Problem Traversal Theory TL;DR
Born from first principles thinking and rooted in Philosophy and Buddhism, Problem Traversal Theory (PTT) is a desire-centric framework created by Shadow Smith for systematically exploring a problem domain, discovering outside-the-box solutions, and generating value.
The Core Idea
Every problem is a desire.
Without desire, there are no problems—only neutral observations. A problem is a sentient entity's desire for a thing to transition from a current state to a specific potential state against resistance.
Problem Anatomy
| Component | Definition |
|---|---|
| Sentient Entity | One or more conscious life forms capable of desire |
| Desire | A wanting for a thing to have a specific state |
| Thing | An object or an idea (concrete or abstract) |
| State | A characteristic or circumstance of a thing |
| Transition | A change from one state to another |
| Resistance | The level of effort required for a transition |
The Formulas
| Type | Formula |
|---|---|
| Problem | [Sentient entity] want(s) [thing] [potential state]. |
| Solution | [Sentient entity] could want [thing] [potential state]. |
| Traverse Up | Why does/do [sentient entity] want [thing] [potential state]? |
| Traverse Down | How could/can [thing] [potential state]? |
| Validate | Does/Do [sentient entity] truly want [thing] [potential state]? |
The Two Phases
Phase 1: Understand
- Identify a problem by writing down a desire:
[Sentient entity] want(s) [thing] [potential state]. - Validate the desire. If invalid, the problem is cleared:
Does/Do [sentient entity] truly want [thing] [potential state]? - Traverse up to a parent problem:
Why does/do [sentient entity] want [thing] [potential state]? - Identify the parent problem from the answer:
[Sentient entity] want(s) [thing] [potential state]. - Validate the parent's desire. If invalid, the problem is cleared.
- Repeat the traverse up → identify → validate loop until you clear the problem or understand the lineage enough to solve.
Phase 2: Solve
- Traverse down to a solution:
How could/can [thing] [potential state]? - Identify the solution from the answer:
[Sentient entity] could want [thing] [potential state]. - Validate the potential desire. If invalid, traverse back up and try again.
- Implement the solution to clear the problem.
Solving vs. Clearing
- Problem Solving is passive—traversing down to discover potential solutions.
- Problem Clearing is active—invalidating a desire or implementing a solution.
True value is generated by clearing problems, not solving them.
Converting for Communication
Once validated, convert your lineage into familiar formats:
| Format | Formula |
|---|---|
| Problem Statement | [Initial problem] because [ancestor's current state]. To solve this, [descendant solution]. |
| User Story | As [sentient entity], I want [thing] [potential state], so that [ancestor's desired state]. |
Key Terms
- Problem Lineage — A hierarchical chain of connected problems
- Ancestor Problem — Higher in lineage, answers "why" (more inspirational, less actionable)
- Descendant Problem — Lower in lineage, answers "how" (more actionable, less inspirational)
- Misproblem — A perceived problem that lacks genuine desire upon evaluation