Jeff Vail has a critique of the mainstream Watts and Strogatz model regarding Small Worlds Theory, and proposes a different approach which would enable the development of a “Diagonal Economy”.

Jeff Vail:

1.

“Notice that, in the hub-and-spoke system, one node in each close cluster is in control–it’s the “hub,” and communication between subordinate nodes through these hubs creates dependency. While the hub-and-spoke system provides a minimally shorter path in many cases, my theory is that the information processing burden imposed at the hubs, combined with the lack of self-sufficiency and resiliency, makes the hub-and-spoke model inferior to the “rhizome” model of more egalitarian connections.

“Without regard for hierarchy or span of control, small worlds theory optimizes the shortest path length (e.g. for airlines flights) by heavy reliance on hubs to minimize connections. However, this theory’s reliance solely on path length optimization fails to account for the information processing burden created at these hubs (e.g. span of control, SNAFU, etc.) nor does it account for the side effects of this necessarily hierarchal structure. For example, the hub-and-spoke small worlds systems suggested by Watt and Strogatz, among other current small worlds theorists, create excessive dependencies on the hubs in these models. This creates a network that is neither topologically flat (there are significant dependencies of most nodes on the hub), nor resilient (a breakdown of a hub causes chaos).

Additionally, the hub-and-spoke models created in traditional small worlds optimization is not compatible with the span of control capability of human nodes in those networks. Span of control is, essentially, the number of other humans that one human can effectively manage in a hierarchy—a number which tends to settle at about 5. Where humans are a component of the networks optimized through traditional hub-and-spoke small worlds systems, the information processing burden at the hubs is exacerbated because multiple layers of human hierarchy are required to manage the activities of the hub.”

2. Alternative to the Watts and Strogatz model

Jeff Vail:

“While the math of the standard hub-and-spoke small worlds optimization process is complex (see, e.g. http://en.wikipedia.org/wiki/Watts_and_Strogatz_model), my intuition is that an effort to balance minimization of path length and minimization of information processing burden of hierarchy (and other more subjective side effects of hierarchal structure) will result in a very different optimal network structure than that suggested by the Watts and Strogatz model, and one that will facilitate far superior information processing by any real world process running on such a network. Basically, I’m suggesting that, because the hub-and-spoke model fails to account for the issues of hierarchy (and the associated issue of span of control), it fails to actually optimize the network for human reality (instead forcing upon us a system that squeezes humans into a machine role). Below, I propose an alternative structure that I think is broadly applicable and that will allow for more efficient coordination and communication in human structures precisely because it is non-hierarchal.

First, one factor that must be considered in formulating this alternative structure is that, while optimization of a network in some theoretical set it may permissible to ignore physical geography, in the Diagonal Economy the demands of production tied to geography (e.g. food, water, energy, family) demand at least some degree of local clustering (as, I think, does our psychology to some degree due to our development in such an environment).

Next, it is necessary when developing such a theory to recognize that, when humans comprise the nodes in such a system, there is a limit to the number of effective connections in which each node can participate (and to avoid span of control issues popping up even in non-hierarchal systems). The concept in anthropology known as Dunbar’s Number suggests that this number for humans is approximately 150. The jury is out on whether new technologies (e.g. social networking software) or psychological developments (such as autism – see “Create Your Own Economy” by Tyler Cowen) may be changing that, but for now Dunbar’s Number seems to provide a reasonable guide.

Next, I think that the effectiveness of people in any system improves when those people are not being squeezed into the role of a cog in a giant hierarchy, but instead are working in a self-directed, self-motivated capacity with peers. Human creativity, passion, drive, and so many other subjective qualities seem to fare better when self-actualized, rather than acting as an, essentially, an insect.

Finally, variable loyalty or strength of connection is simply a reality in any human-based network, and is something that conventional small-worlds theory ignores. Even within the 150 links supported by Dunbar’s Number, some will be far stronger than others. One factor supporting this is the shared connectivity between links (e.g. A links to B and C, but B and C are also linked). Another factor is geographic proximity, though there are certainly proxies in cyberspace (e.g. shared language).

With all of these factors taken in to account, my theory of an optimal flat network is most simply described from the perspective of a single node: a number of close, strong, and generally mutually shared links, and a diverse array of medium and distant, weak or strong links. ”

3. Conditions for a successfull Diagonal Economy

Jeff Vail:

“One clear weakness in this model is that it cannot be objectively and mathematically quantified in the manner of the Watts and Strogatz model. First, the desire to optimize both path length and multiple human factors simultaneously is antithetical to mathematical analysis (you can only optimize for one thing). When there are multiple factors to be balanced, there are probably many different effective structures, and the potential for “local peaks” presents a significant challenge (where slight tweaking of a variable degrades the performance of the model, thereby preventing further exploration that would, eventually, identify a superior structure). There is also the fundamental challenge of conducting controlled experiments or simulations to evaluate highly complex human structures. Therefore, this theory is necessarily based on an intuitive application of these factors and anecdotal evidence. As with the development of all human systems, I think optimization of flat human networks, a cornerstone of the Diagonal Economy, is best achieved through the development and fine-tuning of a series of (rough) guiding principles:

1. (Strong): Approximately 1/3 geographically (or otherwise) close and strong/loyal connections that share significant interconnectivity among each other.

2. (Weak): Approximately 2/3 geographically (or otherwise) distant connections, of variable strength/loyalty that are largely not shared by the above group.

3. (Self-Aware): A self-awareness of these principles in the creation and maintenance of connections

4. (Shared Principles): Particularly within the context of creating a “diagonal” network that overlaps but exists out of phase with a “large world,” a criteria in creating new connections should also be whether that connection understands and applies this theory in its own connections (which can be accomplished through education and facilitation or discrimination)