Mdst3703 graph-theory-11-20-2012


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  • Visualization use space and time to tell stories – provide images of causation and correlation
  • Mdst3703 graph-theory-11-20-2012

    1. 1. Graph Theory Prof. Alvarado MDST 3703/770320 November 2012
    2. 2. Business• Maps can now use ~ in paths (!)• Finish formatting chapters!• Project Prompt now on the site
    3. 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. 4. These visualizations operate at the border between narrative and dataNotice 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?
    5. 5. Stephen RamsayAssociate Professor of English atNebraska. Ph.D. English fromUVA. B.A. English from Rutgers.Worked for IATH and the RosettiProject in the 1990sRecently published ReadingMachines: Toward an AlgorithmicCriticism
    6. 6. Graph Theory
    7. 7. The 5 “Platonic Solids”are the only shapes you cancreate using surfaces of thesame shape and size. Eachcan be circumscribed by asphere.The Pythagoreansrecognized that these arethe only the only regularconvex solids possible.Euclid called them “atomsof the universe.”
    8. 8. The GermanastronomerKepler tried tobuild a model ofthe solar systemfrom it …From the “Mysterium Cosmographicum”(1596)
    9. 9. The Swiss German mathematicianLeonhard Euler (1705-1783) showedthat these solids all exhibited a simpleproperty.If you count and compare the points(or “vertices”) the edges, and the facesof the shapes, you get the followingformula: V–E+F=2
    10. 10. Is it possible to cross all of the bridges of Königsberg and cross each only once?
    11. 11. This abstraction allowed Euler Cto see that one would need tohave an even number ofbridges to get on and off agiven land mass without going A Dover a bridge twice. B
    12. 12. 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
    13. 13. Many things can be represented as graphs – networks of points and linesthat abstract the relationships between parts By representing things as graphs, wecan transform them in interesting ways
    14. 14. How many colorsdo you need tocreate a map inwhich noadjacent regionshave the samecolor? Graphtheory tells usthe answer is 4
    15. 15. What about texts?
    16. 16. A Comedy of Errors, an early farce
    17. 17. Richard II, a history
    18. 18. Cymbeline, a late romance
    19. 19. Coriolanus, a history, battles as limbs
    20. 20. Antony and Cleopatra, a history, battles integrated
    21. 21. Henry IV, Part 1, central place of the Garter Inn
    22. 22. Henry IV, Part 1, Eastcheap Central
    23. 23. Measure for Measure, a room in theprison central
    24. 24. Julius Ceasar, extremely linear
    25. 25. King Lear, linear then divided
    26. 26. Henry VI, Part 1
    27. 27. Henry VI, Part II
    28. 28. Henry VI, Part III
    29. 29. Anthony’s path through the play as a subgraph
    30. 30. Cleopatra’s path
    31. 31. Antony and Cleopatra
    32. 32. Clustering by number of single-incident scenes
    33. 33. Alignments of tragedy and comedy
    34. 34. Comedy and tragedy clusters
    35. 35. So, Ramsay begins by counting and linking scenesThen 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)
    36. 36. 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).
    37. 37.
    38. 38. What does Fish take issue with?
    39. 39. 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)
    40. 40. 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 …
    41. 41. Halfway through “Areopagitica” (1644), his celebration of freedom ofpublication, John Milton observes that the Presbyterian ministers who once complainedof being censored by Episcopalian bishops have now become censors themselves.Indeed, he declares, when it comes to exercising a “tyranny over learning,” there is nodifference between the two: “Bishops and Presbyters are the same to us both name andthing.” 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 chiasmicpattern: the initial consonant in “bishops” is “b”; “p” is the prominent consonant in thesecond syllable; the initial consonant in “presbyters” is “p” and “b” is strongly voiced atthe beginning of the second syllable. The pattern of the consonants is the formal vehicleof the substantive argument, the argument that what is asserted to be different isreally, if you look closely, the same. That argument is reinforced by the phonological factthat “b” and “p” are almost identical. Both are “bilabial plosives” (a class of only twomembers), sounds produced when the flow of air from the vocal tract is stopped byclosing 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” carriesa message, and that message is made explicit when Milton reminds the presbyters thattheir own “late arguments …against the Prelats” should tell them that the effort to blockfree expression “meets for the most part with an event utterly opposite to the end whichit drives at.” The stressed word in this climactic sentence is “opposite.” Can it be anaccident that a word signifying difference has two “p’s” facing and mirroring each otheracross the weak divide of a syllable break? Opposite superficially, but internally, where it
    42. 42. Fish’s Criticisms• In any event, nothing “licenses” one to make interpretive leaps from the data
    43. 43. 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