Breakthrough Ideas (3-09-03 edition)
Richness and Fitness in Networks.
In "Linked: The New Science of Networks," Notre Dame Physics Professor Albert-Laszlo Barabasi (2002) explained how everything is connected to everything else and what it means for science, business, and everyday life. According to Barabasi (p. 72), the economist Vilfredo Pareto's "most celebrated discovery was that income distribution follows a power law, implying that most money is earned by a few wealthy individuals, while the majority of the population earns rather small amounts. This is sometimes called the 80/20 rule. For instance, 80% of the profits are earned by only 20% of the companies. Only a small fraction of 1% of companies makes extraordinary monopolistic profits.
Power laws are at the heart of phase transitions, say, between water and ice, when cold crystalline order spontaneously emerges from the chaotic dance of water molecules. By investigating the physics of phase transitions, physicists discovered that the same power laws emerged as liquids turned into gas, when a ceramic was chilled until it became a superconductor, or when ferromagnetic metals transformed into a magnet as its previously disorganized atom-spins become a set of clustered, communicating, and correlated spins within blocks of atoms before finally emerging as a set of self-organized atoms spinning in unison at the critical point marking the phase transition to magnetization.
According to Barabasi (p. 77), power laws "are the patent signatures of self-organization in complex systems." In the theories of dynamic paths or the gorilla game, a phase transition occurs when profits increase in scale, inflecting from a linear-dynamic to an offscale-dynamic at a critical point as adoption reaches critical mass due to sudden decisions by a pragmatist herd to jump on the forming bandwagon. If the stock market is a complex adaptive system, then it may self-organize, exhibiting a power law in which an extraordinary company reaps monopolistic profits.
A power law is a mathematical expression describing quantities that, unlike a bell-shaped normal curve so often found in nature, exhibit a continually decreasing curve that decays very slowly, which implies that a multitude of small events coexist with a few exceptionally large ones, including the possibility of an extraordinarily large one that is scale free or off the ordinary scale of variability characterizing a normal curve. Yet, most quantitative methods used in statistics rely on assumptions of normality, including regression techniques that extend the linear slope of trends as forecasts.
Barabasi was deeply interested in the self-organization of evolving networks, including the Internet. The number of links between web pages followed a power law where many small nodes had a few links but a few giant hubs acquired an extraordinarily large number. A hub is a node in a network that has an anomalously large number of links. A fundamental property of diverse types of networks, the phenomenon of hubs intrigues diverse scientists drawn from the disciplines of biology, computer science, economics, physics, psychology, and ecology.
At the time when the only network mathematically proven to have hubs was the Internet, Barabasi and his graduate students collected other investigator's data bases on real life networks, including the Western Power Grid, the Kevin Bacon/Hollywood Actors data base, the neural topology of C. elegans, an IBM wiring diagram, and analyzed each of them, discovering that the tail ends of all distributions exhibited a power law. This implied the presence of a universal mechanism operating across diverse networks. Such universal principles are necessarily relevant to forecasting the future of network subscriber and handset growth.
Next, Barabasi (p. 84) and other scientists embarked on a series of computer simulation studies designed to discover the nature of the mechanisms that generated power laws. One of the first things discovered was "that growth alone cannot explain the emergence of power laws." Thus, trend forecasts are limited to unsurprising growth in a normal world of static structures that projects a clear enough future. This pattern of more-of-the-same-growth contrasts with a residually uncertain world of dynamic, evolving, self-organizing networks, where interacting competitive forces may increase scale suddenly and explosively to alter not only the pattern of growth but also to clarify former uncertainties about the future.
In a 1999 study published in Science, Barabasi (pp. 85 and 86) demonstrated that networks characterized by both growth and preferential attachment generated hubs and power laws. Consider the web, although our individual choices are not predictable, our group choices follow a strict pattern of preferring hubs, demonstrating preferential attachment: "when choosing between two pages [nodes], one with about twice as many links as the other, about twice as many people link to the more connected page [a node that as this process iterates becomes a hub]," and "Thus preferential attachment induces a rich-get-richer phenomenon that helps the more connected nodes grab a disproportionately large number of links at the expense of the latecomers." At this point in the still incomplete story, it sure looks good for Modoff and the GSM installed base to get richer-and-richer.
Perhaps it was the preferential attachment to the prestigious journal Science's hub that accelerated the rate of subsequent research that changed the simulations from the scale-free model to simulations more representative of the mechanisms that reside in nature. For Barabasi (p. 92), one question in particular kept resurfacing: "How do latecomers make it in a world in which only the rich get richer?" Similarly, I ask, "How did the brash latecomer Qualcomm make it in a world dominated by the worldwide GSM installed base?"
Barabasi met Larry Page, the founder of Google, and the story of its rapid development intrigued him because in less than three years Google became a hub, the most popular search engine and biggest node on the Internet. This explosive growth violated an assumption in the scale-free model, that the first mover has an ever-escalating advantage based on seniority and growing preferential attachment. Barabasi (p. 94) realized, "in most complex systems each node has unique characteristics that are apparent even if we do not know its connectivity. Web pages, companies, and actors have intrinsic qualities that influence the rate at which they acquire links in a competitive environment." Hence, intrinsic qualities matter in competitions. [This must mean all basketball players cannot compete as well as Michael Jordan, Kobe Bryant, Shaquille O'Neal, or Yao Ming.]
That is, each node has various degrees of fitness. Fitness is a quantitative measure of a node's ability to stay in front of the competition. Barabasi (p. 97, emphasis added) developed a fitness model that demonstrated that nodes still acquire links following a power law, but that the dynamic exponent, which measures how fast a node grabs new links, was "proportional to the node's fitness, such that a node that is twice as fit as any other node will acquire links faster because it dynamic exponent is twice as large. Therefore, the speed at which nodes acquires links is no longer a matter of seniority. Independent of when a node joins the network, a fit node will soon leave behind all nodes with a smaller fitness."
This means that if Qualcomm is twice as fit as, say, Nokia, it will acquire customers and drive sales twice as fast. Because a fit node leaves behind all less fit nodes in acquiring links. This implies that the GSM installed base's ability to acquire customers or to stimulate replacement sales will be left behind by Qualcomm's superior competitive advantage, by its greater fitness.
Next, Barabasi detoured back in time to three giants of quantum theory: Bose, Einstein, and Planck. To his surprise, and based on the ingenuity of one of his graduate students, Ginestra Bianconi, in 2000, they discovered a remarkable and completely unexpected correspondence between networks dynamics and the Bose-Einstein Condensate, a new form of matter created when particles in a gas are forced into their lowest energy state by chilling them to a critical temperature above absolute zero.
"Using a simple mathematical transformation, Bianconi substituted fitness for energy, assigning an individual energy level to each node in the fitness model. Suddenly the calculation took on an unsuspected meaning: They started to resemble those that Einstein ran across eighty years earlier when he discovered the condensate. This could have been coincidental but of no consequence. But there was indeed a precise mathematical mapping between the fitness model and a Bose gas. According to this mapping, each node, in the network corresponds to an energy level in the Bose gas. The larger the nodes fitness, the smaller its corresponding energy level. The links of the network turned into particles in the gas, each assigned to a given energy level. Adding a new node to the network is like adding a new energy level to the Bose gas; adding a new link to the network is like injecting a new Bose particle into the gas. In this mapping complex networks are like a huge quantum gas, their links behaving like subatomic particles." (p. 101)
Networks are rapidly evolving complex dynamic systems. The implication is that networks can undergo a phenomenon analogous to Bose-Einstein condensation. According to Barabasi (p. 102, his emphasis), "The consequences of this prediction can be understood without knowing anything about quantum mechanics: It is simply, that in some networks, the winner can take all." That is, some networks can decisively tip in favor of a single winner.
Moreover, Bianconi's calculations indicated there were only two possible categories. Each network has its own fitness distribution for how different the nodes in a network are from one another. In networks where the nodes are similar, they follow a narrowly peaked bell curve. In other networks, the range of fitness is very wide, and the winner takes all the links. In the first category, the scale-free topology survives, and the networks, following a power law, display fit-get-rich behavior, meaning that the fittest node will inevitably grow to become the biggest hub, but a hierarchy of hubs remains. In the second category, the fittest node takes all links. This winner-takes-all network develops a star topology: all nodes are connected to a central hub, leaving no room for a potential challenger. The computer assembly business, with Dell, Compact, and others competing, would represent the fit-get-rich category. Barabasi used Microsoft as an example of Bianconi's second winner-takes-all category.
When I began to write about the concept of a star-node, I had not yet read Barabasi. And, I was referring to a star-node as a position within a value web rather than a position resulting from an industry-wide competition. In the theory of dynamic paths, I probably will posit that outcomes in industry-wide competitions depend on the ratio of fitness between competitors until that ratio explodes at a critical point of inflection, which locks-in sustainable advantage. The Gorilla Game defines that critical point as the tornado. But also, it may be that intrinsic qualities in an integrated learning base might strongly bias the ratio of fitness indefinitely into the future, making it highly probable that one outstandingly fit hub will emerge as a winner-takes-all star node.
Here is how. The mutual virtues of a platform's stability and expandability, taken together with rapid advances in performance at ever decreasing costs from the combined amplification by Moore's law and increasing returns to scale, attract more and more customers to the star-node's platform as the de facto standard. Architectural control of the platform sustains the fitness of its multiple forms of competitive advantage. The integrated learning base of organizational capabilities, particularly technical and marketing capabilities, powers advanced innovations like, say, Qualcomm's complete standardized solutions for optimized high data rate, multimode world phones, and BREW Distribution System that leverage the platform's reach and depth to create a temporary monopoly. The monopoly company is chosen because it adds the most value to this industry, and hence has the power of fitness transformed into mastery that can grow both its value chain and the industry itself.
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