I agree with Jamie Galbraith and Bill Lear that the Albin/Foley volume is very well done. Duncan's extended introduction is an especially clear exposition of many of the issues involved. I would only warn the the identification that Peter and Duncan make between the third level of Chomsky's linguistic hierarchy and Wolfram's third level of complexity with chaos is probably not accurate. This implies that chaotic trajectories simply fly away from each other. In fact true chaotic trajectories eventually return to be near each other, at least temporarily. This makes chaos more like the fourth (and last) level of the Chomsky/Wolfram linguistic/complexity hierarchy. (I have sent a letter to Duncan which I am sure he will forward to the tragically ill Peter making this point). Barkley Rosser On Thu, 13 Aug 1998 08:57:18 -0500 "William S. Lear" <rael at dejanews.com> wrote:
> Dickens invokes the flavor of chaos in the reflections of Pip on his
> day's uncomfortable and transformative events:
>
> Pause you who read this, and think for a moment of the long chain
> of iron or gold, of thorns or flowers, that would never have
> bound you, but for the formation of the first link on one
> memorable day.
>
> I've been reading the very interesting *Barriers and Bounds to
> Rationality* by Peter S. Albin (whose work was highly recommended to
> me by Jamie Galbraith). Duncan Foley provides a long and thoughtful
> introduction (I suspect, in part, because Albin, though relatively
> young, has had a fairly serious stroke).
>
> One thing that struck me when reading this, is that this mathematical
> treatment of complexity and rationality is not only "neat
> mathematically" (as Doug says) but it does tell us something very
> important about human decision making (social choice) within market
> settings.
>
> It tells us that if you can show (as I believe Albin does) that
> "selection of an optimal social choice" is not only costly, but
> computationally infeasible for an individual to undertake, you might
> then begin to more fully undermine the "rational expectations"
> nonsense and provide openings to economic and social problem solving
> that are not based on the neoclassical vision of homo economicus
> (solitudos).
>
> That is, to spin it Albin-style, if, by relying on individual agents,
> the "solution space" to economic problems is necessarily narrowly
> constricted to only that which can be explored by an individual,
> perhaps this can lead to more efficient (and fair) collective
> solutions, perhaps using computers, but perhaps more generally and
> simply by different social organizations.
>
> The central, dominant contention of that branch of mass propaganda
> known as economics (present company excepted, naturelment) is that the
> computations necessary to communicate and evaluate information to
> undertake efficient market transactions are not only feasible for an
> individual, but are trivial, automatic, and are undertaken properly
> *only* by isolated individuals, lest doom descend.
>
> So, in a hopeful sense, this can not only beat the criminals at their
> own game, it can provide some insights about how to collectively,
> democratically manage our future.
>
>
> Bill
-- Rosser Jr, John Barkley rosserjb at jmu.edu