Mathematics & Logic#mathematics#logic#equality

On Equality

Dedicated to all who seek clarity amid conceptual fog


I

A scale. Zhang San steps on it, the needle points to 100 pounds; you step on it, the needle also points to 100 pounds. This scale would say: your weight equals Zhang San's weight.

What it says is correct. What it says is limited.

What it cannot tell you: whether the one standing on it is Zhang San or you, where the difference between Zhang San and you lies, or even—what these 100 pounds really mean.

It can only tell you one thing: with respect to the attribute of "weight," you have no difference.

This is the essence of "equals."

II

We are taught from childhood: A = B.

But few are reminded: this equals sign is never hung between A and B as two things, but between some attribute of theirs.

A is an entity, B is an entity. A's weight is a value, B's weight is a value. When these two values cannot be distinguished, we say A's weight equals B's weight. Then, out of laziness, we simplify it to "A equals B."

This simplification is the beginning of all confusion.

Because when you say "A equals B," you have quietly flattened two living, space-occupying entities that inhabit different times and places into two interchangeable numerical values. You have erased their coordinates, erased their origins, erased every reason for them to be "this one" rather than "that one."

Then you wonder: why, when A and B are clearly "equal," are they still not the same?

Because "equal" never promised they would be the same.

III

Let us speak clearly.

In mathematics, when we write "a = b," we are not talking about the symbols a and b themselves, but about the numerical values they refer to. a and b are merely names; the number standing behind them—that pure-form, locationless, space-occupyingless abstract existence—is the true object the equals sign serves.

Between the number 2 and the number 2 there is of course no difference. They are not even "two" numbers; they are the same number called twice.

But apples are not numbers.

Two apples, even if everything from genes to color, from atomic arrangement to electron spin is completely identical, are still two apples. Because the universe has given them different coordinates. One is here, one is there. You can eat this one, and that one is still on the tree. This one rots, and that one remains fresh.

The attribute of "position" is the last defense line of entities. It ensures that two entities can never "equal" each other—at least at the level of "the entity itself."

Because if you even merge their positions, then it is no longer "they are equal," but "they are one."

Not A = B, but A is B.

IV

These are two entirely different relations.

Computer languages are more honest than everyday language. They use two sets of symbols to distinguish:

  • "A == B" asks: are the values of A and B equal?
  • "A = B" does: assign B's value to A, making A become B.

The former is judgment, the latter is assignment. The former asks "are they the same," the latter says "make them the same."

Everyday language calls both "equals." Thus we often "assign" when we think we are merely "judging"; and when we should be judging, we cannot resist assigning.

You say "love equals responsibility." Are you judging, or assigning? Are you observing the relationship between two concepts, or binding them together with your own will?

You say "I equal my work." Are you describing a fact, or surrendering yourself?

V

The truly serious question lies here: when someone says "A equals B," which attribute have they chosen as the basis for comparison?

This choice determines the weight of the equals sign.

You and your brother, with respect to the attribute of "father," are equal. The father is both Old Wang. But Old Wang as a person is himself an entity. Thus the attribute "your·father" equals the attribute "your brother·father," and Old Wang as a person is that equal value.

This is the entanglement of attributes and entities: an attribute itself can be an entity. A father is a person, a name is a symbol, a weight is a number, a position is a coordinate.

Thus we can keep interrogating along the chain of attributes until we arrive at a bottom layer that can no longer be interrogated—the thing itself.

VI

Then, can one entity directly equal another entity?

No.

Because the phrase "another entity" itself already declares: there exists a distinction between them. If there is no distinction between them, they are not "two entities" but one entity called by two names.

The "morning star" equals the "evening star." But the morning star and the evening star are not two things; they are the same thing—Venus—seen from different angles and given different names. Their "equality" is not the equality of two entities, but the identity of the referents of two names.

When people say "these two apples are equal," what they truly mean is: certain attributes of these two apples are equal. And the word "certain" is the root of all misreading.

Because what is omitted is often the most important.

VII

What does this mean for our lives?

It means: every time you say "equals," you owe yourself a further question—which attribute am I comparing?

You say "we are equal." Equality of which attribute? Dignity? Rights? Wealth? Capability? Or some ineffable value bestowed by the universe?

You say "this person equals that person." Which attribute led you to this judgment? Intelligence? Character? Social status? Or some bias you haven't even recognized?

The equals sign never lies, but it never tells the whole truth either.

It only tells you what it was asked to tell. And that "being asked" is a responsibility you must take on yourself before pressing the equals sign.

VIII

There is yet a deeper layer.

When you press the equals sign between two entities, you are not discovering their relationship—you are creating a relationship. You are saying: from this perspective, they have no difference.

This is a choice, and also a commitment.

You choose weight as the standard, and you place Zhang San and yourself into the same category. You choose father as the standard, and you place brothers into the same family. You choose dignity as the standard, and you place all people into the same community of value.

Every "equals" is a classification. Every classification is an ethical choice.

IX

Thus, "equals" is far more complex than it appears.

It is not merely a symbol from math class, but our fundamental action of positioning ourselves and others in the world. When we say "I equal you," we may be expressing empathy, or we may be erasing our own uniqueness. When we say "I do not equal you," we may be declaring independence, or we may be refusing understanding.

The equals sign is a mirror. What it reflects is not the world, but the measure by which we view the world.

X

Return to that scale.

It says: your weight equals Zhang San's weight. It is correct, and it is blind. It is correct about the reading; it is blind about: you and he are two different lives.

Within your 100 pounds are the roads you've walked, the hardships you've endured, the nights you've stayed up. Within his 100 pounds are his stories, his struggles, his silence.

The equals sign grasped that reading, and let all this pass.

This is not the equals sign's fault. The equals sign was never meant to grasp everything.

It is a tool, not truth. It is a perspective, not the whole picture.

Understanding this, you can truly use it—with reverence, with clarity, with respect for the world beyond the equals sign.

Because we know: in those places untouched by the equals sign, each of us is simply ourselves.


"The equals sign is the measure of thought, but not the entirety of the world."

Copyright Notice: This is a preview translation — Chinese original is the authoritative version. Copyright belongs to Guangzhou Phaenarete AI Technology Co., Ltd. Unauthorized reproduction, citation, or distribution is prohibited.

© 2026 Liang.World. All rights reserved.

Total words: — | PV: — | UV: —