Monday, October 04, 2010

Networks and liquidity

David Warsh points us to Paul David and an essay on the "flash crash". The end to open outcry may have some effects that allow the transmission of shock or 'catastrophe beyond what would previously have been the case. It is a story of fragmented liquidity and an end to face-to-face dealing.
Still, if it’s the crash itself that is of interest, you’ll do better reading the SEC report. It is the larger dimension of the signal that interests David. He invokes the work of French mathematician RenĂ© Thom, inventor in the 1970s of a formal mathematics of sudden shifts, of qualitative breaks or discontinuities, that he called catastrophes. “To appreciate that quality it is helpful to start from the mathematical rather than the ordinary language meanings conveyed the term,” David writes.

A commonplace physical illustration of a “catastrophic event” – in this formal sense of the term — may be experienced by letting your finger trace the surface of a draped fabric until it reaches a point where the surface (the “manifold” as mathematicians would speak of the shawl or cloak’s three-dimensional surface) has folded under itself; there gravity will cause your finger’s point of contact to drop precipitously from the surface along which it was traveling smoothly – to land upon the lower level of the drapery beyond the fold. That little passage is the “catastrophe.” In the present context, what is especially relevant about this conceptualization of the “event” experienced by your finger is its generic nature: catastrophes thus conceived are not phenomena belonging to a category delimited by some size dimension of the system in which they occur, or according to the severity of their sequelae; nor are they to be uniquely associated with processes that that operate only in one or another range of temporal velocities (whether slow, or fast). Instead, the catastrophes to which this essay’s title refers are fractal, possessing the property of self-similarity.

Similar to what? He compares the conditions that led to the May 6 price break to the phenomenon known as “flaming.” One party breaks off a previously civil exchange with hostile abusive comment. Instead of turning it aside, others sometimes reciprocate. Anonymity is the key part of the process; isolation seems to remove inhibitions that would brake the process if the exchanges took place face to face. Silence ensues, or, worse yet, digital versions of what long ago were called “slam books” – compendia of the faults of others, sufficient to fragment the conversation once and for all. (This is the problem with Glen Beck and much of the rest of Fox News.)

Humans evolved to recognize from infancy the effect of their actions on others – facial expressions, body language, tone of voice, he notes. On the Internet, however, no one knows when they may come across as a flame-throwing tank. It is why humor is so risky on the Web.

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