|Linked: The New Science of Networks|
|summary||An introduction to scale-free networks and their broad applications|
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.
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