Monday, December 28, 2009

The Diagonal Economy 6: Small Worlds Theory

Small Worlds theory is one method of quantifying and optimizing networks, and is often applied to the optimization of networks in business and economics.  Most people are familiar with the theory because it has produced, among other things, the “hub-and-spoke” design for airline routes.  While small worlds theory has broad applicability in business and social networks, it tends to ignore many factors that influence the actual effectiveness and efficiency of coordination and communication in human networks.  My intent with this post is to propose a theoretical structure for the Diagonal Economy that builds on the small worlds theory of network optimization, but that accounts for the issue of hierarchy to create a flat, non-hierarchal network structure that will facilitate coordination and communication in parallel to our present economic system.

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.

While the math of the standard hub-and-spoke small worlds optimization process is complex (see, e.g., 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.  Here is a simple graphic illustrating this concept:

However, it is how these sets are combined that is critical—and that I have previously stated incorrectly (at least per my current theory).  In the past, I suggested that these sets combine as follows:

The structure portrayed in the above graphic portrays more of a lattice structure, and suggests a pattern of interconnectivity that is too uniform to support either flat network optimization (the distant connections are too uniform and too uniformly close) or to support emergence (which, from observation, only seems to exist in situations with very dense, diverse, and variably distant sets of weak connections).

I’ve hinted at the solution in the past:

But in reality this graphic still relies far too heavily on regular and close connections.  The above graphic implies (incorrectly) that these distant and irregular connections (as shown by the bold black lines in the graphic above) are minor parts of the network and only utilized by occasional nodes--in fact, they are the core of the network and are just as critical as the close connections depicted above.  Additionally, the medium-close connections (as shown by the repeated pattern of four connections to nearby nodes) are excessively standardized.  An optimal configuration would show a far more random and variable set of medium and distant/weak connections.

Here's an example:
Compare that to the same nodes networked in a traditional hub-and-spoke system:
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.

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).

That’s pretty simple, but I think largely ignored and potentially revolutionary when applied.  Ultimately, if the Diagonal Economy can develop and latch-on to a superior structure for coordination and communication, it will quickly spread as a means for individuals to maintain and improve quality of life through increased self-sufficiency and resilience despite the troubles besetting hierarchy.

Readers may also find my litigation checklist of interest.

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Ruben said...

Hi Jeff,

A concept that I feel is important is Constructal Theory. CT describes flow--of water, heat, money, information--anything in the natural world. One of the most memorable ruels of thumb of CT is optimizing or distributing imperfections. Optimizing imperfections, how wonderful.

There is a wiki page, a home page and several books on CT, one of which is on applications within human society.

Jeff Vail said...

Hi Ruben,

Very interesting reference--I had not heard of Constructal Theory before, but found at least the wikipedia page to be very informative. Especially this quote:

"For a finite-size (flow) system to persist in time (to live), its configuration must evolve such that it provides easier access to the imposed currents that flow through it." (Adrian Bejan)

I think this is another way of stating my argument (see The Problem of Growth) that peer-polity competition among hierarchal structures leads to the inexorable demand to grow. Similarly, it can be seen to support my argument that, if we want to achive long-term, dynamic stability, we need a structural shift that looks to achieve "easier access to the imposed currents" (resources/outcomes) through elegant simplicity rather than growth...

However, I think the theory holds best in unconscious systems. In our current civilizational model, for example (unconscious), peer-polity competition among structures leads to improved resource flows from the time-constrained (short-term time horizon) impersonal perspective of the system, rather than from a rationally long-term view or from teh view of optimizing the outcome for human ontogeny. I think that humans can consciously implement a system that will provide for dynamic stability without conceding the structure of our world to an unconscious competition that will necessarily result in our own destruction (because the time-horizon limitation prevents the "system" from seeing the approaching cliff, and because it's non-human-centered perspective doesn't care if its optimization eliminates us).

Definitely something for me to keep looking in to--perhaps a very suitable theory for better explaining the structural problem with our current system...

Simon Tegg said...

Hi Jeff,

You may also be interested in this

"Social Contracts on Social Networks: Local Patterns of Interaction, Local Strategy Dynamics and the Emergence of Reciprocity"


establishing reciprocal, pro-social norms requires (partially) closed networks.

terrapraeta said...

Hey Jeff --

How's the fam? Hope all is good :-)

A couple things... I really like the fine tuning you've made on the rhizome network. It's starting to feel right. Graphically and verbally...

You commented on a lot of this being intuitive... but in my mind that is a really good thing. I've been arguing for some time that, in opposition to chaos theory, complexity is understandable and predictable, but not in a way that is mathematically calculatable. Because civ, science, and esp math is reliant on reductionism, and chaotic (complex) systems cannot be reduced, the only way to address them is as a whole... and therefore requires intuitive approaches.

I commented yesterday, much more coherently, I think, but blogger ate it. Figures. Second time through is never nearly as eloquent ;-)


Jeff Vail said...


Thanks for the link to that paper--very interesting stuff. I think they make a good point about the importance of partially closed "local clusters" for development of loyalty. I think local clusters and the set of diverse connections not shared by multiple members of the local cluster serve very different functions--the former build resiliency, provide essential support, and coordinate fusion of information provided by the diverse links, and the latter provide access to innovative solutions, ideas, and applications. I think the key, as you suggest, is to consciously cultivate both the semi-closed cluster and the diverse/diffuse connections non-exclusively (it seems to me that we tend to go too far in either direction, and our networks normally fail to balance these two characteristics very well...

Jeff Vail said...

Hi Janene,

The family is sick at the moment, but overall everything is going very well...

I agree with you that intuition is very valuable in understanding both networks and the broader functioning of civilization. Since civilization is plainly reducible to, among other things, individual human consciousness, and we don't understand how that works yet (a series on emergence is upcoming), we're really only guessing or describing anything that results from human interaction, so I don't think reliance on intuition is in any way "bad." One aspect of my theory of Rhizome, for example, is the intuitive notion that if we structure society more like our brains, and less like a computer, we will reap the benefits of emergence in economic coordination much like individually we reap the benefits of emergence in the form of consciousness...

Jeff Vail said...
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