A discrete computational aesthetics model
for a zero-sum perfect information game
PhD Thesis Abstract by Mohammed Azlan Mohamed Iqbal
One of the best examples of a zero-sum perfect information game is chess. Aesthetics
is an important part of it that is greatly appreciated by players.
Computers are currently able to play chess at the grandmaster level thanks
to efficient search techniques and sheer processing power. However, they are
not able to tell a beautiful combination from a bland one. This has left a research
gap that, if addressed, would be of benefit to humans, especially chess players.
The problem is therefore the inability of computers to recognize aesthetics
in the game. Existing models or computational approaches towards aesthetics
in chess tend to conflate beauty with composition convention without taking
into account the significance of the former in real games. These approaches
also typically use fixed values for aesthetic criteria that are rather inadequate
given the variety of possibilities on the board.
The goal was therefore to develop a computational model for recognizing aesthetics
in the game in a way that correlates positively with human assessment. This
research began by identifying aesthetics as an independent component applicable
to both domains (i.e. compositions and real games). A common ground of aesthetic
principles was identified based on the relevant chess literature. The available
knowledge on those principles was then formalized as a collection of evaluation
functions for computational purposes based on established chess metrics.
Several experiments comparing compositions and real games showed that the proposed
model was able to identify differences of statistical significance between domains
but not within them. Overall, compositions also scored higher than real games.
Based on the scope of analysis (i.e. mate-in-3 combinations), any such differences
are therefore most likely aesthetic in nature and suggest that the model can
recognize beauty in the game.
Further experimentation showed a positive correlation between the computational
evaluations and those of human chess players. This suggests that the proposed
model not only enables computers to recognize aesthetics in the game but also
in a way that generally concurs with human assessment.
About the author
Dr. Mohammed Azlan Bin Mohamed Iqbal – pictured above
at his university's convocation ceremony – is 31 years old and has a bachelor's
and a master's degree in computer science from Universiti Putra Malaysia (Selangor,
Malaysia). For the last seven years he has worked as a lecturer in the College
of Information Technology, Universiti Tenaga Nasional (Selangor, Malaysia).
The last four of those were spent as a part-time student, doing his Ph.D. in
computer science – specifically in the area of computational aesthetics,
a sub-field of AI – at the University of Malaya (Kuala Lumpur, Malaysia).
Azlan doesn't have an official chess rating, but he puts himself, conservatively,
on the level of a club player. He also enjoys reading and playing the piano.
We asked Azlan to tell us more about his career and his doctoral research.
He wrote:
I had always had a keen interest in chess, playing actively since I was eight,
and intended to explore the possibility of computers "recognizing"
aesthetics (i.e. beauty) in the game. There are many books on chess outlining
the various characteristics or features that made chess combinations and compositions
beautiful, e.g. economy, sparsity, chess themes. I wondered if computers –
now playing at the grandmaster level on personal computers – could also
be made to "see" beauty in the game like human players do.
One application of this might be the automatic discovery of aesthetic "gems"
that, given the massive game tree, would perhaps otherwise lie undiscovered
for centuries. I compiled a list of these "aesthetic principles"
based on the literature and developed formalizations (i.e. evaluation functions)
for them. Instead of the typical approach of deriving weights for these aesthetic
principles, e.g. using an artificial neural network, I opted to design their
formalizations from the "ground up" based on the game rules and
using "building blocks" that were consistent in the game, i.e. the
board squares, pawn unit and piece unit from which "higher" properties
such as distance, piece value and piece count could be derived; especially
since, in my experiments, I was going to make comparisons between real games
and compositions in order to isolate the distinguishing aesthetic component.
Previous work in the area, going back some 80 years, was comparatively rudimentary
and lacked experimental rigor when it came down specifically to aesthetics.
Over two years, I coded a program called CHESTHETICA, which I still work on,
that could test my somewhat complex evaluation functions within the scope
of mate-in-3, and managed to show that aesthetics in the game could be identified
"mechanically". I also showed that the computational evaluations
correlated positively with human aesthetic perception in the game.
Even though there may be philosophical objections as to whether or not aesthetics
can be defined in the first place, much less estimated using mathematical
formulas, my research suggests that a computer can indeed be programmed to
identify combinations and compositions, at least within the specified scope
of mate-in-3, that the majority of human players with a reasonable knowledge
of the game would likely consider beautiful. It was not intended to "predict"
precise human player aesthetic ratings, even though chess players in general
might be able to better (and with more consistency) articulate why they find
a certain chess combination beautiful than, say, art critics would be able
to about a particular painting.
The research can therefore be seen as a first step toward pushing the boundaries
of what computers may be capable of in terms of aesthetics; at least in chess.
I am still researching the area actively and will also be working with a couple
of other researchers to see if my proposed aesthetics model can be adapted
for use in chess endgame studies, potentially to aid (not replace)
tourney judges.
Personally, it does not matter if the computer "knows" what it
"sees" is beautiful or not; just like it does not "know"
it is playing grandmaster-level chess. Such machines can still be beneficial
to humans. I did not set out to simulate human consciousness, as might have
been implied, but if computational aesthetic "perception" one day
turns out to be a component of that, I have no objections.