Fred L. writes (among other things): << Another feature of networks [from percolation theory ...] is that they go critical: as traffic approaches the maximum capacity, a small increase traffic precipitates sudden gridlock over a large region. As a result, a crisis arising from other causes is intensified by the inability of the participants to communicate at all.
Percolation theory is really incredibly interesting. For those who don't know about it: One example is, consider the hexagonal tessellation of the plane. Let 0 < p < 1. Suppose each tile is colored White or Black independently with respective probability p or 1-p. Then each tile belongs to a maximum connected piece of the same color. What is the probability I(p) there exists a connected piece of infinitely many White tiles? Turns out there is a number p_crit in (0,1) such that I(p) = 0 for p < p_crit, and I(p) = 1 for p > p_crit for this lattice (and other "lattices" as well). For the triangular lattice, p_crit = 1/2. The proofs of such things tend to be incredibly long and complicated. (For the triangular lattice, I believe I(p) = 1 for p = p_crit = 1/2 as well.) Last I checked there were very few results for this kind of "site percolation" for "lattices" naturally occurring in dimensions >= 3. (The original motivation for studying this stuff was as a model for how a fractal-ish rock decides whether to let water flow through it or not.) ----------------------------------------- << . . . Mr Taleb is credited with making himself 40M$, presumably on the back of short-selling. [I'm not going to criticise him on thos grounds --- if people are permitted to profit by backing stocks to rise, then it makes no sense to forbid them to profit by backing them to fall --- at any rate, provided it's their own money they're risking.]
I wouldn't blame Mr Taleb for the way he made his money, but there are times it may make sense to ban betting that a stock price will go down -- as the U.S. Securities and Exchange Commission did recently. If enough people are betting that stocks will go down, they may use their influence to try to make that happen, and that would add to the probability the stock markets will crash -- or crash worse than it already has. ------------------------------------------ By the way, when I worked for Bank of America Global Trading ('87-'91), I learned (as many of you probably already know) that the Glass-Steagall Act, passed during the First Great Depression, forbade banks from dealing in many kinds of securities, especially stocks. The intent was to add stability to financial markets by decoupling major market sectors. But the Glass-Steagall Act was repealed in 1999. I'm puzzled that I haven't encountered in the media anyone's mentioning that repeal as a possible factor in what's happening now. Anyone have (non-partisan) comments on this? --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele