Nonlinear systems occur when “outputs of a system cannot be expressed in terms of a sum of inputs, each multiplied by a simple constant.” The quote comes from John Brockman, Ed., This Will Make You Smarter (Harper Collins 2012) at 184, a piece on scale analysis. If a formula could capture the output of law departments, life and management would be so much simpler: X times number of lawyers plus Y times number of paralegals and Z times other staff plus A times the dollars spent on outside counsel equals output! For any given law department, its four inputs multiplied by their respective constants would capture it all. Not so, of course.
Law departments are non-linear, with complexity the dominant characteristic: “Unpredictable variability, tipping points, sudden changes in behavior, hysteresis – all are frequent symptoms of a nonlinear world.” We can hold out no hope for a linear function that describes law departments.