It's been a long long time since I wrote one of these, but reading James Gleick's book Chaos got me thinking about all that is going on these days and how much you can apply it to them, albeit in an abstract manner, since I obviously lack the mathematical skills to model it accurately.
Let me start off by introducing this one equation that started a lot of it, the Logistic Difference Equation. It may sound complicated, but all it says is that x_next = alpha * x * (1-x), where x is anything you're modeling. What many scientists found was that choosing different values of alpha can lead to wildly varying behaviors, behaviors which are actually observed in diverse fields such as weather, populations, economics etc. I'll give one small example of populations, that if alpha is small, populations remain constant, or decline, but if alpha rises above a certain threshold, it can rise explosively. Now this is a very simplistic model, but it shows what "non-linearities", i.e. functions that are not a straight line, are capable of.
Why it applies in the current context is because of the attempt to control a number of highly undesirable developments happening these days. The economy is going to hell, education is starting to suffer in a number of notable countries (I know that more than most :P). As a result or otherwise, politics is becoming much more extreme. Since the USA is too easy an example, I'll take my home country, India. Currently, a notable gentleman by the name of Anna Hazare is leading a crusade to wipe out corruption from India, starting with the government. While some may applaud, and others may scoff, my interest for the time being is to see if his approach is viable or not. For a thorough critique of his methods, try reading Greatbong's blog post about it. So Anna's idea for rooting out corruption is to create a body above all others, whose members are not elected, but nominated from the notable members of society. This body, headed by a "Lokpal" would bring forth charges against officials and try them. Now, most engineers would notice the lack of feedback in the system, meaning the system would function wonderfully if we assume the members of this board to be unaffected ghosts bereft of all feeling and earthly connections, i.e. those who cannot be swayed by us common, corrupt folk. However, if an error enters the system, e.g. a corrupt person becoming a Lokpal, can have drastic consequences, since it's very hard for the system to filter out this error. Herein lies the nonlinearity and the scope for drastic and dictatorial repercussions. Like the logistic difference equation, specific values of alpha make this an amazing system, some bad ones have the possibility of making this a mistake of Nazi proportions...
The same idea applies to economics, since this idea owes much of its origins to economics. Markets, the US economy and consequently the dollar are suffering like an enemy of Chuck Norris/Rajnikant. People are quite upset about this brouhaha and want something to be done, what this something should be varies considerably from person to person. The core of the problem is, and still remains, that the US economy does not make enough money to finance the expenditures of its people. Like it or not, that's the plain simple truth, don't believe me, look at the labels on anything sold in the USA and see what percentage is actually made there. Made in the USA is a very rare label to see these days. The one thing that's held the US up is the dollar, since being the world's reserve currency, no one wants to see it depreciate, in spite of rampant injections of fresh dollars. This is one of the reasons that USA has been able to recover atleast partially from the housing bust while other like Greece have not, as borrowing is a lot easier when you can print the payments without seeming loss of value. To those who might not understand this, just imagine a supply-demand system, where the supply of any commodity becomes almost unlimited, what would happen to its price. Truth be told, smaller scale vibrations like this have happened in the world economy in the past, it's just that things could be brought back under control much easier than today, cause the world's economy was simply in much better shape. This time it's so bad, because the USA is stretching the limits of its borrowing power (again, like it or not, it's the truth, see China's reactions, they're the biggest debt provider to the USA), and its people are not yet ready to accept that their spending is beyond their means. Similar situations unfortunately exist in a lot of the developed world. So this time the nonlinearity could be brought to heel, or could spiral out of control.
Why I keep harping about this nonlinearity is cause I work on simulations, and know that like an experimental simulation code, the point where your simulation becomes unstable and explodes is usually preceded by small oscillations in either direction, i.e. the situation becomes better, then worse, then better, then even worse and so on. These oscillations increase in amplitude and at a critical point, take over the system and every bit of expected behavior is overturned. Unfortunately for us, very little is understood about such systems, yet all of nature, physics, and even human behavior is completely non-linear. We have managed so far by approximating these, since our "alpha's" have been small, but it seems like we're quickly getting to the point where these oscillations could escalate into chaos. After all, doomsday prophecies don't always have to mean that the world ends literally...
Let me start off by introducing this one equation that started a lot of it, the Logistic Difference Equation. It may sound complicated, but all it says is that x_next = alpha * x * (1-x), where x is anything you're modeling. What many scientists found was that choosing different values of alpha can lead to wildly varying behaviors, behaviors which are actually observed in diverse fields such as weather, populations, economics etc. I'll give one small example of populations, that if alpha is small, populations remain constant, or decline, but if alpha rises above a certain threshold, it can rise explosively. Now this is a very simplistic model, but it shows what "non-linearities", i.e. functions that are not a straight line, are capable of.
Why it applies in the current context is because of the attempt to control a number of highly undesirable developments happening these days. The economy is going to hell, education is starting to suffer in a number of notable countries (I know that more than most :P). As a result or otherwise, politics is becoming much more extreme. Since the USA is too easy an example, I'll take my home country, India. Currently, a notable gentleman by the name of Anna Hazare is leading a crusade to wipe out corruption from India, starting with the government. While some may applaud, and others may scoff, my interest for the time being is to see if his approach is viable or not. For a thorough critique of his methods, try reading Greatbong's blog post about it. So Anna's idea for rooting out corruption is to create a body above all others, whose members are not elected, but nominated from the notable members of society. This body, headed by a "Lokpal" would bring forth charges against officials and try them. Now, most engineers would notice the lack of feedback in the system, meaning the system would function wonderfully if we assume the members of this board to be unaffected ghosts bereft of all feeling and earthly connections, i.e. those who cannot be swayed by us common, corrupt folk. However, if an error enters the system, e.g. a corrupt person becoming a Lokpal, can have drastic consequences, since it's very hard for the system to filter out this error. Herein lies the nonlinearity and the scope for drastic and dictatorial repercussions. Like the logistic difference equation, specific values of alpha make this an amazing system, some bad ones have the possibility of making this a mistake of Nazi proportions...
The same idea applies to economics, since this idea owes much of its origins to economics. Markets, the US economy and consequently the dollar are suffering like an enemy of Chuck Norris/Rajnikant. People are quite upset about this brouhaha and want something to be done, what this something should be varies considerably from person to person. The core of the problem is, and still remains, that the US economy does not make enough money to finance the expenditures of its people. Like it or not, that's the plain simple truth, don't believe me, look at the labels on anything sold in the USA and see what percentage is actually made there. Made in the USA is a very rare label to see these days. The one thing that's held the US up is the dollar, since being the world's reserve currency, no one wants to see it depreciate, in spite of rampant injections of fresh dollars. This is one of the reasons that USA has been able to recover atleast partially from the housing bust while other like Greece have not, as borrowing is a lot easier when you can print the payments without seeming loss of value. To those who might not understand this, just imagine a supply-demand system, where the supply of any commodity becomes almost unlimited, what would happen to its price. Truth be told, smaller scale vibrations like this have happened in the world economy in the past, it's just that things could be brought back under control much easier than today, cause the world's economy was simply in much better shape. This time it's so bad, because the USA is stretching the limits of its borrowing power (again, like it or not, it's the truth, see China's reactions, they're the biggest debt provider to the USA), and its people are not yet ready to accept that their spending is beyond their means. Similar situations unfortunately exist in a lot of the developed world. So this time the nonlinearity could be brought to heel, or could spiral out of control.
Why I keep harping about this nonlinearity is cause I work on simulations, and know that like an experimental simulation code, the point where your simulation becomes unstable and explodes is usually preceded by small oscillations in either direction, i.e. the situation becomes better, then worse, then better, then even worse and so on. These oscillations increase in amplitude and at a critical point, take over the system and every bit of expected behavior is overturned. Unfortunately for us, very little is understood about such systems, yet all of nature, physics, and even human behavior is completely non-linear. We have managed so far by approximating these, since our "alpha's" have been small, but it seems like we're quickly getting to the point where these oscillations could escalate into chaos. After all, doomsday prophecies don't always have to mean that the world ends literally...
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