Henry wrote: << I'm as upset as anyone by the financial crisis(es?) of the last several years, but I'm even more upset by the lack of mathematical sophistication of those in charge. I'm not at all confident that these folks have a clue, in which case any cure they propose is highly likely to be worse than the disease. Given that these people are often from the best universities (Ivy League, etc.), I think their innumeracy demonstrates that our university educational system has failed society miserably, at least when it comes to some relatively fundamental mathematical concepts. Example 1. A pronouncement that the stock market crash of last Thursday was caused by a "negative feedback loop". Of course, it was far more likely to have been caused by a "positive feedback loop"; negative feedback loops are typically self-stabilizing, while positive feedback loops are the ones that explode exponentially.
It seems hardly worthy of mention if someone was trying to say "vicious cycle" but instead said "negative feedback loop". << Example 2. After all the incessant talk of "chaos" and "fractals" over the past 30+ years, these basic ideas still don't seem to have percolated into brains of the intelligentsia. When a system is chaotic, there may be no amount of "regulation" that can fix it. If a butterfly wing flap can cause a hurricane to hit New Orleans instead of Tallahassee, what do you expect a regulator to do, kill all the butterflies with DDT?
This sounds like saying that because our minesweepers are flawed and can't even detect some mines at all, we shouldn't even try to find them. << Example 3. We've known since Gödel that every sufficiently powerful logical system can have undecidable consequences. . . . This provides a powerful heuristic: the first place to look for instability in a system is where a system is attempting to regulate itself -- e.g., Congress trying to make rules that apply to Congress itself.
There's certainly some truth to this and closely related ideas. For example, recent studies have shown that often, the more that law enforcement tries to clamp down on violent, powerful drug organizations, the more virulent and powerful they tend to become. (A bit like taking a course of antibiotics for an infection, but stopping before it's fully wiped out. Which is not to say we should engage in a battle to the finish with such drug organizations . . ..) And certainly there are computer-automated trading routines whose behavior in many situations is not known and could be (and could have already been) disastrous. I said *some* truth, because there is much regulation that seems successful, like your most basic law enforcement, laws that make many utilities *public* utilities so we don't end up getting gouged for a glass of water, laws that prevent 51% or the population from tyrannizing the other 49%, etc. --Dan ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx