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IT’S A SMALL OFFICE… The evolution of office artifacts and the small-world phenomenon

IT’S A SMALL OFFICE… The evolution of office artifacts and the small-world phenomenon BY: JOSH BYERS & MATT SHIRLEY. References. • Watts, Duncan J. Small Worlds: The Dynamics of Networks between Order and Randomness . Princeton: Princeton University Press, 1999.

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IT’S A SMALL OFFICE… The evolution of office artifacts and the small-world phenomenon

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  1. IT’S A SMALL OFFICE… The evolution of office artifacts and the small-world phenomenon BY: JOSH BYERS & MATT SHIRLEY

  2. References • Watts, Duncan J. Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton: Princeton University Press, 1999. • Winter 2001 STAPLES Mail-Order Catalog • www.santafe.edu/sfi/publications/bulletins/bulletinfall99/work… inprogress/smallworld.html • www.cs.cornell.edu • www.cs.colorado.edu • www.imagix.com • www.wfs.org

  3. Artifact Systems Reengineering(Background) • Offers an approach which draws on the characteristics of “artifacts” or components of legacy systems to develop a new, more evolved and efficient system • Artifacts take much of their significance from the social world. At the same time they mediate our interaction with that world. • Is there a way to study and make use of this phenomenon?

  4. It’s a Small World…(Background) • Six Degrees of Separation (The Kevin Bacon Game) • The Triangle Inequality: states that if three points (a, b and c) are anywhere in the same space, then they can be connected via the three sides of a triangle, and the length of those sides must obey the inequality d(a,c) < d(a,b) + d(b,c). • Small World “violation”: It is quite possible for person A to know both person B and C, yet for B and C to be not even remotely familiar with each other. • Does this apply to the relationships between artifacts?

  5. It’s a Small World…(Background) • • Terms Identified: •  – vertex. Vertices are office products. • V(G) – vertex set of G. • E(G) – edge list of G. Edges are points of connectivity on G. • n – order of graph G = number of vertices in set • M – size of G = number of edges in E(G) • k – average degree of graph • (G) – neighborhood of a vertex, all adjacent vertices • – clustering coefficient, vertex adjacency for vertex  • L(G) – characteristic path length. Shortest distance between vertices.

  6. It’s a Small World…(Background) • • Graph Restrictions • Undirected. Edges exert no direction, relationship is symmetrical. • Unweighted. Edges do not have a priori strength. • Simple. Multiple edges are not allowed between any one or two vertices. • Sparse. Maximum size, M = n(n-1)/2. Here, M<<n(n-1)/2. • Connected. Any vertex can be reached by another by traversing a path • consisting of a finite number of edges. • Characteristic path length, L, is the median of the means of the • shortest path length connecting each vertex V(G) to all others. • Calculate d(,j)  j  V(G) and find for each . L is median of { }.

  7. “Substitutions” • Artifacts which perform “complimentary” functions may become substitutes for artifacts that performed similar functions in the past • Substitution is inevitable as systems become more integrated • Substitution is a slow process • Office Examples: -- Computer/Printer for typewriter -- Hand-held computers for organizers -- E-mail for intra-office memos

  8. Scope • The artifacts of an office system: Past (1970), Present (2000) and Future (2020) • Defined types of interaction that office artifacts may share: -- Type A: sharing component(s) -- Type B: sharing basic function(s) -- Type C: exchange of information (physical) -- Type D: exchange of information (remote) -- Type E: exchange of material (physical) -- Type F: exchange of energy (physical) -- Type G: exchange of energy (remote)

  9. Hypothesis THE SMALL WORLD PHENOMENOM CAN EXPLAIN THE RELATIONSHIPS BETWEEN VARIOUS OFFICE ARTIFACTS/SYSTEMS. MORE SPECIFICALLY, THE SHARING OF FUNCTIONS IN A NETWORK OF OFFICE ARTIFACTS (IN A GIVEN PERIOD) RELATE TO EACH OTHER SIMILARLY TO THE SHARING OF ACQUAINTANCES IN A SOCIAL SYSTEM

  10. Methodology • Identified office functions to be examined • Chose various artifacts from three different periods of time that perform those functions • Construct adjacency matrix M(G) of (n x n) artifacts for each period for each type of interaction (Type A, Type B, Type C, etc…) • Assign binary value of 0 or 1 to describe the Type __ interactions between artifacts in the matrix

  11. Methodology (cont…) • Compute the “clustering coefficient” for each type of interaction in each time period • Compare these matrices/graphs and coefficients to both the “caveman-world” graph and the “spatial” graph • How do they relate? Does it change over time? Does the small world phenomenon apply?

  12. Assumptions (1 of 7) • • Type A Interactions (Sharing Components) • either share the same component physically (such as two • machines running off of one battery) or having same • components as another artifact, but with no interaction • between the artifacts themselves • - two pens both have ink but do not share the same ink

  13. Assumptions (2 of 7) • • Type B Interactions (Sharing Basic Functions) • the same basic function as another artifact at any level of • abstraction • - a ball point pen and a felt tip marker have a type B interaction

  14. Assumptions (3 of 7) • • Type C Interactions (Physical Exchange of Information) • a physical product of information passes from one artifact • to another • - a printer prints a document and a fax machine sends it out

  15. Assumptions (4 of 7) • • Type D Interactions (Remote Exchange of Information) • any transmission of data from one artifact to another that • requires no further processing at its destination • - email, or a computer forces information to a fax machine

  16. Assumptions (5 of 7) • • Type E Interactions (Exchange of Material) • an artifact leaves residue, transfers any material or can be • stored in another artifact • - a pen leaves ink on paper and transfers the ink

  17. Assumptions (6 of 7) • • Type F Interactions (Physical Exchange of Energy) • if two artifacts can be electrically connected to each other, • including sharing multiple connectors • - a keyboard and a computer motherboard

  18. Assumptions (7 of 7) • • Type G Interactions (Remote Exchange of Energy) • any exchange of electricity or information between two • artifacts that have no physical contact between each other • - PDAs checking email through a cellular phone connection

  19. Adjacency Matrix (example)

  20. Past Office Artifacts • Type A interaction -- M = 41 -- k = 0.661 LA-past = 11.64 --  = 0.0054 = 0.0090 • Type B interaction -- M = 117 -- k = 1.887 LB-past = 7.59 --  = 0.0155 = 0.0292 • Type C interaction -- M = 126 -- k = 2.032 LC-past = 6.79 --  = 0.0167 = 0.0092

  21. Past Office Artifacts • Type D interaction -- M = 0 -- k = 0.000 LD-past = --  = 0.0000 = 0.0000 • Type E interaction -- M = 299 -- k = 4.823 LE-past = 3.06 --  = 0.0395 = 0.0215 • Type F interaction -- M = 145 -- k = 2.339 LF-past = 5.67 --  = 0.0192 = 0.0143

  22. Past Office Artifacts • Type G interaction -- M = 0 -- k = 0.000 LF-past = --  = 0.0000 = 0.0000 • Overall -- M = 728 -- k = 11.742 Lpast = 1.96 --  = 0.0962

  23. Present Office Artifacts • Type A interaction -- M = 61 -- k = 0.726 LA-present = 22.66 --  = 0.0044 = 0.0097 • Type B interaction -- M = 190 -- k = 2.262 LB-present = 6.28 --  = 0.0136 = 0.0247 • Type C interaction -- M = 148 -- k = 1.762 LC-present = 9.05 --  = 0.0106 = 0.0114

  24. Present Office Artifacts • Type D interaction -- M = 26 -- k = 0.310 LD-present = 4.37 --  = 0.0019 = 0.0033 • Type E interaction -- M = 520 -- k = 6.191 LE-present = 2.81 --  = 0.0373 = 0.0220 • Type F interaction -- M = 222 -- k = 2.643 LF-present = 5.27 --  = 0.0159 = 0.0131

  25. Present Office Artifacts • Type G interaction -- M = 43 -- k = 0.512 LG-present = 7.65 --  = 0.0031 = 0.0039 • Overall -- M = 1210 -- k = 14.405 LPresent = 1.92 --  = 0.0868

  26. Future Office Artifacts • Type A interaction -- M = 70 -- k = 0.833 LA-future = 28.10 --  = 0.0050 = 0.0088 • Type B interaction -- M = 239 -- k = 2.845 LB-future = 4.90 --  = 0.0171 = 0.0263 • Type C interaction -- M = 125 -- k = 1.488 LC-future = 12.89 --  = 0.0090 = 0.0079

  27. Future Office Artifacts • Type D interaction -- M = 34 -- k = 0.405 LD-future = 5.67 --  = 0.0024 = 0.0041 • Type E interaction -- M = 495 -- k = 5.893 LE-future = 2.89 --  = 0.0355 = 0.0312 • Type F interaction -- M = 269 -- k = 3.202 LF-future = 4.40 --  = 0.0193 = 0.0169

  28. Future Office Artifacts • Type G interaction -- M = 55 -- k = 0.655 LG-future = 12.10 --  = 0.0039 = 0.0045 • Overall -- M = 1287 -- k = 15.321 Lfuture = 1.88 --  = 0.0923

  29. Trends • • Past to Present • M increased for all interactions because n increased from 124 to 168 • k for each interaction category increased except Type C & E •  overall decreased (less connected) but L decreased also • Present to Future • Remote interactions assumed more critical role in office interactions • k trend continues throughout interaction types • More connected matrices (increased M, static n) yield higher order • graph with higher  and shorter L.

  30. Trends (cont.) • Interaction between vs. interaction within categories: -- There is an inverse relationship between the  for an entire interaction and the for that same interaction -- For example, a higher  for the interaction than the for that same interaction means that the interaction between categories was lower than the interaction within categories (Type A and B interations in the past, Type A, B, D and G in the present and future) -- Also applies vice versa

  31. Trends: Clustering Coefficients

  32. Trends: Characteristic Path Length

  33. Caveman Graph

  34. Spatial Graph • Note: the office world • is non-uniform

  35. Relational Graph • • interpolate between ordered and random limits • (Caveman vs. Spatial) • the probability of two vertices sharing a common edge depends only upon pre-existing conditions • Relational graphs admit a particular class of graphs (small-world) • that share L with equivalent random graphs but with much • greater clustering (~ ) • Caveman Spatial • Our real-world graph

  36. Conclusions* • • Various interactions between office artifacts translate into a • relational graph • • Office artifacts interact more as time progresses • These increases in interaction between office systems yield a • decreased characteristic path length • The small-world phenomenon more accurately describes the • office world as time progresses *See also “Trends”

  37. Qualitative Comments (1 of 2) • • L, characteristic path length, is only a valid statistic for • sufficiently connected graphs such that: • M > 62 in the past, & • M > 84 in the present and future • Automate spreadsheet adjacency matrix production and construct • macros to apply binary bridge values of “1” from one workbook • to another

  38. Qualitative Comments (2 of 2) • Develop a macro to determine • Construct the relational graph to compare with caveman and • spatial graphs • Develop a method of mediating or minimizing the effect that • comes from different numbers of artifacts in each time period

  39. Total and Complete Confusion? Questions?

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