9-Boxes of Thought and the 10th Quadrant

I have been examining how thinking behaves and attempted to summarize the movement of thought—from observation to conclusion—in a map composed of nine boxes.

In this article, I will explain the structure of this 3×3 matrix and the meaning of each area in the model.

The horizontal axis represents the process of thinking:

Observation → Inference → Conclusion

The vertical axis represents the layers of thinking:

Reality

Recognition

Thinking

By combining these two axes, we can locate where thinking currently exists within its process and depth.

9-Boxes matrix showing the axes:

Observation | Inference | Conclusion

Reality

Recognition

Thinking

Thinking generally begins in the left column (Observation).

From there, thinking may move vertically between layers, and gradually progresses toward the right side of the matrix.

Below is an explanation following the movement of thinking.

1. Observation

(1) Phenomenon

Events that actually occur in reality.

(2) Interpretation

Recognizing a phenomenon and understanding its meaning, value, or potential problems.

At this stage, different paths may emerge depending on the assumptions involved.

Some situations are:

・handled automatically

・understandable through causal reasoning

・requiring deeper interpretation

・difficult to understand at all

If interpretation alone is insufficient, thinking moves deeper into the thinking layer.

Readers interested in this stage can refer to another article on recognition and interpretation.

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(3) Thinking

Here, new elements are introduced beyond existing assumptions.

Thinking at this stage means attempting to form a hypothesis.

If a hypothesis can be formed, thinking proceeds to the Inference column.

However, if a hypothesis cannot be formed, thinking stoppage occurs.

This situation is referred to as assumption collapse.

The structure behind assumptions can be summarized as:

Assumption =

Fact (phenomenon + interpretation)

+ Recognition (interpretation + thinking)

When part of this structure collapses, thinking can no longer proceed normally.

The details of assumption collapse will be discussed in a separate article.

2. Inference

Once thinking moves to the Inference column, causal reasoning begins.

At this stage, thinking often moves vertically between layers:

・forming hypotheses

・gathering data from reality

・updating interpretations

This movement may repeat multiple times before reaching a conclusion.

Sometimes preliminary decisions are made and tested during this process, creating movement between the inference and conclusion columns.

Thinking stoppage can also occur here.

For example:

when the available information is sufficient but a decision cannot be made

when causal explanations cannot be verified

These situations may also result from assumption collapse, which will be discussed later.

[Insert Diagram 2 here]

9-Boxes diagram showing vertical movement between layers during inference.

3. Conclusion

When thinking reaches the Conclusion column, decisions are finalized.

From the recognition layer, a decision is made.

From the reality layer, action is taken.

Conclusion therefore includes:

hypotheses

decisions

actions

expressions or outcomes

This is where thinking reconnects with the real world.

4. The 10th Quadrant

Beyond the nine boxes lies another space.

Sometimes thinking reaches a point where:

・we do not know what is happening

・we cannot determine the cause

・we do not know what action to take

This area lies outside the 9-Boxes structure.

I refer to this space as the 10th Quadrant.

The 10th quadrant represents a domain of:

・the unknown

・the undiscovered

・the not-yet-understood

In this space, the only possible action is exploration.

Concepts such as thinking outside the box or the nine-dot puzzle have long illustrated similar ideas.

Across many fields—including science, philosophy, poetry, and business—major discoveries and innovations can often be understood as movements into this space.

9-Boxes with an outer area labeled “10th Quadrant.”

A discovery can be understood as an update of recognition.

When something new is discovered or understood, thinking returns from the 10th quadrant into the expanded 9-Boxes structure.

Immediately after returning, the new understanding usually appears first as a hypothesis.

PBT and the 10th Quadrant

Poetic Business Thinking (PBT) activates at the moment when thinking stops.

It operates at the boundary between the 9-Boxes and the 10th quadrant.

PBT can therefore be described as a thinking approach that attempts to enter the 10th quadrant and return with a new hypothesis.