When we’re thinking about solving a problem we’re usually thinking about it on a two-dimensional plane.

This makes it easy to create a simple matrix that allows us an overview of the two dimensions that matter most to us. This is basically why we use Excel’s spreadsheets, graphs, and coordinates to visually represent data.

Two examples of its usage for problem solving are “Covey’s quadrants” and the “Prisoners’ Dilemma”.

The two dimensions in Covey’s quadrants are whether a task important or unimportant and whether it’s urgent or not urgent. The two dimensions in Prisoners’ dilemma are whether prisoner A stays silent or betrays and whether prisoner B stays silent or betrays.

Simple enough, right?

Well, what if there’s a third dimension that’s crucial for making the best possible decision? For example, maybe we want to know whether we have or don’t have the resources required to complete a task in Covey’s quadrants. This could help us reprioritize, delegate, or eliminate some tasks.

The problem is that we aren’t as good at representing possible solutions in 3d as we are in 2d.

Let’s say your band is going to play covers at a birthday party. They want you to play pop and rock, but they don’t want you to play anything slow, just fast and mid tempo songs. They’ve neatly put the requested songs into boxes, like this.You have a 2d overview and can clearly see all the options in front of you. Now, they mention that they’ve compiled a second set of boxes as they want you to play songs specifically from the 80’s and 90’s.

They’ve arranged the boxes as follows.OK, it’s still manageable even though you can’t actually see the box with 90’s pop, as long as you remember it’s there.

After talking it over they change their mind and also want you to play some slow songs, jazz, and 70’s.

This is the final arrangement of the boxes.Now it looks like a damn Rubik’s cube. You went from 4 boxes to 8 boxes to 27 boxes. Also, notice how you went from not being able to see one box when there were 8 to not being able to see 8 boxes when there were 27.

For example, you can make an educated guess what the backside of the device you’re looking at right now looks like. But you can’t see both the front and back at the same time, there’s always some information missing for us to see the whole as it is.

And this is just about having 3 styles of music from 3 decades with 3 different tempos.

Now, if we were to sit in the middle with those 27 boxes in a circle around us it would be easy to sort it out. But as a 3d decision matrix represented on a 2d (flat) surface it isn’t practical.

This kind of matrix will probably remain impractical, unless we can find a way to manipulate the cube. Simple 3d software and VR could easily solve this issue. If we can rotate the cube and explode the cubes that make it up we can wander around and look at and weigh all the options. We’ll have a tool to make better decisions.

Maybe we can stop using 2d solutions to solve 3d problems.If we were 2d beings (flatlanders) we would likely be using 1d tools (linear) to solve our problems. It would be hard for us to see all sides of the 2d plane, just as we have a hard time seeing all sides of our 3d space.

We shouldn’t disqualify 1d and 2d tools, we just need to recognize their limits. They can’t possibly help solve all our problems, and as we’ve seen the more complex a problem is the harder they are to portray in those dimension.

Let’s look at 3 levels of solving a problem.

**1d (line):** To do-list. This prioritizes all the things in order of importance from 1-10 and they’re easy to check off. However, you don’t necessarily know whether they need to get done now or can be done later.

**2d (square):** Covey’s quadrants. This categorizes and prioritizes all the things from your to do-list into what’s important and unimportant, and what’s urgent and not urgent.

**3d (cube):** Trimatrix. This does all of the above and allows us to take into consideration whether we have the resources to complete a task, whether a task is recurring, etc.

That’s why we would gain so much by being able to look at and analyze our problems in a 3d space.

The next step would be to have matrices in 4d (tetramatrix), 5d (pentamatrix), and so on.

As a thought experiment it’s interesting to think about how a 4d being would use a 3d object the way we use screens and paper. Being able to view and manipulate an object or problem in 360 degrees would probably increase their ability to think through and reach better decisions faster.

What would their version of a spreadsheet look like? How would it influence their ability to represent data? How would it enhance research? How would it influence their everyday thinking?

But we need to start where we are, and we need to get people used to this mode of thinking first.

We need a thoughtware upgrade.

For now, we can close our eyes and imagine what it would be like to enter that world. A space where we aren’t merely outside observers looking at a flat square of options, but totally immersed and able to move around, pick up, and look at all the available solutions around us.

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