Dance · public management · complex systems
Choreographies of Complexity
Two workshop exercises translated into walking circles. One comes from Dejan, by way of dance and improvisational theatre. The other comes from Toby Lowe, a professor of public management. Each simulation follows a simple score, and the pattern that appears on the floor is not decided by anyone in particular.
What happens in a workshop like this is hard to picture if you were not in the room. A rule spoken in one sentence turns into forty bodies adjusting to each other, and the pattern that results lives only in the moment. This page uses creative code to make those behaviours visible and interactive: each score is rebuilt as a small simulation you can watch, pause and change, so you can explore what the participants felt from the inside by looking at it from above.
From the body to the space, from the space to the others
Dejan does not start with an exercise. First he invites each person to sense their own body and where they are. Then to observe the space, touch it, smell it. Only then does attention turn towards the other people.
Attention opens in layers, like concentric circles. In the simulation, each circle starts by breathing in place, then explores the room slowly, and finally begins to register whoever is nearby.
How this model works
The room is 16 × 10 m, drawn from above, with a faint line every 2 m like strips of dance floor. Each circle is 48 cm wide, about the width of a body seen from above. The three layers change every 7 seconds unless you pick one yourself.
- Body. Each circle stands still and its size pulses slowly. That is breathing, at a random rate of about 12–19 breaths per minute per person. There are no transparent circles and no lines.
- Space. The circles start walking very slowly (about 0.3 m/s, compared with 1–1.5 m/s in the free walk) and turn more often, which gives a wandering, exploratory path. Each circle gets a large transparent disc with a radius of 0.9 m, also breathing slightly. The disc stands for attention reaching out into the room around the body.
- Others. A bit faster (0.5 m/s) and less wandering. The disc shrinks to 0.55 m, and thin lines appear between any two people closer than 2.6 m, fading with distance. The disc shrinks because attention moves from the surrounding space onto the people.
The discs and lines are drawn, not simulated. In every layer a circle only reacts to others by not bumping into them, the same avoidance used in the free walk.
Forty people, each at their own pace
Before anything is synchronised, each person walks and stops whenever they like. A person walks at 1 to 1.5 metres per second, speeds up and slows down gradually (stopping takes less effort than starting) and steps around whoever crosses their path without much thought.
There is no shared rule here. This is the baseline: a system of individuals who only avoid each other.
How this model works
- Pace. Each person has their own preferred speed, between 0.95 and 1.4 m/s. Every few seconds they drift to a new speed between 70 % and 130 % of it, and ease towards it rather than jumping.
- Acceleration. Speeding up is limited to 1.3 m/s², slowing down to 2.6 m/s², so stopping takes about half as long as starting.
- Walking and stopping. Each person walks for 2–8 s, then stands for 0.8–3.8 s, chosen at random each time, independently of everyone else.
- Direction. The heading drifts with small random turns that fade out, so paths curve gently. Within 1.5 m of a wall, people turn away from it.
- Avoidance. Anyone closer than 1 m pushes you away. If someone within 1.6 m is almost straight ahead (within about 40°), you steer round them.
- Drawing. The trail shows where the person was over the last two thirds of a second, so it lengthens with speed. A ring means they are standing.
Click a circle and that person stops or starts. Notice that nobody else reacts.
When someone stops, we all stop
Dejan learned the basis of this exercise from people working in improvisational theatre. The rule fits in one sentence: when someone stops, we all stop; when someone walks, we all walk. Nobody leads, and anyone can start the change.
The interesting part is time. Nobody reacts instantly: you have to notice that someone has stopped, and people further away notice later. In the simulation each person takes between 0.3 and 0.6 seconds to react, plus a little more for every metre of distance. The result is a wave travelling out from whoever starts it, marked by an expanding ring.
How this model works
- Walking and avoiding. Same bodies as in the free walk: own pace, gradual acceleration, avoidance.
- Who starts. The group walks for 3–8 s or stands for 1.6–4.4 s. When that time runs out, one person picked at random starts the change. Clicking a circle makes that person start it instead.
- Reaction time. Everyone else follows after 0.28–0.6 s, plus 0.055 s for every metre between them and the person who started. Someone 10 m away reacts about half a second later than someone next to them, which is what makes the wave visible.
- Drawing. The expanding ring marks who started the change.
Click a circle to make that person the one who starts. Try someone in a corner and someone in the middle.
You only follow your group
In the second stage, Dejan forms small groups of three or four people. Each group walks and stops together, but only watches its own members. The groups do not stay together: they spread across the whole room, so your colleagues may be on the other side.
Dejan says he is interested in what people sense within the group, and then in slowly opening attention to the whole, so they notice that their small group influences the whole system and the system influences the group. The attention to the system slider models that opening: it is the chance that a group notices another group changing and copies it.
How this model works
- Groups. The 40 people are split at random into groups of 3 or 4, regardless of where they stand, so members start scattered across the room. Each group gets its own colour.
- Inside a group. Each group has its own stop and go timer and works like score 02, but people only react to members of their own group.
- Attention to the system. When one group changes, every other group that is in the opposite state notices it with a probability equal to the slider. If it notices, it copies the change, but more slowly than its own members would: 0.65–1.15 s plus 0.09 s per metre. Those copies are themselves changes that other groups can notice, which is how chains form.
- Links. "Show links" draws a line between every pair of people in the same group.
At 0 % attention, each group lives in its own world and the room looks disordered. Raise it slowly: past a certain point the groups start to chain together and, near 100 %, the system behaves like a single body again.
The groups stop being fixed
In the last stage, Dejan opens the possibility of changing groups. Here, when a person crosses paths with someone from another group, they sometimes join it and take on its colour and rhythm. Nobody decides how many groups there will be or how big they get.
Given some time, things appear that the score never mentions: groups that grow because they pass through busy areas, groups that run out of members and disappear, colours that dominate the room for a while.
How this model works
- Starting point. Same groups and rules as score 03.
- Switching. Each person has a chance to switch group, set by the slider (on average that many times per minute). When it happens, they look for the nearest person of another group within 1.9 m. If there is one, they join that group, take its colour (fading in over about a second) and adopt its walking or standing state. If nobody is close, nothing happens.
- Groups can vanish. The number of groups is fixed at the start, but a group whose last member leaves is empty and never comes back.
- Attention to the system. Works as in score 03.
Proposing a rule is not controlling the outcome
Dejan puts it like this: he proposes a score, but what unfolds depends on the people practising it. He is interested in the playfulness that arises when people have time to make mistakes, to get bored, to sense their own limits and those of the other group.
The circles only reproduce the structure of the score: who watches whom, and with what delay. They do not get bored, laugh, or invent variations. Even so, these thin rules already show the essential point: the global pattern comes from local interactions, and changing a single word of the rule (who you follow, how much attention you pay to the rest) changes the whole room.
Pick two people and don't tell them
This game appears in both transcripts: Dejan uses it as a warm-up, and Toby Lowe uses it so people can feel interdependence. Each person secretly picks two others and has to stay the same distance from both at all times. Since those two are also moving to follow their own rule, nobody can stay still for long.
Geometrically, all the points equidistant from two people form a straight line, the perpendicular bisector. Each circle walks towards the point on that line closest to where it is. Click a circle to see its two people, its line and its destination.
With Same person, same colour, every person who is being followed gets a colour and a ring in that colour. Each circle is split in two halves, painted in the colours of the two people it follows, so people who chose the same person share a half.
How this model works
- Choice. Each person picks two others at random, never themselves and never the same person twice.
- Target. All points the same distance from those two form a straight line, the perpendicular bisector. Each person walks to the point on that line closest to where they are now (the cross when you select someone).
- Perception. People react to where their two were about a third of a second ago, not where they are now. A small, slowly wandering error is added to each person's target, a few centimetres, like misjudging a distance.
- Speed. Up to about 1.15 times their preferred pace, slowing down as they approach the target.
- Personal space. Anyone closer than 0.9 m pushes you away.
- Removing someone. Everyone who was following that person picks a new one at random.
- Colours. With "Same person, same colour", each followed person gets a colour and a ring. Each circle is split into the colours of its two people.
Toby then asks who is responsible for the pattern of movement. The answer is everyone. If you remove one person, those who were following them pick someone else and the whole pattern changes, but you cannot predict how. That is why, he says, in a complex system it is impossible to hold any single element accountable for an outcome, whether a person or a team.
Compositional
An outcome comes from hundreds of factors at once. His obesity systems map had 108, and only four of them were healthcare.
Experiential
Each person experiences the same outcome differently, depending on where they sit in the system.
Dynamic
The system is always moving. What produced wellbeing twenty years ago does not produce it the same way today.
Governance
Nobody controls all the factors. As here: nobody controls all the circles.
Go back to your spot and play again
Toby asks everyone to memorise their exact position. They play once. Then they go back to the same spot, with the same rule and the same two people, and play again. Almost everyone raises their hand: the pattern was very different.
The same happens here. Every round starts from the same positions with the same choices. The only things that change are the things that change between humans: about two centimetres of error when returning to your spot, and small inaccuracies when judging distances. The previous round is drawn in grey; the current one in colour.
How this model works
- Rules. The same equidistance game as score 05, with the same pairs every round.
- Starting spots. Before the first round each person's spot is memorised. Every round, including the first, each person is put back within ±2 cm of it, as if returning to a mark on the floor.
- Variation. The few-centimetre perception error is on. Time also advances with the browser's frames, which are never exactly the same length, so this is a third small source of difference.
- Measuring. A round lasts 13 s. Every tenth of a second each person's position is recorded, and the gap is the average distance between where each person is now and where they were at the same moment in the previous round.
The consequence Toby draws is uncomfortable for classic evaluation. If the same system, from the same starting point, produces something different each time, you cannot build a reliable counterfactual: you cannot say what would have happened without your project. Baseline data describes a system that no longer exists, and a randomised controlled trial cannot control for every variable.
Where does the difference come from?
A computer is about the most repeatable thing there is. So if every round in the previous room is different, something in the model must be making it so. This lab lets you take those things out one by one.
The first round you play is the reference. Every following round starts from exactly the same spots, with the same pairs, and is compared to it. The chart below the room shows how far apart the two rounds are, on average per person, second by second. The scale is logarithmic: each line up is ten times larger.
How this model works
- Rules. The same equidistance game as scores 05 and 06. A round lasts 20 s.
- Fixed time. Unlike the other rooms, time here moves in identical steps of 1/120 s, whatever the browser does. Without that, perfect replay would be impossible.
- Reference. The first round is kept. Every later round is compared with it, not with the round before.
- Start error. Each person is put back somewhere within the chosen distance of their spot, in each direction.
- Start delay. Each person starts moving at a random moment between 0 and the chosen delay. The model handles this to a fraction of a step, so even 1 ms counts.
- Perception noise. The few-centimetre wandering error in judging where your two people are. Off means everyone judges perfectly.
- Collisions. The 0.9 m personal-space push. Off means circles walk through each other.
- Randomness. The model's "random" numbers come from a generator that is restarted with a new seed each round. With noise, start error and delay all at 0, nothing random is used, which is why the replay is exact.
Some experiments to try, in this order:
- Perfect replay. Start error 0, delay 0, noise off. Play the reference, then play again. The gap stays at exactly zero: the circles retrace every step.
- A tenth of a millimetre. Set the start error to 0.1 mm, about the thickness of a sheet of paper. With collisions on, the gap grows roughly tenfold every few seconds until it is wider than a body.
- Remove collisions. Same 0.1 mm, collisions off. The gap stays tiny. The circles walk through each other, but the room comes out almost the same.
- A thousandth of a second. Start error 0, delay up to 1 ms, collisions on. Nobody is out of place; some people are just a blink late. That is enough.
Unpredictable is not the same as undetermined
The model is deterministic. Its whole state is a list of numbers: where each circle is, how fast it moves, and which two others it follows. The rule is a fixed formula that every circle applies in exactly the same way. Time advances in identical ticks of 1/120 of a second, and every circle updates on the same tick. Even its "noise" is not really random: it comes from a pseudo-random generator that produces the same sequence every time it is given the same seed. Same inputs, same outputs, always. Step 1 shows it.
And yet steps 2 and 4 show that it cannot be predicted in practice. That combination has a name: deterministic chaos. In this model it comes almost entirely from collisions. Each time two circles meet, one of them has to go round the other, left or right. A tenth of a millimetre can flip that choice. The person who went the other way now pulls the two people following them along a different path, and those pull their followers, and so on. Small differences do not just survive; they multiply. To repeat a round you would need to know the starting spots with infinite precision.
Without collisions, equidistance on its own is smooth. Nearby starts lead to nearby outcomes, and the room tends to settle. It is still interdependent: nobody controls the pattern, and removing one person reshapes it. But it is not sensitive. Interdependence and sensitivity are two different properties, and a system can have one without the other.
What makes the real room complex
The workshop room shares the model's interdependence and its either-or moments, and it has far more of them: who you glance at, whether you hesitate, whether you laugh. But it also differs from the model in kind, not only in precision.
| In the model | In the room | |
|---|---|---|
| State | Positions, speeds and two chosen names. Nothing else exists. | Bodies, moods, attention, memories, and each person's idea of what the game is. |
| Rule | A formula, applied identically by everyone, forever. | An instruction each person interprets, and reinterprets while playing. Some bend it, some get bored, some cheat. |
| Perception | Exact positions, seen by everyone with the same 0.35 s delay. | Partial and personal. Each person sees a different room, which is Toby's experiential complexity. |
| Time | Fixed ticks. Everyone moves at once. | Continuous. Each body has its own reaction time, and it changes with fatigue. |
| Variation | Pseudo-random numbers that can be replayed. | Genuine variation: breathing, balance, distraction. |
| Repetition | A true reset. Round 2 is the same system as round 1. | No reset. People remember round 1, so round 2 is played by a group that has already learned. |
| Boundary | Closed. Nothing enters the room. | Open. Music, the facilitator's voice, someone arriving late. |
This is the deeper distinction. In the model, failing to repeat a round is a problem of measurement: with perfect knowledge of the start, you could predict everything. In the room, the system itself changes each time it runs, because its parts learn, adapt and rewrite the rules for themselves. Toby calls this dynamic complexity, and it is why the second round in his workshop is not a rerun but a new system.
The lab can also do one thing a real room never can. It can rerun the identical room with exactly one change and show what that single change did. That is a perfect counterfactual, the experiment Toby says public services are never able to run. The model makes it possible precisely because it is not a complex system in the full sense.
One last thought about what the circles can and cannot tell us. They are identical and interchangeable, reduced to a handful of numbers, and still they produce patterns nobody chose and rounds nobody can repeat. Interaction alone is enough for that. A room of people starts from there and adds everything the circles lack: each person's history, what the game means to them, what they learned in the round before.
The model shows how much complexity can come from interaction alone. The room shows how much more there is when the parts are people.
Get most people into this part of the room
Finally, Toby gives the system an arbitrary goal: get as many people as possible into one corner. The equidistance rule cannot be touched, but one more rule can be added. Which one would you propose?
In the room, someone suggested cheating. Toby remarked that, in some respects, that is the perfect example of a public service system. Another group suggested getting as close as possible to your two people. Try the rules and compare: each result is logged below.
- No rounds yet. Pick a rule and press Play.
How this model works
- Starting point. Same pairs and same starting spots every round (±2 cm), with the perception error on. A round lasts 16 s; the result is the share of people inside the 5 × 4 m zone at the end.
- No extra rule. Walk to the point on your equidistance line closest to you.
- As close as possible to your two. Walk to the midpoint between your two people. The midpoint lies on the equidistance line, so the original rule is still kept. Everyone pulls everyone together and the room collapses into a cluster, but nothing steers it towards the corner.
- Equidistant, but towards the zone. Stay on your equidistance line, but choose the point on it closest to the zone. As people move towards the corner, the lines of those who follow them move too, and the whole system drifts there. It is the only rule that steers the system without breaking the original one.
- Cheat. Equidistance is dropped. Everyone walks straight to the nearest point inside the zone.
Toby says the rules people propose say a lot about who they are. And he points to something the results log makes visible: with each iteration the group learns a little more about how the rules of the game work and how to nudge it towards what it wants.
Not controlling, but learning together
Toby's conclusion is that the task of organising, funding and governing public service is to help systems that are unpredictable, that nobody controls, and that give a different result every time, produce desirable outcomes more often. And that this is done by turning complex systems into learning systems.