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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.
... Wolfram's, "New Kind of Science" and Fritjof Capra's, "The Web of Life" to get a tremendous sense of convergence of many fields and principles. The incredible interconnectedness of things makes you wonder how anyone can claim to have " ... found the gene for ..." or dare to think that their actions only have local repurcussions. You listening, George?
"Consensus" in science is _always_ a political construct.
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
BTW, what's this book about?
I don't need no instructions to know how to rock!!!!
This is somewhat of a misleading remark. And I think this comment misses the spirit of the book and topic presented.
For instance, in the game of chess, we understand _completely_ what each piece does, but that doesn't mean we can play a perfect game, or even a good game. Although it certainly is a prerequisite in this case.
And for instance, in a branch of physics known as critical phenomena, where one tries to explain the behavior of things like water evaporating, or magnets losing magnetization, etc. You can construct extremely simple models where there's like one lower level of abstraction to know, but then you can't answer extremely simple questions about higher levels of abstraction.
Let me draw an example, that is widely known as the Ising model of magnetism in physics. We can make a very very simple model of magnetism by saying that all magnetic spins can be UP or DOWN, and the energy is 1 if an adjacent pair of magnetic spins are the same, and -1 if the spins are different. Then we put all these little spins on a lattice, and we call this collection of little spins a _magnet_. Ok, this is a very very simple model, but now we ask, does this thing behave like a magnet? A tough question in 2 and 3 dimensions! Why? It's not because of errors in our assumptions, it's basically because we have very primitive mathematical tools to tackle this type of problem. We are forced to resort to mathematical tools such as infinite transfer matrices, and jordan-wigner transformations.
Yes, in one sense, I agree with your post, that round-off errors cause chaos to occur over very long simulations or models can be inaccurate and have bad predictions. But the spirit of the book is in examining very simple models that seem to have correct predictions, but are complicated enough that we can't manipulate these models with finesse to extract additional information about the system.