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 Networksbetween Order and Randomness. Princeton: PrincetonUniversity 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

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?

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 obeythe 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 remotelyfamiliar with each other.• Does this apply to the relationships between artifacts?

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 setM – 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.

It’s a Small World…(Background)

• Graph Restrictions1. Undirected. Edges exert no direction, relationship is symmetrical.2. Unweighted. Edges do not have a priori strength.3. Simple. Multiple edges are not allowed between any one or two vertices.4. Sparse. Maximum size, M = n(n-1)/2. Here, M<<n(n-1)/2.5. 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 theshortest path length connecting each vertex V(G) to all others.1. Calculate d(,j) j V(G) and find for each . L is median of { }.

“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

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)

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

Methodology

• Identified office functions to be examined

• Chose various artifacts from three different periods of time thatperform 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 __ interactionsbetween artifacts in the matrix

Methodology (cont…)

• Compute the “clustering coefficient” for each type of interactionin 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 smallworld phenomenon apply?

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

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

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

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

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

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

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

Adjacency Matrix (example)

CategoryCopy Paper

Laser Paper

Ink-J et Paper

Multi-Use Paper

Fax Paper

Notebooks

Message Pads

Ink-J et Cartridges

Laser Cartridges

Fax Cartridges

Copier Toner

Printer Ribbons

Typewriter Ribbons

Correction Tape

Correction Film

Correction Fluid

Correction Pens

Ballpoint Pens

Retractable Ballpoint Pens

Rollerball Pens

Mechanical Pencils

Pencil Sharpeners

Markers

Highlighters

Paper Supplies

Cartridges, Toners, Ribbons

Writing Instruments

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

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

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

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

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

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

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

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

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

Trends

• Past to Present1. M increased for all interactions because n increased from 124 to 1682. k for each interaction category increased except Type C & E3. overall decreased (less connected) but L decreased also

• Present to Future1. Remote interactions assumed more critical role in office interactions2. k trend continues throughout interaction types3. More connected matrices (increased M, static n) yield higher order

graph with higher and shorter L.

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

Trends: Clustering Coefficients

00.0050.010.0150.020.0250.030.0350.040.045

typeA

typeB

typeC

typeD

typeE

typeF

typeG

PastPresentFuture

Trends: Characteristic Path Length

0

5

10

15

20

25

30

typeA

typeB

typeC

typeD

typeE

typeF

typeG

PastPresentFuture

Caveman Graph

Spatial Graph

• Note: the office world is non-uniform

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 SpatialOur real-world graph

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”

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

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

Total and Complete Confusion?

Questions?