs Y instead, which I CAN do”

Example from Lectures: PROTAC Story

• Goal A (Failed): Degrade specific therapeutic target
• Goal B (Achieved): Map which kinases ARE degradable
• Value: B is more impactful (general principle + method validation)
• Learning: Target engagement ≠ degradation (important discovery)

Framework:

1. Original goal: [What you wanted]
2. Why it failed: [Specific reason]
3. What CAN you do with current data/tools: [Capabilities]
4. Comparable goals:
   • Option 1: [Different but related goal]
   • Option 2: [Another alternative]
   • Option 3: [Yet another]
5. Which is most valuable: [Analysis]
6. How to frame it: [Communication strategy]

Strategy 3: Answer Seeking Question

When to Use: End-of-project challenges (interpretation, framing, application)

Approach: You got an answer, but not to your original question. What question DOES your data answer?

Mindset Shift:

• Wrong: “This doesn’t answer my question”
• Right: “What interesting question does this answer?”

Example from Lectures: Steroid Receptor

• Original Question: What is THE receptor for this steroid?
• Answer Obtained: Binds multiple receptors at different affinities
• Problem: Can’t answer original question (no single receptor)
• Inversion: “What question does this answer?”
• New Question: How does finite receptor pool sense infinite lipids?
• Answer: Combinatorial sensing (pattern = unique “chord”)
• Impact: More interesting than intended finding

Framework:

1. Original question: [What you asked]
2. Data obtained: [What you actually found]
3. Why it doesn’t answer: [The mismatch]
4. What DOES the data show clearly: [Solid findings]
5. What questions could these answer:
   • Question 1: [Option]
   • Question 2: [Option]
   • Question 3: [Option]
6. Which is most interesting: [Assessment]
7. How to reframe paper/project: [New framing]

Workflow

Phase 1: Identify Your Obstacle

• Type: Technical / Biological / Competitive / Interpretive
• Severity: Run-of-mill / Existential / End-stage
• Description: [What’s blocking you]

Phase 2: Select Strategy

Phase 3: Apply Strategy

Work through the relevant framework above with your specific situation.

Phase 4: Evaluate Alternatives

For each alternative generated:

• Scientific value: How interesting is this?
• Feasibility: How hard to execute?
• Timeline: How long will it take?
• Impact: How does this compare to original plan?
• Your advantage: Do you still have edge here?

Output: Problem Inversion Analysis

Page 1: Current Situation

• Obstacle: [Clear description]
• Why you’re stuck: [Root cause]
• Original plan: [What you intended]
• Current capability: [What you CAN do]

Page 2: Strategy Applications

Strategy 1 (Unfix Parameters):

Strategy 2 (Comparable Goals):

Strategy 3 (Answer → Question):

• Data obtained: [What you have]
• Question 1 it could answer: [Option 1]
• Question 2 it could answer: [Option 2]
• Question 3 it could answer: [Option 3]
• Most interesting: [Selection + reasoning]

Page 3: Recommended Path

• Selected strategy: [1, 2, or 3]
• New direction: [Specific plan]
• Why this is better: [Not just “it works” but “it’s more interesting”]
• Communication approach: [How to frame this pivot]
• Timeline: [New schedule]