About Proofs and Stories, in 4 Parts

Editor’s note: Here’s another new post from a new team member. Shortly after the ‘Lab expanded to include research and design, I attended a workshop on visualizations hosted by a couple of our new team members, Joyce, John and Julia. 

The event was excellent. John and Julia have done an enormous amount of critical thinking about visualizations, and I immediately started bugging them for blog posts. All the work and research they’ve done needs to be freed into the World so anyone can benefit from it. This post includes the first three installments, and I hope to get more. Enjoy.

Part 1

I still haven’t talked anyone into reading Proofs and Stories, and god knows I tried. If you read it, let me know. It is written by the author of Logicomix, Apostolos Doxiadis, if that makes the idea of reading Proofs and Stories more enticing. If not, I can offer you my summary:

H.C. Berann. Yellowstone National Park panorama

H.C. Berann. Yellowstone National Park panorama

1. Problem solving is like a quest. As in a quest, you might set off thinking you are bound for Ithaka only to find yourself on Ogygia years later. Or, in Apostolos’ example, you might set off to prove Fermat’s Last Theorem only to find yourself studying elliptic curves for years. The seeker walks through many paths, wonders in circles, reverses the steps, and encounters dead ends.

2. The quest has a starting point = what you know, the destination = the hypothesis you want to prove, and the points in between = statements of facts. Graph, in mathematical sense, is a great way to represent this. A is a starting point, B is the destination, F is a transitive point, C is a choice.


A story is a path through the graph, defined by the choices a storyteller makes on behalf of his characters.


Frame P5 below shows Snowy’s dilemma. Snowy’s choice determines what happens to Tintin in Tibet. If only Snowy not gone for the bone, the story would be different.


Image from Tintin in Tibet by Hergé

Even though its own nature dictates the story to be linear, there is always a notion of alternative paths. How to linearize forks and branches of the path so that the story is most interesting, is an art of storytelling.

3. Certain weight, or importance, can be suggested based on the number of choices leading to a point, or resulting from it.


When a story is summarized, each storyteller likely to come up with a different outline. However the most important points usually survive majority of summarizations.

Stories can be similar. The practitioners of both narrative and problem solving rely on patterns to reduce choice and complexity.

So how does this have to do with anything?

Part 2

Another book I cannot make anyone to read but myself is called “Interaction Design for Complex Problem Solving: Developing Useful and Usable Software” by Barbara Mirel. The book is as voluminous as its title suggests, 397 pages, out of which I made it through the page 232 in four years. This probably doesn’t entice you into reading the book. Luckily there is a one-pager paper “Visualizing complexity: Getting from here to there in ill-defined problem landscapes” from the same author on the same very subject. If this is too much to read still, may I offer you my summary?

Mainly, cut and paste from Mirel’s text:

1. Complex problem solving is an exploration across rugged and at times uncharted problem terrains. In that terrain, analysts have no way of knowing in advance all moves, conditions, constraints or consequences. Problem solvers take circuitous routes through “tracts” of tasks toward their goals, sometimes crisscrossing the landscape and jump across foothills to explore distant knowledge, to recover from dead ends, or to reinvigorate inquiry.

2. Mountainscapes are effective ways to model and visualize complex inquiry. These models stress relationships among parts and do not reduce problem solving to linear and rule-based procedures or work flows. Mountainscapes represent spaces being as important to coherence as the paths. Selecting the right model affect the designs of the software and whether complex problem solvers experience useful support. Models matter.

 B. Mirel, L. Allmendinger. Analyzing sleep products visualized as a mountain climb

B. Mirel, L. Allmendinger. Analyzing sleep products visualized as a mountain climb

Complex problems can neither be solved nor supported with linear or pre-defined methods. Complex problems have many possible heuristics, indefinite parameters, and ranges of outcomes rather than one single right answer or stopping point.

3. Certain types of complex problems recur in various domains and, for each type, analysts across organizations perform similar patterns of inquiry. Patterns of inquiry are the regularly repeated sets of actions and knowledge that have a successful track record in resolving a class of problems in a specific domain
And so how does this have to do with anything?

Part 3

A colleague of mine, Dan Workman, once commented on a sales demo of a popular visual analytics tool. “Somehow” he said “the presenter drills down here, pivots there, zooms out there, and, miraculously, arrives to that view of the report where the answer to his question lies. But how did he know to go there? How would anyone know where the insight hides?”

His words stuck with me.

Imagine a simple visualization that shows revenue trend of a business by region by product by time. Let’s pretend the business operates in 4 regions, sells 4 products, and has been in business for 4 years. The combination of these parameters results in 64 views of sales data. Now imagine that each region is made up of hundreds of countries. If visualization allows user to view sales by country, there will be thousands and thousands of additional views. In the real world, a business might also have lots more products. The number of possible views could easily exceed what a human being can manually look at, and only some views (alone or in combination) possibly contain insight. But which ones?

I am yet to see an application that supports the users in finding insightful views of a visualization. Often users won’t even know where to start.
So here is the connection between Part1, Part2, and Part3. It’s the model. The visualization exploration can be represented as a graph (in mathematical sense), where the points are the views, and the connections are navigation between views. Users then trace a path through the graph as they explore new results.

J. Blyumen Navigating Interactive Visualizations

J. Blyumen Navigating Interactive Visualizations

From here, certain design research agenda comes to mind:

1. The world needs interfaces to navigate the problem mountainspaces: keeping track of places visited, representing branches and loops in the path, enabling to reverse steps, etc.

2. The world needs an interface for linearizing a completed quest into a story (research into presentation), and outlining stories.

3. The world needs software smarts that can collect the patterns of inquiry and use them to guide the problem solvers through the mountainspaces.

So I hope from this agenda the Part 4 will eventually follow . . . .


  1. Julia, I am most curious about your final point: how to develop a system that can guide users through “mountainspaces”. I think the users’ patterns of inquiry will be meandering, doubleback on themselves, and wander, so the system would need to be able to distill those wandering paths into the most direct, efficient one as a recommendation. This is a very, very common problem I have seen with enterprise software. There is so much functionality, and so many different ways to accomplish a task, that it is very rare that an end user completes the task in the most efficient way.

    Finally, a couple of nitpicky things: I get a 404 error message from your first link (the link you included works, but the link from the Proofs and Stories website does not).

    Also, the “1-pager” is totally not 1 page! It’s 1 webpage, but I think at least 6-7 real, paper-sized pages in academic wording, no less. 🙂 I will read it, though.

  2. @Joyce: Re. the 404 on Proofs and Stories, they want you to email them for permission. I assume they will grant you access to the draft on Dropbox then, if you’re worthy 🙂

  3. @Julia: Did you read Logicomix? Do you recommend it? I’m wondering if perhaps a comic book version would be a better fit for me!

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