There are the usual reactions to George Box's quote about models...

.Essentially, all models are wrong, but some are useful

... to make the wrong headed position that we can't use models for our benefit.

Here's a better basis for our needs ...

*This model will be a simplification and an idealization, and consequently a falsification. It is to be hoped that the features retained for discussion are those of greatest importance in the present state of knowledge*

- A. M. Turing, "The Chemical Basis of Morphogensis, *Philos. Trans. Royal Soc., *London, Ser B, Vol 237, 1952, 37-72*.*

One of the features that distinguishes applied mathematics is its interest in framing important questions about the observed world in a mathematical way. This process of translation into a mathematical form can give a better handle for certain problems that would be otherwise not possible*.*

This is called *Modeling*. It combines formal reasoning with intuitive insights.

The simplest models can be powerful descriptions of the real world and at the same time demonstrate the naive assumptions of some self proclaimed thought leaders. Newton's laws of motion, formulated several centuries ago, provide an early example of mathematical modeling.

*F = ma = m dv/dt = dx ^{2}/dt^{2}*

This is a simple model where acceleration is described as the derivative of the velocity of the object being moved by the force. Note that the second derivative of the position of the object is now NON-LINEAR as all second derivatives are.

So the notion that we've all be taught to think in linear models* *is of course nonsense.

**But What Does This Have To Do With Managing Projects?**

The elements of projects, the processes used to manage them, the variables of cost, schedule, technical performance, and yes the people are non-linear by their very nature. No need to buy that notion that we've all been taught the world was linear and it's a new discovery it's not, unless of course you were asleep in the freshman physics class.

Not only that; all the world is a non-stationary stochastic process. This means everything is random and described by a random process whose probability distribution shifts in time. This really means *the thing that is causing the randomness changes the values it creates as time moves from left to right*. The weather is a nonstationary stochastic process. The stock market, the traffic flow in a major city, supply chains.

So if we are modeling a project, we must come to understand if we are seeking predictive outcomes and not modeling the underlying system as a nonstationary stochastic process, we're going to be disappointed with the outcomes of our model. We'll be late, over budget, and the thing we're building will probably not work as predicted.

We'll be using the naive interpretation of Box. *All models are wrong, some are useful.*

And oh by the way the quote from those who claim *all models fail* should be told to the designers of the very complex system of getting Curiosity on Mars, where many of the systems could only be modeled, not actually tested. And listen to the engineers as they talked about confirming their models worked when Curiosity sent back the first 64x64 picture of the dust settling with the message *I'm Here*.* *

Listen to the first words here. The forecast (model) miss distance was 232 meter over the planned landing. The landing spot was *modeled*. Then listen to how they abandoned an update to their *model* at minute 2:35, since the previous one was *within spitting distance* of the planned landed spot.

All the world's a model, it's just how much fidelity we need for our efforts and how much fidelity we want to search for or are willing to pay for.

**One More Thought**

If we go back to the opening quote from Turning and the Morphogenesis example, we can address a very common populist misunderstanding about *self organizing systems*.

There is a popular quote floating around

*Self-Organization is a process of attraction and repulsion in which the internal organization of a system, normally an open system, increases in complexity without being guided or managed by an outside source.*

The premise is there is organization without management. But of course like most populist descriptions of complex systems, they miss a fundamental concept. Those *repulsions *and *attractions* are GUIDED by the models, equations of motion, and rules of physics, chemistry, and biology. They are MANAGED by these rules.

Morphogensis is the process whereby form and pattern evolve in a biological system. There are two simple models for the purposes of this post. Both models start with an undifferentiated and spatially homogeneous distribution of some biological substance. This distribution represents an unstable equilibrium state, and in both models a slight disturbance permits nonhomogeneous spatial pattern to develop over time. This pattern *emerges* through the *rules of interaction* defined by physics and chemistry - in this example.

Read the paper and learn that the notion of *no external control* is a false analogy. There are always *rules and laws* for the interaction of the individual components of the system. We may not be able to see them, or even understand them if we saw them. But they are there. To be otherwaise would *defy the laws of physics*.

This is the challenge for using actual science analogies for what is very sketchy, untested, anecdotal, and possibly untestable opinions about how human systems work. Be careful. Human systems are complex, but when populist explanations starting with actual science enter in, take a deep breath, and put the models in the stack called *notional*. These models may or may not be useful. The irony of course, is the populist approach fulfills Box's statement, the models are wrong.

**One Final Final Comment**

In the populist world view, emergence has no mathematical basis for forecasting future states. In the science of emergence there are very useful models. Here's and example - Neural Networks and physical systems with emergent collective computational abilities, J. J. Hopfield (the father of Neural Networks).

The popularization skips over the underlying mathematics - for all the right reasons, since it is intractable to many outside the discipline.

But to ignore this when making pontifications of outcomes is sporty at best.