The Art of Problem-Solving Through Analogical Reasoning

The process of analogical reasoning as understood by cognitive scientists. This process involves identifying a target problem, finding a similar problem from past experience (the source problem), determining a solution that was or should have been used for the source problem, and then applying that solution to the target problem.

Two points apply. First, there is no dispute that analogies are the Way of innovation. Second, the framework suggested in Figure 11.1 for achieving strategic innovation is the same as the TRIZ framework for tactical innovation. But there is one enormous difference. Although the TRIZ innovation algorithm is based on a very large amount of hard data (patent database), the algorithm suggested in Figure 11.1 is based on logic only. This is why we say that most current methods of innovation, whether strategic or tactical in nature, are person-centric; they rely on the mental powers of the individual and provide no extra help in converging on the solution needed for business or technical breakthrough.

Solution-positing refers to the act of proposing or suggesting potential solutions to a problem. It’s the stage in problem-solving where you put forth candidate answers or methods for addressing the issue at hand. The term emphasizes the action of placing a possible solution into consideration for further evaluation and testing.

Tapping the Power of Analogy in Problem Solving

What is Analogical Reasoning?

Analogical reasoning is a way to solve problems based on the understanding that if two things (source and target) are similar in some ways, they may be similar in other ways as well. This method helps you adapt a solution from a source problem that you understand well to a new, target problem that you’re trying to solve.

The Process

  1. Target Problem: Start by identifying the problem you want to solve.

  2. Find Source Problem: Think of other situations, either from direct experience or learning, that have similar characteristics to your target problem.

  3. Similarity Mapping: Through a process of finding similarities, identify the source problem that has characteristics most like your target problem.

  4. Source Solution: Once the source problem is identified, examine how that problem was solved. This is your candidate solution.

  5. Application to Target: Apply the candidate solution to your target problem.

Standard Analogical Process

  1. Identify Purpose: Before drawing an analogy, know what you’re looking to achieve. This will guide your search for a suitable source problem.

  2. Find Source Problem: Identify a similar situation, but from a different context.

  3. Understand Source: Study the source problem well enough to understand the solution used there.

  4. Similarity Mapping: Map the similar characteristics of your target problem to your source problem.

  5. Identify Differences: Before applying the source solution to the target problem, actively look for differences that might make the source solution less applicable.

  6. Translate, Decide, Adapt: Take the source solution and modify it to fit the specifics of your target problem.

  7. Fine-Tune: Once the source solution is applied, tweak as necessary for optimal results.

Characteristics

  • Logic-Based: This is not a method assisted by tools; it relies solely on human cognitive abilities.

  • Open-Ended: The process is flexible and accommodates various kinds of problems.

  • Thought-Driven: It’s powered by human thought and creativity.

  • Similarity-Mapping: Central to this method is the idea of finding similarities between two different problems.

  • Solution-Positing: The method is proactive in suggesting potential solutions based on previous experiences or knowledge.

Limitations

  • Poor Reasoning: Analogies can sometimes lead to poor conclusions if not carefully considered.

  • No Extra Help: This process doesn’t offer external assistance; it’s all about your ability to make connections.

Key Takeaways

  • Analogical reasoning is a powerful way to solve problems by mapping a known solution from a similar problem.
  • The method is logical and entirely dependent on human cognitive skills.
  • While effective, it requires careful consideration to avoid pitfalls like poor reasoning or misapplied solutions.

Problem Abstraction and Specialization

It involves moving from a specific problem to a generic one, solving the generic problem using established methods, and then applying that generic solution back to the specific context.

Let’s take a look at an example: A mathematical concept of a quadratic equation, which is an equation that can be rearranged in standard form as (ax^2 + bx + c = 0).

  • Generic Problem: The quadratic equation in its general form, (ax^2 + bx + c = 0), represents the generic problem. This equation lays out the structure of the problem but doesn’t provide specific values for (a), (b), or (c). It gives you the “shape” of the problem but not its “size”.

  • Specific Problem: In this instance, the equation (3x^2 + 5x + 2 = 0) is the specific problem. Here, (a = 3), (b = 5), and (c = 2). Now the problem is fully defined and ready for solving.

  • Generic Solution: The Quadratic Formula (\frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}) is the general solution to the generic problem. This formula tells you how to find the roots of any quadratic equation.

  • Specific Solution: Plugging in the specific values of (a = 3), (b = 5), and (c = 2) into the Quadratic Formula gives us the roots of the specific equation (3x^2 + 5x + 2 = 0). After calculation, the roots can be determined, completing the journey from a specific problem to a specific solution.

In summary, the generic problem helps us understand the structure or form of the problem we are dealing with. The generic solution offers a systematic way to tackle any problem of that form. We then tailor this generic solution to our specific problem to find our specific solution.

In this process, you’re taking a specific problem and distill it to its essential components, abstracting it to a more general form. This process can make the problem easier to solve, and the solution can then be tailored to fit the specific context of the original problem.

  1. Specific Problem –> Abstract Thought –> Generic Problem:

    • The specific problem is the unique, real-world issue you’re trying to solve.
    • Abstract thought helps to isolate the core elements of this problem, removing all the specifics and the noise.
    • A generic problem is the abstracted form of the specific problem. It’s a problem statement that is devoid of the particularities that made the problem unique in the first place.

  2. Analogical Thought –> Specific Solution:

    • Analogical thought involves comparing the generic problem to other problems you have encountered before.
    • A specific solution is found by applying the insights or methods from these comparisons to your initial problem.

  3. Affinity Category has many problems and solutions:

    • An affinity category is a grouping of problems that share similar structures or characteristics.
    • Since they share characteristics, they often also share solutions, albeit tailored to each specific context.

  4. Each affinity group has a label:

    • The label helps in quickly identifying the type of problem and possible approaches to solve it.

  5. General Solution is applied to a Problem Type:

    • A general solution is a broad method or algorithm that solves a generic problem. It can be tailored to solve specific instances of that generic problem type.

  6. Problem Parameters vs Cues:

    • Problem parameters are specific, quantifiable variables that define a problem.
    • Cues are more like hints or indicators that might guide you in understanding the problem better. They may not be as explicitly defined as parameters.

  7. Inventive Principles vs Direction:

    • Inventive principles are general strategies or methods for solving problems.
    • Direction refers to the orientation or path along which you approach a problem. Inventive principles provide this direction, guiding you toward a solution.

Example: Climbing Stairs Problem

  • Specific Problem: How many ways can you climb a staircase of n steps, taking 1 or 2 steps at a time?
  • Abstract Thought and Generic Problem: This can be abstracted to a problem of permutations and combinations.
  • Analogical Thought: Similar problems involving permutations can give insights.
  • Specific Solution: The specific algorithms or formulas that can solve this problem for any given n.

By following this framework, you can navigate from a specific issue to a general problem, find a suitable solution, and then tailor that solution back to your original, specific problem.