Flock logic How groups move in nature by design and on stage
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so
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
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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
like
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
or
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
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so
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you