The Basic Logic of Problem Solving: Optimizing Digital and Analog Thinking
For problem solving, understanding the problem itself is indispensable. If it’s a problem that can be immediately understood, or if you have the ability to grasp the problem intuitively, you can solve it quickly and appropriately.
Otherwise, it is essential to take a rational approach, analyzing the problem thoroughly. For rational problem solving, it’s important to understand the problem logically.
There are many ways in the world to summarize and compare concrete information. In this article, we will organize the logic of problem solving as a foundational concept.
Framing the Problem
Understanding a problem involves understanding its requirements, solutions, and policies.
In a typical problem, multiple requirements and solutions exist. Grasping this is crucial.
It’s not common to exhaust all possible solutions or to satisfy all requirements fully, as it can be wasteful. Normally, you select some solutions and fulfill only some of the requirements. How to choose these is also significant.
Key Concepts in Logical Problem Understanding
When understanding requirements, solutions, and policies, the following characteristics are critically important for rational problem-solving:
Characteristics of Requirements: Essential and Important
Essential: Requirements or conditions that absolutely must be met for problem resolution. If these are not met, the problem remains unsolved.
Important: Not essential, but if included, better results can be expected.
Characteristics of Solutions: Impossible and Challenging
Impossible: Something that cannot be achieved no matter the approach.
Challenging: Hard to achieve, but possible with certain methods or efforts.
Characteristics of Policies: Optimization and Balance
Optimization: A mindset aiming to achieve a specific requirement or objective at the highest level, maximizing efficiency or performance.
Balance: Combining multiple factors or requirements to seek the best overall state.
Clearly Define Essential Requirements and Exclude Infeasible Solutions
Even if you can meet 10 important requirements, if one essential requirement is not met, the problem remains unsolved.
Thus, it’s crucial to clarify what the essential requirements are among the important ones. Once you ignore all requirements except the essential ones, you should think about available solutions. Options that don’t meet essential requirements are a waste of time to even consider.
Discard Impossible Options, Keep Challenging Ones
Similarly, for solutions, it’s necessary to distinguish between the impossible and challenging clearly. Especially when discussing a problem deemed hard to solve, pointing out the difficulty of each solution isn’t meaningful. On the other hand, indicating impossibility is.
There’s no need to keep impossible solutions as options, but challenging ones should be retained.
**An Example with Essential Requirements and Impossible Options**
Consider the process of buying electronic products. After a rough review of products with various features and performance, you would shortlist some candidates.
In the initial research step, it’s efficient to specify essential features or performance while progressing. And when picking candidates, choose only products that meet these essential requirements. If you’re tempted to include a product that doesn’t meet these requirements, you should reconsider what’s essential.
By narrowing down options according to essential requirements early on, you can significantly reduce choices. It’s then efficient to proceed with research focusing on important requirements.
During this process, if you notice products that are no longer available due to discontinuation, you should remove them from the list. Conversely, if you haven’t set a budget limit as an essential requirement, you should keep even expensive products as candidates. If you’re excluding a product because of its price, first add a budget limit to your essential requirements.
Digital Thinking vs. Analog Thinking
So far, the steps discussed represent digital thinking. Whether it’s essential or impossible is binary, digital information. Also, excluding non-essential or impossible options is digital since the criteria are clear.
In contrast, the next steps require analog thinking, where there’s no clear line between 1 and 0 and where the criteria have a range.
When Essential Requirements Can Be Met
After narrowing down options based on the essential and impossible criteria, the next step is to consider which important requirements can be met while being aware of the difficulty of each solution.
Essential requirements are straightforward to meet. On the other hand, important requirements don’t all need to be met, so you need to decide how many to satisfy and which ones to choose.
Moreover, you can’t make this decision by looking only at requirements. You must always think in conjunction with solutions. If all solutions are time-consuming, costly, and uncertain, it’s possible to give up all important requirements. Conversely, if you can easily, almost freely, and certainly meet all important requirements, there’s no need to reduce them.
Typical problems are often somewhere in between, so choices are necessary.
Deciding Whether to Optimize or to Seek Balance
This decision inevitably carries a degree of subjectivity. However, it is essential to determine a policy to make choices as rationally as possible. Once a policy is set, there’s no wavering in direction throughout the thought process.
If you wish to change direction, reconsider the policy. Also, when multiple people are discussing, clarifying the direction and aligning everyone’s understanding will reduce the need for reevaluation.
There are various ways to decide on a specific policy. Abstractly speaking, there are two main policies: optimization and balance.
Optimization involves setting a metric for the whole and choosing options to maximize that metric. On the other hand, balance means setting metrics applicable from multiple perspectives and choosing options to equalize those metrics.
A prime example is deciding on the distribution of rewards within an organization. One policy aims to maximize motivation by allocating more to the most active members, while another policy aims to distribute rewards evenly among all members. Note that it’s not an either-or situation between optimization and balance. You can incorporate both. For instance, 80% of the rewards can be distributed evenly among all members, while the remaining 20% is given as a bonus to outstanding performers. This approach aims to strike a balance between motivation and equality.
When Essential Requirements Can’t Be Met
Unfortunately, there might be cases where there’s no option that meets essential requirements. In such cases, the only solution is to cut back on these requirements. Analog thinking is crucial here.
Under the assumption that not all essential requirements can be met, deciding what to sacrifice is inevitably subjective. Again, it’s essential to consider policies like optimization and balance.
Moreover, you might need to modify the essential requirements. For instance, if budget or schedule requirements cannot be met, you may consider relaxing those constraints. Alternatively, for budgetary constraints, you might look into loans or alternative transactions. For schedule constraints, even if you can’t meet the initial deadline, you may consider personal delivery to meet the final customer’s timing.
There are also options to compensate for unmet requirements by other means. If not meeting a requirement results in a contract breach, one option might be intentionally violating the contract and paying the penalty.
By modifying the essential requirements, you might find a solution. For instance, if meeting a deadline means compromising essential quality and embracing significant risk, it might be more strategic to exceed the deadline, pay the penalty, but manage the risk thoroughly. Among requirements, budgets and deadlines are often the most flexible.
Additional Considerations
Also, it’s important to note the relationships between requirements, the means of resolving them, and the order of considerations.
Nature of Requirements: Contradiction and Trade-off
Requirements might sometimes contradict or trade-off against each other. Contradictions arise when fulfilling one requirement absolutely prevents fulfilling another. Trade-offs happen when fulfilling one requirement restricts another.
There are both full and partial trade-offs. A full trade-off is when choosing one side always limits the other. In contrast, a partial trade-off might not always restrict the other option.
Moreover, trade-offs can be zero-sum or optimizable. A zero-sum trade-off is when one side gains at the exact expense of the other. An optimizable trade-off is when both sides can gain, such as when distributing two apples between two people.
The term “contradiction” is often used, but many situations are merely partial trade-offs. For example, being selfish and altruistic might seem contradictory, but they’re just on a trade-off spectrum. Similarly, individualism and collectivism, idealism and realism, function in the same way.
In problem-solving, it’s rare for requirements to truly contradict. More often, it’s a matter of trade-offs between requirements, and due to constraints, not all requirements can be met simultaneously.
Nature of Solutions: Competition and Dependency
Solutions might compete or depend on each other.
If only one person can work on a problem, it becomes hard to apply multiple solutions simultaneously, leading to competition between solutions. You might need to think about whether to implement them sequentially or in parallel at a slower pace.
Sometimes, one solution needs to be implemented before another. In such cases, the latter should be prioritized.
Therefore, it’s vital to understand the available resources (people, materials, information, money) and the relationships between solutions to organize an efficient and cost-effective approach.
Order of Consideration: Analysis and Evaluation
Investigating, thinking, and organizing requirements and solutions are part of the analysis phase. Evaluating requirements, solutions, and policies is equivalent to the evaluation phase.
Usually, people tend to analyze first and evaluate later. However, it’s during evaluation that new requirements, their importance, and the validity of policies become evident. Therefore, in real problem-solving, constantly switching between analysis and evaluation helps in understanding the whole picture.
It’s also essential to document requirements, means, and policies as much as possible, updating them whenever there are changes. This prevents confusion and ensures that everyone involved has a clear and shared understanding, leading to logical decisions that everyone can agree on.
Examples of Mistakes
When organized in this way, these ways of thinking are basic, and some might consider them to be obvious. However, the reality is that many people do not manage these well. Here are some common mistakes:
- People tend to list important requirements, but neglect to clearly identify which ones are essential. They waste time by getting distracted by non-essential but important requirements.
- They leave impossible options open, or conversely, eliminate difficult options. This also wastes time for deliberation.
- Neglecting clear digital decisions about essentials or impossibilities, they try to make analog decisions, spending excessive time analyzing and evaluating vast amounts of information. In the worst case, they might choose an option that doesn’t meet essential requirements.
- Conversely, by neglecting analog decisions, they adopt options that meet essential requirements but cut out all non-essential but important requirements.
- In analog decision-making, without a clear policy, they make vague decisions. As a result, they choose biased options with low acceptability to stakeholders or regret their choices.
- Despite being unable to meet essential requirements, they continue to waste time looking for a solution.
- They retain essential requirements with alternative means but eliminate essential requirements without alternatives.
- They treat simple trade-offs as if they are mutually exclusive and completely cut out one side.
- They see optimizable trade-offs as zero-sum trade-offs, leading to extreme choices.
- They waste time trying to reconcile conflicting requirements.
- Without a proper understanding of the conflicts or dependencies of manpower, materials, money, and information that can be devoted to problem-solving, they either give up thinking it cannot be implemented within the given time or believe it can be realized quicker than it actually can.
- They spend time on detailed analysis of problems including information that isn’t useful for evaluation, thereby wasting time. Moreover, they might reach the deadline for devising a solution without adequately considering newly found requirements, ending up without finding the best strategy.
- Since the results of past problem analyses aren’t documented, when stakeholders try to share roles and proceed with analysis, they waste time. During decision-making, they cannot understand the background information, reducing their confidence in decisions. The people devising the solutions lack confidence in their analyses and decisions. When they look back in the future, they can’t retrieve the background information of the solution’s formulation.
In Conclusion
In this article, I have summarized the basics of problem-solving. It’s based on my experience in system development and the thought process I use when considering personal purchases.
This logical approach to rational problem-solving can be applied broadly, whether it’s work, daily life, minor problems, or major societal issues.
While some experience and tips might be needed, there are plenty of opportunities for practice as it can be applied to everyday thinking. For instance, as mentioned with the example of buying household appliances, you can accumulate experience by applying this in real life. Whether at work or considering societal issues, there will be numerous opportunities to gain experience.
