From Knowledge to Reusable Structures and Problem Solving

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Related reading: Learning from Models to Performance · From Experience to Understanding and Action.

These questions can be connected by a single thread: how people form knowledge from experience, understand the relationships within it, abstract reusable structures, and then use them to handle new problems.

Below, we first clarify the concepts and then discuss methods of practice. These are “working definitions” intended to make thinking and testing easier; some of these questions have no single universally accepted answer in philosophy.

Essence and explanation

Let us first discuss “essence.” “Essence” usually refers to the fundamental properties that make something the kind of thing it is. In philosophy, there are also different analyses of “what properties it must have” and “what explains what it really is.” :chatgpt-content-reference{index=”0”}

In everyday speech, “seeing through to the essence” often combines two kinds of inquiry:

• What exactly is it? For example, a triangle can change in size, color, and orientation, but the structure of three line segments forming a closed figure cannot simply be removed.
• Why does it behave this way? For example, if a restaurant continually has long queues, what we are looking for is the mechanism producing the queue, involving customer arrivals, service speed, process bottlenecks, and so on.

The former identifies things; the latter explains phenomena. Clear definitions and correct causal explanations need to be established separately.

Asking further, “What is the essence of essence?” can advance the question to: On what grounds do we regard a particular feature as fundamental?

We can test this with three questions:

1. Which details can change while it remains the same kind of thing?
2. Which feature, if removed, would mean it no longer meets the original definition?
3. If we are explaining a phenomenon, changing which condition would change the result as predicted?

Thus, in practical thinking, the core work of investigating essence is distinguishing which differences can be ignored and which structures, conditions, and relationships cannot be ignored. Whether something has a unique, eternal essence requires a separate argument.

Working definitions

The other concepts can be placed in the same table:

Concept	What it is	Its core
Knowledge	Well-grounded command of facts, methods, rules, and the conditions under which they apply	Reliable grasp supported by grounds
Learning	Experience, observation, or practice bringing about relatively lasting changes in knowledge, skills, or behavioral tendencies	Experience changes subsequent judgments and actions
Understanding	Grasping relationships among the parts of something, its premises, and its outcomes	Being able to reconstruct relationships, explain reasons, and handle related changes
Abstraction	Ignoring some details for a particular purpose while retaining relevant features, relationships, or structures	Selectively retaining information so that one representation can cover multiple situations
Transfer	Existing knowledge, skills, or strategies influencing new learning or tasks	Recognizing correspondences between old and new situations and making necessary adjustments
Ability	Being able to carry out a class of tasks relatively consistently under certain conditions	Repeatable, adaptable performance
Thinking	Using concepts, language, images, and experience to compare, infer, imagine, and evaluate	Organizing and changing mental representations of things
Problem	A gap between the current state and the goal, or between the known and the unknown, that remains to be addressed	Goals, constraints, and obstacles that need clarification
Problem solving	Clarifying a problem, seeking, implementing, and verifying feasible answers or actions	Effectively addressing that gap within constraints

Several distinctions here are easy to confuse:

• Learning can produce bad habits. “A change has occurred” and “the change is for the better” are two different criteria.
• Understanding has degrees of depth and scope. Being able to explain a phenomenon does not mean that all its conditions have been grasped.
• Abstraction necessarily discards information. How good an abstraction is depends on whether what remains is sufficient to support the task at hand.
• Transfer can have negative effects. Applying an old method in the wrong setting can also hinder the handling of a new problem.
• One performance is not enough to represent ability. Judging ability requires considering task difficulty, tools, time, and one’s state at the time.

For example, knowing that “in a Euclidean plane, the interior angles of a triangle sum to 180°” is command of a piece of knowledge; being able to explain why using parallel lines and relationships among angles is understanding; ignoring the triangle’s color, size, and orientation while grasping the relevant geometric structure is abstraction; using triangles to derive the sum of a polygon’s interior angles is transfer; only by continuing to choose the right method and complete the derivation across different problems does ability gradually develop.

Learning ability

Learning ability is the ability to effectively develop, retain, and use knowledge and skills, and to adjust one’s learning methods. Its core is being able to keep improving one’s learning process through experience and feedback.

To improve it, you can take the following approaches:

1. Write learning goals as observable performance. For example, change “learn statistics” to “be able to judge whether a study’s conclusions go beyond what its data support.”
2. Identify prerequisite knowledge. When you encounter something you do not understand, locate the particular word, step, or inference; if a foundation is missing, fill that part in first.
3. Close the material and retrieve actively. Try writing down the key points, answering questions, or carrying out an operation, then check. Research shows that retrieval practice can also improve performance on some tests of understanding and inference. :chatgpt-content-reference{index=”1”}
4. Spread practice across different times. For example, test yourself again the next day, several days later, and a week later, adjusting according to how much you forget. Spaced practice helps long-term memory, but suitable intervals depend on the material and how long you intend to retain it. :chatgpt-content-reference{index=”2”}
5. Obtain specific feedback. Divide errors into “unclear concepts,” “overlooked conditions,” “wrong method selected,” and “execution errors,” applying different corrections to different errors.
6. Test your own judgments. Before doing a problem, estimate how confident you are; after completing it, compare that estimate with the result. Gradually identify the situations in which you tend to overestimate or underestimate your command of the material.

To evaluate learning outcomes, consider how much you still remember after some time, whether you can complete the task independently, whether you can still apply it in a different situation, and how much time you invest in doing so.

Understanding ability

Understanding ability is the ability to establish, check, and revise relationships among things. Its core is organizing scattered information into a grasp supported by reasons and qualified by conditions.

For each concept you learn, you can answer six questions:

• How would you express it in your own words?
• What concrete examples are there? What examples look similar but actually do not qualify?
• What existing knowledge is it related to?
• Why does it hold? Are any steps omitted from the reasoning?
• If a condition changes, what will happen to the result?
• Under what circumstances does it not apply?

For example, understanding “fairness” requires comparing different situations: equal distribution, distribution according to contribution, and distribution according to need—under which goals does each make sense, and what problems might each produce?

Clear expression is one clue for testing understanding; it also needs to be combined with distinguishing new examples, performing actual operations, or completing inferences, to avoid treating fluent speech alone as sufficient understanding.

Understanding regularities

The key to the ability to understand regularities is distinguishing what kind of regularity you have found.

Type of regularity	What support it needs	What to watch for
Logical and mathematical relationships	Clear definitions, premises, and valid derivations	Changing the premises may change the conclusion
Statistical tendencies	Sufficient and appropriate data, comparisons, and analysis of uncertainty	A group tendency cannot guarantee every individual case
Causal mechanisms	Temporal order, evidence of mechanisms, and comparisons or interventions that can rule out other explanations	Occurring together does not mean causing one another

You can practice in this sequence: observe a phenomenon, propose a relationship, list other explanations, derive different predictions, seek evidence, and establish the scope of application.

For example, suppose you observe that “students who ask more questions generally get better grades.” Asking questions might help learning, or students who were already more engaged might both ask questions more often and get better grades. Understanding the regularity requires further distinguishing these explanations.

After finding a regularity, it is especially important to ask: “Which conditions, if changed, might cause it to fail?”

Understanding people and groups

Understanding what other people and groups say, do, and think requires separating facts, interpretations, and conjectures that remain to be tested.

You can directly observe what a person says and does; their inner thoughts can usually only be inferred through what they express, the context, and ongoing interaction.

When analyzing a person’s behavior, you can ask the following questions in turn:

• Information: What do they know? What might they mistakenly believe?
• Goals and concerns: What do they want to achieve or avoid? What values and relationships matter to them?
• Constraints: How much time, resources, authority, and choice do they have?
• Context: To whom was this said? What pressures and role expectations were present at the time?
• History: Is this an isolated behavior, or does it recur under similar conditions?
• Verification: What questions can be asked directly? What subsequent behavior could help you judge?

For example, if a colleague has not replied, they may be busy, lack information, not know how to respond, disagree, or have missed the message. Keep several hypotheses open first, then ask: “Do you currently need more information, or do you have other considerations about the proposal?”

Research also offers a reminder: merely imagining yourself in the other person’s position does not necessarily improve judgment accuracy; in the situations tested in the research, talking directly and obtaining the other person’s perspective provided more effective information. :chatgpt-content-reference{index=”3”}

When understanding a group, you need to look one level further: How do individual opinions become collective decisions?

Find out who has decision-making authority, how information flows, what behavior is rewarded, whether dissent can be expressed, and what disagreements exist among members. What the group says publicly, the actions it ultimately takes, and what each member privately believes may differ. Silence in a meeting is also insufficient on its own to demonstrate agreement.

Abstraction ability

Abstraction ability is the ability to identify and represent key features and relationships according to a purpose. Its core is being able to move back and forth between concrete cases and general structures.

The most practical exercise is “comparing cases”:

1. Choose two or three examples that differ on the surface but may share the same structure.
2. List the roles, variables, constraints, and relationships in each.
3. Write down the common structure.
4. Find a counterexample to check whether you have overgeneralized.
5. Test the structure with a new case.

For example:

• A restaurant accumulates uncompleted orders.
• A team accumulates documents awaiting review.
• An inbox accumulates unprocessed emails.

They can share an abstract relationship:

Uncompleted amount at the end of the period = uncompleted amount at the start of the period + amount added during the period − amount completed during the period − amount canceled during the period.

This representation retains the relationships among inflow, outflow, and accumulation. From this, we can see that reducing a backlog may involve adjusting the incoming amount, processing capacity, or the items that no longer need to be handled.

Next, return to the concrete situation: a restaurant’s bottleneck may lie in its equipment, while document review may be constrained by one person’s authority. The same abstract structure requires different concrete actions.

Research on analogy supports promoting transfer by comparing examples and forming common structures; whether it can be used successfully still depends on recognizing the relevant structures and differences. :chatgpt-content-reference{index=”4”}

Problem-solving ability

Problem-solving ability is the ability to organize problem definition, knowledge, reasoning, action, and feedback. Its core is continually finding an effective next step and adjusting according to the results.

You can practice with the following process:

1. Define the problem. What is the current situation? What do you hope to change? Whose needs are affected?
2. Set success criteria and constraints. What counts as improvement? What requirements are there for time, cost, quality, or other aspects?
3. Distinguish what is known from assumptions. What has been observed? What is only the current explanation?
4. Identify the main obstacle. Is what is missing information, skills, resources, or coordination, or are the goals themselves in conflict?
5. Propose several comparable options. Make clear why each option might work.
6. Take actions that provide information. Where possible, try them out in ways that keep costs manageable.
7. Check results and side effects. Does the improvement persist? Have costs been shifted to other people or other parts of the process?
8. Retain reusable experience. Record the conditions under which it works and those under which it fails.

For example, when facing “I study very inefficiently,” you can first make it specific: “After reading a chapter, I cannot independently answer its main questions the next day.” Only then can you examine whether the cause is insufficient prerequisite knowledge, failure to grasp relationships while reading, lack of retrieval practice, or something else.

To improve your ability, after each problem-solving attempt you can review three things: how you initially understood the problem, which evidence changed your judgment, and how to obtain that evidence earlier next time.

Seeing through to the essence

Improving the ability to see through to the essence requires combining domain knowledge, structural analysis, and self-correction.

You can regularly practice five things:

• Rewrite abstract labels as concrete descriptions. For example, change “poor execution” to “after the decision was made, no person responsible or deadline was designated.”
• Distinguish description, explanation, and evaluation. “Submitted late three times” is a description; “the workload exceeded capacity” is an explanatory hypothesis; “irresponsible” is an evaluation. Separating them makes testing easier.
• Consider several levels at the same time. An individual’s knowledge and motivation, interactions among people, organizational rules, and external conditions may all play a part.
• Have different explanations make different predictions. If the issue is insufficient information, what should change after information is provided? What would happen instead if the issue is insufficient authority?
• Revise your views with new evidence. Being able to explain “what evidence would make me change my conclusion” makes it possible to keep approaching a more reliable explanation.

Domain knowledge also needs to accumulate. To see the key elements of a field clearly, you must gradually become familiar with its facts, common mechanisms, typical cases, and failure modes. General questioning methods can help organize thinking, but specific judgments still require specific knowledge.

A daily twenty-minute practice

You can start with one small problem each day and complete the following exercise in about twenty minutes; the time is simply an arrangement to make it easier to carry out:

Step	What to write down
Description	What have I actually observed?
Explanation	What are at least two possible causes?
Abstraction	Which roles, conditions, and relationships are involved?
Testing	What evidence can distinguish these explanations?
Transfer	Where else does this structure apply? Where does it not apply?
Revision	After receiving feedback, which judgment did I change?

Today, you can choose a small recent matter you have not understood and first write down “the facts, my explanation, another explanation, and how to verify it next.” Look back a few days later and check where your predictions differed from the results.