Linked: The New Science of Networks 160
| Linked: The New Science of Networks | |
| author | Albert-László Barabási |
| pages | 229 |
| publisher | Perseus Publishing |
| rating | 10 |
| reviewer | kurtkilgor |
| ISBN | 0738206679 |
| 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.
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.
Book's site (Score:5, Informative)
This [nd.edu] is the photos page, with photos like.. umm... this [nd.edu].
More reviews (Score:5, Informative)
Nature [nature.com] (ho-hum)
Computer User [computeruser.com] (thumbs-way-up)
Duhh.... (Score:1, Informative)
Re:Duhh.... (Score:3, Insightful)
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.
Re:Duhh.... (Score:1)
Re:Duhh.... (Score:1)
And the proof of a GoL TM is exactly a prediction. I might be wrong, but a mathematical "prediction" of the existence of a GoL TM seems to me far more likely than the accidental discovery of one (gosh! It's a Turing machine! Who'ould've thunk it!).
So, as proven by the proof of the existence of a GoL TM
More complex than you think. (Score:5, Interesting)
A question of assumptions (Score:1)
It turns out the all the mathematical deductions weren't valid, since observed network traffic consists of bursts of emission, instead of regular streams. So the author suggested that a whole different theory needed to be developped to understand networks better.
So I think assuming a Poisson distribution falls in the 'theoric' branch... or does it?
Read in conjunction with ... (Score:3, Insightful)
Re:Read in conjunction with ... (Score:2, Insightful)
Re:Read in conjunction with ... (Score:1)
Barabasi, Wolfram and all that. (Score:1, Informative)
Barabasi and co-author Albert are literarily inventing a new field of physics/math; I'm not even quite sure of what to call it. However, they are very much in touch with current research in the field, and their work is very timely (who else could tell you that the "degree of separation" on the web is 19 and not 6?)
As for Wolfram, however, I cannot say the same. I've seen Wolfram present his book in a special seminar (but haven't read it), and my impression is this: he is an exceptionally bright guy, but not in touch with current research. Wolfram is able to explain a wide variety of fields within physics and mathematics with great confidence, and I would be the last to call him un-educated (no two-week crash course in particle physics on his behalf! Actually, I think he was the only grad-student that Richard Feynman supervised!). I realize that when you "invent paradigm-changing science", you will necessarily meet some opposition from other researchers, but Wolfram's problem is this: he had a good idea some 20 years ago (cellular automata), secluded himself in a room since then developing his idea (as well as various sales-pitches for Mathematica), and forgot to consult with the rest of the scientific community. I understand very well why he's being critizied by his peers.
Re:Barabasi, Wolfram and all that. (Score:2)
-Carter
Re:Read in conjunction with ... (Score:1)
Re:Read in conjunction with ... (Score:2)
This is a bit of a pet peeve of mine: people making assumptions about the behavior and motivation of scientists that have nothing to do with the way real scientists actually do their jobs, and a lot more to do with catchy headlines and fear-mongering. Sorry if I'm overreacting.
Re:Read in conjunction with ... (Score:1)
Another point, Galileo didn't exactly pass peer review, either.
Re:Read in conjunction with ... (Score:1)
Your opinion is a pathetic misinformed regurgitation of others' equally pathetic 'reviews' and 'comments'.
The fact of the matter is that there is _nothing_ in the past like the approach that wolfram advocates. As for specific results, how about a model for shell growth that contradicts widely held ideas about evolution? Or in math, the shortest possible axiom system for logic? Or in physics, obliterating time, space, and matter and still being able to derive special and general relativity from a far simpler structure? Or in CS, the simplest known universal system? Not to mention an absolute mountain of important and interesting results in the notes.
>sciences have been investigating complexity theory and >the emergence of complex phenomena from simple rules >for years now, and have produced work of far greater
Like what? how many popularized accounts of fractal dimensions and power laws do we need? The fact of the matter is that the establishment has produced very few meaningful results. And the fact of the matter is almost no one investigates simple, abstract systems. Just look at the literature.
The New Science (Score:4, Insightful)
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
Re:The New Science (Score:3, Insightful)
"... What is really interesting is that game theorists will borrow from network theorists, network theorists from game theorists, game theorists from evolutionary theorists, evolutionary theorists from game theorists, network theorists from evolutionary theorists, evolutionary theorists from AI theorists, and all of them from linguistics, philosophy, cognitive sciences, economics, and the other social sciences, computer modeling, agent-based modeling, etc. and visa versa..."
True, very true. Not only that, but the author of this book is a physicist!
95% of this book was familiar and/or easy to understand, coming from an AI and maths background. Where it occasionally lost me was in the sudden jumps and links between seemingly unrelated fields.
The Bose-Einstein condensation analogy with Microsoft's OS monopoly is one example of this. In the terms of the models Barabasi et al used, the discussion around this makes perfect sense*. It's only in the atmosphere of a physics department that such a connection would have been made, but the non-physicists reading the book could have done with a little more explanation. Most of the book, however, was extremely thorough and accessible.
*If I understand it correctly, the scale-free model predicts (and accounts for) the formation of hubs, but it is possible to modify the model such that the hubs can all converge to one level. This is governed by equations Einstein formulated in the 1920s. Nice to know, but not very clearly explained.
Re:The New Science (Score:3, Informative)
and visit http://www.santafe.edu. It is very interesting. Santafe.edu is a college that gathers researchers from a wide number of fields in a shared environment, so that they can share ideas between fields of study.
Re:The New Science (Score:1)
it is better to say that this is an institute. there are no teaching positions at the santa fe institute. but everything else is quite true.
Re:The New Science (Score:2)
Re:The New Science (Score:1)
( :
Re:The New Science (Score:1)
A few years ago it would have been practically impossible to use these kinds of theory. We are just now getting the computing speed and memory (at an affordable price) needed to simulate, millions on molecules in a cell, or millions of cells in a body, or millions of neurons in a brain, or millions of atoms in a stream of water etc...
Of course now that we have the computers we can advance our knowledge in the field of cellular automata, being able to test the theories and refine them.
And I am of the same opinion as Barabási or Wolfram: I think this kind of aproach is incredibly powerful, enabling us to predict things and create artificial intelligence in a way never possible before.
This however does not make algebric solutions or aproximations less usefull. Math is a tool wether it is in the algebraic form or in the form of cellular automata. BOTH methods are aproximations of reality. Unless we find the grand unified theory of everything and we simulate things to the smalest most elementary particle, we will always make aproximations. And even if we find the basic rules to the univers its going to be a long time before we get to computing power to simulate large systems from "infinitely" small particles.
Of course maybe cellular automata model is a little closser the real world. But the aproximation we have to make is worst. In every iteration of these simulations we make a small error. These error add with time so that if we simulate something for more than a few seconds we need have a result that is far from reality. Algebraic solutions dont have that cummulative error problem.
P.S. I have to admit I haven't read Wolfram's book or Barabási`s book because I was lacking free time. So I hope I am getting the idea of these theories right. Tell me if I don't make sense.
Re:The New Science (Score:1)
i think you are basically right. the big difference is computation power. but then again I think more things have changed than that which have encouraged these approaches.
Re:The New Science (Score:3, Interesting)
It seems to me that most of the dynamics and mechanics of multi-agent networking behaviour are closely related to the structure they are confined to - and by structure I mean the physical implementation constraints of the working model - more so than what it is the agents themselves do, associated with a certain probability density function.
I've done some research in Neural Networks and I was amazed by the importance of the dimensionality of the network. There is a subfield in NN's that tries to generate appropriate networks for appropriate computing tasks. Still the difference between real neurons and neural networks, is that the first one has an analog clock, while the second one has at least a discretized clock per node, if not per layer or for the whole cell. Also the importance of having a feedback or recurency can make all the difference in the right / wrong places.
I have the feeling - but could not proove this yet - that a dynamic combination of local optima searches and global optima searching leads to self-modifications to the structure in which the agents live, in such a way that the structure suits the needs of the original fitness function, which desribes the problem that we are trying to solve. Since the fitness function itself is a variant in time in most problems, it is logical to assume that the networks are never in a static state, so global optima searching will modify the network constantly, while local optima searching will try to exploit network capabilities best.
Seems like interesting material, I'll have to check out this book!
Re:The New Science (Score:1)
Firstly:
of the emerging science of complexity
Damn funny, that...
Secondly, it was in New Scientist, years ago ( paper edition ) where it was noted that each dimension of complexity is equivalent to about an order-of-magnitude increase in detail: Having neurons ( synthetic neural-net ) that stimulate other neurons, only, in one system, and having neurons-that-stimulate and neurons-that-suppress in a second system, the first system would require 10x~100x ( IIRC, it actually may have been a factor of 10 000 ) as many neurons to get the job done, as the second.
Interestingly, our neurons communicate by stimulative synapses, by suppressive synapses, by pattern-of-signal, and by nitrous-oxide diffusion ( as well as possibly electrical conduction ), so the mere 100 000 000 000 neurons we're born with
( with ~100 synapses, and ~1000 dendrites on each one, +/- an order-of-magnitude, in short a stunning quantity of connections )
can accomplish as much as many-more of a less-dimensionally-deep neural-net...
And that is boggling, but the principle, that each extra ( necessary ) dimension removes the need for a quantum-order-of-magnitude of detail-level-things, holds reasonably well...
... is elegant, and very useful ( try simplifying your business/processes/anything this way... 'The 7 Habits..' does this, unconsciously... )
PS, here's the link from above, clickable, for your incconvenience:
http://www.santafe.edu/ [santafe.edu]
"The Santa Fe Institute is a private, non-profit, multidisciplinary research and education center, founded in 1984. Since its founding SFI has devoted itself to creating a new kind of scientific research community, pursuing emerging science."
"Operating as a small, visiting institution, SFI seeks to catalyze new collaborative, multidisciplinary projects that break down the barriers between the traditional disciplines, to spread its ideas and methodologies to other individuals and encourage the practical applications of its results."
Worthy intention, 't seems...
SFI's Kaufmann explains the origins of order (Score:3, Informative)
However, the work of Sante Fe researcher Stuart Kaufmann (The Origins of Order, etc.) gives a whole new direction, showing how complex, interlocked systems can arise in some circumstances by winnowing a more complex chaotic system that arises naturally. It sounds circular until you look at it carefully, but Kaufmann backs up his analysis with extensive computer simulation as well as a deep analysis of genetic control processes (Kaufmann's original specialty).
These ideas can be used far beyond the biological settings for which they were first developed. Examples range from the crystallization of activity patterns in a new organization or cultural area to the process of learning itself, where the "aha" experience marks the emergence of a set of coherent concepts from the overflowing cloud of ideas that sets the stage for it.
Adding Kaufmann's ideas to your set of explanatory tools will permit you to resolve many complex-systems questions that are otherwise intractable. And computer types are particularly well-situated to understand and use his arguments.
In the Foundation series... (Score:5, Interesting)
"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 =) )
Re:In the Foundation series... (Score:3, Insightful)
You cannot use the knowledge of individuals to analyze society, just as you cannot use the knowledge of society to analyze individuals.
It's also -- forgive me for saying -- a little old-fashioned. It implies that there's a complete break between the individual and the society of which that individual is a part. One must have nothing to with the other. Given that every action by every individual has an impact in the society (however small) this seems unlikely. Like air in a room, the overall behaviour of the system will not be based on the behaviour of one gas molecule, but the system is still just an aggregation of gas molecules.
Might well be that it's of more practical value to study the two separately. Going from mass and electrical charge to "how to build a nice car" might be a long and twisty road. It's probably easier to model it with math that might be a little crass, but gets the job done. But it doesn't mean mass and charge have nothing to do with what the car is made of.
Re:In the Foundation series... (Score:1)
Maybe I should have been clearer in my statement saying "You cannot use...".
The complexity that arise from trying to analyze a "macro situation" with a "micro theory" becomes so unwieldy and overwhelming that it is more practical to pretend that there is an uncrossable barrier between the two.
Re:In the Foundation series... (Score:1)
But what if we discovered general principles which would allow us to easily extrapolate macro behavior from known micro behavior? It would cause a revolution in all branches of science.
My personal opinion is that this particular line of research will be like fractals, NP-completeness, complexity, etc in that it will make a big splash, but in the end will only make a small contribution to our total knowledge of the universe. But you never know.
TTFN
Re:In the Foundation series... (Score:3, Interesting)
Re:In the Foundation series... (Score:3, Interesting)
With all due respect to Asimov (who I don't think believed it himself), the theory is a load of crap and really is just fantasy. History proves over and over that single individuals can make a world-changing difference. Would the mongols have taken over asia with Gengis Kahn? Doubtful. Would Europe have been carved up the way it was without Hitler? Again, doubtful.
And hell, what if Lincoln had not been elected President? We might have TWO "United States of Americas" occupying our current continent. I can't even imagine what the world would be like with a divided US. And how long would it have taken to free the slaves in the Southern US?
I mean, you can go on and on. What if Lee Harvey Oswald had missed? What if what's-his-name didn't get assassinated, causing WW/I? What if Ghandi hadn't been born?
Re:In the Foundation series... (Score:1)
Re:In the Foundation series... (Score:2, Interesting)
> And hell, what if Lincoln had not been elected President?
> What if Ghandi hadn't been born?
The truth is, no one knows. Just as psychohistory was largely statistical, human societies are non-linear. Individual humans ("heroes") do come in, do act as inflection points -- but it is not as if other inflection points could not have existed.
Lincoln's opponent could have risen to the occasion as well. Many historians argue that India would have become free, Gandhi or not, because Britain was much too weak after WWII to deal with the "restive natives" (not all Indians were non-violent, a good many that were sentenced were called "seditionists" then, and almost certainly would be called freedom-fighters^W terrorists today).
Social behavior in the 1900s middle-east was pretty predictable: who in the middle of it would have predicted Kemal Atatürk? Yet, the really interesting thing is, given the almost-repeating patterns common to non-linear systems, how what will Turkey evolve into a hundred years from now? (e.g. Now a pro-Islamic party has been voted in there. Is this a major inflection or something that'll be damped out in no time? again, no one knows...)
> With all due respect to Asimov (who I don't think believed it himself
You are right, Asimov used it simply as one of the building blocks of a good yarn. Like the 3 laws of robotics. (In fact, in Forward the Foundation, written in the late 80s (or early 90s?), contains references to 'achaotic equations' he had to dream up because he could bear not acknowledging the growing body of evidence that the future is essentially non-linear).
Re:In the Foundation series... (Score:3, Insightful)
If you were to read carefully, Hari makes the point that an individual does make no difference in the history of the Empire. The role that the indivudal plays in history can be predicted, but the individual to fill it (and when it's filled) doesn't really matter.
Even Hari was just filling a role. In Hari's case he was selectively bred for over a millenia by the Robots. His role was important but exactly why and what effect he would have, Daneel couldn't fathom. They bred him because long-term planning for humanity was just beyond the grasp of Robots.
Had Hitler never arrived, maybe Stalin would have gone rampaging through Europe. If Lincoln had not been president, another Unionist might have fallen into his place. If Lee Harvey Oswald had missed, maybe JFK would have died of drug overdoses. If Caesar hadn't been born, perhaps another with his ambition would have eventually become Dictator and Emperor. And so on.
Hari's larger point being that Stalin, Hitler, Lincoln, and Gandhi would all have been unimportant anyway. Even a figure whose impact was as dramatic as The Mule didn't really throw off the predictions of psychohistory by much. The Plan compensated even for him -- and he was completely unforseen.
100 or 200 years is a myopic view of history. Larger factors like nationalism, resource pressures, population expansion, steady trends in technology, industrialism, and so on drive history -- not individuals. Taking the longer view, psychohistory (acting in hindsight) may have predicted that near 100 BCE a large seafaring empire covering the entire Mediterranian, with effective military technology, efficient government structure, rigid social classes, and a strong military influence over government would have risen. It might not have been Roman, but should have happened anyway. It might have predicted factors which would cause the Empire to fall, and the feudalism which took hold shortly thereafter; inevitably the nation-states that arose out of the fuedalism would colonize to relief resource pressures; and so on...
Re:In the Foundation series... (Score:2)
Asimov speculated that it took more than a suitable person to fill roles like Lincoln and Ceasar. In his books, it took entire societies being ready and needful of such figureheads.
Interestingly enough, Seldon's own plan became hypocritical after the 2nd Foundationers took over "management" of history in Foundation and Empire. According to Seldon's published theories, there needed to be no management for history to conclude the formation of a 2nd Empire. After the Plan was re-established (the Mule and aftermath), the 2nd Foundationers would still meddle in the affairs of mortals.
The Mule DID throw the plan completely off, and Seldon's plan and even the 2nd Foundation would have been unable to survive the Mule intact if it weren't for the planet consciousness of Gaia stepping into the picture in Foundation's Edge (the fourth book of the "Trilogy"), much like the 2nd Foundationers were trying to do themselves.
Actually, I think Foundation's Edge was Asimov's revision of his view of the world of foundation. In the trilogy, his books pointed toward a class-based rulership of the masses based on selected elite mind-bending super-men, not totally unlike George Lucas's universe, actually. Foundations edge revised that to become a collective consciousness where everyone shares in the control by their needs and their connection with said "collective consciousness". To wit: Gaia for a single planet and Galaxia as the entire galaxy (not just the people) being psychicly linked.
And all in all, Asimov's entire message from all his Robot books and Foundation books and everything else was: "Can't we all just get along?"
Re:In the Foundation series... (Score:2)
The empire DID collapse without interference from the 2nd Foundation. The Great Sack of Trantor was the first time 2nd Foundationers ever influenced the outside world. Hehe I just happen to be rereading the series at the moment.
Re:In the Foundation series... (Score:2)
Well, we seem to agree that on the time scales of hundreds if not thousands of years the history of man is essentially chaotic and thus impossible to predict.
Personally I think this is true for larger time scales as well. Events like nuclear war, or Earth colliding with a big comet could change everything and cannot be predicted.
For anyone who thinks differently, the burden of proof is on you to make correct predictions for tens of thousands of years into the future. Saying that in hindsight something was inevitible will not do.
Tor
Re:In the Foundation series... (Score:1)
Okay. Predictions are in. It's *your* job to prove me wrong. Good luck.
Re:In the Foundation series... (Score:2)
Seems reasonable. But not inevitible; populations are decreasing in industrial countries and could start doing so elsewhere as well. And then we have my earlier examples of comet collisions and nuclear war, they could happen and put an end to it all.
Okay. Predictions are in. It's *your* job to prove me wrong. Good luck.
I think you missed my point; I don't claim to be able to make these predictions - I think it is impossible. The only way to tell is to wait for a couple of thousands of years and see what happens.
If you consistently make correct and useful predictions then I will start to listen. Call me skeptic, but getting it right once in a very general prediction is not enough for me.
Tor
Re:In the Foundation series... (Score:2)
It wasn't the individuals who made the difference, per se. It was the society reacting to those individuals.
Basic tenet of sociology is that humans seek leaders, heros, and villains of various kinds -- people who cause a large segment of the society to engage in a common social behavior.
What Asimov was saying is that we don't have to understand Oswald's specifics to understand that under given conditions, individuals attack their leaders; and, in fact, we can better predict social behavior by ignoring Oswald's specifics and just looking for other patterns in society.
If you don't believe this premise, ask any advertiser who puts billions of dollars into researching aggregate behavior and demographics. That research always pays for itself....
possible in principle (Score:2)
Now with societies, this might be the only way to go. We don't really have enough examples of societies to be able to glean at a macroscopic level the abstract features of societies while not being tripped up by merely accidental and inconsequential features. Thus modeling individual behavior might give more insights. However, constructing such a model accurately is likely to be even more difficult than constructing an accurate model of a nuclear explosion, since people tend to behave in less predictable ways than atoms and electrons do.
Re:In the Foundation series... (Score:2)
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.
Ugh. Please intelligently explain to me how a system of components following well understood rules cannot be studied based on the behavior of the components. If you care to mention how cases like the 3-body problem introduce chaos into the behavior of the system and make it impossible to predict based on observation, please tell me why this difficulty makes it not intellectually worthwhile to study an observed cross-discipline phenomenon. Also, what should be done in cases like physics where the extremely accurate but incompatible theories of quantum mechanics and general relativity describe the macro and micro scale?
Re:Emergence (Score:1)
Heard of emergent behaviours?
This is behaviour that only arises through the complex interactions of many components, and it is not deducable from analysing a single component in isolation.
OK, maybe collect these behaviours and look for similarities between components and emergent behaviours. But it cannot be determined analytically beforehand.
I've heard of it, but seen no real research nor read up on it in any more than a casual way. Frankly, even though I respect Wolfram, I don't buy into it as an explanation for all that exists. And based on my math background, it doesn't sound likely that this behavior can't be determined beforehand.
Just because something is almost intractably complex doesn't mean it _cannot_ be determined beforehand.
Re:In the Foundation series... (Score:1)
I agree that from a empirical perspective it makes sense to study large systems as they are to understand them on a basic level. I disagree that ignoring the individual constituents is a wise course of action.
In a thermodynamics course I am taking we don't use the conventional approach - starting from large empirical observations and generalizing empirically. Instead, we start with basic assumptions from quantum mechanics and build upwards to show that thermal physics has a mathematical foundation. This is an example of a well-understood system.
It is important to look at general principles to get preliminary clues of its behavior, but if you can't connect it to the individuals I don't think you can truly say you understand it.
While many systems exhibit complex 'emergent behavior'; I think the key to understanding large systems is building it up from smaller ones.
Re:In the Foundation series... (Score:1)
Do "we"? Seems that psychologists and psychiatrists would be out of work.
We can't? Crowd behavior may be better understood than individual behavior. Example: an individual's response to "fire!" is less predictable than a crowd in a theater.
Sociology studies the behavior of entire societies (Score:3, Informative)
There just happens to be an entire discipline dedicated to exploring the behavior of entire societies. It's called sociology.
Within society, there's an entire sub field that's been studying social networks for years. Things like how information is spread, how people get jobs, how diseases like AIDS spread, all have been explored using social network analysis.
If you want a mathematical description of "tipping points", take a look at Mark Granovetter's work on threshold models of collective behavior. Gladwell's book is based his work (though he only references Granovetter's work on how people get jobs).
Re:Sociology studies the behavior of entire societ (Score:1)
could you give a more thorough description of sociological threshold models? thanks
Re:Sociology studies the behavior of entire societ (Score:2)
I took two Sociology courses at Humber College and York University and both times my teachers and advanced students were ardent Marxists.
There was no math to speak of either. I think Sociology is a bogus discipline designed to get communists into our school system.
Re:Sociology studies the behavior of entire societ (Score:3, Informative)
-Carter
Re:Sociology studies the behavior of entire societ (Score:2)
And you've just agreed with author. Sociology doesn't study individuals. It studies flocks and swarms. Sociology does not study large numbers of individuals, then try to predict how those individuals will react socially. Instead, it looks for trends in societal behavior without much weight being given to the individual units.
Sociology huh? (Score:1)
Sociology is full of these things. There is simply no one view of how we humans work by design, not to mention to which extent we are affected by external circumstances. One of the most significant splits lie in the idea of the "natural" behaviour of man. There is still a great many people, mainly in social sciences, who believe in the ideas mainly formulated by Rousseau, that all the moral faults of man, all vice and egoism, can be blamed on society itself (an idea that I believe helped form the ideologies of the anarchist movements). Experiments (and quite heartless experiments by todays standards btw) conducted as early as during the 1700s, failed ingraciously to support this idea. (Example: A young native child was taken from his mother in a colony (I believe it must have been the island St. Bartholomy, the only real colony ever held by the Swedish crown) and taken to Stockholm to be brought up at the court without any moral guidance or rules of any kind. The idea was that if the ideas of Rousseau were correct, he would grow up something of a saint with an unquelchable thirst for knowledge, moral enlightnement etc. As the common sense of most people would dictate, the kid grew up a total pest, pulling evil little pranks on everybody in his surroundings and eventually had to be sent home).
Gee. That was a long post. But this kind of topic really gets me going.
How? (Score:4, Funny)
How does information spread through society?
Rumors.
Re:How? (Score:1)
Re:How? (Score:2)
through Slashdot, of course.
Re:How? (Score:1)
Actually, when I said "rumors" was the way in which information spreads through society, it was both a joke and a real comment.
I think if you want to understand paterns in a society, you need to understand how rumors work - especially the way "truth" changes (loss of info, gain of false info, exageration of certain points of view, etc.) as it is passed from person to person.
Even in non-human groups, this is true - think about a herd of elk. If one elk standing on the outside thinks that it smells the presence of another animal in the area, it will snort and/or move into the herd a bit. This creates a ripple affect through the herd that may or may not trigger a stampede, based on the way the other elk interpret the actions of the first.
I'm not a psychologist or anthropologist or behavioralist, but I think it's obvious that there can be no reasonable study of how a society acts without having understanding of how perceptions of the same information varies from person to person, and of how it is therefore 'retransmited' to others.
Anyway, I'd have to say that most if not all of what I know is complete hear-say, including what school teachers have taught me.
Really. (Score:2)
Uh... you mean... uh... chemistry?
'Cause if you're talking about some other big picture of matter, fill us in.
Re:Really. (Score:1)
I assume that is the 'big picture' referred to in the post.
Please do not mix sociopolitics with physics (Score:2, Insightful)
Please stop drawing analogues between socioeconomical politics and physics.
Wasn't it enough that darwinism was used to promote fascism and ultraliberal capitalism and Einstein's relativity was used to promote moral relativism. All out of context, of course, but still bought by the people and - even worse - the politicians.
Re:Please do not mix sociopolitics with physics (Score:1)
Please stop drawing analogues between socioeconomical politics and physics.
But that's the very point of this book... that if you look at normally separate fields in a certain way (in this case, forming networks of relationships) you can use common tools to analyse them.
What you're saying is almost like saying "stop using statistics in chemistry and football". Why should we, when statistics can tell us so much in both areas?
Re:Please do not mix sociopolitics with physics (Score:5, Informative)
If you had read the book (pp.93) and maybe this paper [nd.edu], 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.
Re: (Score:3, Interesting)
Re:Please do not mix sociopolitics with physics (Score:1)
Re:Please do not mix sociopolitics with physics (Score:1)
Multi-Agent Systems + Evolutionary Computation (Score:1)
Don't know how to build networks? (Score:1)
Snow Crash... (Score:4, Informative)
I really don't think there isn't much complexity that can't be explained by the mere fact that we are all actually living on top of a Giant's head
Re:Snow Crash... (Score:1)
In other news... (Score:3, Funny)
Where's Hari Seldon when you need him? (Score:3, Informative)
Read this book about six months ago.. (Score:2, Insightful)
Re:Read this book about six months ago.. (Score:1)
I'm with you. This book should have been a 10 page paper. I kept thinking there was going to be a big revelation. But there wasn't. He just kept rehashing the same thing over:
If you want to bring down the air traffic system, it would be more effective to take out a couple of big airports rather than a couple of small ones.
If you want to take down the internet, it would be easier to do so by removing the more heavily trafficked nodes than the undertrafficked, small nodes.
And on and on...
The first couple of chapters were interesting, but even those were inflated with historical digresssions.
--t
Re:Read this book about six months ago.. (Score:1)
If you want to take down the internet, it would be easier to do so by removing the more heavily trafficked nodes than the undertrafficked, small nodes.
If you want to take out the movie industry, it would be more effective to take out Kevin Bacon.
Related topics (Score:4, Interesting)
I won't research for you, but if you're interested, the preprints archive at LANL [lanl.gov] has a lot of relevant theory [lanl.gov]. 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 [wikipedia.org] (three-satisfiability). Brian Hayes has a very readable article [sigmaxi.org] about this phenomenon, with references. The authority in this field seems to be Gabriel Istrate [lanl.gov].
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 [stanford.edu] 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
Re:Related topics (Score:1)
If you had a "scale-free" network, AFAIK you have an unlimited amount of independent computational nodes, most NP problems would be trivial to solve in polynomial time. Imagine, just spawn a new node for each possible solution to the problem. Each node can check if its solution is valid in polynomial time.
This is similiar how genetic algorithms should be executed. Each packet of genetic information in such an algorithm is a point in a very large state space you're searching for optimal solutions. Each mutation is a random jump around that state pace, and the fitness function tries to seek a local optimal point.
Except in the 'real-world' this algorithm is not executed linearly, but concurrently. Each animal is an concurrent node able to spawn an arbitrary amount of new nodes.
Your computational power then grows exponentially, not the problem. (Sounds like in mother Russia... eh, not worth it).
How to factor prime numbers really quickly:
advance nano-technology to the point where your nano-pc is able to construct duplicates of themselves when you issue a fork() command.
Like I said, talking out of my ass.
Excellent summary (Score:3, Insightful)
another "science of networks" book (Score:2, Informative)
S/N:R
Small Worlds by Duncan Watts (Score:2, Interesting)
Amazon link [amazon.com]
From the Amazon reviews:
Duncan Watts uses this intriguing phenomenon--colloquially called "six degrees of separation"--as a prelude to a more general exploration: under what conditions can a small world arise in any kind of network?
The networks of this story are everywhere: the brain is a network of neurons; organisations are people networks; the global economy is a network of national economies, which are networks of markets, which are in turn networks of interacting producers and consumers.
Food webs, ecosystems, and the Internet can all be represented as networks, as can strategies for solving a problem, topics in a conversation, and even words in a language. Many of these networks, the author claims, will turn out to be small worlds.
Interesting but...... (Score:1)
Re:Interesting but...... (Score:2, Informative)
Great Analogy (Score:1, Interesting)
The preaching continues (Score:1)
Most of these books are journalistic endeavours indulging in overcooked analogies. They all drivel on - its like revelationary religious evangelism as each book includes the phrase "and suddenly I looked at X understanding its full Y for the first time" - be it chaos, complexity, self-organisation, wolfram, barabasi...
Curious that these books including the damn Wolfram tome typically just rephrase computer science. It should have been called information science and then peeps might realise that its fundamental.
Read 'em by all means but keep your scepticism until they actually say something useful.
Zu
mathematical description of tipping points? (Score:2, Funny)
- bill x .15 for good service .20 for great service
- bill x
- $.01 for crappy service
2,532 squared not 6,441,024 (Score:1)
mathematical description of tipping points (Score:1)
Yep, catastrophe theory
Barabasi ignores routing (Score:1)
His description of the neuron network in the brain, for example, talks about how some neurons link some parts of the brain with others, and that random links help the brain (and networks) function. But nowhere does he say how a signal actually gets from point A to point B - just that the loose coupling and random connections between brain areas make everything closer together.
. Maybe he doesn't know? Maybe nobody knows? But the whole point of the book is "connect tightly at the micro level, connect the micro groups with their immediate neighbors, and connect each micro grouping randomly with other non-local micro groupings for better connectivity."
Ok Encyclopedia Brown... here we go (Score:1, Troll)
Have you heard of this "internet" thing yet? Al Gore created it and all your friends are doing it.
We know how people act individually, and yet we can't extrapolate the behavior of entire societies from this.
Its called "demographics". Yep, you're part of it.
How does information spread through society?
People have been reading and writing for centuries now.
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
Alright! Now that's my idea of a good time... I'd hate to come down with the flu, lose my stocks, and suffer a DDOS attack all on the same day. Oh, AIDS too? Even better.
new "science" of networks (Score:3, Interesting)
"We know how people act individually..." (Score:2, Insightful)
Our lack of progress in sociology is a testament to our lack of understanding of the individual.
Slashdot as a scale-free network (Score:3, Interesting)
Here's a couple of examples of networks that exhibit a scale-free topology.
WikiWiki.
This [reseaucitoyen.be] shows that Wiki sites are characterized by the Pareto distribution (a.k.a. power law distribution).
RPM dependency graphs [slashdot.org].
Out of curiousity, I wrote a quick script to compute the distribution of the number of links in the RPM dependency graph. It does seem to follow the Pareto distribution.
Slashdot
Although I have no easy way of verifying this, my gut feeling is that the network of Slashdot users is also scale-free, if we define the notion of a link between two users as follows. User bobdc is linked to user bugbear, if bobdc has replied to any of bugbear's post (or submissions) at least once.
This definition allows us to introduce the notion of a CmdrTaco number, similar to the Kevin Bacon number [virginia.edu]. Specifically, user Joe Schmoe has the CmdrTaco number of 1, if CmdrTaco has replied to any of Joe's comments. If Joe responded to wuliao's post, then wuliao has the CmdrTaco number of no greater than 2, and so on.
Pareto distributions are pretty common. For example, the number of downloads on SourceForge follows the Pareto distribution [cam.ac.uk].
This page [innovationwatch.com] provides a fairly comprehensive list of further reading on the subject.
Companion reading: Chaos (Score:2)
A closely related field, where there is probably lots of overlap, is Chaos Theory.0 092501/qid=1043352869 [amazon.com]
For a good starter on that I recommend "Chaos" by James Gleick, a most excellent book. It both describes chaos theory extremely well and is engaging and readable.
Gleick's site is here:
http://www.around.com/ [around.com]
His page on the book is here:
http://www.around.com/chaos.html [around.com]
And here is an Amazon.com link:
http://www.amazon.com/exec/obidos/tg/detail/-/014
Happy reading and thinking.
I'm afraid that this "New Science" is quite old... (Score:5, Informative)
If you're interested in learning more about the large body of literature in this area, be sure to visit the INSNA [www.sfu.ca] web site. I think you'll find it much more informative than reading popular books on the subject.
-Carter
Re:I'm afraid that this "New Science" is quite old (Score:2)
If you want a more technical (but still approachable) introduction to social network analysis, you might want to look at Wasserman and Faust's 1994 Social Network Analysis: Methods and Applications. This one is a getting a little dated, but it's a still the broadest methods text available. John Scott wrote a little book simply called Social Network Analysis some years back (don't recall the publication year) which may be more approachable yet, although it is much more limited. Really good, up-to-date texts are hard to find in such a rapidly evolving field, but these are adequate to get you sufficiently prepared to start reading the scientific literature (which is where the real action is).
-Carter
Global Scaling (Score:1)
regards
Gerald
Another similar book (Score:1)
Give me a four digit number... (Score:1)
'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.'"
Actually the square of it is 6,411,024
Cause and effect (Score:2)
If you know how the network works, you can make very high level decisions based on calculated cause and effect. For example, what might seem like a bad decision at first may eventually give you the outcome you desire.
In a world where all avenues seem tapped out and it's hard to get ahead, I believe networks are one of the keys to breaking through.
Re:Would people (Score:1)