Lee’s Stories

Lee’s Stories

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posted on July 23, 2016 | Teaching and Learning
Perfect Circles

Luis Sobrino in his kitchen at home
making perfect


One great pleasure
of working in UBC’s
Science One
Integrated Sciences Programs is to
observe and interact with colleagues from
other science disciplines
in the classroom.  For
the one who is ‘up’ in front, colleagues’ engage-
ment brings surprise, uncertainty, enrichment,
and very often challenge.  And
engaging in
others’ teaching sows seeds for growth
in our own.  That is one of many
rewards of real
time team

Here is an example.

Luis Sobrino
was the first physicist to
teach in in Science One, where he
taught two years before retiring in 1995.
Many things about his teaching were superb.
He was wonderful to work with and fascinating
to observe,
and his articulate English prose, delivered
in the accent of his birthplace in Cadiz, Spain, inspired
me to use my own language more mindfully.  His
stories about his hero, Galileo, captivated
me. They encouraged me to use more
stories  from the history of
my own discipline.

His nearly
perfect perspective drawings
on the blackboard amazed me, especially
since so many teachers’ drawings done in the
heat of the moment, or carefully, are horrid. Luis
appeared to sketch them casually with no thought
or planning, but no student ever misunderstood any-
thing in any of his drawings.  If
you don’t already
know it, physicists and mathematicians draw a
lot of circles.   Most must merely call their
drawings circles
 just as biologists
must label their drawings fish or
rats so we know what to
see in them.

Luis’ circles
were perfect.  They had no
corners, flat places, innies, outties,
or any other irregularities (their radii
were constant),
and it was impossible to see
where their ends met.  They were perfect and
everybody knew it, including Luis, but didn’t
talk about it. 
Over the months I marveled
at his circles.  As a biologist, I wondered
how he made them and  how he came
to make them so well.
Slowly, I
realized something significant
about his  circle drawing
behaviour.  It appeared
stereotypic to me.

Same starting place,
same speed, same direction, same
fairly large size that engaged his entire torso
in the drawing and allowed everyone in the room
to view both the result, the circle, and Luis Sobrino’s
perfect circle-drawing performance.  T
hat told me
when Luis drew circles, he engaged the same
muscles in the same way and the same
sequence every time , and it
gave me an idea of
something to do
in class.

One day
at the start of the class,
before anyone said anything serious,
I asked the class to tell me the difference
between ballistic and guided missiles. After a
few minutes’ discussion among themselves, they
realized that ballistic missiles are Newtonian
particles in motion.  Once moving, their mass,
speed, and direction of motion determine
where they will land.  Guided missiles
tune direction during flight, usually
using information about where
they are in relation to the
target to guide the action.

We talked for
a while about what would
have to be known to aim ballistic missiles
accurately or tune trajectories of guided missiles
and how missiles could get it, and
when I was
sure they ‘got’ ballistic vs guided,
I gave a quick lecture about
the organization
of behaviour.

In 1974,
Ernst Mayr argued that
animals likely don’t control complex
actions by controlling each component
act independently.  That would require vast
processing power, make coordination difficult,
and be too slow to work in the real world.  Instead,
he thought, they package actions into complete
sequences he called behaviour programs, and
control them as coordinated wholes.  Behaviour
programs vary in openness to modification
during execution, and he suggested
two kinds of factors influence
that plasticity.

First, he expected
short-lived animals with little
opportunity to learn from experience,
to have relatively closed behaviour programs
that may even be specified genetically.  Similarly,
communicative behaviours like courtship, which
must be interpreted and responded to correctly
by other individuals of the same species, are
relatively stereotyped and closed

to real-time modification.

In contrast,
because foraging for food
and avoiding predators must be
performed under widely varying conditions,
it must be open to modification, especially
in long-lived animals who learn from experi
to execute the same basic programs many
If predator and prey animals
had words for things like this,
“Chase Sequence” would
a good one.


We discussed
a few examples of open
and closed behaviour programs,
then I asked whether anyone had noticed
anything interesting about Luis’ circle-drawing
The class lit up and quickly agreed that
Luis drew the most perfect circles anyone had ever
seen.  Luis beamed proudly.
When I asked them
to predict whether that action was guided or
ballistic, all also agreed, including Luis,
it must be guided to be so good.

It was harder
to agree on a way to test
that hypothesis.  Someone noted that
by Mayr’s definition, guided programs must
be open, and suggested probing them
ally with various
perturbations.  When a student asked
Luis to draw a perfect circle slowly and deliber-
ately, he failed and was surprised and
visibly embarrassed by that.

gave them the
sense they knew what
to do as scientists, so I turned
them loose in teams to devise and per-
form tests of their own circle-
drawing.  They
tried slow circles, fast circles, backwards circles,
upside down circles, and wrong-handed circles.
Overwhelmingly they concluded, again to
everyone’s great surprise, that Luis’
circle-drawing, and theirs,
was ballistic.

In a short
concluding discussion,
we wondered about the structure
of ballistic circle-drawing programs,
and wondered how they came to be ballistic
instead of guided. We tried to remember what
it had been like as kids to learn to draw circles.
Some described the head-drawing behaviour
of younger siblings, which seemed guided.
That led us to wonder whether programs
grow progressively more ballistic
with practice, and to wonder
how that happens with
no conscious control
or awareness.

The discussion
continued informally for
weeks outside of class, and I
gave interested students copies
of a paper I had published on a related
Luis was not pleased that for the
next several weeks he was too self-
conscious to draw perfect circles.
Eventually he returned to his
normal perfect style
and forgave me.

In a talk
I gave at a national
convention of educators,
about Stories
, I told a favourite Luis Sobrino
story, about Galileo discovering the
concept of momentum in
a coffeehouse.

In a book
chapter I wrote about
surprise, Behavioural Foundations
of Adaptation
, I discussed Mayr’s notion
of behaviour programs at length,
including their development
and control 

In editing,
I realized that the
using the idea of behaviour
programs in Perfect Circles is a
perfect example of the value of theory.
No one has ever seen a behaviour program.
Mayr made up the idea to help understand
something.  Others find it useful in the
same way.  It is a figment of
Mayr’s imagination.

Edited January 2019

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