Flock logic How groups move in nature by design and on stage

[Music]

hello my name is naomi eric leonard i am

professor of mechanical engineering at

princeton university in the u.s

and today i’m going to share with you

some of what i know about

flock logic how groups move in nature

by design and on stage with a focus on

my contribution to the making of a dance

piece

called there might be others the piece

is what’s referred to

as a structured improvisation

performance instructions and rules are

choreographed but it’s the dancers who

make compositional choices

in the moment as the dance unfolds on

stage

the project intrigued me because of my

interest and work more broadly

on the logic that explains how groups

move there might be others offered

a unique opportunity to explore that

logic

with highly trained artists who make

movement choices

with respect to constraints that we

could introduce and manipulate

by design in my research i

investigate and apply the logic of group

motion

to explain the remarkable movement of

groups in biology

and to enable similarly remarkable

movement of groups

in engineering but because groups in

biology engineering and the arts

seem maybe quite unrelated my

first goal today is to convince you that

there is a

common logic behind how these different

kinds

of groups move to do so i’m going to

talk specifically about

the logic behind the collective motion

of birds

of robots and of the dancers and there

might be others

so my second goal is to convince you

that mathematics

provides an elegant language for

abstracting out this logic

allowing us to unify our understanding

of the underlying principles of

collective motion across these seemingly

unrelated groups and providing an

opportunity to draw

inspiration from one type of group and

use it to inform how we think about

another

and this was decidedly the case in the

making of there might be others

so by logic i mean a set of rules

that govern how individuals in a group

respond to what they sense about their

neighbors

and their environment and how it is that

these responses lead to

the richly coordinated movement of the

group as a whole

so to appreciate the possibility of

there being a common logic consider

that the beautiful shifting pattern

of a flock of birds emerges from the

evolved responses of individual birds to

what they

observe of their neighbors and their

environment

and the beautiful shifting motion

patterns of a team of robots

emerges from the designed responses of

individual robots to what they

observe of their neighbors and

environment and the beautifully shifting

motion pattern of a group of dancers

emerges both from

choreographed and from artistic

responses of individual dancers to their

neighbors

and environment and this is particularly

striking in a rule-based piece like

there might be others and so so watch

this clip

from the new york city premiere of there

might be others in march 2016 and you’ll

see

these shifting patterns among the

dancers in time and in space and as you

watch consider what

rules and responses might be governing

those patterns

[Music]

and there might be others the dancers on

the fly compositional

choices involve jointly negotiating a

catalog

of defined movement modules with a set

of rules

the catalog concludes 44 modules each of

which corresponds to a composed

set of rules or a gestural idea

or a task some modules are boisterous

jump bean where the instruction is to

bounce and interact with fellow dancers

and other modules are

more meditative such as ore where the

body gently shifts forward

and backwards the performers are

instructed

to dance their way through most if not

all of the 44 modules

choosing in the moment the sequencing of

modules as well as how to introduce

juxtapose vary and abandon modules

in support of the aesthetic of the work

the rules which impose constraints on

the dancers choices

are designed explicitly to encourage the

dancers to experiment

with timing with spacing with

relationships

even with unpredictability and the

result is that the dancers through their

collective in the moment decisions

create and invent ever new beautiful and

complex

patterns and create moments of human

connection

so my contribution to the making of

there might be others was to

introduce new ways to experiment with

composition

using the logic of how groups move in

nature and by

design and so the first step in

understanding the logic is to recognize

that for birds

robots and dancers the choices that

individuals make

don’t just lead to beautiful patterns

they also allow groups

to manage the challenges of an uncertain

and changing environment

especially challenges that individuals

can’t manage on their own

and this is possible only if individuals

regularly and

frequently observe their motion of the

neighbor of their neighbors

and adjust their own motion in response

to what they observe

so the logic of group motion therefore

is built on a rule that describes how

individuals continually respond to what

they observe about the motion of their

neighbors

and furthermore to allow for the

richness of group motion

the rules should include dials such that

the turn of a dial

tunes the quality of the group motion

for example a dial might

refer to how many neighbors an

individual observes

and turning up the style which means

increasing the number of neighbors

improves the cohesiveness of the group

as it moves

so to motivate take a look at this

spectacular

display of starlings specifically notice

how sensitive

the group is to the motion of the

predator

and at the same time how cohesive the

group is despite the uncertainty

and presumably disturbances in the air

furthermore notice that this happens

and it’s all the more remarkable given

that the individual starlings have

limited attention what looks so

effortless is actually an amazing

balancing act

the individual birds use some of their

attention

to observe neighbors for coherence but

reserve

the rest of their attention to look out

for

predators this is the well-known

explorer versus exploit

tension which is ubiquitous in nature

and

design to exploit means to focus on the

well-known and to explore means to

check out the unknown but the two are

intentioned when resources like

attention

are limited so the second step in

understanding the logic of a group

in motion is to use the language of

mathematics to encode the rules

the dials and the explorer exploit

tension

the result are mathematic mathematical

equations that provide

a unified framework for investigating

the relationships between

rules individual responses and the

emergent group

behavior importantly we can use the

mathematics

to examine how turning dials tunes

features

of group motion so i’m going to

illustrate briefly

by describing application to the logic

of the in a study

of a flock of birds and in the design

of a team of robots and then i’m going

to show you how the results inspired

our novel approach to compositional

experimentation

in there might be others so birds will

flock

if every bird follows a rule to

regularly observe the direction of

motion of its neighbors and turn in the

average direction of these neighbors

so picture a single bird that makes a

sharp turn by the rule

any bird that observes this this uh the

bird that turned

will turn with it and then anybody whose

neighbors those birds

are among those birds who’ve turned will

turn with them and so on until the whole

group turns

cohesively the cohesion gets better when

each bird pays attention to more

neighbors

but this is in tension with exploring

for predators

which requires paying attention to fewer

neighbors so we let the number of

neighbors

be a dial the scientists who

filmed and studied the starlings in the

video showed that every bird pays

attention to its

seven closest neighbors but it was not

clear why the number seven

with my research group we hypothesized

that

seven might be the dial setting that

best balances the explore

exploit tension so using the mathematics

we derived a score

that quantifies how well a group

balances

the tension given a snapshot of the

birds and given a dial setting

so then using over 400 snapshots and a

dozen dial settings we found

that the score was greatest when each

bird pays attention to its six or seven

closest neighbors which matches the

number found by the scientists

and provides evidence in support of our

hypothesis with my students and

collaborators we use the same kind of

logic to design

strategies for a group of ocean-going

robots called underwater gliders

these were equipped with sensors to

measure ocean temperatures

salinity and currents and the goal was

to enable the robots to coordinate into

motion patterns that were mel well

matched to the

spatial and temporal dynamics in the

ocean so that the collected data the

collected measurements would best reveal

the ocean physics in monterey bay

california

however underwater gliders are limited

in how fast they can go especially

relative to

stiff currents and this creates an

explore exploit tension

a robot either moves to where currents

are known to be manageable

or it explores where currents have not

been well measured

so for each robot the rule was to

regularly observe

the direction of motion of its neighbors

but this time to move in the opposite

direction so as to allow the group to

spread out

over coordinated patterns on rectangular

tracks and

the dials in the rules govern which

robots were paying attention and

responding to which other

robots on which tracks and so with the

mathematics we showed how these dials

would tune the group motion pattern to

manage the changing environment given

the explore exploit tension so in august

of 2006 we programmed a group of six

robotic gliders with these rules and the

robots used them to move in and around

monterey bay for 24 days straight nearly

and here’s an animation of the

experimental results you’re looking

overhead

at the six robots each represented by a

color circle

the gray lines governed by the dials

show which

robots are responding to which other

robots and you can see how changing the

dials

tuned the motion patterns and despite

the fact that the gliders got pushed

around by the currents our design led to

an unprecedented

data set that has advanced understanding

of the coastal ocean

now an important lesson we learned from

our work with birds and robots

was that rules derived for agents faced

with an explorer exploit tension

provide a wide range of tunable

collective motion patterns

and so we sought out a constraint that

we could

impose on the dancers

by way of the performance rules and

there might be others to create and

explore

exploit tension and with it rich

compositional opportunities

and through experiments and rehearsal

and analysis

of the mathematical equations that

encode the rules we found a useful

constraint in imposing a strict limit on

the number

of modules that could be active could be

danced at the same time during the dance

piece

and there might be others a dancer

exploits when experimenting with an

existing module

and explores by introducing a new module

these are both creative choices but

their intention

if there’s a strict limit on how many

modules can be active at the same time

for example if the limit is three then

either the dancers

experiment with the three active modules

they complete one of the modules so that

they can introduce a new one

the limiting number of modules is a dial

and we turn the dial down to two to

heighten the tension

a two module limit means that a dancer

can only add

a new module if all of the dancers have

converged on a single module

so without any advanced discussion we

tried the two module limit

in rehearsal with the dancers and the

dancers did describe

feeling the tension and finding new

challenges and creative opportunities

we could also see this in the richly

varied

switching between exploring and

exploiting as well as

in provocative and playful playful new

moments that we saw them create for

example we saw

changes in who could influence the

pacing of a piece

any dancer could speed up the pace by

introducing a new module but now with

the limit any dancer could slow down the

piece

by taking their time to converge on a

single module

like the dancer on the floor is doing in

this photo

we also saw dancers invent ways to coax

others into a single module

like the dancers standing in a circle

are doing at that same moment

in one rehearsal a dancer gently folded

other dancers

from one of the two existing modules

into

another and then quickly introduced a

new module

and then a little while later another

dancer created a lovely

playful moment when she folded other

dancers without actually intending

to introduce a new module and so the

other dancers then in sequence

unfolded themselves we also use the

mathematical equations to find other

dials in the rules that could produce

and provide interesting tunability of

the qualities

of the collective motion patterns one

such dial

represented the dancer’s resistance to

switching between active modules

which when turned up slowed the pacing

of the piece

in rehearsal we used a drumbeat to

signal to the dancers

a dial up or down of this resistance to

switch

and we observed how we could effectively

this way tune the pacing of the piece

further more the dancers reported liking

these external cues like the drum beat

since it gave them a chance

to focus from inward looking to outward

looking with respect

to the group so there might be others

prospered from compositional

experimentation

informed by the logic of group motion

with the help of a mathematical

framework inspired by studies

of groups in biology and engineering and

my research

in biology and engineering has prospered

from

what we learned from working with highly

trained dancers about the logic of group

motion

i am grateful to choreographer rebecca

legere who led the collaboration

composer dan truman postdocs caihan

osinder and biswadup day

and an extraordinary group of dancers

and musicians

for exploiting their great talent and

taking a risk to

explore in the making of there might be

others

with that i thank you for your attention

and leave you to enjoy

one final clip from the performance

[Music]

you