Different people perceive the same object or event differently. We usually say people have different “cognitions” or see things from different perspectives.

After gaining more experience, you might suddenly understand someone else’s way of thinking at a specific moment. This expands your own cognition, or what we might call your “worldview.”

Is there a model to describe this phenomenon?

The Matrix Mindset

If we treat everything in the world as “information” composed of variables, then looking at something from different angles is equivalent to extracting information from a specific dimension.

Take an object, for example. From angle A, it has a specific use; from angle B, it might be completely useless; from angle C, it’s a necessity. The more angles a person can see, the more clearly they understand the “value” of that object.

This entire process is a judgment of the original object. The information of the original object remains unchanged from start to finish. The process of calculating these “values” is exactly like performing matrix multiplication on the original information—a linear transformation to obtain a new matrix. This new matrix reflects the person’s full understanding of the matter:

• Dimensions: How deep is the person’s cognition? How many dimensions can they use to analyze things?
• Eigenvalues: Within these dimensions, which ones do they find valuable, and to what degree?
• Rank: Overall, is their cognitive dimensionality rich? Or, how many dimensions of this object actually hold “value” within their cognition?

A matrix is essentially a dynamic transformation of space.

Cognitive Matrix Theory

Based on this, I’ll propose a “Cognitive Matrix Theory”:

Assume an objective thing or event in the external world is a matrix $X$.

Due to genetics, experience, and knowledge, everyone has a unique cognitive weight matrix $W$ (essentially a “filter”) naturally formed in their brain.

The resulting $P$ is the “Subjective Analysis Matrix” mapped into the mind after personal reflection.

The Essence of Value

From this, I infer:

• Eigenvector $v$ (Direction): Represents which dimension this thing maps to in a person’s cognitive system (e.g., emotional dimension, academic dimension, interest dimension).
• Eigenvalue $\lambda$ (Magnitude): Represents the “magnitude of value” or “absolute influence” this thing generates for that person in that specific dimension.

This explains why different people have different views and actions regarding the same thing. After the cognitive matrix transformation, everyone calculates different “values (eigenvalues)” for different dimensions. Generally, people act according to the dimension with the largest eigenvalue.

A Simple Example

For simplicity, let’s use two dimensions.

Suppose for the cognitive weight matrix $W$, Person A has a high emotional dimension weight, and Person B has a high rational dimension weight. Faced with the task of “comforting someone”:

• A: Makes them happy, distracts them (high eigenvalue in the emotional dimension).
• B: Rationally analyzes the cause, objectively verifies the problem to solve it (high eigenvalue in the rational dimension).

Inspiration from Computer Vision

Thinking about this reminds me of Computer Vision (CV). CV essentially treats images as matrices and uses matrix transformations (convolution kernels) for machine learning or image processing.

Effects like grayscale, blurring, and edge detection are all achieved through specific operator matrices.

This leads to deeper reflection.

Cognitive Change Theory

I’ll also propose a “Cognitive Change Theory.” Since people can change, cognition can also change.

Changing our specific matrix might involve famous quotes, universal truths, or significant life experiences. These act as “preset universal cognitive matrices.” By introducing these new matrices to view things, we perform linear transformations on our own cognitive matrices or even expand their dimensions. This improves a person’s cognitive level (rank) and changes their $W$.

Similarly, arguments, persuasion, and even empathy between people can be seen as a form of cognitive matrix game and parameter fine-tuning.