1. Graph Theory
Prof. Alvarado
MDST 3703/7703
20 November 2012
2. Business
• Maps can now use ~ in paths (!)
• Finish formatting chapters!
• Project Prompt now on the site
3. Review
• Maps and Timelines used as devices for
visualizing information and generating ideas
• Spatial narratives, object stories Database
literature
• Maps -> Map of texts -> Texts of Maps
4.
5. These visualizations operate at the
border between narrative and data
Notice how we move from a map, to a
story based on a map, to a map of a
story …
How is this possible? What can maps
and texts possibly share?
6. Stephen Ramsay
Associate Professor of English at
Nebraska. Ph.D. English from
UVA. B.A. English from Rutgers.
Worked for IATH and the Rosetti
Project in the 1990s
Recently published Reading
Machines: Toward an Algorithmic
Criticism
9. The 5 “Platonic Solids”
are the only shapes you can
create using surfaces of the
same shape and size. Each
can be circumscribed by a
sphere.
The Pythagoreans
recognized that these are
the only the only regular
convex solids possible.
Euclid called them “atoms
of the universe.”
11. The Swiss German mathematician
Leonhard Euler (1705-1783) showed
that these solids all exhibited a simple
property.
If you count and compare the points
(or “vertices”) the edges, and the faces
of the shapes, you get the following
formula:
V–E+F=2
12. Is it possible to cross all of the bridges of Königsberg and cross each only once?
13. This abstraction allowed Euler C
to see that one would need to
have an even number of
bridges to get on and off a
given land mass without going A D
over a bridge twice.
B
14. Graph Theory
• Regions and boundaries can be represented
by “vertices” and “edges”
– AKA nodes and links
• Links can be represented as having a
direction or not
– Directed vs Undireced
15. Many things can be represented as
graphs – networks of points and lines
that abstract the relationships between
parts
By representing things as graphs, we
can transform them in interesting ways
16.
17.
18.
19.
20. How many colors
do you need to
create a map in
which no
adjacent regions
have the same
color? Graph
theory tells us
the answer is 4
42. So, Ramsay begins by counting and linking
scenes
Then he finds metrics for these graphs (e.g.
number of scenes, etc.)
He ends by correlating these metrics to
known genres
(comedy, romance, tragedy, history)
43. Metrics
• the number of unique scene locations
• the total number of scenes
• the number of single-instance scenes
• the number of loops (scene locations that
appear consecutively)
• the number of switches (consecutive scene
locations with an intervening location).
46. Fish’s Criticisms
• Quantitative approaches produce banal and
nearly tautological results
– “The low frequency of initial determiners, taken
together with the high frequency of initial
connectives, makes [Swift] a writer who likes
transitions and made much of connectives” (Milic)
47. Fish’s Criticisms
• These methods cannot discover things that
real critics can, such as the rhetorical use of
word and sound play
– Milton’s use of p’s and b’s …
48. Halfway through “Areopagitica” (1644), his celebration of freedom of
publication, John Milton observes that the Presbyterian ministers who once complained
of being censored by Episcopalian bishops have now become censors themselves.
Indeed, he declares, when it comes to exercising a “tyranny over learning,” there is no
difference between the two: “Bishops and Presbyters are the same to us both name and
thing.” That is, not only are they acting similarly; their names are suspiciously alike.
In both names the prominent consonants are “b” and “p” and they form a chiasmic
pattern: the initial consonant in “bishops” is “b”; “p” is the prominent consonant in the
second syllable; the initial consonant in “presbyters” is “p” and “b” is strongly voiced at
the beginning of the second syllable. The pattern of the consonants is the formal vehicle
of the substantive argument, the argument that what is asserted to be different is
really, if you look closely, the same. That argument is reinforced by the phonological fact
that “b” and “p” are almost identical. Both are “bilabial plosives” (a class of only two
members), sounds produced when the flow of air from the vocal tract is stopped by
closing the lips.
[…] In the sentences that follow the declaration of equivalence, “b’s” and “p’s”
proliferate in a veritable orgy of alliteration and consonance.
Even without the pointing provided by syntax, the dance of the “b’s” and “p’s” carries
a message, and that message is made explicit when Milton reminds the presbyters that
their own “late arguments …against the Prelats” should tell them that the effort to block
free expression “meets for the most part with an event utterly opposite to the end which
it drives at.” The stressed word in this climactic sentence is “opposite.” Can it be an
accident that a word signifying difference has two “p’s” facing and mirroring each other
across the weak divide of a syllable break? Opposite superficially, but internally, where it
49. Fish’s Criticisms
• In any event, nothing “licenses” one to make
interpretive leaps from the data
50. Ramsay’s Response
• Liberman’s response to Fish misses the point
• Fish does not understand that data too can
be read like a text
– In other words, what licenses us to make
interpretive leaps from texts?
• Correlations between form and content are
interesting and useful for redirecting research
Editor's Notes
Visualization use space and time to tell stories – provide images of causation and correlation
