Mark Webb


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S-Curves for Trend Forecasting

Yes, I think it's an excellent article, especially the observation about constraints. If we can correctly identify which elements are constraining a system we have a path to return to exponential growth.

Still, we'll see articles lamenting that "despite how we've overcome Constraint X, growth hasn't returned." The world is multi-causal/multi-factoral, though. More than one factor can constrain growth. It is often an engineering problem, and focusing on the system as driven by rationally understandable forces is important. Otherwise the default seems to be to view trends as 'magical growth' and make illogical predictions based on that thinking.

In the case of growth in the computer hardware industry, where you have a veritable army of engineers focused on the problem, is it any wonder we continuously overcome constraints?

S-Curves for Trend Forecasting

If you want to slow growth, pick any limiting factor and apply pressure. One will do.

Sometimes a trend continues growing exponentially for a long time before bumping up against a limiting factor. The thing to remember about an S-curve is that if you plot it on a log scale the first half of the curve looks like a straight line all the way backward. That's because it's exponential growth at the beginning, so every new observation dwarfs all those that came before. Sometimes we spend a lot of time in exponential growth phase and people write articles about how it'll go on forever, and The Singularity, and whatnot. When you don't know the limiting factor, it's very tempting to fit your model to exponential growth, only to get burned later on.

S-Curves for Trend Forecasting

I think you'll always be working in S-curves if you're in a finite system. The trick is to be able to detect the rate-limiting factor. That's the factor that marks the inflection point between exponential growth and the beginning of the slowdown. For classic examples like bacterial growth that might be nutrients, space, elimination of waste, etc.

The hard part is determining whether you've considered all the rate-limiting factors involved. Going back to bacterial growth, if you think food is the rate-limiting factor and you predict your culture will continue to grow for six hours, you might be surprised when you hit an inflection point after three hours because waste products start killing bacteria off. This same principle can be applied in technology and elsewhere, where people often aren't even looking for rate-limiting factors and appear to assume exponential growth in a finite system.