Network Theory

Paper reacting to an article on the risk created by a power law structure.

I can tell that John Mauldin enjoys reading interesting books. In this week’s newsletter, Mauldin discusses the ideas of Mark Buchanan in his book entitled Ubiquity: Why Catastrophes Happen (Buchanan 2002). I read this book when it first came out. It is a very interesting book. It argues that power laws are ubiquitous in the way that the world is organized. Power laws establish exponential relationships in a system. For example the inverse-square law of gravitation is an example of a power law. Likewise, the 80/20 Rule (aka the Pereto Principle) is an example of a power law. For example, 20% of the people receive 80% of the income. In fact much of the world does seem to be organized on the basis of power laws.

In his book, Buchanan gives the example of fault lines. The earth’s crust is riddled with fault lines, a few big, but most are small. You can imagine these fault lines like the branches on a tree. There is the main trunk that branches out into ever smaller branches and twigs. The smaller the size of the branches, the more numerous they are. Likewise, smaller and less dangerous fault lines are much more numerous in the earth’s crust than large and very dangerous fault lines. If you assume that slippage on fault lines is random, then we would expect many small, unnoticeable quakes and only rarely should we see massive quakes registering 8.0 or more on the Richter scale. In fact, this is what we do see. However, if the total number of large fault lines were to double in number, then we would see both a doubling in the number of great earthquakes. But, we would see an even more dramatic increase is smaller quakes, since the relationship between large and small fault lines is based on a power law.

I often argue to my students that to properly understand the functioning of a free market economy, it must be viewed as a large network, and thus “net work theory” applies to economics. In his book entitled Linked, Albert-Laszio Barabasi does an excellent job of describing network theory for the lay person. Using the Internet as the quintessential network, consider how it is organized. The organization of the Internet is based on a power law. Each website on the network is a node. There are millions and millions of very small nodes. These are websites (much like mine) which receive only a small amount of traffic. Think of all the MySpace pages, family newsletter pages, personal blogs, etc. The Internet is tied together through a system of links from one node to another. This system of links is critical to our navigation of the Internet. As websites increase in size as measured by traffic, we can see that the number of links to and from that website increase. In Network theory, these larger websites are called hubs. Currently, the biggest hub of all is Google. This power law organization is not very egalitarian, but it is vital to the functioning of a network. Hubs like Google, Yahoo, Amazon and eBay give the Internet is functionality and thus its value. As the total size of the Internet grows, because of its power law structure, the hubs must also correspondingly grow in size. If we were to abolish the power law structure of the Internet and require that all websites contain the same number of links and receive the same amount of traffic, the Internet would grind to a halt and be functionally worthless.

Accepting my argument that the economy is a network and has to thus be organized based on a power law structure, we can see why John Mauldin is under the impression that as Globalization precedes the number of serious economic disasters also increase. As the global economy grows in size and more and more people and firms become a part of the system, the hubs of the world’s economy also must grow in size to support the entire network. Mauldin used Long-Term Capital Management (LTCM) as an example of a hub, which nearly brought down the US economy in 1998, when it collapsed.

Just like the small fingers of the fault lines in our earthquake example, problems and disturbances involving individuals or even small and medium size participants in the market place are not going to bring down the system. But, as hubs become more numerous and larger in size, there is an increasing random chance of serious problems developing in a major hub and crashing the entire economic system. When you look strictly at that math, I agree, this is an obvious conclusion.

At the same time, this is the very process which is lifting hundreds of millions of people out of grinding poverty. This is the same process, which is delivering a better standard of living to each of us as the year go by. Thus, I was happy to see that at the end of his newsletter, John Mauldin made it clear that he is not advocating that we dismantle globalization. But, it is important that we give serious thought to these problems.

Think of the world before the process of globalization began. You might have a small town of village dong a small amount of business with another town a few miles away. However, the links were so small, weak and isolated that the destruction of a village would only impact those in the immediate area and have no impact on places farther away. This meant that you would not have to worry about the impact of an event on the other side of the world. But, it also meant that almost everyone was very poor. It was a world of hunger, a world of poverty and a world in which you were old if you happened to reach forty. Thus, when we worry about the dangers of globalization and the complexities of the global network, we also have to consider the dangers that would be caused by an end to globalization.

Last week, I discussed how “mind” changes things. I love to read books on science, just like I love to read about economics. There has been a great deal of cross pollination between economics and science, ever since Darwin sat down, read Malthus and decided to apply survival of the fittest to biology. This is a very creative process. For example, the mathematics used in the Black-Scholes option pricing model was adapted from a mathematical model of Brownian motion, describing the quantum jitteriness of molecules in a liquid. However, while math is deterministic, mind is not. Awareness of a problem can alter its outcome.

James Mahar, a finance professor at St. Buenaventura University in New York often mentions in his class lectures that people are REMs (Resourceful, Evaluative, Maximizers). In other words, people do not sit around waiting to be run over by the next disaster. Rather, they use their minds to bend alter the outcome. (Mahar 2007)

I think that LTCM is a great example of exactly this principle. While LTCM is widely cited to show the vulnerability of the global economy, in the end disaster was averted. People refused to stand idly by and await their fates. Instead, with the Federal Reserve leading the way, market participants recognized the danger and took action to avert the disaster.

While mathematical models and the application of scientific ideas to economics are very helpful, and they can give us important insights into the functioning of the economy, I also think that we need to recognize that economics is a human endeavor and that people through the use of their minds and the exercise of their wills can alter outcomes for the better.

References

Barabasi, Albert-Laszio (2003). Linked: How Everything Is Connected to

Everything Else and What It Means. New York,

NY: Penguin Group.

Buchanan, Mark (2002). Ubiquity: Why Catastrophes Happen. New York,

NY: Three Rivers Press.

Mahar, James (2007). FinanceProfessor.com. Retrieved December 10, 2007, from

PodCast Blaster Web site:

http://www.podcastblaster.com/directory/podcast-15899.html

Mauldin, John (2007, December, 7). Black Swans and Endogenous Uncertainty.

Thoughts from the Frontline Weekly Newsletter.

Taleb, Nassim Nicholas (2007). The Black Swan: The Impact of the Highly Improbable.

New York, NY: Random House.

		December 11, 2007 *Economics, Network Theory and Power Laws*
	Paper reacting to an article on the risk created by a power law structure. I can tell that John Mauldin enjoys reading interesting books. In this week’s newsletter, Mauldin discusses the ideas of Mark Buchanan in his book entitled Ubiquity: Why Catastrophes Happen (Buchanan 2002). I read this book when it first came out. It is a very interesting book. It argues that power laws are ubiquitous in the way that the world is organized. Power laws establish exponential relationships in a system. For example the inverse-square law of gravitation is an example of a power law. Likewise, the 80/20 Rule (aka the Pereto Principle) is an example of a power law. For example, 20% of the people receive 80% of the income. In fact much of the world does seem to be organized on the basis of power laws. In his book, Buchanan gives the example of fault lines. The earth’s crust is riddled with fault lines, a few big, but most are small. You can imagine these fault lines like the branches on a tree. There is the main trunk that branches out into ever smaller branches and twigs. The smaller the size of the branches, the more numerous they are. Likewise, smaller and less dangerous fault lines are much more numerous in the earth’s crust than large and very dangerous fault lines. If you assume that slippage on fault lines is random, then we would expect many small, unnoticeable quakes and only rarely should we see massive quakes registering 8.0 or more on the Richter scale. In fact, this is what we do see. However, if the total number of large fault lines were to double in number, then we would see both a doubling in the number of great earthquakes. But, we would see an even more dramatic increase is smaller quakes, since the relationship between large and small fault lines is based on a power law. I often argue to my students that to properly understand the functioning of a free market economy, it must be viewed as a large network, and thus “net work theory” applies to economics. In his book entitled Linked, Albert-Laszio Barabasi does an excellent job of describing network theory for the lay person. Using the Internet as the quintessential network, consider how it is organized. The organization of the Internet is based on a power law. Each website on the network is a node. There are millions and millions of very small nodes. These are websites (much like mine) which receive only a small amount of traffic. Think of all the MySpace pages, family newsletter pages, personal blogs, etc. The Internet is tied together through a system of links from one node to another. This system of links is critical to our navigation of the Internet. As websites increase in size as measured by traffic, we can see that the number of links to and from that website increase. In Network theory, these larger websites are called hubs. Currently, the biggest hub of all is Google. This power law organization is not very egalitarian, but it is vital to the functioning of a network. Hubs like Google, Yahoo, Amazon and eBay give the Internet is functionality and thus its value. As the total size of the Internet grows, because of its power law structure, the hubs must also correspondingly grow in size. If we were to abolish the power law structure of the Internet and require that all websites contain the same number of links and receive the same amount of traffic, the Internet would grind to a halt and be functionally worthless. Accepting my argument that the economy is a network and has to thus be organized based on a power law structure, we can see why John Mauldin is under the impression that as Globalization precedes the number of serious economic disasters also increase. As the global economy grows in size and more and more people and firms become a part of the system, the hubs of the world’s economy also must grow in size to support the entire network. Mauldin used Long-Term Capital Management (LTCM) as an example of a hub, which nearly brought down the US economy in 1998, when it collapsed. Just like the small fingers of the fault lines in our earthquake example, problems and disturbances involving individuals or even small and medium size participants in the market place are not going to bring down the system. But, as hubs become more numerous and larger in size, there is an increasing random chance of serious problems developing in a major hub and crashing the entire economic system. When you look strictly at that math, I agree, this is an obvious conclusion. At the same time, this is the very process which is lifting hundreds of millions of people out of grinding poverty. This is the same process, which is delivering a better standard of living to each of us as the year go by. Thus, I was happy to see that at the end of his newsletter, John Mauldin made it clear that he is not advocating that we dismantle globalization. But, it is important that we give serious thought to these problems. Think of the world before the process of globalization began. You might have a small town of village dong a small amount of business with another town a few miles away. However, the links were so small, weak and isolated that the destruction of a village would only impact those in the immediate area and have no impact on places farther away. This meant that you would not have to worry about the impact of an event on the other side of the world. But, it also meant that almost everyone was very poor. It was a world of hunger, a world of poverty and a world in which you were old if you happened to reach forty. Thus, when we worry about the dangers of globalization and the complexities of the global network, we also have to consider the dangers that would be caused by an end to globalization. Last week, I discussed how “mind” changes things. I love to read books on science, just like I love to read about economics. There has been a great deal of cross pollination between economics and science, ever since Darwin sat down, read Malthus and decided to apply survival of the fittest to biology. This is a very creative process. For example, the mathematics used in the Black-Scholes option pricing model was adapted from a mathematical model of Brownian motion, describing the quantum jitteriness of molecules in a liquid. However, while math is deterministic, mind is not. Awareness of a problem can alter its outcome. James Mahar, a finance professor at St. Buenaventura University in New York often mentions in his class lectures that people are REMs (Resourceful, Evaluative, Maximizers). In other words, people do not sit around waiting to be run over by the next disaster. Rather, they use their minds to bend alter the outcome. (Mahar 2007) I think that LTCM is a great example of exactly this principle. While LTCM is widely cited to show the vulnerability of the global economy, in the end disaster was averted. People refused to stand idly by and await their fates. Instead, with the Federal Reserve leading the way, market participants recognized the danger and took action to avert the disaster. While mathematical models and the application of scientific ideas to economics are very helpful, and they can give us important insights into the functioning of the economy, I also think that we need to recognize that economics is a human endeavor and that people through the use of their minds and the exercise of their wills can alter outcomes for the better. References Barabasi, Albert-Laszio (2003). Linked: How Everything Is Connected to Everything Else and What It Means. New York, NY: Penguin Group. Buchanan, Mark (2002). Ubiquity: Why Catastrophes Happen. New York, NY: Three Rivers Press. Mahar, James (2007). FinanceProfessor.com. Retrieved December 10, 2007, from PodCast Blaster Web site: http://www.podcastblaster.com/directory/podcast-15899.html Mauldin, John (2007, December, 7). Black Swans and Endogenous Uncertainty. Thoughts from the Frontline Weekly Newsletter. Taleb, Nassim Nicholas (2007). The Black Swan: The Impact of the Highly Improbable. New York, NY: Random House.