Jurgen Appelo used the double pendulum on page 42 of his Management 3.0 book to explain the differences between simple, complicated, ordered, complex, and chaotic. He defines the term Chaotic as “very unpredictable.” Like many of Jurgen’s definitions, they are *localized* to suit the needs of the story line.

There is no universally excepted definition of chaos. But almost everyone would agree on the following ingredients:

Chaos is an aperiodic long-term behavior in a deterministic system that exhibits sensitive dependence on initial conditions.

In this context, the phrase aperiodic long-term behavior means that the motion does not settle down to a fixed point or a periodic orbit. Since the double pendulum loses energy to the environment, after some time the motion does become periodic and it eventually stops at a stationary fixed point. In this sense it is only the theoretical double pendulum without energy losses that would really be a chaotic system.

Please read that last sentence again. It is critical. As well the “sensitivity” to initial conditions is a parametric measure in itself. The starting angle of the pendulum is one parameter. Low starting angles result in different “sensitivities” than larger starting angles. This is an exercise for students in the introductory classical mechanics class as an undergraduate in Physics.

A deterministic system means that the system has no random or noisy inputs. The irregular behavior is intrinsic and arises from the system’s non-linearity rather than from any noisy driving forces.

Please read this last sentence again. It is critical to understanding the definitions needed to describe the behavior of the double pendulum.

Sensitive dependence to initial conditions means that nearby trajectories separate exponentially fast, i.e. two identical systems set up together in the same way such that the initial conditions are arbitrarily close together will have their trajectories rapidly diverge. To make this more concrete, consider two trajectories, where at some time *t* the trajectories are at position x(*t*) and x(*t*) + d(*t*), then the statement of chaos would be that d(t) ~ d(0) exp [ L t] , where the average value of L is called the Lyapunov exponent, and if this is positive it means that the two trajectories are quickly separating from each other.

Why is this an issue in the management of agile software projects? Good question?

*Management 3.0* - and now #NoEstimates advocates - proffers a solution to a complex problem of managing the development of software. The book, while providing advice to managers on how to manage, mixes pseudo-scientific references and concepts – like the double pendulum – in support of essentially sound staffing and personnel management. I came to the book, through Jurgen’s himself. But on first reading I ran straight into what seemed like a collection of ideas that have no actual basis in fact. The double pendulum is just an example of this approach.

So here's the fix for these conjectures. There's a paper "Distilling Free-Form Natural Laws from Experimental Data," Michael Schmidt and Hod Lipson, *Science, Vol.* 324 3 April 2009, showing not only the *equations of motion *for the double pendulum, but a *machine* that can deduce these equations by observing the double pendulum in motion.

Here’s the core problem. When we can't get the analogies right, what else isn’t right in the foundational principles proposed by those suggesting we can't operate in the presence of uncertainty? If those analogies miss the mark on the underlying principles of these analogies, are the other suggested approached equally flawed? Maybe, maybe not, but for someone like me, trained and experienced in the application of approaches to solving complex problems, many of the fundamental approaches used in the book are simply muddled thinking. It’s too bad. A good editor, with experience in the analogies Jurgen uses could have established that they are just notional, analogies, or possible just anecdotal experiences. Instead Jurgen states them as the foundations of the principles of *Management 3.0.* In the same way the original posters of #NoEstimates state their case that decisions CAN be made without estimating, when in fact that violates microeconomics, managerial finance, and several other principles.

And of course, this plays directly into the #NoEstimates conjectures, based on even less credibility than Jurgen's management processes - minus the illformed analogies.

There is no principle stated to date by the advocates of #NoEstimates that supports the conjecture that decisions can be made in the presence of uncertainty with estimating the impact on the business of those decisions.