Matrix Thinking
Ideas hide what's missing. A matrix makes the gaps visible — connect dots, fill cells, develop strengths, mitigate weaknesses, delegate ownership.
"The representation is part of the cognition." — Judy Fan
Principles
A matrix does not organise what you know. It manufactures the space where you can wander into what you don't.
| Default thinking | Matrix thinking |
|---|---|
| "I have an idea" | "I have a gap in a matrix" |
| Narrative hides what's missing | Empty cell reveals what's missing |
| One domain at a time | Cross-domain patterns visible |
| Insight feels random | Insight has coordinates |
Explore the space to understand what matters most. An empty cell is not nothing. It is potential with coordinates.
Naps Fill Gaps
Hunt the Void
Edge hides where no one has coordinates.
Known unknowns are locatable — they have a ? cell waiting. Unknown unknowns have no cell — no row, no column, no axis. You cannot ask about them because the grid has no place for the question.
The hunt is not for answers. The hunt is for the meta that manufactures new coordinates. Name a new dimension and an entire axis of void appears. That axis is where edge lives, because no competitor has even drawn it.
| Layer | The hunt | The instrument |
|---|---|---|
| Meta | What dimension would name what the grid cannot see? | A new axis |
| Coordinates | Where on that axis does the thing sit? | Row + column |
| Cell | What lives at those coordinates? | A ? becomes a ✅ |
| Edge | Who arrives first? | Private time at cell |
Cells age. A ✅ today is the answer every competitor knows tomorrow. When a column floods with ✅, the grid is dying — not because the work failed, but because the dimension stopped manufacturing void.
- Hunt the meta, not the cell. The instrument is the axis you name, not the square you tick.
- Hoard the path. The route to a cell compounds even when the cell commoditises.
- Watch for flood. A column full of
✅is a prompt to grow the grid, not celebrate.
Edge is not ownership of a cell. Edge is resolution — seeing a dimension others have not drawn.
Meta of Matter
Use the meta of the matter to explore a matrix of potential for improvement. Matrices are the method. Patterns are the instrument. Both work the same way — structured gaps that pull thinking toward an answer. Fill enough gaps and the picture evolves.
Matrix Thinking manufactures the grid. Knowledge Schema fills it fast by anchoring to a domain you already own — direct mapping, different model, absence, genuinely new. Same instrument, two verbs. Locate the void here. Fill it there.
Cartesian Product
All you know is all you can see. Pick two subjects. Define the meta of each. Cross them. Every cell becomes a question you can answer, a gap you can see, or a job you can hand off.
| Tool \ Job | Find prospects | Qualify fit | Write proposal | Deliver work | Collect payment |
|---|---|---|---|---|---|
| Spreadsheet | ✅ know | ✅ know | ❌ gap | ❌ gap | ❌ gap |
| ✅ know | ❓ unknown | ❌ gap | ❌ gap | ❌ gap | |
| AI agent | ❓ unknown | ❓ unknown | ❓ unknown | 🤝 delegate | ❌ gap |
| Specialist contractor | ❌ gap | ❌ gap | 🤝 delegate | 🤝 delegate | ❌ gap |
| Payment rails | ❌ gap | ❌ gap | ❌ gap | ❌ gap | ✅ know |
Cross them and every cell asks: can this tool do this job?
Subject A — Tools. Meta: instruments you can wield. Members: the ones you own, the ones you rent, the ones you have never touched. Dimension: capability on offer.
Subject B — Jobs To Be Done. Meta: progress a customer is trying to make in a situation. Members: the jobs you serve now, the jobs you could serve, the jobs you refuse. Dimension: demand to be met.
Read The Cells
| Mark | Meaning | Move |
|---|---|---|
| ✅ know | You have proof this tool does this job | Reuse, document, standardize |
| ❓ unknown | You suspect it works but have not verified | Run a small experiment, close the loop |
| ❌ gap | No tool in your kit serves this job | Find a tool, buy one, build one |
| 🤝 delegate | Another agent does it better than you | Hand off with a contract and a receipt |
The value is not the individual cell. It is the shape of the grid. A row full of ❓ marks means you own a tool you have never tested. A column full of ❌ marks means an entire job is unserved — the gap is the business. A column full of 🤝 marks means the job is ready to be a product.
Two Modes
The grid has two modes. Discovery finds which cells to fill. Density tracks how much you have built there.
| Mode | What changes | Colour |
|---|---|---|
| Discovery | Empty cells glow — they're prompts | ? marks the void |
| Density | Filled cells darken with capability depth | Green = strength, Red = threat |
Discovery asks "where?" Density asks "how strong?" Same coordinates, different data. A GitHub heatmap for competitive positioning. The scoring instrument is three cells deep — Wedge (can you sell?), Moat (can you defend?), Scale (can you compound?).
Top Priorities
Take most important subjects and five most important forces that impact that subject.
| Industry \ Force | AI | Blockchain | Crypto | Devices | Energy |
|---|---|---|---|---|---|
| AI Data | verification at scale | provenance ledger | data marketplace tokens | edge collection | compute-per-watt pricing |
| Manufacturing | closed-loop QA | supply chain integrity | production capacity tokens | robotic sensing | grid optimisation |
| Robotics | multi-agent planning | machine settlement | task bounties | embodied autonomy | autonomous power harvest |
| Gaming | adaptive gameplay | trustless rewards | play-to-earn incentives | spatial play | useful proof-of-play |
| Education | personal tutors | credential rails | learning incentives | learning-by-doing rigs | simulation energy markets |
Five rows, five columns, twenty-five located cells. Start here: Industries x ABCDE forces.
Expectations vs Outcomes
A matrix is a prediction instrument. You build one to forecast what an investment of time, energy, and capital will return before you spend it. Each cell is a bet with a known shape — known inputs, known effort, estimated yield. Fill one cell with a receipt and every neighbouring cell sharpens. The grid turns guesswork into a schedule.
| Input | What the grid predicts |
|---|---|
| Time | How many cells close per cycle |
| Energy | Which rows drain, which compound |
| Capital | Cost per filled cell, cost per gap closed |
| Attention | Which column returns the most per unit spent |
The goal is tight alignment between rules, generators, and plans so every change is predictable in effort, cost, and time to ship. That is why the matrix exists — not to describe the past, to price the future.
The Pattern Generalises
Any two subjects whose meta you can define will produce a useful space.
| Subject A | Subject B | What the space reveals |
|---|---|---|
| Skills | Roles | Which roles you can staff, which gaps to hire or delegate |
| Industries | Forces (ABCDE) | Where a transformation wedge exists |
| Principles | Decisions | Which principle governs which decision |
| Agents | Jobs | Which agent owns which job, who is idle |
| Agents | Trace Quality × Governance | Which deployments compound, which plateau, where the scoring system is the product |
| Standards | Artifacts | Which artifacts conform, which drift |
Define the meta before you cross the subjects. Without the meta, the grid is a doodle. With the meta, the grid is a thinking instrument that sells the story, exposes the unknowns, and routes the work.
Question The Void
All you can know is all you can experience. The grid gives the unknown coordinates.
| State | What It Is | Without Grid |
|---|---|---|
| Known known | Filled cell | Scattered knowledge, no pattern |
| Known unknown | The ? cell | You sense a gap but can't locate it |
| Unknown unknown | The row or column you haven't added yet | Invisible — no coordinates, no wander space |
Each dimension you add to the grid is a new axis of void. Industries x Forces gives you 20 cells. Add a third dimension — maturity stage — and you have 60. Most are empty. That's the point. More meta in the grid, more space to explore.
Naming is the resolution mechanism. Taxonomy defines what dimensions the grid has. Nomenclature defines what goes in each cell. Ontology defines how cells relate. Better names, finer grid, more void to wander in. The data model IS the grid. Understanding the data model is understanding the domain.
The empty cell is not absence. It is where you help someone see who they could become. Love is seeing potential in others and helping them move toward it. The matrix is that love, mechanised.
What are the best questions you can place in that each space?
Excel Spreadsheets
See cash-flow projection — the canonical worked example of a grid that narrates before the numbers do.
Excel is the most valuable thinking tool ever shipped. It won because the grid is universal and the setup tax is zero — type headers, fill cells, read the story. Sparse rows expose weak coverage. Dense columns expose over-investment. Empty cells beg to be filled. A spreadsheet sells conviction faster than any dashboard because the shape of the grid narrates before the numbers do.
| Strength | Weakness |
|---|---|
| Universal grammar — anyone reads rows x cols | Each sheet invents its own schema |
| Zero schema tax at birth | Column meaning dies at the file boundary |
| Empty cell = visible prompt | Filled cell = claim with no provenance |
| Sells the story by showing strengths + gaps | Hard to connect cells to the world in a true way |
| Guides conscious investment decisions | Merging two sheets collapses the shared meaning |
Every cell holds potential. Realise it by asking the right questions of the space — the whole grid, not one cell. What does this row mean? What dimension is this column? What would an empty cell here prove? Which axis is missing? The questions interrogate the space; the cells answer. A claim becomes a bet, a bet becomes a move.
The fix is not a better spreadsheet. The fix is the meta layer Excel never got: named rows, typed columns, cells bound to a source, empty cells as verifiable intents. Keep the grid ergonomics. Add the provenance. Every cell becomes a question waiting for a receipt.
A spreadsheet is an asset of persuasion — it moves the reader from scattered belief to located bet. Logos through shape.
Walk The Pipe
When learning how a system works, you walk the pipe — trace the flow from input to output, record what you see, map each item to a standardized name, then arrange them into good flow. This is how P&ID engineers survey a plant before drawing the diagram. The same method works for any domain.
| Step | Action | What You Produce |
|---|---|---|
| Walk | Trace the flow end to end | Raw observations |
| Name | Map each item to taxonomy | Standardized labels |
| Arrange | Place names into a matrix or A&ID | Structure with coordinates |
| See | Read the empty cells | Gaps, strengths, risks |
The naming system IS the resolution of the grid. Better nomenclature, finer grid, more void to wander in. Once the names are right, cartesian products generate the matrix mechanically — every row x every column = a cell that either has something or reveals a gap.
Applied example: The Capability Router is this method applied to software. Categories (taxonomy) x Dimensions (essentiality, verdict, coverage, ROI) = a matrix where every empty "Top Build Features" cell with a "Build (core)" verdict is a known gap with coordinates. A "Defer" row is a conscious decision to leave the void unfilled until demand pulls.
Opportunity Map
Convert one promising cell into a build thesis.
| Industry | Force | Current friction | Opportunity wedge | First proof |
|---|---|---|---|---|
| AI Data | AI | Data quality and provenance | Verification and pricing protocols | 1 paid pilot |
| Manufacturing | Devices + AI | QA bottlenecks and rework | Closed-loop quality system | Defect rate down 20% |
| Robotics | Devices + Cloud | Coordination across actors | Shared task and settlement protocol | 1 live deployment |
| AI agents | AI | Eval harness absent — loops run blind | Scoring system tied to business value, not proxy metrics | First domain loop closed with receipt |
If you cannot express the move in one row, keep mapping.
Context
- Knowledge Schema — How to fill the grid fast using an anchor domain you already own
- Gates of Knowledge — Rhetoric x Senses: knowledge bounded by what we can experience
- Inner Space — Matrix thinking applied inward: the modes, loops, and states within you are dimensions waiting for coordinates
- Inner Game / Outer Game — What becomes possible when matrix thinking makes the invisible inner game navigable
- Idea Discovery — force-to-friction method
- Naming Standards — The resolution mechanism: better names, finer grid, more void
- Persuasion — Matrices are assets of persuasion; the grid sells the story before the numbers do
- A&ID Template — P&ID nomenclature applied to AI + Crypto systems
- Performance — proof that value is real
- The North Star — the fixed reference that tells you which gaps matter
- Software Jobs To Be Done — Applied matrix: software categories x essentiality x verdict x coverage x ROI
- Potential — why gaps matter
- Strategy — the Capability-Demand Matrix is matrix thinking applied to positioning
Links
- Judy Fan: Cognitive Tools — "The representation is part of the cognition"
- Mapping Alignment of Priorities
- Customer Growth Charts
- Problems and Opportunities
- Strategic Priorities
Questions
If all you can know is all you can experience, what dimensions are missing from your grid?
- What row or column would you add if you had a sense you don't have?
- When the grid reveals a gap, is the gap in reality or in your perception?
- What's the difference between a matrix that extends your cognition and one that merely confirms what you already believe?
- How do you know whether your grid's dimensions are named well enough to see what's actually there?