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Matrix Thinking

How do you create gaps for your imagination to fill?

Diagrams | Matrices | Thinkers

Explore the matrices of your mind by using charts and tables to visualise the journey ahead and progress that has been made, by understanding what decisions need to be made when versus the decisions that have been made and why.

Mantra

Identify gaps for your unconscious to fill and dots to connect

Cognitive Tools: Making the Invisible Visible​

External representations — matrices, diagrams, drawings, data visualisations — are not outputs of thought. They are active components of thinking that make hidden structure, assumptions, and possibilities perceptible so your brain can work on them.

"The representation is part of the cognition." — Judy Fan

When you put things into a structured visual form, you force choices about what is important, how pieces relate, and what's missing. Those choices themselves drive learning and insight.

A matrix is a constrained visual space where you externalise your internal models. Empty cells reveal unexplored options. Mismatched rows expose faulty assumptions. The format itself does cognitive work that verbal thought cannot.

The Cognitive Tools Stack​

LayerPurposeTools
CaptureGet thoughts out of your headMind maps, sketches, notes
StructureFind patternsMatrices, 2x2s, flowcharts
CommunicateShare with othersDiagrams, decks, data viz
ComputeMake it executableCode, algorithms, workflows

Five Questions Before You Draw​

  1. What invisible thing am I trying to make visible? (assumptions, bottlenecks, mechanisms, capabilities)
  2. Which tool would make it most concrete? (matrix, diagram, map, code, data vis)
  3. What simplifying assumptions am I making? Externalise them so you can critique them.
  4. Who needs this and at what time horizon? Personal insight vs team alignment vs investor story.
  5. What's the smallest experiment this enables? Only invest in tools that would change a decision if results surprised you.

Core Concepts​

Matrix thinking involves moving between different points of thought in seemingly unrelated ways, constantly absorbing and synthesizing information from the world around us. Unlike linear thinking, it allows us to find patterns and creative connections between concepts that may appear unrelated to others but make perfect sense when viewed through a matrix lens.

The Triple Reframe: Never settle on your first axis pair. Try at least three framings—the third often reveals what the first two missed.

The Process​

Step 1: Create the Structure​

Draw out the dimensions you're exploring. A 2x2 is the simplest:

           Low Y         High Y
         ┌────────────┬────────────┐
High X   │     ?      │     ?      │
         ├────────────┼────────────┤
Low X    │     ?      │     ?      │
         └────────────┴────────────┘

The ? marks are gaps. Gaps are where insight lives.

Step 2: Fill What You Know​

Place known concepts in their positions. Don't force it—let what's obvious fall into place first.

Step 3: Question the Gaps​

For each empty cell, ask:

  • What belongs here?
  • Why is this gap empty?
  • What would fill this if it existed?
  • Is the gap real or is my framing wrong?

Step 4: Connect the Dots​

Look for relationships:

  • Horizontal: How do things differ at same level?
  • Vertical: How do things differ across levels?
  • Diagonal: What unexpected connections exist?
  • Inverse: What's the opposite of each cell?

Step 5: Reframe and Repeat​

If the matrix feels forced, change the axes. The right framing makes connections obvious.

Common Matrix Patterns​

Capability × Demand (Work Charts)​

           Low Demand    High Demand
         ┌────────────┬────────────┐
Human    │  Eliminate │  Differentiate  │
Edge     ├────────────┼────────────┤
AI       │  Automate  │  Scale     │
Edge     └────────────┴────────────┘

See Work Charts for the full coordination framework.

Certainty × ROI (Investment)​

           Low Certainty   High Certainty
         ┌────────────┬────────────┐
High ROI │  DREAMER   │  DO NOW    │
         ├────────────┼────────────┤
Low ROI  │  KILL      │  QUICK WIN │
         └────────────┴────────────┘

See Investing Decisions for decision frameworks.

Push × Pull (Motivation)​

           Low Action    High Action
         ┌────────────┬────────────┐
Push     │  Paralyzed │  Reactive  │
(Fear)   ├────────────┼────────────┤
Pull     │  Drifting  │  Flow      │
(Desire) └────────────┴────────────┘

See The Game for the consciousness loop.

Toolkit​

What tools can help you explore the matrices of your mind?

ToolBest For
Matrix TableComparing options, finding gaps
2x2Prioritizing, categorizing
Flow DiagramProcesses, causation
Concept MapRelationships, taxonomy
Work ChartHuman/AI capability routing

Context​

Benefits​

What can be gained?

  1. Explore gaps
  2. Reveal strengths
  3. Make connections

Enhanced Creativity

  • Helps break out of mental ruts
  • Enables innovative problem-solving
  • Facilitates connection-making between disparate concepts

Improved Decision-Making

  • Provides multiple viewpoints for analysis
  • Reduces cognitive biases
  • Enables more comprehensive problem assessment