Monday, January 18, 2010

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.


Saturday, January 9, 2010

Problem Solving, the Brain, and the Enneagram [Matt Schlegel]

On the topic of problem solving and the brain, I want to bring to your attention a fascinating book called Personality and the Brain written by a local computer scientist and entrepreneur, Peter Savich. Peter became interested in the Enneagram and realized that there must be a link between how the brain operates and the core modality described by the Enneagram. His book makes a very compelling case for this link.

Peter asserts that there are two parts of the brain that drive personality, an old brain component, the amygdala, and a new brain component, the prefrontal cortex (PFC). The amygdala is in essence the fear processor, and the PFC is the optimism/pessimism processor. He goes on to describe how each of these brain components has a right side and a left side, corresponding with the right side and left side of your brain. And, each half invokes dominant characteristics. For instance, one side of your amygdala is your fear-aware processor (the flight processor) and the other is your fear-unaware processor (the fight processor). Likewise, one side of the PFC is your optimism processor (glass half full) and one side is your pessimism processor (glass half empty).

Just like there are 3 states of handedness, right-handed, left-handed or ambidextrous, Peter asserts that both the amygdala and the PFC have three dominant modal states, and it is the combination of these states that give us the 9 states of the Enneagram. How cool is that! He goes on to examine studies from the body of neuroscience literature to show how pathologies in these brain components accentuate or diminish the behaviors that map to the behaviors described by the Enneagram, thereby making a very compelling case for connecting the dots between the brain and the Enneagram. I cannot thank Peter enough for developing and publishing this fascinating thesis.

With the help of this understanding, we are able to connect the dots from 1) a problem-solving process described by the Enneagram, to 2) the behaviors and capabilities important for each phase of that problem-solving process, to 3) our own unique set of behaviors and capabilities and, finally, to 4) our brain which governs those behaviors and capabilities. Just like the brain determines whether we end up being right-handed or left-handed, it also plays an important role in how we contribute to the problem-solving process.
According to Peter Savich’s framework, Matt Schlegel has an amygdala that is fear-aware dominant and a prefrontal cortex that is pessimistic processor dominant. This makes Matt uniquely suited for that part of the problem-solving process he characterizes as “finding the path of least danger.”


Saturday, January 2, 2010

Take stock of your problem-solving talents [Matt Schlegel]

In the last blog, I wrote about a talented right-handed pitcher. When it comes to throwing a ball, it is pretty easy for most of us to figure out which arm throws best. But what about problem solving? Each of us has a style that lends itself to contributing to the problem-solving process. How do we figure out what that style is and how we best contribute?

As you have read through the previous blogs describing the problem-solving process (and I hope that if you are reading this you will have done that), you may have been thinking to yourself about how you contribute at each phase in the process. You may have recognized those areas in which you feel you are strong or which you enjoy the most. Those are important clues in understanding where your personal talents lie when it comes to solving problems.

If we accept the 8 steps of the problem-solving process and acknowledge that as individuals we are strong in a few of the steps but perhaps not all of them, what happens when as individuals we attempt to solve problems? I can tell you from personal experience, I will focus on the steps in which I am strong and minimize or skip over the steps where I am weak. Here is how I would characterize myself: Firstly, I am not one to even make a big deal about problems. I may ignore them, live with them or tough them out. On the other hand, occasionally I get a “brilliant” idea that I want to try out. This idea will be a solution to a problem that I may or may not actually have. Yet, I will be so enthused about the idea that I will move forward and implement it, and I will be tenacious in doing so. After implementation, I will take steps to measure how effective the idea is in order to determine if it performs as I envisioned. At this point I usually stop and move on to the next thing.

So, which steps of the problem-solving process are my strengths and which are the weaknesses? Let’s start with weaknesses. I did not start off by having a clear problem statement, nor did I have any goals. I did not enlist the help of others. I did not consider many ideas, just the one that popped into my head. I did not explicitly analyze my idea, but there was the implicit analysis that my brain did to come up with the idea in the first place. I got very enthused about the idea, but I did not necessarily get others enthused about it. And, I worked hard to implement the idea and went back to see how well it worked. From this, you can see that I am personally weak in steps 1, 2, 3, 4, and 6 of the process. On the other hand, I tend to be strong on steps 5, 7 and 8. Good to know.

And, dear reader, in terms of the problem-solving process, which steps do you identify in yourself as strengths? I encourage each of you to take stock of your strengths and understand how you best contribute to the problem-solving process.

Matt Schlegel lives in a household of 5 people, each contributes differently to the problem-solving process and two are teenagers. Matt’s keen awareness of his own problem-solving inadequacies may come from the constant and frank reminders of these inadequacies voiced by these teenagers. Kindly, his wife reminds him of his strengths.