of Heart of Anima. This is a a 3D
graph with its front faces removed to
reveal internal structure. Model and
sculpture by Lee Gass.
choreographer and director of
Experiments, a dance production expressing
the essence of scientific creativity, suggested that
I mount a sculpture exhibition during our performances.
There was room for only one actual sculpture, so we
agreed that in addition to an exhibition of photos
of my work, I would exhibit The Granite
Madonna as a rotating laser light show
at the end of a long mirror.
Gail wanted two
things from her video interview
with me represented as posters in the photo
exhibit. How I described the movements involved
in carving stone reminded her of dancing. As dancer
and choreographer, she resonated with what I said
about carving stone. With that in mind, Gail
asked me to create the poster on movement
that I wrote about in On Moving
Forms Into Being.
Gail also found
what I said about graphs and
graphing interesting from a choreographic
perspective, especially 3D graphs that move.
With the idea that graphing connects science and
sculpting in mind, she asked for a poster on
graphing as well, and that’s what I’m
writing about here.
Gail Lotenberg is
a professional choreographer.
Before that, as this video preview of
Experiments shows, she was good at math
and science in school. They are still in her
mind, still in her bones, and still in her
dance and choreography. And as
she and I know, scientists can’t
live without graphs or
that pictures are worth thousands
of words. Any kid can tell you that. To a
scientist, graphs can be worth thousands of
pictures. It could take that many pictures just
to make a graph, and that many more to inter-
pret it. They help describe complex relationships
with few words and fewer pictures. They keep
Big Pictures and Details clearly in mind
and help us communicate more
deeply than without them.
Really good graphs
say what we’re about to say
before we say it, so to speak. Some-
times, one look at a graph and we don’t
even need words to get the picture – – –
the graph is the picture and we get it,
just like that. We still need details,
and graphs do that too. But
with Big Pictures
clearly in mind,
help us see Big Pictures.
That’s what a
graph can do. It’s what makes
pictures worth thousands of words
and graphs worth thousands of
pictures. What a lot of
words to save!
The point of all
this is that graphs illustrate
relationships that might not be clear
just from looking directly at data or reading
many words. The first thing first-year university
students need to learn to see in graphs is what I call
The Big Picture. Does the line go up, down, or sideways?
Is it straight or curved, concave or convex-up? If any-
thing changes over time, does it speed up, slow
down or reach a steady state? Humps.
Bumps. Things like that. How
many Big Pictures?
Big Pictures are
easy to see. Anyone can see
them. Everyone must see them to
understand detail. The shapes of curves
make all the difference, as do the shapes of
surfaces in 3D graphs. A simple example
of a 3D graph that moves is this video
of the South African flag waving
in a steady breeze.
programmed a computer
to make a surface wave up and down in a
wave pattern. Waves of a certain height, with a
certain spacing of crests and troughs, moving across the
surface at cerain speed and direction. The program
coloured and lighted this surface in certain
ways and displayed it from a
Coloured and lighted
like that, the graph represents
a South African flag waving in a breeze.
With different details, the same graph could
represent the surface of a pond with
waterstriders striding on it
(Walking on Water).
Even if all you had
was one static snapshot from
a moment in time, a graph like this still
shows the size, spacing, and axis of movement
of the waves. With the movement
in the video, the graph
A long thin
graph might show
the density of drivers on a
certain stretch of freeway, travelling at
certain speeds over certain periods of time. It
could display real data about real cars or be the
outcome of a model of driver behaviour. The graph
could be sound waves, vibrating windowpanes, drum
heads, eardrums or anything, really, with wave-
like behaviour that varies spatially and/or
changes over time. The only thing that
makes the graph of a flag a flag
is that somebody made
it that way.
Another kind of graph is this one about
hummingbirds that illustrates
A Story for Twyla Bella.
The graph tells
the following short story:
“An adult female
rufous hummingbird sat on
a perch at three different air
This result was
part of the work of my first
undergraduate research student at UBC,
Bob Purdy. The hummingbirds’ response to
temperature, as shown by the shapes and sizes
of their silhouettes, were remarkably uniform
both within and among individuals. With
the colours I added, Bob’s graph is easy
to understand even without numbers.
When it’s cold, hummingbirds
are a different shape, are
bigger, and perch with
are made of details and
they display details magnificently,
but they’re not as much about details
as about how details relate to other
details and how those relation-
ships make a whole. Graphs
are great for that.
I could go on
forever about graphing in
science, but I need you to see how
it relates to sculpting. Here are a graph
and a photograph of my basalt sculpture
Heart of Anima. The graph displays real,
measured data about the sculpture.
In this rendering
of the model I displayed the
convex and concave surfaces of the
sculpture differently. Dark, softly lit,
matte concavities. Polished gold
convexities in broad daylight,
reflecting a cityscapes.
As if the concavities
were warped sheets of graph
paper, I displayed the so-called isolines
or meridians that define them, like a webbing
to emphasize the forms. Note that in the image
at the top the web is on the convexities and the
concavities aren’t there at all. These ways
of graphing model surfaces emphasize
different things and inform me
differently about what
I’ve done and need
Bobbles in reflected
cities reveal bobbles in mirrors
that reflect them, whether the mirrors
are polished surfaces of real sculptures or
models of those surfaces. On broad surfaces
where curvature is low, the quality of reflections
is high and the model is accurate. They are poor near
upper and lower points; that is obvious in the image at
the top. Except those two problem areas and one
on the back, careful measurement showed that
the model was accurate to about a millimeter
everywhere else. That was accurate
enough for what I needed
and I continued.
Back in the
beginning, while Heart
of Anima was just a rock in my
stoneyard and I admired it for years
wondering what to make of it, something
in the shape of the rock grabbed my attention.
I simplified it and made it real. It wasn’t very
creative to let a rock tell me what to carve like that,
but I was fine with that. In terms of graphing,
what mattered was that as I ate into the stone
I found a system of very fine cracks. There
were only a few of them, and the deeper
I carved the more I feared for one of
the most beautiful stones I had
ever seen. I worried a
lot about it.
To stabilize the
boulder and hold it together,
I needed to insert long steel pins to tie
the sectors on either side of each crack
together and prevent the sculpture
from falling apart.
Pins had to
cross all cracks, not touch
each other, not touch the long central
mounting pin or its sleeve, and no pin could
break the surface of the stone. They had to be
invisible. But where did each crack go beneath
the surface and how could I pin it? There’s not
much room for steel in a rock that size, so I
needed a good plan for the holes for the pins
and the only way I could think of to
work all that out was with
a computer model.
Using Microscribe, a
mechanical 3D digitizer I’ve had for
many years, I built a 3D computer model
of my sculpture, a graph, late in its development.
In the image below, you look past the hip of the
real sculpture on your right to the model of
the sculpture on my computer screen.
Sculpture and model are at slightly
different angles of rotation.
Here is how I
made the model. On the surface
of the real sculpture, I drew a net of meridians
with coloured pencils, digitized points along those lines.
Then I constructed smooth curves through the points
of each line and lofted smooth surfaces
over the network of curves.
When I was
satisfied with the accuracy of
the model, I digitized the cracks where
they broke the surface and studied them. To
my delight, each crack was a flat plane. That greatly
simplified the challenge; I could extend what I called
“crack planes” through the model stone, slicing it into
various sizes and shapes of model pieces. Studying
crack planes revealed what the pins must
accomplish. I installed 6 long and 1
short pin through only 5 holes
in the surface of the
In addition to the
convex surface, this rendering
are an orange vertical 5/8″ mounting pin
and two blue 8″ x 1/4″ steel pins running through
the invisible inside of the stone. If I had shown
all the pins you would get the point that I had
to plan holes carefully. I could never
have done anything so precise
without the aid of
That might seem too
technical and scientific for art, but
I don’t apologize for that. I am scientist as
well as artist, after all, and model building was
all I could think of to solve the problem. I’ve used
computer models of sculptures in several other
ways as well, including the large basalt
sculpture Girlchild Reflected in
her Mother’s Eye, outside the
design of Girlchild is ridiculously
simple – – two large spheres with a spherical
bite out of one of them. With limited budget and
time, I experimented with the model to see how to
maximize the visual power of the sculpture
while minimizing the amount of
carving I had to do.
I could have
experimented with clay. But
working with the model was faster,
more accurate, and I could save as many
versions as I wanted and compare them.
The plan of action was simple: digitize
the column and the spheres, adjust
the spheres in relation to each
other and the column
until I liked it,
then make it
Another example is
The Granite Madonna. I didn’t
need a model of the sculpture itself, but
I needed to design a base of jet black granite.
Instead buying a circular base or cutting a rectangle
from a granite headstone, I wanted to carve a big, black,
sharp-edged crystal to contrast with the smoothly curving
light coloured sculpture above it but how big, how many
facets, what geometry? Would reflections from sloping
flat surfaces distract viewers? With a computer
model I could try ideas ideas out before
spending several days making
In this rendering, I
used a brushed gold matte surface
everywhere on the sculpture, with simulated
laser lines in different colours on the three surfaces.
That helped me visualize those surfaces, in
relation to each other and to the
faceted base below it.
sculpture and constructing the
model took a while. But once I had the
model of the sculpture I could hack out base
after base under it in minutes. I threw out 15
or 20 virtual black granite bases before I
found the one I wanted. After that,
it was simple to carve it
I hope this helps you
see sculptures as graphs and see
how sculptors can use graphs in their work.
The story of
Buzz Holling’s manta ray
sculptures in Heroes, Masters and Wizards:
Buzz Holling, provides another example of my use
of computer models in sculpting. Though Frank Spear
and the Pea Seeds doesn’t refer explicitly to graphs, Frank’s
hypothesis is quite graphable and he would have had to
graph aspects of it for me before I would get off his
back and agree that his explanation for the
phenomenon was brilliant.
The stories in
Architects of Their Own Education
are all about graphs: straight lines on log-
log graph paper expressing power laws. Hypotheses
were not about graphs or lines, but about the laws they
expressed. Arguments rested on how well hypothetical
power laws fit real data. All of that was evident in the
graphs. Walking on Water is about high school
teachers confronting the same sort of scientific
problem, again resting on the fit of hypo-
theses to real data, as evident in
certain kinds of graphs.
For a pivotal moment
in my development as a scientist that
relates directly to graphing, see Dan Udovic’s
audio-only comment and my reply
to him, at the end of the video
Grizzly Lake Story.
First published in the Vancouver Observer.
Edited January 2019