|U n i v e r s i t é Y O R K U n i v e r s i t y
ATKINSON FACULTY OF LIBERAL AND PROFESSIONAL STUDIES
SCHOOL OF ANALYTIC STUDIES & INFORMATION TECHNOLOGY
S C I E N C E A N D T E C H N O L O G Y S T U D I E S
NATS 1800 6.0 SCIENCE AND EVERYDAY PHENOMENA
Lecture 7: It's a Small World
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Readings, Resources and Questions
Here is another recent example of the applicability of small-world networks to real systems: Small World Networks Key to Memory
"If you recall this sentence a few seconds from now, you can thank a simple network of neurons for the experience. That is
the conclusion of researchers who have built a computer model that can reproduce an important aspect of short-term memory.
The key, they say, is that the neurons form a 'small world' network. Small-world networks are surprisingly common. Human social
networks, for example, famously connect any two people on Earth—or any actor to Kevin Bacon—in six steps or less."
A very good overview is offered by P Shulman in the December 1998 issue of Discovery Magazine: From Muhammad Ali to Grandma Rose..
The literature on social networks is vast. Here are a couple of very good, accessible books:
- Albert-László Barabási, Linked: The New Science of Networks. Perseus Publishing, 2002
- Mark Buchanan, Nexus: Small Worlds and the Groundbreaking Theory of Networks. W W Norton & Co, 2002.
- Steven Strogatz, Sync: The Emerging Science of Spontaneous Order. Theia Books, 2003.
- Duncan J Watts, Six Degrees: The Science of a Connected Age. W W Norton & Co, 2003.
Check also the Small World Phenomenon entry in Wikipedia,
where you will also find additional references.
Here is a good collection of links to articles on Scale-Free / Power Law Networks.
The articles are generally quite technical, but you may find them useful when comparing the original scientific discourse with
the 'English' version presented here.
Read D J Watts' article The Internet, The Small World, and The Nature of Distance, Boston Science Museum Exhibit on Messages (May 1999).
Unfortunately this article does not seem to be available any longer.
Here is an example of a special type of degree of separation:
"Most practicing mathematicians are familiar with the definition of one’s
Erdös number [ … ] Paul Erdös (1913–1996), the widely-traveled and incredibly
prolific Hungarian mathematician of the highest caliber, wrote hundreds
of mathematical research papers in many different areas, many in
collaboration with others. His Erdös number is 0. Erdös’s co-authors
have Erdös number 1. People other than Erdös who have written a joint
paper with someone with Erdös number 1 but not with Erdös have Erdös
number 2, and so on." [ from The Erdös Number Project ]
For an amusing twist, see Thumbing His Nose at Academe, a Scholar Tries
to Auction His Services:
"Late last month an independent scientist auctioned off his services
as a co-author on eBay, with the promise of helping the highest bidder
write a scientific paper for publication. The offer even had the added
allure of a linkage with the legendary mathematician Paul Erdös [ … ]
The auction began as a bit of fun, admits William A Tozier, a
consultant in Ann Arbor, Mich., who specializes in machine learning and
artificial-intelligence research. "I undertook it as a combination of a
joke and conceptual art and a bit of an experiment in social networks,"
he says. The idea builds on the reputation of Erdös, a Hungarian
mathematician who died in 1996. A prolific researcher, with more than
1,400 published papers, he spent the last several decades of his life
moving from one colleague's house to another's, staying for extended
periods at each place and collaborating on solving problems."
Here is an example of application of the small-world model to technology: Circuits are Small Worlds
"Recent theoretical studies and extensive data analyses have revealed a common feature displayed by biological,
social, and technological networks: the presence of small world patterns. Here we analyze this problem by using
several graphs obtained from one of the most common technological systems: electronic circuits. It is shown that
both analogic and digital circuits exhibit small world behavior. We conjecture that the small world pattern arises
from the compact design in which many elements share a small, close physical neighborhood plus the fact that
the system must define a single connected component (which requires shortcuts connecting different integrated
[ from Topology of Technology Graphs: Small World Patterns in Electronic Circuits ]
C Kelty, at Rice University, in Stanley Milgram's Small World Experiment, poses
very interesting questions:
"Milgram and the science of social networks focuses on the network itself, especially the complex ones. It is
not interested in what anthropologists have traditionally focussed on, namely the kinship relations of the people
involved. What's the difference?
To begin with, there is a classic distinction in anthropology. Emic vs
Etic. The explanation that we as observers give of any phenomena can be different from the explanation
that those observed themselves might give [ … ] The small world problem doesn't capture this
difference [ … ] However, the anthropological question does not go away. Just as people can describe
their relationships with each other on the basis of their understanding of biology, so too might they describe their
relations on the basis of their understanding of a network. The phrases 'six degrees of separation' and 'it's a
small world after all' are just two examples of such explanations. Some people who understand how the internet and
the telecommunications system work might have a different understanding of the shape of society from those people
who only ever talk with their neighbors and the mail man. What difference does it make to have a different
understanding of the shape of society?"
Material related to these topics can be found in Lecture 3.