Graph Theory

  Prof. Alvarado
 MDST 3703/7703
20 November 2012
Business

• Maps can now use ~ in paths (!)
• Finish formatting chapters!
• Project Prompt now on the site
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
Mdst3703 graph-theory-11-20-2012
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?
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
Mdst3703 graph-theory-11-20-2012
Graph Theory
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.”
The German
astronomer
Kepler tried to
build a model of
the solar system
from it …




From the “Mysterium Cosmographicum”
(1596)
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
Is it possible to cross all of the bridges of Königsberg and cross each only once?
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
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
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
Mdst3703 graph-theory-11-20-2012
Mdst3703 graph-theory-11-20-2012
Mdst3703 graph-theory-11-20-2012
Mdst3703 graph-theory-11-20-2012
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
What about texts?
A Comedy of Errors, an early farce
Richard II, a history
Cymbeline, a late romance
Coriolanus, a history, battles as limbs
Antony and Cleopatra, a history, battles integrated
Henry IV, Part 1, central place of the Garter Inn
Henry IV, Part 1, Eastcheap Central
Measure for Measure, a room in the
prison central
Julius Ceasar, extremely linear
King Lear, linear then divided
Henry VI, Part 1
Henry VI, Part II
Henry VI, Part III
Anthony’s path through the play as a subgraph
Cleopatra’s path
Antony and Cleopatra
Mdst3703 graph-theory-11-20-2012
Clustering by number of single-incident scenes
Alignments of tragedy and comedy
Comedy and tragedy clusters
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)
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).
www.graphviz.org
What does Fish take issue with?
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)
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 …
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
Fish’s Criticisms

• In any event, nothing “licenses” one to make
  interpretive leaps from the data
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

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Mdst3703 graph-theory-11-20-2012

  • 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
  • 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.”
  • 10. The German astronomer Kepler tried to build a model of the solar system from it … From the “Mysterium Cosmographicum” (1596)
  • 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
  • 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
  • 22. A Comedy of Errors, an early farce
  • 23. Richard II, a history
  • 24. Cymbeline, a late romance
  • 25. Coriolanus, a history, battles as limbs
  • 26. Antony and Cleopatra, a history, battles integrated
  • 27. Henry IV, Part 1, central place of the Garter Inn
  • 28. Henry IV, Part 1, Eastcheap Central
  • 29. Measure for Measure, a room in the prison central
  • 31. King Lear, linear then divided
  • 35. Anthony’s path through the play as a subgraph
  • 39. Clustering by number of single-incident scenes
  • 40. Alignments of tragedy and comedy
  • 41. Comedy and tragedy clusters
  • 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).
  • 45. What does Fish take issue with?
  • 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

  • #5: Visualization use space and time to tell stories – provide images of causation and correlation