shapes and squiggles

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.

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matrix power

How much of your life can you fit into rows in columns? Well, enough of it for you to cherish the matrix as a valuable organizational and analytical tool.

Spreadsheets, tables, and matrices are used in every aspect of life. We track finances, monitor tasks, plan our future, and analyze potential relationships with rows and columns. And we are surrounded by this information as individuals, as part of small social groups, and as part of large organizations such as classes, companies, or governments.

More simply, matrices and tables give a new structure to elements of our life that are not always so two-dimensional. From the new structure, we can glean new insights and inspire new visualization of those same elements to make best-informed decisions. To me, a matrix is a valuable analytical tool that helps organize information for insight and action.

(Note that I am using the term “matrix” to represent that much more than numerical arrays of the math world. I am including categorical mappings, tables, lists, and spreadsheets too.)

The University of Cambridge Institute for Manufacturing nicely defines the matrix as an essential decision support tool:
  

“A two by two matrix is a useful tool for initial sorting of qualitative data. The axes should be chosen so that, e.g., the data with the most desirable characteristics will fall into the upper left quadrant and the least desirable in the lower right quadrant. While groups may be unable or unwilling to assign absolute values to qualitative data, they usually find it relatively easy to come to a consensus as to which quadrant something belongs in.

Generally, the two by two matrix is a useful tool for categorising things that can be reduced to two simple variables, particularly when quantitative information is unavailable and qualitative judgments must be made.

It enables a rapid clustering (or separating) of information into four categories, which can be defined to suit the purpose of the exercise. It is particularly useful with groups as a way of visibly plotting out a common understanding or agreement of a subject.”

Authors Alex Lowy and Phil Hood describe the matrix as “the most flexible and portable weapon in the knowledge worker’s intellectual arsenal”.

What’s best about the matrix is that flexibility. Depending on need, you can get as much power out of a 2×2 matrix as you can from a 5×5 matrix. Increased dimension does not translate to increased power. The matrix is flexible and dynamic to the needs of your analysis. You control the path to discovery.

And although matrices do a nice job of pairing categorical relationships, you can also translate these pairs to numerous other visualizations to better contextualize the information at hand. Turn your row and column headers into scaled concepts, map them to some x- and y- axes, and try and fit your qualitative information to a line that describes the relationship between x and y. Is the relationship directly proportional, inversely proportional, linear, parabolic, or along some other path? What do each of these types of relationships mean for your categorical variables?

It’s important to note that there can be fuzzy lines too. Not all cells need to have values and not all relationships need any sort of defined continuity. Empty cells and undefined relationships provide insights that are just as valuable as the populated and defined ones. Lack of data is data in itself, and that’s a great thing.

In the end, the matrix is just one part of the analytical toolbox and can provide a wide range of insight for your personal and professional life. Box up your data, organize it, visualize it, and use new structure to optimize your life.

Examples

Business/Leadership: Gartner, an IT research and advisory company, has created the “Magic Quadrant” to analyze types of entities in the business world. By plotting the ability (or inability) to execute against the completeness (or incompleteness) of vision, businesses can be categorized with those sharing similar characteristics, as Leaders, Challengers, Visionaries and Niche Players. This is a useful example of turning abstract qualities into groups for targeted strategy and decision making.

Product Development/Management: For analyzing how to grow a business from the product side, one matrix shows how plotting types of markets vs types of products can help guide that growth strategy.

Math/Statistics: Type I and Type II error tables are used to describe possible errors made in a statistical decision process. This is a great example of mapping relationships between categories, naming the cells, and using the matrix to understand what each cell represents.