The "Impossible" Filter: Why Complexity is Only Half the Equation

There is a recurring ghost in innovation: the "simple" idea that everyone wants, yet no one can seem to build. Take, for example, the concept of a smart digital wallet that automatically switches to the credit card offering the highest reward for any given purchase. To a consumer, this feels like a weekend project for a talented coder. To a seasoned fintech veteran, it is a nightmare of legacy processors, data privacy barriers, and the fierce protectionism of banking ecosystems. This disconnect highlights a fundamental tension in entrepreneurship.

We often measure a problem by its technical complexity, but we forget to measure it by its institutional friction and its ultimate worthwhileness.

When we look at why certain problems remain unsolved, we have to look past the "how" and start asking "why," and more importantly, "for whom?"

The Two Types of "Impossible"

To understand the lifecycle of a problem, we must distinguish between two types of difficulty.

The first is Technical or Physical Complexity.

This is the domain of EUV lithography machines or Mars rovers. These problems are governed by the laws of physics. They are incredibly hard, requiring billions and decades of research, but the "gatekeepers" are atoms and photons. If you figure out the science, the universe lets you build it.

The second is Systemic or Incentive Complexity.

This is the domain of the smart credit card switcher or universal healthcare records. These problems aren't necessarily "hard" in a scientific sense—the code required to check a reward category is trivial. Instead, these are "impossible" because they require the cooperation of entrenched incumbents who have zero incentive to help you. In this case, the gatekeepers are boards of directors, legal departments, and competitive moats.

The Filter of Worthwhileness

Complexity alone doesn't deter innovation; it merely filters the pool of people willing to dive in. The real deciding factor is the "Prize." If a problem is High Complexity but High Worthwhileness (e.g., carbon capture, curing a disease, or manufacturing the chips that power AI), it attracts the world’s most brilliant minds and deepest pockets. The difficulty acts as a moat, ensuring that whoever solves it will own a generational monopoly.

The danger zone for an entrepreneur is the High Complexity/Low Worthwhileness quadrant. This is where many "clever" consumer apps live.

Using the smart wallet example: solving the technical and legal hurdles to automatically switch credit cards is a Herculean task. But the "prize"—saving a consumer 1.5% on a latte or a few dollars on a flight—might not be large enough to justify the war against the banking establishment. The "worth" to the user is a convenience; the "cost" to the builder is an institutional crusade.

Who Shows Up to Solve the Problem?

The intersection of complexity and value defines the "Who":

• The Feature Builders: When the problem is low complexity and moderate value, you get a crowded market of features. These are the apps that get swallowed by Apple or Google within two years.

• The System Architects: When the problem is high systemic complexity, you need "insiders." These are the people who have spent twenty years at American Express or Visa and know exactly where the bodies are buried. They don't win with better code; they win with better relationships and regulatory navigation.

• The Moonshotters: When the problem is high technical complexity and high value, you get the ASMLs and SpaceXs of the world. They aren't interested in "hacks"; they are interested in breakthroughs.

The Founder’s Dilemma

When you are pitched an "impossible" idea, the first question shouldn't be "Can it be done?" In the 21st century, the answer is almost always "Yes." The better questions are:

• Is it "Physics Impossible" or "People Impossible"?

• Does the value of the solution outweigh the friction of the gatekeepers?

Many entrepreneurs fail because they mistake a "People Problem" for a "Technical Problem." They think if they just build a better interface, the banks will play ball. They won't. True innovation requires an honest accounting of the terrain. Sometimes, building a machine that uses extreme ultraviolet light to etch nanometer-scale transistors is actually easier than getting five major banks to share their data for the benefit of the consumer.

Before you try to solve a problem, make sure the prize is big enough to survive the journey—because the more complex the system, the more the system will fight back.