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Linked: The New Science of Networks
It turns out that in the past few years, a decent amount of progress has been made on this front, largely thanks to the Internet. The Internet allows scientists to exchange information and speed up research, but more pertinently it is a test subject for these kinds of large-scale interaction problems. Linked: The New Science of Networks presents both the story of how the science has developed, and what it means. Unlike much popular scientific literature, the author himself is an active participant in the field.
The biggest surprise and most important lesson of the book is that the Internet, cellular biology, society, matter, and an incredible array of other seemingly unrelated things all form a particular type of structure called a scale-free network. These types of networks have only been described in detail recently, and their study promises to be as fundamental and rewarding as, for instance, waves or diffusion. The presence of the same structure in many unrelated situations suggests that there is a deep physical or mathematical principle which governs them.
The discovery of this principle is the subject of the first half of the book, which is a sort of detective story that leads from the most primitive concepts of graphs, as pioneered by Euler, to the state of the art. It is very interesting in itself to see how inconsistencies in mathematical models have led people to develop more and more accurate ideas of how such networks function. There is a tiny amount of math in the footnotes available for those who want it, but generally no prior knowledge is required. The author writes with plenty of anecdotes, especially in the beginning starting out with such introductions as this one of Paul Erdos:
"One afternoon in late 1920s Budapest, a seventeen-year-old youth cantered with a weird gait through the streets and stopped in front of an elegant shoe shop that sold custom-made shoes ... After knocking on the store's door-an act that would have seemed just as odd back then as today-he entered, ignoring the saleswoman at the counter, and went up to a fourteen-year-old boy in the back of the shop.'Give me a four digit number,' he said.
'2,532,' came the wide-eyed boy's reply . . .
'The square of it is 6,441,024,' he continued. 'Sorry, I am getting old and I cannot tell you the cube.'"
For another example of both the writing style and the unusual content, the author humorously describes the discovery of a similarity between Bose-Einstein condensation and economic monopoly:
"Essentially Microsoft takes it all. As a node, it is not just slightly bigger than its next competitor. In the number of its consumers it simply cannot be compared. We all behave like extremely social Bose particles, convenience condensing us into a faceless mass of Windows users. As we purchase new computers and install Windows, we carefully feed and maintain the condensate developed around Microsoft. The operation systems market carries the basic signatures of a network that has undergone Bose-Einstein condensation, displaying clear winner-takes-all behavior."
The rest of the book devotes a chapter to a particular example of a network: epidemics, the Internet, economics, etc. One thing is abundantly clear: the more we know about how these things work, the better we'll be able to curb DDOS attacks, stop disease, and control economic failures. An unlikely example of a scale-free network is the cell. It turns out that the interactions among a cell's proteins can be modeled this way, and if we could only understand it, we would be able to come up with treatments analytically, instead of by trial and error as it is done now.
It seems to me that with a greater understanding of networks, we will be able to finally advance in many fields in which progress is currently stalled. From firefly research to AIDS treatment, this is the Next Big Thing.
You can purchase Linked from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, read the book review guidelines, then visit the submission page.
Here is the book's official site.
This is the photos page, with photos like.. umm... this.
CS Monitor (thumbs-up)
Nature (ho-hum)
Computer User (thumbs-way-up)
One of the required classes for my Engineering degree was a course in the mathematics behind networks. It was without a doubt one of the most difficult coursework I have ever experienced. Even with all of the work we performed to create mathematical models of network nodes, etc., they were still unrealistic due to the overall complexity of "real" networks. For example, basic router queuing assumes the packets have an incoming probability Poisson distribution and outgoing has an exponential distribution. This is just an approximation used to allow us to get our arms around the problem. If you examine this model closely, you will find out that it implies that the packets that enter aren't necessarily the same size when they leave! Other issues like probabilistic routing rather than trying to model "smart" routers that adjust based on traffic patterns, etc. aren't usually modeled either.
The science of networks is not so new, but it is gaining importance rapidly. I'm interested in the application of network theory to the flow of information in structured populations. Network theory would be part of this, but so would other social theories (kinship, information, psychology, etc.)
for interesting papers on networks go to:
http://www.santafe.edu
the center for the science of complexity
Logic, macros, and more
"societies", and you don't even have to know how the individuals act individually.
I agree with him, we knew how the solarsystem (society)worked long before we knew how atoms (individuals) worked.
You cannot use the knowledge of individuals to analyze society, just as you cannot use the knowledge of society to analyze individuals.
If you want to know how society works, study society, not individuals.
These are just my opinions though.
(Don't call me redundant if somebody else wrote something similar while I wrote this =) )
"GNU's not Unix....it's Linux" / Kami "kokamomi" Petersen
How does information spread through society?
Rumors.
I won't research for you, but if you're interested, the preprints archive at LANL has a lot of relevant theory. Basically, the current research is trying to come with a unified framework for so-called "phase transitions" in stochastic discrete processes. One of the most studied problems is the transition between "easy" and "hard" problems in 3-SAT (three-satisfiability). Brian Hayes has a very readable article about this phenomenon, with references. The authority in this field seems to be Gabriel Istrate.
The emergence of the giant component in random networks is a mature field of research, of course pioneered by Erdös, and with players of the likes of Don Knuth and Doron Zeilberger.
From a mathematical standpoint, Graph Theory per se is not really complicated, what actually is is the asymptotic analysis of stochastic processes.
HTH,
Matas
Please stop drawing analogues between socioeconomical politics and physics.
If you had read the book (pp.93) and maybe this paper, you would have noticed that Bose-Einstein condensation is used to mathematically explain monopolies in the economic network. So, the analogy is a) explained and b) may be even valid.
From the book: "It is, simply, that in some networks the winner can take all. Just as in a Bose-Einstein condensate all particles crowd into the lowest energy level, leaving the rest of the energy levels unpopulated, in some networks the fittest node could theoretically grab all the links, leaving none for the rest of the nodes. The winner takes all."
Just my 2 Eurocents.
I feel so sig.
If you're interested in learning more about the large body of literature in this area, be sure to visit the INSNA web site. I think you'll find it much more informative than reading popular books on the subject.
-Carter