What is Problem Traversal Theory?

Problem Traversal Theory is a desire-driven framework for systematically identifying, understanding, and solving problems. It operates on a simple but powerful idea: all problems stem from desire—a want for something to be different.

Without desire, there are no problems, only ideas—neutral observations of the world, most of which don’t need chasing. This distinction is critical for avoiding wasted time and effort. By focusing on desires, Problem Traversal Theory helps you tackle authentic problems, identify meaningful solutions, and generate undeniable value.

“Without desire, there are no problems, only ideas—neutral observations of the world, most of which don’t need chasing.”

The framework is divided into two structured phases: Understand and Solve, guiding you to uncover root causes and resolve problems with clarity and efficiency.

Why learn Problem Traversal Theory?

“Solving the right problem wrong is better than solving the wrong problem right.”

Every problem you face is based on something that is believed to be desired, but not all things truly are. These inauthentic problems are not worth solving.

Think about how often effort is wasted on problems that feel real but aren’t. Imagine knowing, with confidence, which problems deserve your attention and which ones don’t. Imagine focusing only on problems that, when solved, create real value.

Problem Traversal Theory gives you the tools to:

• Identify whether a problem stems from a genuine desire.
• Separate problems from ideas to avoid unnecessary effort.
• Focus your energy on solving problems that matter.

Let’s explore how it works.

Phases of Problem Traversal

In *Problem Traversal Theory * problem-solving is broken into two phases: Understand and Solve. Both are built around actions—Identify, Verify, Traverse, and Clear—that help you explore problems and their solutions systematically.

Phase 1: Understand

The goal is to uncover the root cause of a problem by exploring the desires that came before it and validating their authenticity.

Every problem is a desire—more specifically a sentient entity’s desire for a thing to transition from a current state to a new potential state. In this phase, the goal is to determine whether the desire is real and identify the underlying desires that give the problem meaning.

1. Identify a problem by writing down a desire using this formula:
   Thing current state. Sentient entity desire thing potential state.
2. Verify that the desire is authentic. If it isn’t, the problem is cleared.
3. If it is authentic, Traverse Up to a parent problem by asking “Why?”.
4. Identify a parent problem by writing down a desire found in the answer to “Why?” using the formula again.
5. Verify that the desire is authentic. If it isn’t, the problem is cleared.
6. If it is, repeat the Traverse Up, Identify, Verify loop until you Clear the problem or understand the problem’s lineage enough to begin to solve.

Phase 2: Solve

The goal of Phase 2 is to generate actionable steps and resolve the problem.

1. Traverse Down the problem’s lineage to a potential child problem—a solution—by asking “How?”.
2. Identify a solution by writing down a potential desire found in the answer to “How?” using this formula:
   Thing current state. Sentient entity could desire thing potential state.
3. Verify that the potential desire is an authentic desire. If it isn’t, Traverse Up and repeat the Traverse Down, Identify, Verify loop until you identify a potential desire that is wanted.
4. Clear the problem by executing the solution.

Why was Problem Traversal Theory created?

In 2020, I came across the story of Juicero, a failed $120M startup that engineered a solution to a problem no one had. It fascinated me—not because of its failure, but because it highlighted a deeper issue: how often talented, passionate people dedicate time and resources to solving problems that aren’t real.

I started calling these Juicero Problems—problems that feel real but lack an important authentic desire somewhere in its problem lineage. I saw this in my work, where engineers often build solutions to poorly defined problems, only to discover they didn’t matter.

This led me to ask:

• How do we distinguish between authentic problems and mere ideas?
• How can we avoid wasted effort on problems that don’t create value?

To answer these questions, I developed Problem Traversal Theory, a framework that starts with desire as the foundation for identifying, understanding, and solving problems. Now, I’m sharing this approach to help you focus on what truly matters in your life.

Who am I?

I’m Shadow Smith, a self-taught, Principal Software Engineer passionate about solving complex problems and helping others do the same. Since 2014, I’ve worked in the business credit and insurance industries, collaborating with Product Managers, Engineering Managers, and business partners to eliminate assumptions, minimize waste, and maximize the impact of executed solutions.

You can learn more about me and my work at shadowsmith.com.