Friday, December 19, 2008

Zeno's Paradoxes

Paremenides was a philosopher who rejected change and motion as illusory (I've mentioned him before). One of his students was Zeno, who set up a series of paradoxes (some 40) to show that the concept of motion was absurd. Most of them ultimately stem from the problem of the infinitely divisibility of finite spans of space and time. Nonetheless, they present perplexing problems, which certainly weren't soluble with Greek mathematics, and even strain modern mathematical theory (George Cantor notwithstanding).

The two that are the most characteristic are the arrow paradox and Achilles and the tortoise. The arrow paradox first defines a thing at rest as something that occupies its own space, then says that when you throw an arrow through the air, then it always occupies its own space, therefore it must always be at rest. Why we should say that a thing that occupies its own space must be at rest and can't also be in motion is unclear. It might have something to do with the idea that if it occupies its own space and nothing more, then how can it continue to propel itself forward after it leaves the hand. This was a problem that vexed Aristotle, but which we can now can take for granted, leaving Zeno's arrow paradox not so vexing to us.

The Achilles and the Tortoise paradox is more interesting though. Achilles was reputed to be a fast runner. If Achilles is racing with a tortoise and he gives him a head start, then when Achilles starts running he will catch up to where the tortoise was when he first started running, but since time will have elapsed the tortoise will no longer be there, so he'll run to where the tortoise is now, but he won't be there by the time he reaches that spot, and so on. Thus, Achilles would never reach the tortoise. We should remind ourselves of the ultimate purpose of this argument, which is to show that motion is absurd; therefore, nothing is in motion, there is no change.

Aristotle's response to this paradox, is that it is irrelevant, since we can clearly see that things move. But Aristotle's refutation wouldn't convince Zeno since he and Parmenides both realize that we perceive motion, but they think that the perceived motion is an illusion. George Cantor, will also come along with a resolution to this with new mathematics of infinite sets and actual infinities.

I think, though, even without this sophisticated mechanism we can already see that it is problematic. The problem with Achilles and the tortoise is that, if the paradox is valid, then we should actually see Achilles being unable to catch up with the tortoise. The way the paradox is set up, it should affect both real and apparent motion. And yet we have many times seen faster runners catch up to faster and pass by them. We shouldn't even be able to see this occur. And yet we do see it occur.

In other words, Zeno's paradoxes prove too much. They prove both the absurdity of real and apparent motion. Whereas we don't observe any problem with apparent motion. This shows us that there is a problem with Zeno's paradoxes, though it doesn't show us what that problem is. It is up to later and more sophisticated mathematics to point out those problems.

Saturday, December 13, 2008

Freedom and the Ability to do Otherwise

Theological absolutism can frequently lead to certain contradictions. For example, it is supposed that God is omnipotent and all powerful and yet that humans have free will. If God is all powerful then God must control everything, including my actions. But if God controls my actions, then I can 't have free will. One way to dodge the problem is to speak of potential omnipotence. In other words, God could control me, but God permits me to have free will.

Yet another solution is to approach the problem by dividing up the concept of freedom. Freedom is proposed to have two parts: autonomy and choice. Autonomy just means that I do my actions myself. I am not a puppet in any sense. For example, the somnambulist Cesare in The Cabinet of Dr. Caligari has no autonomy since he is controlled by Caligari, or in Being John Malkovich, John Malkovich loses his autonomy when his body is taken over by Craig Schwartz the puppeteer.

Though I think none of use would deny that autonomy is necessary for freedom, I think we assume there is something more. We usually also want to include choice, namely having multiple options. To be unambiguous this is sometimes called the ability to do otherwise. Now, I don't really care to quibble over terms and debate whether "freedom" means just autonomy or means the ability to do otherwise plus autonomy. When this is put in a metaphysical-theological context to try to guarantee free will, it doesn't really work. How can I be blamed for doing any action when I could do nothing else?

Descrates uses this distinction too in his discussions of freedom. He becomes convinced that reason leads to good action, and he even goes so far as to say that reason compels good action. Once you see the truth of something (with clear and distinct perceptions) you can't help but believe it, and once you see the goodness of something, you can't help but do it. But, being a faithful Christian, he can't deny free will. So, he has to demarcate this separation between choice and autonomy. He then claims that autonomy is sufficient for free will. But how can you possibly permit responsibility in the full Christian sense and still embrace this idea of the compulsion of reason?

Sunday, December 7, 2008

Market Bubbles and Tinkering

There's been a lot of talk these days about the psychology of speculative bubbles, which is not always entirely useful for helping us understand the situation. Most of these theorists provide little insight, since they don't explain why they happen when they do. If bubbles are simply caused by human psychology we should expect them all the time, since human psychology doesn't change, and yet we don't see this in reality. Despite these shortcomings, I think there are useful insights to be found.

The leads to an article from this month's The Atlantic about how market bubbles are inevitable. I've seen other articles like this one, but this one is particularly useful because it gives us some details about a number of different experiments in this area and their results. It's important to see direct results of the experiments themselves, since it's often the experimental results, and not the experimenters' conclusions that provide the most insight.

The experimenters created a very simply low-stakes financial market where volunteers can trade stocks and will receive dividends. These experiments show that in a very simple and brief trading market, volunteers will tend to create financial bubbles, which will duly crash, resulting in lower profits for everyone involved. To reduce the problem of poor information, the subjects are given constantly updating information about expected dividends (dividend payments vary randomly, but will average 24 cents). Thus, it seems to show that people are irrational, since they would have been better off if they hadn't tried to profit by speculation, thereby creating the bubble.

Admittedly, there are many are many artificial features of this market which don't seem to replicate reality. The amount of money is low (one can only expect to earn a few dollars), so there is little at stake for the subjects. The experiment is short, only lasting an hour. There is an artificial end to the trading, which can cause rash trading just before the close. And subjects aren't allowed to talk to each other, restricting the flow of information more than in a real market.

But as it turns out, one of the biggest artificial features is that the experiments are all and equally inexperienced. What happens when the same group repeats the whole experiment once more with the same market conditions? Well, it turns out, on the second try, they anticipate the bubble and then try to ride it up some of the way and then cash out before it bursts. This causes the bubble to happen sooner and be smaller, and be followed by a long period of stability. When they repeat it again, the same trend continues, with the bubble happening even sooner and being even smaller. Replicate the experiment enough times and you'll only have tiny bubbles and tiny pops, probably happening multiple times in the one hour session. But, no one would call these bubbles anymore. This would just be normal market fluctuation as a rational model would predict.

Behavioral economists sometimes fail to to distinguish bad decision making due to irrationality and bad decisions made due to poor information. It's not surprising that people don't maximize self-interest when they rely on limited and sometimes incorrect information to make their decisions. These experimenters had tried to reduce the effects of limited information by giving accurate and constantly updated calculations of expected dividends. But the subjects still had little to no information of how markets behave, and most importantly of how this market would behave over the course of the one hour. This experimental market has many unusual features and so knowledge of stock markets or futures markets might not translate into an ability to profit from this tiny experimental market. But real investors in the real economy do know how various markets behave and they tend to stick with markets that they understand. Thus, behavior of the subjects after a few tries, unsurprisingly best reflects the behavior of real markets.

But there's another little detail that experimenters further revealed. When they put subjects experienced in one set of parameters through the experiment one more time, but this time with a different set of parameter, this led to bubbles all over again. The bubbles weren't quite as bad as subjects doing it for the first time, but the subjects did overall perform more poorly when they had readjust to a new market system.

Thus, the conclusion seems simple: investors inexperienced in the behavior of a particular market will tend to create bubbles. Thus, when federal regulators constantly try to tinker with the market, they force investors to constantly relearn the game. This includes the actions of the Federal Reserve, the Treasury and the lawmakers. They are all constantly creating new parameter of which investors have little or no exact experience. In addition, these new rules and decisions don't come out of the blue, as they do in the experiment. Investors try to anticipate the next move of the Fed or Congress and respond in advance, which further complicates the markets and makes it more unpredictable for investors, since now they're trying to second guess the regulators and second guess each other's second guessing.

These insights are consonant with the Austrian theory of the business cycle, which better explains why the bubbles start to begin with when they do and how they get started. The Austrians explain that credit expansion leads to the appearance of prosperity, which distorts usual economic signals, triggering excessive, unsustainable investment. With the insights from these experiments, I think we can see another factor contributing to how bubbles get out of control. Cheap credit and the resultant boom create novel conditions which experienced investors struggle to adapt to and the cheap credit and apparent abundant prosperity can attract inexperienced investors, who are prone to tulipmania and herding. Add to this ideas like Robert Higgs' concept of regime uncertainty and you can see how intervention can be, by nature, whether well-considered or ill-considered, counter-productive.

Politicians frequently characterize the economic system as a car that needs to be tinkered with, so that it runs more smoothly, or needs to be jump started when it slows down. But the economy is much more like a living breathing thing, filled with sentient, dynamic cogs that adapt to the conditions around them. Politicians are not tinkering, but performing surgery on the economy. Politicians need to learn to set down the scalpel long enough to let the wounds from their last intervention heal before they start to assume that the economy is dying because it is inherently flawed.

Thus, the simple policy recommendations to our lawmakers and regulators would be: do nothing, preferably even try to scale back on what you're already doing. The economy needs to heal.