*Armed with a pencil and paper, you can simplify about 99% of the world’s problems.*

Despite a couple decades of extra-substantial technological growth, there are two things that can never be replaced: the pencil and paper. For the toughest analytical challenges, only so much can be done computationally to simply and digest such problems. For these challenges, the solutions should start with a pencil and paper.

The first step in breaking down a problem is the conversion of the problem from the brain’s three dimensional space to a the two dimensional space of paper. In mathematics, there are several examples of such similar breakdowns: matrix decompositions, polynomial factorizations, projections, transforms, etc. The breakdown is necessary to see things in a new light, a simplified light, and a light that otherwise may not have been turned on.

Step 1. Grab a pad of paper. Do not put boundaries on where you can write and draw.

Step 2. Grab a pencil. Sharpen it and keep the pencil sharpener close.

So now that we have pencil and paper in hand, what do we draw? Well here’s my point. There is a geometric toolbox that provides a valuable framework for the problem solving environment. These are the shapes and squiggles.

**1. Matrices**Two-by-two matrices are especially valuable for initial sorting of qualitative data. Assign a binary variable to each axis, name the cells, and define the relationships. Categorizing concepts and attacking each cell independently can help find hidden relationships and provide insight for subsequent analyses. See my previous post on matrix power for more on matrices.

*2. Graphs*For more quantitative and scaled concepts, draw a set of axes to start. Visualize relationships between variables by drawing lines or curves and then attack each extremum and graphical sector. Plot knowns and/or hypotheticals on the graph and decipher the meaning of specific coordinates. Jessica Hagy’s blog ‘Indexed’ is a good example of translating mind to graph.

**3. Lists and Mind Maps**

The proper organization of information is often the most valuable visual tool in solving complex problems. Of course there are technologies to assist in the visualization and organization of information (mind maps, spreadsheets, etc.) but it’s important to use pencil and paper as the primary stepping stone to using some software/web app. Check out a mind map on different mind mapping software and a post on five great uses of mind maps.

**4. Circles**Circles have shape and have a shape that is unique. They overlap well, fill space comfortably, and are easy for the human mind to spatially interpret. Eulerian circles (or Venn diagrams) are the simple example of circles put to use on paper for analytical means. There are several other adaptations of circles for comparative reasoning, such as with GL Hoffman’s “gruzzles”.

**5. Doodling**The mind works in mysterious ways. Drawing without bounds can release otherwise inexpressible thought. There’s the somewhat structured doodling such as with UI mock-ups, schemas, and decision trees, and very unstructured doodling that might look like an impossible maze of dots and lines. The importance lies in the fact that your brain knows most about the problem, and the pencil is driven by the brain. Any new representation put forth on paper, by your brain, is a new representation of that problem not previously seen. In other words, “doodling allows the unconscious to render in symbolic expression”.

The shapes and squiggles live on. And the shapes and squiggles will always live on because they are the simplest yet most powerful functional tools our mind can use to express our conscious, subconscious, and unconscious thoughts.