In my early training in mathematical and computational modeling, an idea was drilled into my head by many teachers: make your models as simple as possible. But somehow, I’ve always resisted this urging. I’ve instinctively gravitated to greater complexity; even intractable complexity. Sometime later in my career, I encountered the slightly more refined principle: start with the simplest model of the problem that you don’t know how to solve.
Still, I did not like the advice. Even with Einstein’s credibility behind it (“a theory should be as simple as possible, but not too simple”), something seemed wrong about the advice to me.
A few years ago, I found the key clue to the simplicity principle. A work colleague offered the principle: how you model something depends on what you want to do with the model.
This is the critical piece of the puzzle. Simplicity is important precisely in those situations where you hope to accomplish something specific. A purpose-driven, instrumental model benefits from maximal simplification. If you want to model an airplane to compute basic range, a simple point-mass model with drag coefficients will do. If you want to model an airplane to figure out aeroelastic stress thresholds where wings break off, a considerably more complex model is needed. If you want to compute how much paint you might need to paint it, a scale design of the paint job and an estimate of the surface area constitute the right model.
My instinctive preference for complexity made sense from the perspective of purpose. I like purposeless models. Or equivalently, models that exist before clear purposes do. It makes sense that such models are often more complex. It isn’t that I like complexity for its own sake, but that I like purposeless models, which are often complex. They help me appreciate something on its own terms, rather than through the lens of something I want to achieve.
This non-purpose (or universal purpose or meta-purpose) is appreciation. An appreciative model is a model you use simply to make sense of a situation. While they are not always complex, in the absence of a very elegant organizing insight that illuminates the essential nature of the thing, complexity is not avoidable. When such elegance is present, we often say the model is “intuitive” even when it is not. Einstein’s Special Relativity is an example of a deeply elegant appreciative model of the results of the Michelson-Morley experiment, but it is the opposite of intuitive.
Good appreciative models are fertile. They may not have been constructed with a specific purpose in mind, but they tend to inform the pursuit of most purposes in useful ways. They suggest lines of attack and simplification. Bad appreciative models are seductive without being fertile. They are often elegant and appealing, but go nowhere.
So in the quest for good appreciative models, it is important not to be seduced into a hopeless quest for such intuitive elegance. Appreciation needs can often be met by relatively complicated and ugly models. It is good to recognize elegance when you see it, but important not to get enraptured by it.
The opposite of an appreciative model is a manipulative model: a model optimized for a specific worldly purpose. Note that this is NOT manipulation in the sense of Machiavelli. This is manipulation in the unloaded sense of goal-oriented.
These terms are due to urbanist John Friedman, and are discussed in his book Planning in the Public Domain:
The social validation of knowledge through mastery of the world puts the stress on manipulative knowledge. But knowledge can also serve another purpose, which is the construction of satisfying images of the world. Such knowledge, which is pursued primarily for the world view that it opens up, may be called appreciative knowledge. Contemplation and creation of symbolic forms continue to be pursued as ways of knowing about the world, but because they are not immediately useful, they are not validated socially, and are treated as merely private concerns or entertainment.
On the spectrum from purely manipulative to purely appreciative, we can find many examples illustrating different mixes. A how-to instruction manual that teaches you how to set up your DVR to record programs, but conveys no appreciation for how the thing works is at one extreme.
At the other extreme are poetic musings on the human condition.
In the middle, you find framing models that highlight some broad aspect of a thing. They convey a certain amount of appreciation, but can serve as starting points for construction of more precise manipulative models. Dilbert cartoons are an example. They suggest a vastly more complex tacit, appreciative model of work and organizations than the reductive-manipulative ones found in most business textbooks (whose manipulative purpose has to do with management goals). They highlight the darker side of work. They help you appreciate the political dynamics of a typical workplace, and arm you with the ability to build manipulative models to (for example) navigate meetings better.
Closer to home, the models I describe in Tempo are primarily appreciative models of decision-making. I will be the first to admit that they are not particularly elegant.
Sometimes it is easy to get confused by the form in which an idea is presented. Boyd’s OODA loop looks like a system-and-process diagram, a classic way to capture manipulative knowledge. But it is actually a nearly pure appreciative model. This leads to a lot of unnecessary confusion. To eliminate it, all you need to ask is what is this model for? If the answer is not immediately obvious, the model is likely an appreciative one.
A key point to note about appreciative and manipulative models is that each can transform into the other. Through pruning of the unnecessary, and the addition of practical but arbitrary details that further a purpose but add nothing to appreciation needs (such as the specific value of a spring constant) an appreciative model can be turned into a manipulative one.
The reverse process is much harder. A manipulative model requires the addition of insight, the judicious elimination of arbitrary details, and inductive reasoning, to be turned into an appreciative model.
An excellent example is Pythagorean triples like 3, 4, 5 and 5, 12, 13. These were recognized as being useful in practical applications of geometry, such as architecture, long before the Pythagorean theorem was discovered in an an appreciative sense. In the latter form, it is basically purposeless, but it is the foundation of vast areas of modern mathematics, including all of trigonometry.