“How to Solve It” never goes out of style
by Kate RutterIn the daytime, I work on creating experiences, building models of abstract concepts, making interfaces, feeling deluged by email and navigating the myriad of human contacts that make work and life play nice together.
But when I get home, I sketch, hum and play with math.
I’ll make one thing clear: I’m terrible at computation. I still count of my fingers on occasion. I thank the heavens for the little digital calculator on my computer. But conceptual math? I’m all over it…Archimedes, Fermat, Bernoulli, Babbage, Lovelace, Mersenne, Fourier, Turing, Pascal, Fibonacci, Mobius, Descartes, Erdos, Polya…yum, yum.
There’s something elemental and patternist about math. The principles are ripe with metaphor and opportunities to apply to everyday life. Looking for transformation over time? Have a ball with combinatorics. Wondering why your inbox always approaches zero but never gets there? Hello, calculus! Yearning to think outside the box? Welcome to Abbot’s Flatland.
So today, when I picked up George Polya’s 1945 classic How to Solve It I was again inspired by the beauty, the simplicity, the utter power of math as a system to better understand life. Starting with the basics of thinking through a problem, Polya’s approach is applicable to a wide range of problems well outside the realm of numbers.
For example, I’m about to head into a series of field research interviews with people in their homes. I’ve been working to center my brain to prepare for the interview sessions. And here is what Polya says about Getting Acquainted with a problem:
Q: Where should I start?
A: Start from the statement of the problem.
Q: What can I do?
A: Visualize the problem as a whole as clearly and as vividly as you can. Do not concern yourself with details at the moment.
Q: What can I gain by doing so?
A: You should understand the problem, familiarize yourself with it, impress its purpose on your mind. The attention bestowed on the problem may also stimulate your memory and prepare for the recollection of relevant points.
That’s a clear, concise message with direct applicability:
- Know the problems and questions: What are we trying to accomplish with this research? What do we need to learn?
- Prepare yourself to wear the experience: Be vivid…what issues exist for people? What are their experiences in day-to-day life?
- Open your mind to seeing the right things: Be in tune with the problem so that your brain is primed to receive the most relevant, potent learnings from the experience.
Math, like design, is best when the concepts are so simple they become obvious. And design work, like math, is best when it’s clearly focused on solving important problems. That’s good stuff.
Thanks, Polya. You’re the best.
October 9th, 2008 at 6:43 am
It is interesting to relate conceptual mathematics to design. However, there are many problems with characterizing design as problem solving. For one, it implies that the design begins with the statement a problem. In fact, early stages of design are much more about problem setting than problem solving. Your example of field research interviews is a case in point, as the purpose is to understand what problems (and goals and context and opportunities, etc) exist in order to define a design purpose.
October 9th, 2008 at 8:10 pm
Dave, thanks for your comment. I agree, there is a lot of territory for design that lives outside of problem-solving, and figuring out the right problems or situations to explore and address are a big part of it. I think Polya’s advice still holds if you identify a field research “problem” as “what don’t we know that we should/could/need to know?” Through this lens, the rest falls in place.
October 10th, 2008 at 5:24 am
Love the conceptual stuff. Last week I came across a similar line of problem-solving questions that might fit in with the theme. The logic is to put a positive spin on the problem so your mind is better prepared to come up with a solution and then to take ownership so that the buck doesn’t get passed.
1. What’s good about this problem?
2. What created the problem?
3. What am I willing to change to solve the problem? (defined by time, effort, money and people)
4. What am I no longer willing to do to solve this problem?
5. What action needs to happen?
What’s clear about any problem is that the change required to solve it needs to be driven by pain. If it’s less painful to live with the problem than to solve it, it may never be solved.