Networks and Interconnection (last changed 5/24/04)

More thoughts, articles, links, etc. on networks and interconnection are on my Networks and dialectics web log.
Post a comment on my web log on Networks and Dialectics.

Introduction

The first principle of dialectics listed in the 1930s Soviet primer "Dialectical and Historical Materialism" is that "Nature is connected and determined":

Contrary to metaphysics, dialectics does not regard nature as an accidental agglomeration of things, of phenomena, unconnected with, isolated from, and independent of, each other, but as a connected and integral whole, in which things, phenomena are organically connected with,dependent on, and determined by, each other.

The dialectical method therefore holds that no phenomenon in nature can be understood if taken by itself, isolated from surrounding phenomena, inasmuch as any phenomenon in any realm of nature may become meaningless to us if it is not considered in connection with the surrounding conditions, but divorced from them; and that, vice versa, any phenomenon can be understood and explained if considered in its inseparable connection with surrounding phenomena, as one conditioned by surrounding phenomena. (Stalin)

For two books building on several years' research to be published in the same month (Mark Buchanan's Nexus: Small Worlds and the Groundbreaking Science of Networks and Albert-Laszlo Barabasi's Linked: The New Science of Networks, in May, 2002), both arguing that to understand phenomena we can't just dissect and reduce it to it's constituent parts; instead we need to look at the parts working together:

Today we increasingly recognize that nothing happens in isolation. Most events and phenomena are connected, caused by, and interacting with a huge number of other pieces of a complex universal puzzle. We have come to see that we live in a small world, where everything is linked to everything else. We are witnessing a revolution in the making as scientists from all different disciplines discover that complexity has a strict architecture. (Barabasi, 7)

It's enough to make a dialectician living in anti-communist intellectual exile, well ...

Buchanan's and Barabasi's books both describe a new cross-disciplinary field of "network science". Network science is an offshoot of the broader trunk of complexity theory.[1] This apparent re-discovery of dialectics, or aspects of dialectics is of interest for several reasons.

First, the constant development of the productive forces demands a constant expanding of understanding how the universe works (which in turn speeds the development of the productive forces). Philosophy, as a world outlook, must look out on the world as it is, as science reveals it, or become useless.[2] As new things become known, do they change our outlook? Do they extend our philosophy? Do old concepts need to be re-thought? Philosophy must keep up with science.

Second, network science is not just a re-hash of Stalin's summary on interconnection. Rather, network science, building on the resources of modern scientific practice (in particular, computers and other forms of electronics), extends and deepens our understanding of dialectics as "the science of universal interconnection." (Engels 356)

Third, the re-emergence of an academic discussion of dialectical interconnection as "network science" reveals something of the social practice of science. The practice of science -- the systematic, experiment-based, peer-reviewed investigation of the world -- is a human endeavor, and hence a social act. It takes place in social institutions within class society. There is nothing pure about it. The struggle between capitalism and socialism infected every institution of society. One may assume that the Cold War also infected science, and that dialectics, being linked to Marx and Engels and hence to socialism, would be a delicate matter within the world of politically-driven tenure and corporate-based research funding. That is, Cold War politics blocked, or at least retarded scientific research into areas like interconnection, change, and leaps.[3] Nevertheless, production takes place in the real world. The demands of production cannot ignore or subvert or violate the laws of nature and continue to develop. If dialectics is "true", that is, if it accurately describes how things develop and change, then eventually production, and its sidekick science, must grapple with the same concepts.

This paper has two goals: 1. To convey the significance of network science for dialecticians, looking at how network science deepens our understanding of interconnection. 2. And vice versa, to convey the significance of dialectics to network scientists, outlining contributions dialectics can make in addressing some of the shortcomings in network science.

Interconnections

Before exploring the new concepts developed in network science, it will be useful to review the concept of interconnection in dialectics.

In dialectics, "connections" are a special kind of relation between things: "Only a relation that presupposes the dependence on the changes in one phenomenon or aspect on changes in other phenomena or aspects is called a connection." (Sheptulin 179)

Cause and effect is a familiar and universal type of connection. Cause and effect is not just one body acting on another. Where this understanding is perhaps sufficient for understanding simple mechanical motion, it cannot explain more complex motion or development. (Sheptulin 196) Rather, it is the interaction of the parts of phenomena that causes things to happen. Effects are the changes in phenomena arising as a result of the interactions. Besides causes, "without which an effect cannot materialise" (Sheptulin calls these "basic causes", 199) there are non-basic causes or "occasions." "The occasion itself cannot give rise to any phenomena, but acts as the impulse which brings the actual cause into operation." (Kuusinen 73) In addition to causes (arising from within the phenomena or node) Kuusinen describes "conditions": "Conditions are those phenomena which are necessary for the occurrence of a given event, but do not bring it about themselves." (Kuusinen 73)

Cause and effect describe a sequence in time -- cause precedes effect. But cause and effect also interpenetrate: effect becomes cause and cause becomes effect -- hence the understanding of interaction. Also, one cause may have multiple effects, and effects may be the result of multiple, interacting causes (this is in fact the general rule).

Causality is evidence of a structured, knowable universe. "If cause exists, effect will inevitably follow, provided nothing interferes." (Kuusinen 72-73). "Laws" are simply the necessary connections between things -- "profound, essential, stable and repeated connection or dependence of phenomena or of different sides of one and the same phenomena." (Kuusinen 77) The totality of the laws that describe the connections within phenomena is a "law system."

Laws operate within a range of conditions, or a "field of phenomena." Some laws are general to all phenomena (e.g., all societies), and some are particular to specific fields (e.g., modes of production). The law of the correspondence of productive relations to productive forces operates throughout all human history; the law of value operates during commodity production; the maximization of profit operates only within capitalist production relations.

Interaction or causality can describe the routine interactions which enable the process to function (e.g., respiration in the organism or production and circulation in the economy). Causality can also describe how processes develop and change from one quality to another. Causality enables us to understand the overall process of history.

Network science

The term "network", rooted in hunting/gathering and handicraft, became a way of envisioning the expanding transportation system of the industrial era. Cities became dots (nodes) on a map connected by lines (links) representing highways, canals and railroads. This abstraction was also useful for working with electricity distribution as that technology developed, for communication systems (telephones, radio, television), and later, computers linked together (and referred to as "computer networks"). From this practical abstraction in the production process, the concept could jump to other disciplines which were using the tools already conceived of as parts of "networks" (especially computer networks used in scientific research and communication, the roots of the Internet).

"Networks" are an abstraction, looking at phenomena as collections of nodes connected together via links. Network science explores the structure of complex, dynamic systems -- i.e. actual phenomena -- as networks. Network science has identified remarkably similar patterns in phenomena as different as cell metabolism, ecosystems, and markets.

Network science takes us beyond the idea that "everything is interconnected" to the understanding that those interconnections appear in specific patterns. Understanding the principles or laws that govern the patterns provides insights into the behavior of phenomena (networks).

The principles or laws of real-world networks include:

-- Links are not randomly distributed among nodes. Instead, a few nodes have many links while most have very few. This distribution of links tends to follow a "power law" (e.g., half as many nodes have twice as many links). This distribution is also referred to as "scale-free", in that there is no center of the distribution, unlike the distribution along the common bell curve.

-- The nodes with many links, referred to as "hubs" or "superconnectors", give these networks a "small-world effect", making them very efficient. To get from any one node to any other node takes relatively few hops.

-- This structure gives networks "robustness". Because most nodes have few links, removing nodes at random has little effect on the network.

Network science provides insights into the way networks develop. Barabasi argues that the power law distribution of hubs arises because of a phenomena he calls "preferential attachment". Nodes with many links tend to attract more nodes (or new nodes link to the already well-linked). "No matter how large and complex a network becomes, as long as preferential attachment and growth are present it will maintain its hub-dominated scale-free topology."[4] (Barabasi, 91)

These laws of networks are practical and relevant to scientists, including social scientists and hence Marxist revolutionaries, because they provide tools for understanding and acting in the world.

Marxism regards laws of science -- whether they be laws of natural science or laws of political economy -- as the reflection of objective processes which take place independently of the will of man. Man may discover these laws, get to know them, reckon with them in his activities and utilize them in the interests of society, but he cannot change or abolish them. (Stalin, 1952 2)

Understanding that proteins within a cell comprise a network connected by chemical interactions helps researchers understand the dynamics of cancer and the effects of various treatments. (Vogelstein, Lane and Levine). Understanding the network of the food chain within an ecosystem enables biologists to see the danger of destroying key species. (Buchanan, 140) Understanding that social networks are structured in specific ways allows propagandists to scientifically plan how to disseminate ideas.

Links and connections

In networks, links are simply the things that connect nodes. Links are connections in the sense of mutual dependence (two nodes are required for a link to exist; a link that goes nowhere is not a link).

Links can be seen as conduit or pipe or pathway (a physical channel), or the interaction (causes and effects) between nodes. The former is of interest to the engineer or traffic controller or dispatcher or propaganda planner. The conduit represents the potential of interaction. The interaction, however, is what brings the system to life.

The interaction and the conduit are in a dialectical (interdependent, interacting) relationship. Relationships between people, for example, affect and are affected by the communication channels through which those relationships are mediated. The relationship between interaction and the infrastructure within which it takes place expresses the same underlying interaction that dictates that productive relations must correspond (in the sense of setting boundaries on what is possible) to productive forces. Productive forces are the interaction of human beings and their tools. Human beings develop through interacting with the universe using tools. (See, e.g., Engels, 452-464, "The Role Played by Labour in the Transition from Ape to Man") This interaction itself interacts with the relations (another set of interactions) between human beings in the production process. The links within the network of society are shaped by and expressed by, the connection between the context of interaction and the interaction itself.

We can think of causality in the network at the node level and the network level. Interactions within nodes cause changes that can then be communicated across the network. For example: "New research suggests ... that microbial life is much richer: highly social, intricately networked, and teeming with interactions. [R]esearchers have determined that bacteria communicate using molecules comparable to pheromones. By tapping into this cell-to-cell network, microbes are able to collectively track changes in their environment." (Silberman) The bacteria release the communicating molecules in response to changes in their environment (conditions), and in response to what other bacteria nearby are doing (interaction). Out of these interactions across the system or network, changes take place in the network/phenomena. Some bacteria glow, others release toxins, but only when a biological quorum is reached.

Networks and law systems

Links are not haphazard interactions. Using the insights of dialectics, we can add another dimension to understanding networks. The network operates within an environment or a "field of phenomena", and the links are the "necessary connections" between nodes. The connections belong to a law system that gives a network its behavior.

Both Barabasi and Buchanan are especially weak when they look at the economy as a network. The distribution of wealth in capitalism follows "Pareto's Law", a kind of power law. "Giving people random amounts of wealth to start out, and letting the economy run for a long time, Bouchaud and Mezard found that a small fraction of the people always ended up possessing a large fraction of the entire wealth." (Buchanan, p. 192) The principal of "preferential attachment" in this case is literally "the rich get richer." Such a behavior, though only happens under a system of social production and private ownership.

The law system of capitalism, including the laws of value and the maximization of profit, define the connections between the economic nodes: between capitalist and worker, capitalist and consumer, and between capitalists. The nature of the capitalist law system results in the constant distribution of wealth within the capitalist network/economy towards the already wealthy. Under another mode of production, the links between the nodes obey different laws. We can envision an economy where production for use and maximum satisfaction comprise the law system, and nodes interact such that each contributes as able; and each takes as needed. The behavior of such a network would be radically different. The nature of the links -- the law system -- defines the behavior of the network.

A network exists within an environment of networks (or a process within an environment of processes):

Every internal process is the environment for some other internal process. The earth is internal to the solar system. But the earth is the environment for all earthly processes. The means of production is the environment for society. Society is the environment of the class struggle. The list is unending. This is the way that nature is united into a whole. (Peery)

In addition to a hierarchy of networks, we can also think of clusters of networks interacting, e.g., to make up the fabric of social life. Base is a network and superstructure is a network, but the networks interact and interpenetrate.

How networks grow and die

Engels also describes dialectics as "the science of the general laws of motion and development of nature, human society and thought." (Engels 131) Networks (processes) grow and die.

Growth can be seen as a process of adding connections, or nodes (and by definition, links). Networks go through phase changes as the result of quantitative changes (the addition of new nodes), and qualitative changes through the complex process of adding quantities of an antagonistic new quality. (Miller) "Phase change" (or "phase transition") is a term from physics which refers to changes in properties of phenomena at certain nodal points. Water-to-ice or non-glowing to glowing tungsten are examples of phase changes. "Tipping point" is another description of this phenomena of simple quantitative addition resulting in new behavior. (Gladwell) Isolated actions tip into a general fad; incidences of disease tip into an epidemic. The individual actions of millions of electronically-connected investors at a certain point tip into violent stock market price swings.

Traditionally, dialectics has referred to phase changes as qualitative changes -- "the transformation of quantity into quality." Most of Engels's examples of qualitative change in Dialectics of Nature refers to phase changes. Qualitative change which results from the stage by stage introduction of quantities of an antagonistic new quality though, is different in that it represents the replacement of one law system with another.[5] That is, the laws that govern the connections between nodes are replaced by new laws.

Because the superconnector nodes within a network are more critical to the network, they also represent weak points for the network. A random attack on a network has little effect, because most nodes (per the power law) have few links and so are relatively inconsequential. However, a deliberate attack that concentrates on the superconnector nodes can quickly destroy a network. Such a strategy has been used in hacker attacks on the Internet; it has also suggested a strategy for halting the spread of sexually-transmitted diseases.[6]

One gene in the cell, referred to as "p53", appears to be a superconnector of a gene. It plays a special role in responding to damage to a cell. "An attack on p53 (by mutation) will disrupt basic cellular functions, particularly the responses to DNA damage and tumour-predisposing stresses." This is a direct attack on the node. However, nodes may also be attacked indirectly, by attacking the links or the nodes that link to the super-connector. "One should also expect that combined attacks on many nodes linked to p53 should have progressively more severe effects that more and more closely resemble an attack on p53. This is exactly what has been observed." (Vogelstein, Lane and Levine)

The destruction of capitalism is a process of the destruction of relations or connections within the interconnected economy and society. In this case the initial cause is technology of a new quality, electronics. As noted above, the fundamental connection between productive forces and productive relations in society is disrupted as the connection between human being and tool is upended. The nature of the productive forces is transformed, expressed as cascading failure of the connections in society:

The Capitalist system (and the system of state socialism) developed upon and in compatibility with the industrial means of production. A leap begins as qualitatively new means of production are introduced into the industrial system. The intricate network between industry and banking, between all the various forms of buying and selling becomes disrupted as wage labor, the source of increase of all wealth, falls in value and price. The highest form of industry, electromechanics, cannot compete with the more efficient new means of production.

Each invading quantity of the new quality further disrupts the system. Since profit is surplus or unpaid labor time, and machines, including robots, simply transfer their value to production, the very high profitability in robotic production comes from placing products, without labor power on the market at the same price as commodities, that contain labor power. The accelerating shift to electronics creates untold wealth along side untold misery. The new electronics creates a hitherto unknown want in the midst of a heretofore unknown plenty. More and more workers are permanently unemployed and a polarization between absolute wealth and absolute poverty begins. Unseen and often unknown productive and social relations that correspond to electromechanics are abandoned or begin a subtle transformation. (Peery)

The other aspect of revolution is the construction of new links. expressing the new law system or "necessary connections", in correspondence to the new tools and productive forces.

Interconnected phenomena (networks) should not be seen as a static circuit diagram, mapping out fixed relations (although such a map is often useful). Rather, phenomena/networks, vibrate with exchanges and interpenetrating causes and effects, punctuated with phase changes and dramatic destruction and reconstruction.

More thoughts, articles, links, etc. on networks and interconnection are on my Networks and dialectics web log.
Post a comment on my web log on Networks and Dialectics.

Notes

1. For some good summaries, see the papers by Brand and Miller at http://www.scienceofsociety.org/discuss/dialectics/dialectics.html.

2. This isn't to say that science is necessarily either dialectical or materialist (in some cases one or the other, in some cases neither, and of course in some cases both). (See, e.g., Levins and Lewontin) But dialectics does need to at least assess the new.

3. There is some continuity between socialist-bloc science and complexity theory. And therefore quite possibly between dialectics and complexity theory and its offshoot network science. Although the history from dialectics to complexity, as far as I know, has never been written, there are enough references to Soviet or socialist-bloc science and education to suspect that the field of complexity was at least fertilized by dialectics.

...Western scientists have often repeated work that already existed in the Soviet literature. This blossoming of chaos in the United States and Europe has inspired a huge body of parallel work in the Soviet Union; on the other hand, it also inspired considerable bewilderment, because much of the new science was not so new in Moscow. Soviet mathematicians and physicists had a strong tradition in chaos research, dating back to the work of A. N. Kolmogorov in the fifties. (Gleick, 76)

In the field of network science, much of the initial theorization about graph theory (a field of mathematics that has served as a precursor to network studies) and networks was done by scientists trained in the socialist bloc. Alfred Renyi, a Hungarian mathematician, who, with Paul Erdos (also Hungarian), laid down the foundation for network theory in the late 1950s and early 1960s, studied in Leningrad right after World War II. "There his [Renyi's] creativity exploded." (Barabasi, 20). Lev Landau, a leading theorist of "phase transitions" in physics, studied at the Institute of Physical Problems in Moscow and worked in the Soviet Union during and after World War II. (Buchanan) And Barabasi himself, the author of Linked and a leading researcher in the field of network theory, is from Transylvania, and studied physics and engineering at the University of Bucharest. While none of these biographical tidbits proves anything, it is not far-fetched that some dialectics perhaps rubbed off on these thinkers during their studies in Eastern Europe.

4. There are other important properties of networks. For example, the cost of adding nodes affects the distribution of links. Adding new links to a web site has relatively little cost, so the power-law distribution emerges more dramatically. The cost of adding links to O'Hare airport, however, is high (increased congestion on the runway, competition for gates, etc.), so the power law distribution and growth potential is suppressed.

Some nodes are capable of attracting, or grabbing many links. The "fitness" of a node is its ability to attract or gain links. Networks therefore display a "fitness distribution." The "preferential attachment" property and the "fitness" property will determine the shape of a growing network. If two nodes have the same number of links, new nodes will gravitate to the more "fit" node. In some networks, some nodes are so compelling that they display a "winner takes all" behavior. For example, in the world of computer software, there is clearly a drift towards de facto standards, because of the obvious benefits of everyone using the same program, so monopolies tend to emerge.

Links in networks may be "directed", where the interaction is not reciprocal. On the Internet, e.g., links have a "direction". Establishing a link from web page A to web page B does not mean that web page B will add a link to A. This feature leads to specific network structures.

Networks have a diameter (the average number of connections to get from any node to any other node), which in relation to the total number of nodes is an indication of the "small-world" effect. Networks, as information processors or circuits (e.g., the circuit of production), also have a speed property. The speed with which interactions can be communicated across the network has an effect on overall behavior. Network diameter makes for more efficient communication (fewer connections), but the speed of the connections (e.g., communication by courier vs. email) also has an important effect. "While computers don't create volatility, they do accelerate and exaggerate processes to the point where certain properties in the process can emerge. One report of experiments at IBM in the use of 'smart agents' in the factory, where software programs ('agents') were used to automatically make routine decisions like selling goods, noted that when the agents competed, 'they created a never-ending cycle of widely fluctuating prices.' ("Agents of Change on the Factory Floor", Business Week, Aug 7, 2000) (Davis). The speed of a network can also be thought of as a decision-making cycle.

Although not discussed in network science per se, other behaviors related to networks have been observed: "Metcalfe's Law" states that "the usefulness, or utility, of a network equals the square of the number of users." (http://www.mgt.smsu.edu/mgt487/mgtissue/newstrat/metcalfe.htm) "Reed's Law" goes even further: "Networks that support the construction of communicating groups create value that scales exponentially with network size." (http://www.reed.com/Papers/GFN/reedslaw.html)

5. More work needs to be done on the nature of qualitative change in relation to phase changes vs the overthrow of law systems. E.g., the transition of water to ice is in fact a re-ordering of links between water molecules, and goes through definite stages of water becoming ice. However, in the sense that we think of qualitative changes as "progressive" (from "lower" to "higher", or from less to more complex) and irreversible -- that leaves out phase changes. Water becomes ice under certain conditions, but can becomes water again under new conditions.

6. Think of sexual interactions as a network, with a relatively few highly active individuals, the superconnectors. Working with the superconnectors through education and prevention is a shortcut to halting an epidemic. (Buchanan 182) In the case of SARS:

"Top disease specialists are debating the theory of whether some people with SARS might be "superinfectors" or "superspreaders " -- that is, unusually contagious and able to transmit the illness to larger numbers of people. "Robert Breiman, head of a World Health Organization team investigating severe acute respiratory syndrome in China's Guangdong province, said one patient with the virus spread the disease to more than 30 people, two of whom died.

"He recovered, but only one of the 30 people he infected went on to transmit the illness, and that person infected just two others, who didn't pass it on to anyone else. "There are stories like that," Dr. Breiman says. "We're hoping to get them to look more closely at superspreaders ."

"Dr. Niman argues the number of superinfectors is low as a percentage of the total SARS population and that they "stick out like sore thumbs."