Mr. Carpenter,
Although, at first, the following article appears to belong on a different thread I assure you it belongs right here. Mathematics just may provide a new metaphor to describe the current conditions. It's been a little while since Henry has posted so let's just consider this bear bait and see if we can provoke a comment or two from him.
The Skeptical Investor in your previous posting suggests that the idea of contagion does not adequately describe what is happening in the currency markets. "The global financial crisis is frequently described as a "contagion" which began in Thailand, spread through Asia, then to Russia, Latin America and other countries, and is now "infecting" North America and Western Europe. Although almost everyone else has been using it, I have avoided using the word "contagion" in The Skeptical Investor like the plague (joke!). It is a very misleading way to describe what is going on."
(I hope that my naked appropriation of the following article from my favorite periodical can be compensated by a sincere and enthusiastic endorsement at the end of this lengthy posting.)
<<Once upon a time, in a village of uncertain location, there lived fifty married couples. Now, the rigid statutes of the village required that if a woman could prove her husband had been unfaithful, she had to kill him that very day. Moreover, the women were highly intelligent and aware of one another's intelligence, and they always abided by the statutes. They were also terrible gossips, but they were careful to spare one another's feelings. As a result, each of them knew immediately when another woman's husband had been philandering, but never when her own had been doing so.>>
<<As it happens, all fifty of the men had been unfaithful, but since no woman could prove her own husband's guilt, the village proceeded merrily -- and warily -- along. Then one fateful morning the tribal matriarch came to visit from the far side of the forest. The matriarch's honesty was acknowledged by all; her word was taken as law. Still, when she announced darkly that there was at least one philandering husband in the village, she hardly raised an eyebrow -- after all, she was only repeating to all what every woman already knew.>>
<<There followed forty-nine peaceful days, as one might expect. But on the fiftieth day a massive slaughter took place, and every woman killed her husband. How could that be?>>
<<To follow the reasoning, imagine what would have happened if there had been only one unfaithful husband in the village, Mr. A. In that case, before the matriarch arrived, everyone except Mrs. A would already have known about his infidelity. So when the matriarch made her announcement, only Mrs. A would have learned something new from it. Being intelligent and well aware of her neighbor's penchant for gossip, Mrs. A would have realized that if any other husband were unfaithful, she would have known about it. Thus she would have inferred that Mr. A was the philanderer and killed him that very day.>>
<<Now suppose there had been only two unfaithful men, Mr. A ad Mr. B. Every woman except Mrs. A and Mrs. B would have known about both cases of infidelity; Mrs. A would have known only of Mr. B's and Mrs. B would have known only of Mr. A's. Thus Mrs. A would have learned nothing from the matriarch's announcement, but when Mrs. B failed to kill Mr. B the first day, she would have inferred that Mr. A must also be guilty. The same holds for Mrs. B who would have inferred from the fact that Mrs. A had not killed her husband on the first day that Mr. B was also guilty. The next day both Mrs. A and Mrs. B would have killed their husbands.>>
<<If instead, there had been exactly three guilty husbands, Mr. A, Mr. B and Mr. C, then the matriarch's announcement would have had no impact on the first day, but by a reasoning process similar to the one just described, Mrs. A, Mrs. B and Mrs. C each would have inferred from the inaction of the other two on the first two days that their husbands were also guilty and therefore killed them on the third day. By a process of mathematical induction one can conclude that if all fifty husbands were unfaithful, their intelligent wives finally would be able to prove it on the fiftieth day, the day of the righteous bloodbath.>>
<<Now replace the matriarch's warning with the currency problems that began to appear in Thailand, Malaysia and other Asian nations in the summer of 1997; the uneasiness of the wives with the uneasiness of investors; the wives' contentment as long as their own bulls weren't goring with the investors' contentment as long as their own bulls weren't being gored; killing husbands with selling stocks; and the fifty-day gap between the warning and the killings with the long delay between the East Asian problems and the recent big sell-offs worldwide. Big financial players with substantial investments in Asian economies were vulnerable, but the process that eventually revealed the investors' own vulnerability and caused them to act did not begin until the problem was publicly exposed.>>
<<Thus the Malaysian prime minister's speech criticizing Western banks in August 1997 -- a kind of matriarch's warning -- may have precipitated, more than a year later, the very crises he most feared.>>
<<Happily, unlike the husbands in the story, markets can be resurrected. When they will be, however, is anyone's guess. Such is life, death, buying and selling in the global village.">>
Comments, Henry? Anyone?
Jerard P
P. S. The above quotation comes via The Sciences, published by the New York Academy of Sciences, November / December 1998 and was adapted from the forthcoming book by John Allen Paulos called; Once Upon A Number to be published in December by Basic Books.
The Sciences, a perennial winner of award after award, has IMO the best science writing out there. Best of all almost all the illustrations are culled from collections of fine art. I urge all to get a subscription. |
