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Volume 12, Issue 19;   May 9, 2012: Nonlinear Work: When Superposition Fails
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Nonlinear Work: When Superposition Fails

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Much of the work we do is confounding, because we consistently underestimate the effort involved, the resources required, and the time required to get it done. The failure of superposition can be one reason why we get it wrong.
Congestion on a U.S. highway

Congestion on a U.S. highway. One common example of the nonlinearity of systems is the traffic jam. At low densities, adding one more vehicle to the stream of traffic has no measurable effect on the speed of the other vehicles. But as density increases, traffic slows, until it reaches a state like the one shown. How can this be? This phenomenon occurs because of interactions between the vehicles. That is, the natural flow rate is a nonlinear function of vehicle density. Photo courtesy U.S. Department of Transportation.

More often than we'd like, our projects are late or over budget. Or we find that the problem we've tackled is much more difficult than we thought. We aren't stupid (though some might argue otherwise), and we aren't trying to gild lilies our build empires (though some might argue with that, too). Still, these things happen with such regularity that there must be an explanation.

Part of the answer might be that much of the work we do is of a nature that our minds have difficulty comprehending. One property that gives us trouble is nonlinearity.

For example, consider the issue raised by Fred Brooks in The Mythical Man-Month. If three people can complete a task in six months, many would suppose that nine people can complete it in two months. We now understand that this belief is unfounded, and that our expectations are rarely met.

To understand why, let's begin by defining linear work. Work is linear when the outcomes are directly traceable from, and scale with, inputs. When work is linear, we can successfully plan the outcomes before we begin, because we can predict the course of the effort. To make linear tasks go faster, we can divide them into parts that we execute in parallel, without risking complication.

For example, two identical, independent assembly lines can produce output at double the rate of one single line, assuming that their supply and delivery chains are also independent. A manufacturing process implemented as independent assembly lines is a linear process.

But In a system that doesn't
obey superposition, the whole
can be different from
the sum of its parts
nonlinear work doesn't follow this pattern. Although most of the work we do in project-oriented organizations behaves linearly in response to small adjustments, the nonlinearities dominate when we scale those adjustments to a size where we expect to derive large benefits. One attribute of nonlinear work that explains this phenomenon is its failure to obey superposition.

In a system that doesn't obey superposition, the whole can be different from the sum of its parts. In such cases, as we apply more and more resources, the yield per unit of resource can decline. In the case of Brooks's mythical man-month, this can happen because of increased need for management and communication, and increased difficulty in scheduling.

But superposition can fail for a wide variety of reasons. For example, when we decompose a problem into parts, and try to work on the parts separately, one task team might require — solely for scheduling purposes — that another task team take an approach that is less effective than it would have taken if it were free to act independently. We can easily generate numerous examples like this that show failures of superposition that confound our expectations.

In three weeks, we'll continue this exploration of the reasons why nonlinear work is so difficult to manage. Next in this series  Go to top Top  Next issue: Handling Heat: I  Next Issue

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