So when we speak of defining aesthetics, creativity, computational intelligence, and so on,
it’s not a question of creating dictionary entries.
It’s really about creating fleshed-out theories.
And if we understand something, then we
should know how to, at least in principle, build
it. And if we don’t know how to build it, then
it’s questionable whether we really understand
it. So this art making as experimental philosophy is both a way to generate new theories and
concepts as well as a kind of empirical attempt
to verify theories and concepts through physical
instantiation.
So I wondered two things. First, in what
specific ways did they all look alike? And then
second, why in the world should solutions to an
optimization problem have any kind of common aesthetic at all?
For the first question, I did a statistical analysis of angles, lengths, areas, and so on. It turned
out that those distributions were very consistent across a number of different problem solutions.
For the second question further analysis
showed that optimizing the path for minimization had inevitable formal effects. Indeed, these
were the same effects that showed up as being
statistically significant.
PS: You express your thoughts on emergence—new,
unforeseen ‘products’, so to speak, of a system that
emerge following interactions between smaller components of that system—in The Traveling Salesman
(2008). Can you walk me through the process of devisFor example, I devised a simple geometric
ing and eventually executing the piece?
proof that given four points, and connecting
two pairs of points with a line segment each,
PG: The left-brain versus right-brain model of
the total length of the two line segments would
cognition is an exaggerated oversimplification,
always be longer when they crossed than when
but it’s a useful metaphor in this case. One day
they didn’t. Thus, crossed lines always indicated
I was studying evolutionary computing, and one a suboptimal path, and the optimal path would
of the sample problems was the traveling sales- not have crossed lines, and thus it would have
man problem. This is a canonical problem in
to create one single large shape.
optimization theory. The goal is to start with a
set of cities and then plan a route that visits evThe statistical analysis also showed that angles
ery city once and only once such that the total
close to 60-degree angles were favored. This
distance traveled is minimized. This presumably makes sense from the point of view of optimisaves the salesman time and gas money. This
zation because when connecting three points
problem gets exponentially more difficult as the with two line segments, sharper angles result
number of cities increases linearly.
in longer paths than connecting those points a
different way.
I was looking at a diagram of cities as points
connected by an optimally minimized path. At
The traveling salesman aesthetic became, for
some point, the right-brain aesthetics of the
me, a variable icon representing the way form
plot somehow pushed aside my left-brain techcan emerge from optimization. To present this
nical interest. The solution was, in fact, a very
result, I decided to paint the resulting shapes as
interesting-looking line. And as I looked across murals. Scale always matters, and at a scale that
a number of solved problems, they all had a
envelopes the body, the figure-ground reversal
common aesthetic despite the fact that the
of the image is emphasized.
initial points were randomly placed and spread
over areas of different shapes.
The murals are created in a site-specific manner in that an entire wall is used. In the comSo I scanned the page from the programming puter, the wall is populated with random points,
book, pulled it into Adobe Photoshop, and then and then those points are connected using a
filled in the enclosed areas with color. Aestheti- traveling salesman problem solver program. The
cally, I liked what I saw. There was a very strong resulting image is then projected back on the
figure-ground reversal effect. And oddly enough, real-world wall, the borders are outlined with
none of the lines crossed. A single maze-like
masking tape, and the shape is then painted
figure was always created.
with house paint.
SciArt in America December 2014
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