Project Title:
Quantifying Degrees of Randomness in Word Rhythms of Literary Works
Advisor: John Konvalina
Description:
When we read a poem, a novel, or a scientific article, our
intuition senses a qualitative difference independent of the meaning of the
words. Each literary work seems to have its own “rhythm” based on the sequence
of words used. Poems tend to be more rhythmic than novels, and novels tend to
be more rhythmic than technical scientific articles. What factors shape the
rhythm of the words, and can we quantify the observed qualitative differences?
Our goal is to isolate some of the factors that determine the rhythm of the
work based on just the structure of the word sequences. The formal measure we will use is the number
of characters in a word. Next, we will consider various literary works and
interpret them as time series. We will apply traditional linear methods, such
as Fourier analysis, as well as nonlinear methods, such as chaos theory and
fractal dimensions, to determine the degrees of randomness in the literary
works.
The
student will perform the following tasks:
A.
Become familiar with research in the literature involving the application of
linear and nonlinear mathematical methods to computational linguistics and text
processing.
B.
Become familiar with the Matlab software in order to
be able to write and run several programs related to time series analysis and
nonlinear modeling.
C.
Analyze and interpret the resulting
time series data from various literary works including poems, novels and
scientific articles. Apply the various entropy measures available in Matlab to determine the degrees of randomness in the
literary works.
D.
Create a final research report to be presented at
the MAM Symposium.
OTHER
REQUIREMENTS: The students interested in the project
above are expected to have had a course in time series and a course in chaos
theory and fractals. Experience with a computer algebra system, such as Maple
or Matlab, is essential.
NOTE: The results of this research will represent the core of a
research paper that later will be sent for publication to a suitable journal.