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.
About Tempo
Say you’re trying to derive some conclusion by looking at a purposeless model. Do you find it more convincing if
1) it’s complicated, so you didn’t twist it with your preconceptions by pruning important stuff away, or
2) it’s simple, so you didn’t have as much room to stuff your preconceptions into it?
I favor (2), myself. (Krugman is another favorer of (2), I gather.) You don’t seem to have mentioned Occam’s Razor anywhere.
This looks suspiciously like a false choice to me.
I think leaving things out can be as dangerous a mechanism for acting on preconceptions than putting them in.
Occam’s Razor is an independent axis I think. It determines elegance once you’ve determined scope of interest. Of course, elegant explanations tend to be generative ones as well, and open up new scope. Once you realize that “speed of light is a constant” is a good elegant compressor of the facts of the case around Michelson-Morley, you quickly realize that the model opens up new vistas in terms of scope, that you wouldn’t have even considered if you’d stuck with the non-generative phenomenological descriptions (Lorentz contraction formula).
Kepler vs. Newton is perhaps a clearer example. Newton is not just more compact in Occam terms, it is more generative because it opens up the space of parabolic and hyperbolic orbits, an explanatory attack on asteriods etc.
So a theory of generativity/fertility is needed to complete this picture I think. Occam is not as important. Generativity is also not the same as nominal falsifiability. If a theory only suggests a couple of falsification tests, but no new domains of imagination, it is hardly useful. General relativity is interesting for reasons other than predicting anomalies in the orbit of Mercury and gravitational lens predictions during eclipses. Those tests are actually quite uninteresting as implications of the theory.
In a way, all thinking is modelling. And to borrow your language this is a nice fertile appreciative model.
It certainly touches on an aspect of modelling behaviour that is frequently left out – intention. I also think there is a reduction-production axis in play. I could almost characterise this as a basic there-are-two-types-of-people-in-the-world dichotomy in the way humans think. I like to think of the kind of football play-books Aristotle and Plato would produce respectively. The first would be studying games and trying to understand the virtues of the players, the ball, and the game itself from which he would derive the principles that motivate the actions. The later would start with the formal rule book and seek the most ideal and perfect expression of those rules in action.
There is no comfortable pair of opposites for this in English. But I have observed models are generally produced with either a bias to empiricism or rationalism. They rationalists tend to be creative and productive, building elegant systems the test of which is more rational coherence than workability. The empiricists tend to be descriptive and reductive, being concerned with simplification and predictability.
To my thinking Lucretius is the father of both – an odd historically unique hybrid the first truly rational reductionist. He made up his entities – he had to, there was no observational technology that could get him even close to the phenomena he was trying to deal with. But for him there were simple basic forces at work to which the wonderful complexity of the observable world could be reduced. He cast off the need for intentional explanations, for a “haecceity of the system”, in favour of an explanation of the parts – of which the system is to him an “emergent phenomena” (Today’s language – not his).
So began the yin and yang of modern science. The empiricists model in the spirit of Lucretius’ reductionism – paring back their models to the least number of entities and relationships, seeking predictability and manipulation above all things. The rationals model in the spirit of Lucretius’ hypothesising rationalism – establishing elegant principles and producing edifices of ever increasing complexity that allows them to appreciate and test the power and efficacy of their ‘atoms’.
I like that you brought up management. In essence I think of today’s management theorists as being in the same position as Lucretius. There is a reductionist urge. They want to find the ‘atomic’ causes for the complex effect-systems in which the find themselves. But as yet human behaviour – even in the constrained domain of economic organisation – is too complex. They lack tools that will allow them to be sufficiently empirical. So they must guesstimate their ‘fundamental forces’ and build their models out from their. As a result, management theory, is, by and large, a very intelligent, well crafted mess – a dog’s bowl of competing theories, incomplete evidence and anecdotes.
I am an optimist however. I think we came as far as we did in the arts and sciences because, on average, we managed to yoke these impulses together. Or perhaps it just turned out that way in the inevitable unfolding of a fully determined universe, and we got lucky.
Thanks again.
Interesting. I hadn’t thought of Aristotle v. Plato, but I think the same point has been made using mythology as Dionysus v. Apollo.
It is more than rationalism and empiricism though. Both can be harnessed in service of either particularity or generality and towards either appreciation or manipulation.
Human affairs tend to yield better to particularist approaches, unless you are a government or some other actor who stands to benefit from certain aspects of aggregate behavior.
This reminds me of Schopenhauer’s big idea of “The World as Will and Representation.” http://en.wikipedia.org/wiki/The_World_as_Will_and_Representation
Wow, thank you. I’ve been thinking a lot about this dichotomy between models for a long time, but had never quite been able to formalize it. I’ve personally been working on a model more towards the appreciative side and was having trouble explaining it to others. Thank you!
-Luke
P.S. Book ordered almost solely based on enjoying this post