Tuesday, September 18, 2007

The small world of contract bridge

In the spread of a new idea, which is more important: the speed at which information flows or the speed at which we absorb it?

I have no doubt that modern communication, including the net, has increased the speed of information, but let's not underestimate our forebears. From a recent New Yorker book review on contract bridge:
The modern version, contract bridge, was created in 1925 by the railroad heir and master yachtsman Harold Stirling Vanderbilt, who had been annoyed by what he felt were deficiencies in the previous version, auction bridge. Vanderbilt was a passenger on a ship that was travelling from Los Angeles to Havana by way of the Panama Canal, and on the evening of October 31st, while playing with three friends, he introduced several improvements that he’d been mulling over, including a method of scoring that required players to more accurately assess, during the bidding, the number of tricks they would take, a prediction known as a contract. Vanderbilt shared his ideas with a few other friends in Newport and New York, and his game spread across the country and around the world at almost unbelievable speed. “Half a year after Vanderbilt’s voyage,” McPherson writes, “a notice appeared in the Los Angeles Times announcing that a Chicago woman was suing her husband for divorce on the inexcusable grounds that he trumped her ace.”
I doubt that communication speed was the limiting factor here. More likely, it was the time required for a player to try out the new rules, mull them over, deem them good and decide to try to introduce them in their next game. By the small world principle, it doesn't take too many such hops to reach the entire community.

From a graph theory point of view, you have a set of players connected by lines of communication (we play with the so-and-so's at our Tuesday game; I correspond with such-and-such; we all read thus-and-such's column in the Times). Propagation through the graph is a matter of incubation time (playing, mulling it over) and transmission time (the epidemiological terms are deliberate here; I'm sure there is quite a bit of relevant research in that field).

In the present case, there is probably a classic small world graph, with a few well-connected nodes (major celebrities like Vanderbilt and the major columnists) and lots of less-connected nodes (the Tuesday night games of the world). It would be interesting to see when the new rules first appeared in print. It would also be interesting to see how long it took contract bridge to supplant auction. That's clearly not a matter of propagation speed.

These days communication time is much more limited by the reader than by the medium. If a headline appears in a major news source, it may still take some amount of time before everyone gets around to reading it. Blogs and online news sources shorten the time from writing to availability to practically nothing, but they don't necessarily make me read it that much sooner.

Which has had more impact overall: "Old-school" electronic communication (think telegraph, radio, TV) or the internet? One could make a decent case for the old school.

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