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minimax

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I am, quite happily, heading far afield from my usual paths of thought and research. Summer-time. Reading Charles Stross’s Accelerando, which you can read right this very minute via a download from Stross’s personal site.


This free ebook edition is made available by kind consent of my publishers, Ace and Orbit, under a Creative Commons license with certain restrictions attached. In particular, you may not create derivative works or use the work for commercial gain.

That’s putting your CC money where your CC mouth is.

Anyway, it’s a nifty novel, and way thought provoking. And, a bit weirdly, it delves (more deeply than I) into some of the issues that I’ve been tapping at here. Namely this and this

In fact, the epigraph of the second section comes from John Von Neurmann, of the Von Neumann bottleneck below…

Life is a process which may be abstracted from other media.

– John Von Neumann

Anyway, I’m through the first section of the novel and will try to report a bit more as I get further in. But for now, a paragraph or two from wikipedia on Von Neumann’s economic work, and the minimax concept:

His first significant contribution was the minimax theorem of 1928. This theorem establishes that in certain so-called zero sum games (games in which the winnings of one player are equal and contrary to the losses of his opponent) involving perfect information (in which, that is, each player knows a priori both the strategies of their opponent as well as their consequences), there exists one strategy which allows both players to minimize their maximum losses (hence the name minimax). In particular, for every possible strategy of his own, a player must consider all the possible responses of his adversary and the maximum loss that he could derive. He then plays out the strategy which will result in the minimization of this maximum loss. Such a strategy, which minimizes the maximum loss, is called optimal for both players just in case their minimaxes are equal (in absolute value) and contrary (in sign). If the common value is zero, the game becomes pointless.

Von Neumann eventually improved and extended the minimax theorem to include games involving imperfect information and games with more than two players. This work culminated in the 1944 classic The Theory of Games and Economic Behavior (written with Oskar Morgenstern).

Sounds almost like a materialist ethics, a morality of realism.

Written by adswithoutproducts

May 15, 2006 at 2:08 am

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