The Fractal Geometry of Problem Solving: how chaos becomes progress [Matt Schlegel]

I remember reading “The Fractal Geometry of Nature” by Benoit Mandelbrot many years ago. Mandelbrot made chaos cool. Since then the term “chaos” has been picked up by many disciplines, not the least of which is software product development. Often, chaos is the term we use to describe a messy, complex situation that we do not fully understand but that is required for creativity. Perhaps our perception of chaos is simply a lack of understanding of the fundamental geometric shape that can elegantly describe that creative process. Is there a fundamental geometry for problem solving and the creativity that comes with it?

Prior to Mandelbrot’s work on fractals, generating interesting graphical images by computer was extraordinarily processor intensive. Taking inspiration from Mandelbrot, Loren Carpenter realized he could create complex and realistic graphical simulations of nature using mere triangles, thereby greatly reducing the computation requirements. If you have not seen the movie he presented at SIGGRAPH in 1980, check it out here. Imagine creating all that from just triangles! This breakthrough was a turning point in the computer industry.

Isn’t problem solving another artifact of nature just like natural landscapes? Might not there be a fundamental fractal geometry for problem solving as well? In previous blogs, I have described an 8-step problem-solving process (9-steps by Enneagram count.) I often invoke an 8-section wheel to describe the process. I imagine that there is another 8- section wheel connected to each section of the main wheel, and another to each section of that, and so on in recursive fashion. This structure might form a problem-solving fractal.

Take the simple example of starting with step 1, defining the problem. At step 1, the problem is that “the Problem” is not yet defined. We need to find someone to clearly articulate that problem. We need to consider various ideas for how we might articulate the problem. We need to understand the impact of any articulation and the pros/cons of such articulation. We need to settle on one articulation and to make sure that everyone is in agreement with that articulation. We need to move on and use that articulation to drive the problem-solving process. And, we need to review that articulation periodically in order to ensure that it remains the correct articulation in light of any new data. In this fashion, we just used the entire problem-solving process to describe one section of the overall process.

Having an awareness of the scalability of the problem-solving process helps us better understand the ebbs and flows of the process and helps keep the team moving forward through the process. And, like using triangles for graphical simulation, it can be used to efficiently address the current problem confronting you, your team or your company, regardless of scale.
_________________________________________

Matt Schlegel remains a fan of Benoit Mandelbrot and recently enjoyed reading Mandelbrot’s book on markets entitled, The (Mis)behavior of Markets.