Our Interlocked Universe

(Tema 2.4, ver programa)

+ Mafia Boy & Jesus of Nazareth:

“Both were masters of the network (...) the key to their success was the existence of a complex network that offered an effective medium for their actions” (4).
“Everything Touches Everything” JLB
“Riding reductionism, we run into the hard wall of complexity” (6).

• We live in a Small World

+ The Random Universe

• Leonard Euler.

“Graph theory is the basis of our thinking about networks” (10).

• Koningsberg Bridges.1736. 4 areas of land, and 7 bridges connecting them.
  

• Graph: collection of nodes connected by links.

• With a configuration of a link, comes a set of new possibilities.

• Paul Erdós & Alfred Rényi: At a party with 10 guests, none of whom initially knows one another, ties between assistants emerge during interaction. Even if not everyone has talked to each other by the end of the party, a cluster will consolidate, connecting all the attendees with either direct or indirect paths. Therefore, all guests will have formed at least one link.
  

“As time goes on, the guests will be increasingly interwoven by such intangible links, creating a fine web of acquaintances that includes a sizable portion of the guests” (15)
“Random network theory tells us that as the average number of links per node increases beyond the critical one, the number of nodes left out of the giant cluster decreases exponentially” (19).

• Poisson distribution.

+ Six degrees of separation

• Frigyes Karinthy, Everything is different, 1929. Chains or “Lancszemek”. (Karinthy quote, pg. 26).
• Stanley Milgram, 1967. “Six degrees of separation” ---- John Guarre, 1991.
• We live in a small world: society is a very dense web.
• The magic comes from the links
• Small Worlds: Mark Granovetter Strong and Weak Ties.

“The clustering coefficient tells you how closely knit your circle of friends is” (47)
“Humans have an inborn desire to form cliques and clusters that offer familiarity, safety, and intimacy” (49-50).

• Watts and Strogatz: “only a few extra links are sufficient to drastically decrease the average separation between the nodes”

+ Hubs and Connectors

• Malcom Gladwell, The Tiping Point. There are people that function as connectors, the have the knack of making acquaintances.

FUENTE: Princeton

• Random worldview demystified

“The most intriguing result of our Web-mapping project was the complete absence of democracy, fairness, and egalitarian values of the Web” (56)
“Hubs are the strongest argument against the utopian vision of an egalitarian cyberspace” (58)
“How do hubs appear? How many of them are expected in a given network? Why did all previous models fail to account for them?” (64)

+ 80/20 Rule

• Vilfredo Pareto....1900 Gustav von Schmoller asks Pareto: “Are there laws in economics?”
• 80 percent of the profits are produced by 20 percent of the employees
• Extrapolating the notion towards network theory: 80 percent of the links are concentrated by 20 percent of the nodes.
• Power Laws vs. Bell Curves

• Many small events coexists with a few large events
• Scale Free Networks
• Water Molecules and Brownian Movement (Order and Entropy)
• Theory of Phase Transition, “powerful forces of self organization and is paved by power laws, which determine self-organization in complex systems” (77)
• Features of Scale Free-Networks: Growth (beyond static models), Preferential Attachment (When choosing between two pages, one with twice as many links as the other, about twice as many people link to the more connected page (85))

“Each node attracts new links at a rate proportional to the number of its links” (88)
[Metcalf vs. Reed]

• Scale-Free Model cannot explain the evolution of a complex system, hence, it is constricted to its development, not its reproduction [Dawkings; Generative Systems; Cómo mezclar las exigencias? ---- Trabajo del módulo ---- Can we incorporate entropy to a delimitated approach?] ---- “The New Kid on the Block Effect” and the fitness notion within competitive environments

“Each nodes decides where to link by comparing the fitness connectivity product of all available nodes and linking with a higher probability to those that have a higher product and therefore are more attractive” (96)

“It tells us that nodes still acquire links following a power law, tB. But the dynamic exponent, B, which measures how fast a node grabs new links, is different for each node. It is proportional to the nodes fitness” (97)

• Can we identify a topology for information?

+ Achilles´Heel

• Topological robustness is a feature of networks.

“Errors and failures typically corrupt all human designs” (110)
“Vulnerability due to interconnectivity” (110)
“It seems that nature strives to achieve robustness through interconnectivity” (111)

• Crash of hubs

+ Viruses and Fads

• Diffusion through Networks
• Innovations (The Myths of Innovation, Scott Berkun)

“Diffusion models assign a threshold to each individual” (131)

• Spreading rate
• Critical threshold: where innovation spreads

+ The Awakening Internet

• Paul Baran

“Structurally, the Internet is closer to an ecosystem than to a Swiss watch. Therefore, understanding the Internet is not only and engineering or a mathematical problem. In important ways, historical forces shaped its topology” (146)

• http://www.peacockmaps.com/

• [Terrence Sejnowski, Edge´s “What is your dangerous Question”]

“Interplay of Growth, preferential attachment, distance dependence, and an underlying fractal structure” (153)
“Parasitic computing demonstrated that we can enslave computers located thousands of miles away, forcing them to perform computation on our behalf. This fundamental vulnerability of the Internet raised a barrage of computational, ethical, and legal questions” (157)

+ The Fragmented Web

“They wisely [the robots] avoid sharing the crowded Euclidean space with us, where real estate is at a premium. The robots of the twenty first century are invisible and immaterial. They have taken up residence in the virtual world, which allows them to hop with enviable ease from continent to continent” (161).

FUENTE: Opte Project

• They do the most boring job: read and index millions of web pages [ The Machine is Us/ing Us]
• Territories escape their reach.

• Hierarchies & Communities ( continents: Central Core, IN continent, OUT continent, Tubes, Tendrils, Islands. pg. 166)

“A side effect of our digital lives is that our beliefs and affiliations are publicly available” (170)
Ovelapping Communities
Lawrence Lessig: Code & Architecture
“Its architecture is far more richer than the sum of its parts” (174)
“Without robots it will be a black hole” (178)

+ The Map of Life

“If we want to understand life (...) we must think in networks” (180)

• Intra-cellular network organization
• Genes are part of this celular network
• Diameter of a Network: degree of separation between nodes
• History is awarded by scale-free topologies
• Map the network behind cellular biology in order to understand the vulnerabilities and possibilities of approaching the “Achilles’ Heel”

+ Network Economy

“ In a network economy the hubs must get bigger as the network grows” (200)
“As companies face an information explosion and an unprecedented need for flexibility in a rapidly changing marketplace, the corporate model is in the midst of a complete makeover” (201)
“As research, innovation, product development, and marketing become more and more specialized and divorced from each other, we are converging to a network economy in which strategic alliances and partnerships are the means for survival in all industries” (208)

• Links quantify interactions between institutions

+ Web Without a Spider

• Real networks are not static & self-organizing: change and randomness: growth plays a crucial role
• Scale-Free Networks: language, proteins, sexual relationships, transistors, cellular metabolism, Internet, Hollywood, WWW, Scientists, Economy, etc...
• “Irregular army”: terrorist networks

“The goal before us is to understand complexity” (225)

+ Scale-Free/Modular Networks

• Hierarchical modularity makes multitasking possible

“Complexity starts when networks turn nontrivial” (238)