Mdst3703 graph-theory-11-20-2012

Graph Theory

Prof. AlvaradoMDST 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

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

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?

A

B

C

D

This abstraction allowed Euler to see that one would need to have an even number of bridges to get on and off a given land mass without going over a bridge twice.

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

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

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 counts, the same.

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