Mental Scaffolding and Informal Proofs

In order to understand an idea, people need to work through the layers of understanding in a simplified, but similar way to how you first did when you discovered the solution. This allows them to test each step along the way until they reach a deeper proof that confirms the idea’s validity. This process is akin to constructing a logical proof, even if it’s done intuitively rather than formally. It is “standing on the shoulders of giants”.

When an answer seems overly simple, people may instinctively doubt it because they haven’t worked through the “proofs” that make the simplicity credible. As they reason through discussion, they’re effectively piecing together the mental  steps that satisfy their need for validation. This pattern reflects the cumulative nature of knowledge—each new idea builds upon what is already understood, creating a foundation for accepting new truths.

Mental scaffolding and informal proofs of understanding can provide the structure that makes it easier for others to accept new ideas based on previously accepted knowledge.

To lead a person up to an idea (rather than presenting it outright as a solution) is to build up to it with a mental scaffolding, like an informal math proof, to lead the listener through the process you took to get to the answer. Formal math proofs build upon axioms, but in other areas of life, we don’t have the benefit of those axioms so we have to rely on other building blocks.

In some ways, all reasoning relies on a foundation of prior knowledge and collective beliefs. This concept of mental scaffolding and informal proofs provides us a mechanism to build complex ideas from simpler ones (like the process I’m doing right now in this book).

But mental scaffolding and informal proofs are just one way to help you disseminate your ideas and prevent initial rejection. Here are some other strategies counteract these biases:

  1. Start from First Principles – First Principles thinking periodically breaks down ideas into their core components, questioning assumptions and working back from foundational truths (similar to Working Backwards or Reverse Engineering, which will be discussed later). By resetting to first principles, they can “replant” the Idea Tree when needed, creating space for innovation.
  1. Build in Discussion and Dialogue – Discussing ideas with others can not only satisfy their need for understanding and ultimately accepting the answer, but it also aligns with one of the the 48 Laws of Power by Robert Greene, “Law 31: Control the Options: Get Others to Play with the Cards You Deal,” which emphasizes the importance of framing choices and influencing decisions before they are publicly debated or decided upon.
  1. Seek Elegant Simplicity, not Complex Compromise – Encourage readers to actively seek solutions that are both simple and profound. Explain that simplicity doesn’t mean sacrificing quality; rather, it requires distilling the core of the solution. Recognizing elegant simplicity allows us to see the strength in straightforward answers.

The main idea is to occasionally reflect on how you engage with ideas. Challenge yourself and others to think differently about simplicity and to approach solutions with a mind open to the elegance within straightforward answers.

This is chapter 5 in my book, Think Again, on Amazon Kindle.