Lagrangian and Eulerian Decision-Making

by Venkat on June 24, 2013

This metaphor is not for everybody, but if it works for you, it will probably be very useful.

Writing Tempo has sparked a lot of  fascinating conversations for me. People either seem to immediately get the decision-making model, or find it completely counter-intuitive and bizarre. Some tell me, “this is exactly how I think, thank you for describing the process clearly.” Others tell me, “nobody could possibly think this way, this is ridiculous.”

In reflecting upon the bimodal responses, it struck me that they were coming from two very different kinds of people. The ones who find the model natural are (predictably) somewhat like me: they do most of their thinking inside their heads with models. The ones who find it unnatural seem to do most of their thinking outside their heads by “watching machines work” as it were. What Myers-Briggs types refer to as the Ti vs. Te distinction (ask your friendly neighborhood Jungian to explain this to you). In terms of concepts in the book, this is the difference between narrative thinkers and situated thinkers.

Narrative thinkers tend to process by following a flow of causation, by keeping an evolving model of it going in their heads. Situationist thinkers focus on the logic of the events flowing through a particular static block of space and time: the one they happen to inhabit at the moment. It’s like following a case as it winds its way through the police investigation, different courts, judges and jurys, versus sitting in a courtroom all day and watching slices of different cases each evolve through a chapter locally.

Both are useful patterns of decision-making, and most people use some blend of the two, but with a strong bias. The two modes correspond to two distinct ways of modeling flow in fluid mechanics. In the Lagrangian approach, you follow the course of a little “parcel” of fluid as it moves. In the Eulerian approach, you watch the flow through the boundaries of a specific static “cell.” Boat perspective versus buoy perspective.

In my experience, Lagrangian decision-makers are much better at probing the internal consistency of decision-making processes, and are better able to detect errors in models when reality deviates from expectations. They are also better at long-term thinking when long-term thinking is possible at all.

Eulerian decision-makers are much better at empiricist thinking, detecting “coincidence is not correlation” and “correlation is not causation” errors. They are also much better at short-term thinking because they are more likely to notice situational coincidences and juxtapositions, because they are paying attention to an entire situation, and less subject to model or narrative bias. They are more used to dealing with juxtapositions of unexpected things.

But the general equality seems to break down a bit when it comes to action. Eulerian types are generally far more decisive and action-oriented, and get things done more effectively.  Their learned understanding of specific real situations is much richer than the modeled understanding of Lagrangians, who are just “passing through” along with the stories they are tracking. Eulerians are less derailed by chaos, while Lagrangian types tend to freeze into inaction when chaos increases too much. Greater capacity for armchair analysis is the consolation prize for us Lagrangian types. Only very rarely in history are “flow conditions” such that Lagrangians have an action advantage.

The fluid-flow analogy suggests a reason why this might happen. When flow gets turbulent, the fluid mixes a lot. To properly follow a “parcel”, you have to let it expand as flow lines diverge and churn. This means there is more fluid in your parcel than you started with, more “noise.” Eventually you are trying to analyze world hunger — the entire body of fluid.

But the Eulerian static parcel stays the same size. It just bleeds causal structure and gets more entropic. The action gets a lot more random and choppy, but still tractable in size. It is also easier to shrink what you’re paying attention to when things get complex — it’s called focusing – than it is to reduce the ambition of a model you’re tracking (generally called pruning).

So if there is a bias in Tempo, it is that I have written it for people who are fundamentally weaker at decisive action. Becoming aware of the nuances of this distinction has actually improved my situational decision-making skills, and I now get less anxious when I am in situations that are full of arbitrary juxtapositions of unrelated causal flows that are interfering with each other.

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