How to Solve Complicated Problems — The Art of Deconstruction

The thing about the flag structure is I didn’t have to invent composition.  —Jasper Johns

Imagine that you have a string of 100 interchangeable lights: they have a plug on each end, and you can plug each individual light into any other light. Each time you plug in a light that is off to another light that is off, there is a 50/50 chance it turns on. Your job is to turn off the entire strip.

It’s a problem with 100 variables with two outcomes each. The chance of finding the answer is thus:

2 ^ 100 = 1.267 x 10^30 choices (that’s 1.267 with 30 zeros after it)

Now what if you could break the problem down into 10 sets of 10, and you knew that each set of 10 could be plugged into each other without a problem. You’d have 10 sets of problems each with two variables:

10 x 2 ^ 10 = 10 x 1,024 = 10,240 choices (reduced from an outcome set with 30 zeros)

Maybe we can go one more step; maybe we can actually break it down to 20 sets of 5, or we can break each set of 10 in half. We’d end up with 20 sets of 5 two-variable problems:

20 x 2 ^ 5 = 20 x 32 = 640 choices (reduced from 10,240)

In narrowing the problem into congruent sets, we’ve reduced the possible outcomes from a hopeless number with 30 zeros to a manageable set of 640 choices. This example is from Notes on the Synthesis of Form by Christopher Alexander, an architecture book that defined the language and approach of much of architecture and design since the 1960s. Alexander sets out a process by which we first understand the requirements (the program), we chunk the requirements into sets that are solvable and congruent, and then we work through each set, eliminating the “misfits,” in search of “fit,” which is the unification of form and function. It’s through this process that seemingly complex design problems, like building a house, are solved.

In my art, I deconstruct, and then I reconstruct.   —Chuck Close

The trick is knowing how to deconstruct the problem and how to form the sets — and also knowing that the sets are congruent with each other when you assemble them. When you stand back from a Chuck Close painting and realize all those little squares perfectly form a face, you see that the real design trick — the art — is in the deconstruction.

I don’t work with inspiration. Inspiration is for amateurs. I just get to work.  —Chuck Close

This process is very different from the idea of starting with a blank slate, that art and design are somehow completely intuitive and spontaneous. The reality is that design is a process, and it’s the deconstruction of that process that allows us to take perceivably inconceivable problems and reduce them to a manageable problem set. That’s not to say that it’s easy, of course. Deconstructing complex problems is hard and often requires synthesizing knowledge on a variety of subjects. But it is certainly manageable and demystifies that which is often perceived as pure genius or ineffable art, and thus unattainable by most of us. And this ability — the ability to synthesize and deconstruct — is more important than ever in an increasingly specialized yet more complex world.

Further Reading

Notes on the Synthesis of Form, Christopher Alexander, 1964
Chuck Close: Work, by Christopher Finch, 2010


1 reply
  1. RG says:

    Per Charlie Munger, imagine trying to sell a beverage around the world at scale – Coca-Cola’s distribution system is a great example of this model of problem solving: utilizing a few syrup-making plants to serve independent bottling plants scattered all over the world. By deconstructing the problem and creating congruent sets product consistency and lowest cost are ensured across globe.


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