Heuristic Thinking

The Question is the Answer

Oftentimes the question is more important than the answer.

“If I had an hour to solve a problem, I’d spend 55 minutes thinking about the problem and 5 minutes thinking about solutions.” Albert Einstein.

This quote emphasizes the importance of asking the right questions and deeply understanding the problem before rushing to a solution. It aligns with the idea that the majority of the answer lies in properly defining and framing the problem.

Let’s take a look at this through the lens of AI chat programs.

With AI chat programs, the value has shifted from the solution to the question being asked, which is called the prompt. Compared to the question, the answer is relatively free. It’s the question that matters the most because it informs the answer. In that way, the question is the answer.

This is because the quality of the output heavily depends on the clarity, context, and precision of the prompt, which is what some people now call “prompt engineering”, which contains the following attributes:

  1. Framing the Problem: The way you phrase your prompt often determines whether the AI fully understands the intent behind your request. A well-structured prompt leads to more relevant and actionable responses.
  2. Iterative Refinement: Crafting AI prompts is often an iterative process, much like problem-solving. You refine the input until it aligns with the desired output, emphasizing the importance of the question.
  3. Creativity and Precision Balance: Sometimes, the creativity or flexibility of an AI’s solution stems from how open-ended or detailed the prompt is. The better the question (or prompt), the more nuanced or insightful the output can be (like an “idea tree”).

In the world of AI, crafting the perfect prompt has become an art and science of its own, echoing the idea that the solution’s quality depends largely on how well the problem is framed. It’s not just about what the AI can do but how effectively it’s asked to do it.

Questions as Functions

Let’s look at another example in mathematics. Imagine a function, which is agnostic to the output. Compared to the function, the answer is relatively free. However, oftentimes the function itself was difficult to create.

In mathematics, crafting a function can often be much harder than simply using it to produce an output. Take Einstein’s equation, E=mc², for example. It looks incredibly simple, but it contains a depth of understanding that embodies a large sum of mathematical principles. This is similar to how asking the right question or crafting the perfect prompt for AI leads to better answers.

1. Function as the “Question”

  • In mathematics, a function represents a structured way of mapping inputs to outputs. However, defining the function often requires deep understanding, creativity, and problem-solving to ensure it models the desired relationship or behavior correctly. Similarly, creating a prompt or framing a problem for AI requires clarity and precision, as it determines how the “mapping” (or solution) will work.
  • The function doesn’t “care” about the output—it’s a generalized mechanism. Its value lies in its ability to transform various inputs effectively.

2. Input as Context

  • Once the function exists, the inputs determine the outputs. The challenge of crafting the function mirrors the effort in refining the prompt. A robust function (or prompt) will handle a wide variety of inputs gracefully, just as a well-posed question will yield rich, meaningful answers.
  • The output of a function is often trivial to compute once the function is defined. Similarly, generating an answer from an AI becomes straightforward once the question is properly framed. The hard part is designing the system (or question) that leads to that ease.

4. Higher-Order Functions and Flexibility

  • In mathematics, higher-order functions (functions that take other functions as input) are incredibly powerful but also abstract. These resemble the art of refining prompts for AI to create meta-level queries or cascading effects, where the crafting process is even more intricate than the outputs themselves.

Why This Matters

The intellectual and creative weight of problem solving often lies in defining “the question” (the function or the prompt) rather than solving individual instances. Once the question, function, or system is in place, solutions can be generated repeatedly with minimal effort.

This underscores the idea that the solution is often secondary to the process of structuring the problem—whether in mathematics, AI, or any other creative or problem-solving domain.

Let’s take a look at a few philosophical, scientific, and problem-solving methodologies:

1. Socratic Method / Inquiry-Based Learning

  • Definition: A form of inquiry and discussion where asking the right questions leads to deeper understanding and discovery. This is an educational approach where questions drive the learning process, encouraging learners to explore, investigate, and construct knowledge.
  • Relevance: In the Socratic method, the question itself is often more important than the answer, as it shapes the journey of exploration and critical thinking. Inquiry-Based Learning emphasizes that the quality of the question determines the depth and relevance of the discovery. The idea is that the answer lies in crafting the right question.

2. Epistemological Pragmatism

  • Definition: A philosophy that prioritizes practical inquiry and problem-solving. The formulation of a question or problem is key to uncovering truth or utility. It’s like a  “function” for evaluating truth, where the input is an idea, belief, or hypothesis, and the output is determined by how well it works or aligns with practical outcomes.
  • Relevance: Epistemological Pragmatism often focuses on actionable questions, suggesting that answers are less important than how the question frames the pathway to discovery or progress. If the idea consistently works and adapts under real-world conditions, it’s considered “true” within the scope of its application.

3. First Principles Thinking

  • Definition: Breaking down a problem into its most fundamental parts to rebuild understanding from the ground up. This method is often used by Elon Musk and is famously key to how he decided to start SpaceX, reasoning that the sum of the parts and the labor to make them were less expensive than buying a pre-built rocket.
  • Relevance: By asking foundational questions, this approach ensures that the framework (or “function”) is correct, leading to solutions that are both accurate and scalable. It is also occasionally a remedy for “planting a new idea tree”.

This is chapter 6 of my book, Think Again, on Amazon Kindle.