The Structure of Thinking and Learning, and The Power of 2x2 Matrices

Due to the fact that we are accustomed to draw on paper in 2 dimensions, for many people the maximum graspable complexity is the 4 quadrants that come to be when we cut the plane in half twice, with 2 perpendicular axes.

But this is no real limitation. 2x2 matrices go a long way, if we choose the axes smartly. And they can add a lot of extra meaning to a model which uses only one dimension.


It is common sense, that it is wise to think of actions and learning as feedback cycles, where we plan an action, execute it, and review the result, which is the starting point of the next cycle. The iteration represents the fact that we want to learn from the process, and incorporate the findings about the result of a cycle into the planning of the next one.

This model exists in different flavors, examples are the Lean Cycle (Build — Measure — Learn), or a classical one going back to several decades, the PDCA Cycle (Plan — Do — Check — Act), first proposed by Edward Deming.

How many dimensions are in play here?

The time dimension is obvious, but there is also a hidden one, which we can call “Real World” vs “Theory”:

  • If we want to learn from the process, we need to interpret some factual data which is some kind of transition from “Real World” to “Theory”.
  • And vice versa, when we plan the next cycle, we have to make the transition from some theoretical goals into actions that are supposed to make some real world impact.

And if this additional dimension is implicitly used, why not make it explicit? It can happen that we gain a lot in clarity and usability of the model.

A general model for Thinking

This is actually what has been accomplished by the late Roger Fisher Harvard law professor, who is best known about the book on the art of negotiation he coauthored, Getting to Yes (see the book’s analytical table of contents here).

In the book he introduces a 4 step cycle along the 2 axes Time (what is wrong now, vs what might be done in the future), and Real World vs Theory, for thinking up possible solutions for a problem:

In another book coauthored by him, which I think is for businesses even more important, (Getting it Done -. How to Lead When You are Not in Charge) he uses the Circle Chart in a very similar format to the one above, as a general framework for Thinking:

(In the book Getting it Done Thinking and Learning are 2 elements of a tool set for making things happen.The whole tool set consists of the elements Purpose, Thinking, Learning, Engagement, and Feedback — see the analytical table of contents of the book, which is a very well structured outline of its content, here)

The 2 dimensions are here, as mentioned above:

  • Now vs Later (a simplified form of Time)
  • Real World vs Theory

And the cycle of Thinking, which goes through the 4 quadrants, created by cutting the plane in half along these 2 dimensions, is the following: Data — Diagnosis — Direction — Do next

  • Data is real world facts that can be measured now
  • Diagnosis is the theoretical interpretation of the now existing Data
  • Direction is the theoretical goal setting projected into the future
  • Do next is an action derived from Direction, and supposed to have some real world impact in the future.

The clarity of the model, compared to the above mentioned models (Lean Cycle, PDCA Cycle), comes from the fact, that with each step, we do one and only one clearly defined border crossing:

  • When transitioning from Data to Diagnosis, we cross only one border, separating Real World from Theory, but remain in the realm of Now — call this step analysis
  • When transitioning from Diagnosis to Direction, we cross only one border, separating Now from Later, but remain in the realm of Theory — call this step conclusion and goal setting
  • When transitioning from Direction to Do next, we cross only one border, separating Theory from Real World — call this step breaking down the goal into concrete action
  • And the cycle is closed by transitioning from Do next to Data, when we capture data produced by our Do next action — here again, we cross only one border, separating Later and Now, but remain in the realm of Real World. The transition from Later to Now is of course only possible due to the fact that time is going by in the meantime, and what was “Later” in the planning phase, becomes “Now” by the time we get there. An even better model than the cycle is thus the sine graph, which accounts for the time passing by, see below.

And the big advantage of crossing exactly one border at a time is that the consistency of the steps is much easier to check and demonstrate, than if we tangled up 2 dimensions, hence 2 border crossings in one step, like in the Lean Cycle or the PDCA Cycle.

One step further: Learning as the integration of Thinking and Doing

The invention of the 4 Quadrants model in itself is a big achievement, but Fisher goes a step further, when he shows how Thinking is integrated with Doing in the form of Learning, and how it can be represented by a sine graph:

In addition to the Thinking cycle, introduced above, there is an additional layer of Real World, so there are 2 levels of reality in play here:

  • the upper level, above the water, represents observing Real World
  • the lower level, in the water, represents Doing, which takes in as input your operational plans, and puts out the results of the actions, as observable data, the starting point of the next Thinking cycle.

We would say in a corporate environment that this is a swim lane diagram (no pun intended).

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