Saturday, October 07, 2006
instability
Back in the 1980s, I read a book called Weather at Sea. Those familiar with Charlie Munger of Berkshire Hathaway (Warren Buffett's children say that Charlie is the smartest person they've ever met, which says good things about both Charlie and Warren Buffett) would recognize this as one of those "mental models" that Munger is always talking about. The whole point of mental models is that by studying the current theoretical and practical knowledge about real-world complex systems, you can gain a certain understanding of many principles of how complex things works.
Some complex systems are things like global weather, a large suspension bridge, a silicon chip microprocessor (the actual electrical characteristics), a large corporate organization, an ordinary animal like a housecat, or the stock market. The point of these things is that none of them are truly "solved" and completely understood. There are regions of operation where our understanding, our "model" of these things is able to predict their behavior very closely. But every complex system has third order, fourth order, and higher effects that may have negligable impact on the system in most conditions. They may be totally hidden and unknown until the system gets into some rare state where they may unexpectedly cause our model of the system to diverge greatly from what the actual system will do.
A famous example of this was the Tacoma Narrows Bridge which collapsed in 1940. Before that time, bridge engineers were far less concerned about (and perhaps less knowledgable about) underdamped resonance characteristics [combined with aerodynamics] in structures than they have been since. Today, the field of control theory within engineering has done a great deal of work to understand and model resonance in complex systems, thanks to a huge number of brilliant, hard-working, and results-oriented people. It's not surprising that this model of resonance carries over into all complex systems: that's usually the case. When you develop an accurate model for some aspect of a system, it will typically apply to other systems.
If you were to take a block of air from, say, 5,000 feet above sea level and then move it up slightly higher in altitude, because of the lower air pressure at that slightly higher altitude and because of the model of PV=nRT, the block of air will be slightly colder. But the interesting question is What is the temperature of the surrounding air at that higher altitude? If the surrounding air at that higher altitude is actually colder than the slightly cooled block of air, then because it will have a lower density (again due to PV=nRT), the warmer block of air will be pushed up to a higher altitude. And once again, if the surrounding air at that even higher altitude is colder than the rising block of air, the block of air will continue rising. And adding to this effect is the fact that, at a lower pressure and temperature, water from within the block of air may condense into water droplets which will cause the block of air to heat up, which causes it to rise even faster.
This situation is why we see puffy clouds so often in certain atmospheric conditions. It's actually an instability within the air. Some small perturbation causes a small amount of air to rise slightly, causing it to be warmer than the surrounding air, causing it to rise even more, etc. Eventually water condenses out causing it to rise even faster. When the unstable temperature gradient extends through a large vertical section of the air, then you get very tall clouds. And then lots of other effects kick in, such as electrical charges building up as the rising air passes through falling rain and hailstones.
The basic principle of instability is that it exists when a small push against some part of the system in one direction causes it to move in that direction and that the conditions are such that the more it moves in that direction, the more force it experiences in that same direction.
Logically, you might think that this would continue indefinitely, but all real-world systems are finite. And because they're finite, eventually some other factor will kick-in to override the instability. In the weather example, the air is only so tall. Also, there are factors that kick in above around 50,000 feet that will make it difficult to maintain an instability. The rising air column will flatten out horizontally forming the classic anvil shape of thunderclouds. In all real-world systems, the farther away from the normal equalibrium you get, the more you'll bump into other factors that will become more important than the instability. Complex systems in the real world are stable overall because, if they weren't, they wouldn't exist. They would be very temporary.
In early 2000, at the peak of the Great Bull Market, I was reading the Motley Fool book, Rule Breakers, Rule Makers. The book had been out for about a year in hardcover and was very popular. The final rule for identifying a "Rule Breaker" stock was this:
In the case of the stock market bubble, it continued until the overriding factors reached a certain point and then fear took hold. The fear in this recent bubble wasn't as bad as the fear during the 1930s because the people running the economy were a lot more knowledgable about avoiding Great Depressions and because investors are a lot more knowledgable about stocks, businesses, and markets today than in the 1930s. This is what experience is all about. Ignorant idealism not founded on lots of experience with, and accurate models of, the complex system of the economy and markets, on the other hand, causes a great deal of economic stupidity.
In the past week, the Dow Jones Industrial Average reached an all-time high point three times in a row. The NASDAQ composite (which was a better representation of the glamourous stocks), would need to more than double to do the same. And when you look at the Dow chart, the bigger picture it portrays is one of a long, continuous increase in the overall wealth, interrupted by the stupidity of the 1930s, the 1970s, and the more recent period from 1995 to 2003: localized instabilities within an overall stable system.
Some complex systems are things like global weather, a large suspension bridge, a silicon chip microprocessor (the actual electrical characteristics), a large corporate organization, an ordinary animal like a housecat, or the stock market. The point of these things is that none of them are truly "solved" and completely understood. There are regions of operation where our understanding, our "model" of these things is able to predict their behavior very closely. But every complex system has third order, fourth order, and higher effects that may have negligable impact on the system in most conditions. They may be totally hidden and unknown until the system gets into some rare state where they may unexpectedly cause our model of the system to diverge greatly from what the actual system will do.
A famous example of this was the Tacoma Narrows Bridge which collapsed in 1940. Before that time, bridge engineers were far less concerned about (and perhaps less knowledgable about) underdamped resonance characteristics [combined with aerodynamics] in structures than they have been since. Today, the field of control theory within engineering has done a great deal of work to understand and model resonance in complex systems, thanks to a huge number of brilliant, hard-working, and results-oriented people. It's not surprising that this model of resonance carries over into all complex systems: that's usually the case. When you develop an accurate model for some aspect of a system, it will typically apply to other systems.
In theory, there's no difference between theory and practice, but in practice there is.Weather at Sea is an intense tutorial about the physics of weather for people who need to be able to be their own meteorologists while travelling a great deal across oceans. While there are a lot of interesting models in the book, one that I've found very useful is the stability or instability of a local air mass.
If you were to take a block of air from, say, 5,000 feet above sea level and then move it up slightly higher in altitude, because of the lower air pressure at that slightly higher altitude and because of the model of PV=nRT, the block of air will be slightly colder. But the interesting question is What is the temperature of the surrounding air at that higher altitude? If the surrounding air at that higher altitude is actually colder than the slightly cooled block of air, then because it will have a lower density (again due to PV=nRT), the warmer block of air will be pushed up to a higher altitude. And once again, if the surrounding air at that even higher altitude is colder than the rising block of air, the block of air will continue rising. And adding to this effect is the fact that, at a lower pressure and temperature, water from within the block of air may condense into water droplets which will cause the block of air to heat up, which causes it to rise even faster.
This situation is why we see puffy clouds so often in certain atmospheric conditions. It's actually an instability within the air. Some small perturbation causes a small amount of air to rise slightly, causing it to be warmer than the surrounding air, causing it to rise even more, etc. Eventually water condenses out causing it to rise even faster. When the unstable temperature gradient extends through a large vertical section of the air, then you get very tall clouds. And then lots of other effects kick in, such as electrical charges building up as the rising air passes through falling rain and hailstones.
The basic principle of instability is that it exists when a small push against some part of the system in one direction causes it to move in that direction and that the conditions are such that the more it moves in that direction, the more force it experiences in that same direction.
Logically, you might think that this would continue indefinitely, but all real-world systems are finite. And because they're finite, eventually some other factor will kick-in to override the instability. In the weather example, the air is only so tall. Also, there are factors that kick in above around 50,000 feet that will make it difficult to maintain an instability. The rising air column will flatten out horizontally forming the classic anvil shape of thunderclouds. In all real-world systems, the farther away from the normal equalibrium you get, the more you'll bump into other factors that will become more important than the instability. Complex systems in the real world are stable overall because, if they weren't, they wouldn't exist. They would be very temporary.
In early 2000, at the peak of the Great Bull Market, I was reading the Motley Fool book, Rule Breakers, Rule Makers. The book had been out for about a year in hardcover and was very popular. The final rule for identifying a "Rule Breaker" stock was this:
Finally, given this confluence of positive factors, you must find documented proof that it is grossly overvalued, according to the financial media.Think about that for a minute. The final proof that a stock is a good investment is that people with experience are saying that it's overvalued. If just a small portion of the investment dollars are moving by this principle, then the system would not be changed by it. But when a large percentage of the investment dollars are applying this principle, then you clearly have created an instability in the stock market system. The more a stock goes up into overvalued prices, the more it's considered a good invesment and the most the price will continue going up. While this one book did not create the stock market bubble, the same kind of thinking that inspired the book did.
In the case of the stock market bubble, it continued until the overriding factors reached a certain point and then fear took hold. The fear in this recent bubble wasn't as bad as the fear during the 1930s because the people running the economy were a lot more knowledgable about avoiding Great Depressions and because investors are a lot more knowledgable about stocks, businesses, and markets today than in the 1930s. This is what experience is all about. Ignorant idealism not founded on lots of experience with, and accurate models of, the complex system of the economy and markets, on the other hand, causes a great deal of economic stupidity.
In the past week, the Dow Jones Industrial Average reached an all-time high point three times in a row. The NASDAQ composite (which was a better representation of the glamourous stocks), would need to more than double to do the same. And when you look at the Dow chart, the bigger picture it portrays is one of a long, continuous increase in the overall wealth, interrupted by the stupidity of the 1930s, the 1970s, and the more recent period from 1995 to 2003: localized instabilities within an overall stable system.
// posted by Bruce @ 9:30 AM 
