Lagrangian and Eulerian Decision-Making

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.

Get Ribbonfarm in your inbox

Get new post updates by email

New post updates are sent out once a week

About Tempo


  1. Second edition material?

  2. I might be wrong but I categorize myself as neither, I see some sort of fuzzy big picture with a few “hard points” here and there, i.e. some patterns which more reliably inform on the situation when spotted.
    Though I am not that much “action oriented”, which may explains…
    Nevertheless your model fails here ;-)

  3. Count me among those who find this metaphor useful.

    Another way to think about it is that Lagrangian decision makers naturally place decisions in context, and therefore care more about meaning, whereas Eulerian decision makers are more concerned with the literal internal logic of the situation in question.

    The challenge for the Lagrangian decision-maker is to find stable boundaries to prevent scope creep. I found it much easier to act decisively when I had a traditional 9-5, i.e. when I had a firm boundary between work life and personal life. Within a constrained decision-making environment I believed Lagrangian thinking to be an advantage because it was easier for me (as compared to many of my coworkers) to act decisively, with the confidence that the chosen course of action would be appropriate given the broader contextual objectives.

    But without those natural boundaries it is easy to get caught up in developing models for their own sake rather than as a guide to decision making. One reason is that unbounded models are more intrinsically interesting…at least for the Lagrangian type. A bounded model is boring and therefore naturally lends itself to utilitarian usage.

    On the upside, Lagrangian decision-making does make it much easier to spot the kind of tasks that lead someone to be busy but not productive (urgent but not important). Lagrangian types are probably better at acting opportunistically whereas Eulerian types are better at acting intentionally (willfully).

    This also relates to the dual-mind limitation that I’ve written about several times ( and If we accept that it impossible to engage in performance, learning, and meta-learning all at once, then a bounded environment focuses attention away from meta-learning and onto performance and learning. And a Lagrangian approach applied to a performance/learning environment (e.g. Boyd types) may outperform the Eulerian approach.

  4. When an individual appropriately uses their two eyes to integrate a singular visual 3D perception of the world they transcend a limitation of each single eye. Likewise when one uses the two thinking modes you described in a singular integrated way that puts together the different perspectives of thinkers one transcend a limitation of each single being.

  5. Alexander Boland says

    I think this may cover *exactly* the same theme as Rader’s post on “The Dual Mind Problem.” (I mean that in a good way–it’s good to see consistency in all these different approaches.) Metacognition is more adaptable and helps deal with certain ambiguities, but it comes an incredible amount of cognitive/epistemic overhead.

    One thing that’s important to note is that the Eulerian thinkers are doing one of two things in their pursuits:

    a) Working in a domain where there is a static backdrop with stable rules (chess, firefighting, software engineering, musical instruments, etc…)

    b) Working in a domain where there is wild randomness, BUT, not being held back by meta-cognition. This means that 99% of them may fail (and retreat to some more Eulerian-friendly career), but we see the other 1% who wildly succeed. We want to know their “secret”, but it was really that gambling was the necessary (but not sufficient) condition and they were not held back by too much meta-cognition.

    This always leaves me wondering whether Lagrangian thinking has any true upside or if we just want to believe that insights are more than noise (I say this as someone who is your “typical reader” to a T.) The “cheap trick” concept frames them as a fulcrum, but of course it’s hard to know how it can be verified as such.

    At the moment, I’m starting to think that most insights are not actually fulcrums, but that in the right domains, it’s beneficial to have 99 cheap tricks that don’t work and 1 cheap trick that does. So Lagrangian thinking may work in the case that it’s used in a way similar to Nassim Taleb’s investment strategy.

  6. This does look like a fertile analogy and a line of thought you should expand. While it is the N (as opposed to the S) type that makes someone look for patterns, your take on Te vs Ti and deciding based on the coherence of patterns is intriguing.

    I guess Lagrangians (it’s shorter to say that and I like the sound of it) would like and do more of meta learning and happily deal with multiple models and changes to model than Eulerians, who may adopt a pattern or a technique and stick to it. Perhaps Eulerians temporarily agonize over a decision but don’t look back afterwards whereas Lagrangians keep connecting the dots and try to learn from history while not too worried about the outcome of a decision taken.

    Are Lagrangians less prone to very high levels of happiness or sadness than Eulerians? While also being a little lower on average on the satisfaction/happiness scale than the Eulerians?

    • Alexander Boland says

      Personally I’d assume that Lagrangians are manic-depressive due to swings between the thrill of possibility (evolving mental model) and the stress of metacognition (plus the frustration of success not being so straightforward.)

      Eulerians by contrast probably get a nice trickle of satisfaction since they’re not too skeptical of what they do, but don’t have the mania of constantly thinking about the next big possibility.

  7. I tend to flinch/shudder with dualistic archetypes presentations… that juxtapose alternatives as an either/or, especially when there exist better story-lines with emergent properties; the total is more than the sum of the parts kind of thing. Understanding how particles move, how the parcel exists and the interaction between them can lead to a much broader understanding of each individual part with an overall enriched shoreline. The map, the territory, and the distinctions of each of them can facilitate exploring and transforming them each. The tree, the forest, and the complete emergent ecosystem. Working in the abstract to solve the problem can be a practical adaptation and the most efficient way to deal with the particular situation.

    Yea it can require an increased amount of cognitive/epistemic overhead to get going, which can be recuperated by the increased effectiveness. Consider sharpening an ax before cutting the wood kind of situation. Well that of course assumes that one has got an ax to sharpen… and wants to cut the wood… one could be in a situation where one first has to procure the ax to sharpen (or procure a chain saw)… and even require to cultivate the trees to get the wood.

  8. Ignore N at your peril.

    A well-developed N will “run” repeated iterations of both and bound solution space.

    “Eulerian types are generally far more decisive and action-oriented, and get things done more effectively.”

    Nothing beats watching teams of S get themselves trapped in local maximas and hunker down while N’s ride in and save the day. Once they’re out, they knife the N’s (who never see it coming) and go back to clearing minefields.

    As long as you can ensure neither side ever decisively wins, watching this unfold is one of life’s smaller pleasures.

    • In the interests of full disclosure, I believe Ti and Te are smokescreens. On the flip side, I suppose my views on MB are not exactly mainstream.

      “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”

      I read: “Since I have enough N to admit that a F bias infects Tempo, I have, at minimum, summoned enough J to not be off-putting to actual Js. Becoming self-aware of the nuances of F has actually improved my J, and I now get less anxious when I am in EJ situations that are full of arbitrary (typically social) juxtapositions of unrelated bullshit that I must process like a traffic-judge.”

      Sorry. I always feel mildly bad dinging anything you write, since I’m typically (always?) 90% on the train with you. Hopefully it’s appreciated in its spirit.

      • Abbreviations and acronymania ensures you are only talking to yourself, hope you enjoy it…

  9. N S Ti Te MB F J Js EJ… can ensure confusion… well at least it did on me… I am sure that the loosing side longs for neither side to ever decisively win… even when the wining side has long realized who eventually won… besides the crux of the situation may be in something else… like learning a thing or two, passing a good time, enjoying the moment…

    Its a bit humorous the schemas addictive thinkers* will resort to in order to keep their delusional logic going… ‘watching this unfold is one of life’s smaller pleasures’.