From Information to Ability: A Boiling-Water Example
A nineteen-part example connecting information, understanding, memory, knowledge, transfer, ability, and learning ability.
Chinese original: From Information to Ability: A Boiling-Water Example.
Editorial note: Full English translation of the user-supplied
knowledge.txt, added on September 27, 2026. The original’s claims and illustrative scenarios are preserved; this is not an independent scientific fact-check or evidence of the learner’s mastery. This article is distinct from the earlier From Boiling Water to Learning Ability.
Yes. This example is particularly useful for connecting those earlier abstract concepts into a complete chain.
Rather than treating “water boils at about 100°C under standard atmospheric pressure” as a sentence to memorize, let us imagine someone who genuinely wants to understand it, remember it, use it, and ultimately develop ability.
Here is the overall path first:
See a sentence → acquire information → establish concepts and causal relationships → form knowledge → build durable memory through retrieval and use → solve problems in new situations → develop ability → reflect on how you learned it → improve learning ability.
1. The first layer: encountering “water boils at about 100°C under standard atmospheric pressure”
Suppose a book says:
Under standard atmospheric pressure, water’s boiling point is about 100°C.
After reading it, you can repeat:
“Water boils at 100°C.”
Do you now have knowledge?
A little, but it is very shallow.
What your mind has mainly acquired is a piece of information:
Water + 100°C + boiling.
If the teacher asks the next day:
“At what temperature does water boil?”
And you answer:
“100°C.”
That shows you have remembered an answer.
But it does not yet prove that you genuinely understand it.
If the teacher changes the question:
“Then why can water boil below 100°C on Mount Everest?”
You might suddenly have no idea.
This reveals a very important distinction:
Remembering an answer is not the same as mastering knowledge.
2. Real learning begins with “why”
Now you are no longer satisfied with remembering:
Water boils at 100°C.
You begin to ask:
Why 100°C?
This question matters greatly.
Your mind begins moving from “storing a sentence” to “building a model.”
First, you need to understand:
Water molecules do not suddenly begin entering the air only when water reaches 100°C.
Even a glass of water at 20°C, left on a table, will gradually evaporate.
So:
Evaporation ≠ boiling.
Evaporation mainly occurs at the liquid’s surface.
During boiling, large numbers of vapor bubbles can also form inside the liquid.
A new question follows:
Why does water sometimes evaporate slowly only at the surface, while at other times the whole glass can boil vigorously?
This introduces a deeper concept:
Vapor pressure.
3. Moving from a sentence to genuine understanding
For now, you can understand vapor pressure like this.
Water molecules are constantly moving.
The higher the temperature, the more vigorous their average motion.
Some water molecules can leave the liquid and become water vapor.
As temperature rises, water’s vapor pressure also rises.
But the surrounding air is also “pressing down” on the water.
So there are two opposing influences:
The liquid’s tendency to form vapor
and
The restraint imposed by external pressure.
When water’s vapor pressure reaches the external pressure, vapor bubbles can form stably inside the liquid.
At that point, we say:
The water is boiling.
You suddenly discover that the real regularity is not:
Water = boiling at 100°C.
Instead, it is:
A liquid boils when its vapor pressure equals the external pressure.
This is a deeper layer of knowledge.
And:
“Water boils at about 100°C under standard atmospheric pressure”
is simply an outcome of this general regularity under one particular set of conditions.
4. Beginning to see “the nature of knowledge”
Earlier, we said:
Knowledge is a model of regularities in the world.
Now you can begin to understand what that means.
Initially, your mind contained only:
100°C → water boils
Later, it becomes:
Temperature rises → water’s vapor pressure rises → vapor pressure gradually approaches external pressure → the two become equal → boiling occurs.
Instead of an isolated answer, your mind now contains a causal model:
Temperature → vapor pressure → comparison with external pressure → whether boiling occurs
This is “understanding.”
We can now distinguish the following quite clearly:
| Level | What your mind contains | When you encounter a new problem |
|---|---|---|
| Information | “Water boils at about 100°C” | You can only repeat the sentence |
| Memory | You can answer “What is water’s boiling point?” | You may struggle if the question changes |
| Understanding | You know boiling depends on vapor pressure and external pressure | You can begin to reason |
| Knowledge | You have formed a complete, accessible model of boiling | You can explain various phenomena |
| Ability | You can use the model to handle unfamiliar problems | You can solve real-world problems |
This is why “knowledge” cannot simply mean “remembering many sentences.”
Genuinely useful knowledge is:
A structure you can reason with.
5. The first genuine application
Suppose someone now asks:
Why does water boil below 100°C on a mountain?
If you have only memorized:
Water boils at 100°C.
You encounter a contradiction.
You might think:
“How is that possible? Doesn’t water have to reach 100°C?”
But if what you have mastered is the model:
Boiling condition = vapor pressure reaches external pressure
Then you can reason.
On a mountain:
Altitude increases → atmospheric pressure decreases → water does not need such a high vapor pressure → it does not need to reach 100°C → it can boil at a lower temperature.
You do not even need to have memorized:
“Water has a lower boiling point on a mountain.”
You can derive it yourself.
This is a very important phenomenon:
Genuine knowledge can generate new knowledge.
You originally learned just one principle.
But with that principle, you derived an answer you had not directly memorized before.
This is what makes understanding more powerful than rote memorization.
6. Testing you in the opposite direction
Now reverse the question:
If water is placed in a pressure cooker, why can it remain liquid above 100°C?
You can call on the same model again.
Inside a pressure cooker:
Pressure rises → water needs a higher vapor pressure to boil → it must reach a higher temperature → the boiling point rises.
A pressure cooker therefore lets water and steam reach higher temperatures than an ordinary pot, so food can usually cook through more quickly.
Notice something important.
You have not added many separate pieces of “isolated knowledge.”
You did not independently memorize:
“Higher altitude → lower boiling point.”
“Pressure cooker → higher boiling point.”
“Standard atmospheric pressure → 100°C.”
Instead, you mastered one model:
The boiling point depends on external pressure.
Then you used that one model to generate many answers.
This is what we meant earlier by:
Knowledge has a capacity for compression.
Many phenomena are compressed into a small number of regularities.
7. Understanding “the essence of knowledge is compression”
Imagine a million different situations in the world.
Boiling water by the sea.
Boiling water on a mountaintop.
Boiling water in a pressure cooker.
Water in a vacuum.
Liquids on Mars.
Water in different pressure vessels.
Without a theory, you might need to remember:
Situation A → a particular temperature.
Situation B → another temperature.
Situation C → another temperature.
And so on.
This is:
Memorizing large numbers of individual cases.
But if you know:
A liquid boils when its vapor pressure equals the external pressure.
Then many individual cases can suddenly be explained by one regularity.
So:
One principle → explains 1,000 phenomena.
This is the “compression” of knowledge.
One important characteristic of someone with strong understanding is:
They do not merely collect answers; they look for regularities that can generate answers.
8. What role does memory play?
At this point, it is easy to go to the opposite extreme:
“If understanding matters, does that mean memory is unnecessary?”
No.
Understanding and memory work together.
If every time you encounter boiling water you cannot remember vapor pressure, external pressure, or the condition for boiling, you cannot use the model.
Effective memorization therefore involves more than repeatedly reading:
Water boils at 100°C under standard atmospheric pressure.
It involves retrieval.
For example, close the book and answer for yourself:
- Why does water boil?
- Is 100°C always fixed?
- Why does the boiling point fall on a mountain?
- Why does the boiling point rise in a pressure cooker?
- How does evaporation differ from boiling?
Your mind is no longer doing:
Recognition — I see it, and it feels familiar.
Instead, it is doing:
Recall — can I bring it to mind myself?
There is a huge difference.
When you see an answer:
“Oh, yes, of course. I know that.”
That sense of familiarity can easily create an illusion of having learned.
Genuine memory should face this test:
Without the answer in front of me, can I reconstruct the model?
9. What memory should retain is structure, not just sentences
For this topic, the memory in your mind should ideally be more than:
100°C
It should be a network:
1
2
3
4
5
6
7
8
9
10
Water
↳ Molecular motion in the liquid
↳ Evaporation
↳ Vapor pressure
↳ Higher temperature → higher vapor pressure
↳ External pressure
↳ Vapor pressure = external pressure → boiling
↳ 1 atm → about 100°C
↳ Lower pressure → lower boiling point
↳ Higher pressure → higher boiling point
This is structured memory.
If you later forget whether the boiling point on a mountain is higher or lower, that need not be a problem.
You can reason it through again:
Mountain → lower air pressure.
Lower external pressure → vapor pressure does not need to rise as high.
That pressure can be reached at a lower temperature.
So:
The boiling point falls.
You did not directly “remember the answer.”
You used the model to reconstruct the answer.
This is much more powerful than isolated memorization.
10. The most important relationship between understanding and memory
You can think of the two like this:
Understanding builds the path; memory lets you find that path again later.
Understanding without memory:
You feel that you understand now, but a few weeks later you cannot find the path.
Memory without understanding:
You remember some signposts, but do not know how they connect.
The ideal learning process is:
First build a meaningful structure, then stabilize it through repeated retrieval.
Understanding is not memory’s enemy.
On the contrary:
Good understanding itself helps memory.
Five isolated pieces of information—100°C, mountains, air pressure, pressure cookers, and vapor pressure—are difficult to remember.
But if they form the causal chain:
Pressure → boiling point
They become much easier to remember.
11. Moving from knowledge to ability
Suppose you now know everything described above.
Do you already have ability?
Not necessarily.
Because:
Knowing how to do something and actually being able to do it are different things.
Here is an unfamiliar situation:
An experimental apparatus gradually lowers the air pressure inside a container. You have no thermometer and can only observe when the water begins to boil. Do you predict that the water will become easier or harder to bring to a boil?
If you can immediately think:
External pressure falls → the vapor pressure required for boiling falls → boiling can occur at a lower temperature,
Then you are beginning to possess the ability to apply knowledge.
Try another situation:
Why does liquid water behave very differently in the vacuum of space?
And another:
Why do some foods take longer to cook at high altitude?
If you can analyze these from principles, rather than depend on whether you have memorized the same question, knowledge is beginning to become:
Problem-solving ability.
12. What is ability?
Now the distinction becomes easier to understand.
Ability is not:
“I know water’s boiling point.”
It is not even:
“I understand the principle of boiling.”
It is:
When faced with a relevant real-world problem, I can call on knowledge, reason, and produce an appropriate action or judgment.
For example, someone who genuinely possesses this part of physical reasoning ability can:
Encounter a new phenomenon → recognize that pressure and vapor pressure are relevant → select an appropriate model → reason → make a prediction → check it experimentally.
That whole chain constitutes ability.
So we can conclude again:
Knowledge is part of ability, but knowledge itself is not the same as ability.
13. Reconsidering what learning means
Suppose yesterday all you knew was:
Water boils at 100°C.
After learning today, you can:
Explain why → predict what happens on a mountain → explain a pressure cooker → distinguish evaporation from boiling → handle unfamiliar problems.
What has actually happened today?
Your mind has not simply “stored one more sentence.”
Your internal model has changed.
Before:
Water → 100°C → boiling
Now:
1
2
3
4
5
6
Temperature
↓
Vapor pressure
↔ External pressure
↓
Determines whether boiling occurs
This gives a concrete way to understand:
Learning is a relatively lasting change in your internal model caused by experience, which changes your future thinking and behavior.
This is why “reading for three hours” does not automatically mean “learning for three hours.”
The real question should be:
How is your mind different now from three hours ago?
If there has been no change in models, memory, judgment, or behavior, much of that time may have been spent merely on exposure to information.
14. Going further: what is deep learning?
It does not mean “studying for a long time.”
Nor does it mean “reading difficult books.”
For human learners, deep learning can be understood as:
Connecting a piece of knowledge downward to principles, sideways to other concepts, and upward to phenomena and applications.
For example:
“Water boils at about 100°C.”
Ask downward:
Why?
You reach vapor pressure and external pressure.
Go further downward:
Why does vapor pressure increase with temperature?
You enter molecular motion, energy, and statistical distributions.
Then sideways:
What other concepts are related?
Evaporation, condensation, air pressure, phase changes, latent heat, and so on.
Then upward:
What can it explain?
Cooking on mountains, pressure cookers, boiling under vacuum, weather phenomena, and so on.
The original isolated point:
100°C
Gradually grows into a network of knowledge.
This is:
Moving from “knowing an answer” to “having a system of models.”
15. What is transfer? A key test of genuine understanding
Now let us deliberately stop using water.
Suppose you are asked:
Does alcohol also always have to reach one fixed temperature before it boils?
If you genuinely understand the model of “a liquid’s vapor pressure and external pressure,” you immediately realize:
This regularity does not apply only to water.
It applies to the boiling of liquids.
You have moved from:
Knowledge about water
To:
A general model of liquid phase changes.
This is called:
Transfer.
For another example, suppose you have never studied a particular liquid, but know that at a certain temperature its vapor pressure equals the external pressure.
You can still predict:
It will boil.
This is a very important step.
Advanced learning is not:
The teacher teaches A, and I can do A.
It is:
The teacher teaches A; I extract a regularity from A and can also use it in B, C, and D.
16. Understanding learning ability
Suppose two people, A and B, both study this topic.
A’s approach is:
“Standard atmospheric pressure, water, 100°C.”
Repeat it twenty times.
Answer correctly on the exam.
B asks:
“Why?”
Finds the concept of vapor pressure.
Draws the causal relationships.
Explains them without the book.
Tests their understanding with the mountain problem.
Tests it with the pressure-cooker problem.
Recalls it again three days later.
Finally, tries applying the principle to other liquids.
Both people may answer the first question:
“At what temperature does water boil under one standard atmosphere?”
With:
100°C.
On the surface, both “have learned it.”
But change the question:
“What if the air pressure changes?”
And the difference appears immediately.
B has learned more than an answer.
B has also practiced this mechanism:
Question → model → understand → retrieve → apply → feedback → transfer
That mechanism itself is:
Learning ability.
17. Improving learning ability means repeatedly practicing this chain
You can use the same approach whenever you learn something new.
For example, you encounter:
“Inflation is a sustained increase in the overall price level.”
Do not stop there.
Ask:
What exactly is it?
Why does it happen?
What situations do not count?
What mechanism lies behind it?
Which variables are involved?
If one variable changes, what happens to the outcome?
Can I explain it with a real example?
Can I predict a new case?
Can I explain it without the textbook?
You can take the same approach to programming, economics, law, medicine, management, and history.
Genuine learning ability is therefore not:
“I read quickly.”
It is closer to:
“I can quickly turn unfamiliar information into models that are structured, memorable, accessible, and transferable.”
18. Compressing the whole water example into a cognitive map
You first encounter:
Water boils at about 100°C under standard atmospheric pressure.
This is:
Information.
You remember:
Water, 1 atm, about 100°C.
This is:
Memory.
You discover:
Boiling is not determined by “100°C” itself, but by the relationship between vapor pressure and external pressure.
This is:
Understanding.
You form:
Temperature → vapor pressure → comparison with external pressure → boiling.
This is:
A knowledge model.
You can derive:
Mountains → lower boiling point; pressure cookers → higher boiling point.
This is:
Reasoning.
You can still use it in a situation you have never encountered before.
This is:
Transfer.
You can reliably use it to solve practical problems.
This is:
Ability.
You know that you learned it through:
Question → model → retrieve → apply → feedback → revise → transfer.
And you will actively use the same process next time you learn something else.
This is:
Learning ability.
19. Looking again at the original sentence, it is now completely different
At first:
Water boils at about 100°C under standard atmospheric pressure.
What you saw was:
A sentence to remember.
After deeper learning, what you see is:
Standard atmospheric pressure is a condition; 100°C is an outcome under that condition; the relationship between the liquid’s vapor pressure and external pressure is what actually governs boiling.
Someone who genuinely knows how to learn usually asks more than:
“What is the answer?”
They continue asking:
What phenomenon does this describe?
Under what conditions does it hold?
Why does it hold?
Which variables lie behind it?
If I change a condition, how does the result change?
What other phenomena can it explain?
Can I explain it myself without the original text?
Can I use it to solve a problem I have never seen before?
If you can answer these questions, the knowledge is no longer merely something you have “looked at.”
It is beginning to become:
Part of your cognitive system.
This also provides a very practical set of criteria:
Knowing means being able to state the answer;
understanding means being able to explain why;
remembering means still being able to retrieve it independently after time has passed;
mastery means still being able to reason when conditions change;
ability means being able to use it reliably in real-world or unfamiliar problems;
learning ability means being able to consciously repeat that entire process.
If I compressed all our earlier discussion into a formula, I would write:
Information → questioning → understanding → modeling → memory → retrieval → application → feedback → revision → transfer → ability
And:
The speed, depth, and accuracy with which a person completes this chain, and whether they can complete it again in another unfamiliar domain, constitute that person’s learning ability.