"The Science of Prompt Factorization mini" — "Good Prompt" = P×R×C×F [Column] Science of Thinking (No. 80)

🎯 The Goal of This Column (3 Points)

• To visualize how AI responses change by altering the quality of questions from the perspective of "factorization"

• To redefine prompts not as "output of thought" but as an "interface for thought"

• To provide the joy of thinking meta-cognitively about "questions" themselves through the fictional discipline of "Prompt Factorization Science"

We often say "That's a good question," but

Have you ever thought the following while using ChatGPT?

Actually, that might be becausethe "design" of your question was vague.

People tend to throw out what they "want to ask" based on intuition.
However, ChatGPT is amachine that reads things logically.
In other words, how you ask is the key.

ChatGPT is a partner sensitive to the "shape of the question"

For example, if you just say "Fix this text," ChatGPT will be troubled.
But what if you say it like this?

Then, just like a human, it will return text that is easy to read and a bit gentle.
By just changing how you ask, you should feel as if the AI's "personality" has changed too.

If we break down a prompt into four parts

The "questions" you throw at ChatGPT are, in a sense,blueprints.
These blueprints can actually be divided into four "factors (parts)."

1. Purpose (What do you want to do?)
→ For example, "I want to explain it clearly," "I want you to summarize it," etc.

2. Role (As whom?)
→ "As a teacher," "As a friend," "As a professional editor"

3. Context (About what?)
→ The "subject" such as text, product, idea, or consultation

4. Format (How do you want it answered?)
→ "In bullet points," "within 200 characters," "in a gentle tone," etc.

The health checkup prompt above also properly includes these four elements.
When the question is clear, the answer becomes clear too. This is truly thepower of factorization.

🧮 Prompt Factorization Formula

$${\text{Prompt} = P \times R \times C \times F}$$

Here,

• $${P}$$ = Purpose
  　┗ What do you want it to do? (e.g., summarize, explain, compare...)

• $${R}$$ = Role
  　┗ Who do you want it to answer as? (e.g., as an editor, as a friend, as a teacher...)

• $${C}$$ = Context
  　┗ What is the topic? (e.g., health checkup results, job hunting, philosophical themes...)

• $${F}$$ = Format
  　┗ In what form do you want the answer? (e.g., in bullet points, within 200 characters, casually...)

✳️ Written as a concrete example, it becomes like the example from earlier.

🎯 Prompt example:

The factorization in this case is:

$${\text{Prompt} = (\text{want to explain}) \times (\text{friend's perspective}) \times (\text{health checkup results}) \times (\text{easy to understand in 200 characters})}$$

By using this formula, you will be able tostructurally reviewthe quality of your questions.

And, ChatGPT's answer to this question looks something like this.

What do you think?
Don't you think the content is easy to understand and the tone is friendly?

A scene imagining factorization (By ChatGPT)

🔍 Explanation by ChatGPT itself on the visual elements of factorization contained in the image

1. The tree in the center: A symbol of integration (the whole = product)

• The tree standing in the center of the image symbolizes a single meaning/result (the entire prompt) created by the "product of factors" that have been factorized.

• To use an analogy, it is the "completed form of the question" or the "AI response output."

2. The rows of fields divided left and right: Separation of factors (constituent elements)

• The left side shows lushly growing crops, while the right side shows tilled land. Each row is clearly separated and visually presented as distinct "factors" (elements).

• This corresponds to the image of factors that make up a prompt, such as "purpose," "role," "context," and "format."

3. The repetition of furrows: Logical decomposability

• The way the furrows in the field are lined up neatly in a straight line corresponds to patterns of thinking that logically extract factors.

• This "patterned repetition" symbolizes the method of structurally designing and revising prompts.

4. The horizon and the sky: Separation of abstraction and concreteness

• The sky is abstract and expansive, while the fields are concrete and divided.

• This implies the separation of "conception of the question (abstraction)" and "design of the question (concreteness)," which overlaps with the process of factorizing thought.

5. Light source (morning sun): The "realization" or starting point of thought

• The morning sun illuminates the whole while simultaneously symbolizing the beginning of thought and the birth of a question.

• It can also be taken as a metaphor for light shining on the "structure of the question" revealed through factorization.

✳️ Summarized in a diagram:

Question (Prompt) = Tree
　　↓
P (Purpose) → Part of the field (how to till)
R (Role) → Direction or depth of the rows
C (Context) → Type of crop
F (Format) → Alignment or arrangement of furrows
　　↓
Answer = Tree is born

🪞 What "shape" does your prompt have?

Finally, here is a small question for you.

When you try to ask ChatGPT something,
how do you choose your words, from what perspective, and in what form do you present your query?

For example—

• When you ask vaguely, "Fix this text."

• When you ask politely, "Summarize this as if you were explaining it to a boss."

• When you clearly state the purpose, such as, "Make it ready to use on Twitter."

The “shape” of that questionmay even reveal your habits of thought, your sense of distance from others, and your attitude toward language.it might be seeping through.

A prompt is not just a command.
It is a small mirror that reflects your own “thinking style”.

This column was written in co-creation with generative AI, ChatGPT.
It is an attempt to explore the future of learning between AI and humans through the theme of “question design.”

Profile | Kazuomi Matsunaga

🧭Thinking Navigator

Biography:Graduated from Kyushu University, Faculty of Engineering (Materials Engineering) ⇒ Engineer at a metal materials manufacturer in the Chukyo region (Production Technology) ⇒ Advertising sales for a local free paper in Nagasaki Prefecture ⇒ University staff member (← currently here). A person in his 50s living in Nagasaki Prefecture. Both children have graduated from university and left the nest, and I am currently living with my wife. I am a writer who lets my thoughts play every day at the intersection of “questions” and “curiosity.” Recently, I have been writing about my own unique perspectives on themes such as education, stories, psychology, AI, and design, centered on the serial column series “The Science of Thought.” I am exploring “free design of knowledge” that goes beyond existing frameworks. My motto is “Imagination opens up the world.” In my main job, while being involved in university and education-related work, I value carefully observing “the moments when people come to ‘like’ something” and “scenes where questions sprout.” 🧭 I would be happy if I could deliver an article that leaves you with a “new perspective” after reading it. 📮 Impressions and messages of support are always welcome!