## Friday, 14 October 2011

### Robert Lucas attacked by chaos machine

Robert Lucas, a godfather of the rational expectations movement has come in for a lot of criticism recently.  Here's my own brief attempt.

Imagine an artificial economy with just two actors, who each have to guess game theory style at the likely behaviours, economically, of the other.  They both are fully cognisant of each other's economic models.  All they need to do is apply those rules to apply a decent best guess of model parameters - the legendary sloppy assumptions - and we'll sit back and watch well known macro-economic phenomena emerge from their identically specified micro-level models of themselves as economic actors.

Now lets imagine those models shared a similar property (as many many models do) with the logistic function, $X(n+1)=rX(n)(1-X(n))$, namely they are riddled with chaos.  Our two agents might agree perfectly on each other's model and what's more be correct but when it comes to apprximating the model parameters, needless to say, they cannot guess the other's starting value with infinite precision.  The result, over certain wide ranges of the parameter phase space - is utter chaos.  All it takes for rational expectations to be shown to be inadequate is some likelihood of such radical non-linearity in real (no pun intended) sets of micro-founded models of agent interactions within the wider rational expectations movement.

How would a rational exceptions robot respond to the possibility, or even more strongly, the knowledge that their models had 'dark areas'.  I guess the sensible thing to do is to apply probabilistic approximations around those regimes.  And those heuristics too would probably be amenable to the rational expectations approach.  I guess the rational expectations agent can operate under radical uncertainty.  But what if there were clear patterns of information which cry out for some kind of rational expectations model to develop, while an entirely different initial parameter set results in a different rational-seeming system to lure the unsuspecting rational economic agent.  And what's worse, where do you draw the line between uncontroversially certain parts of your model, and the stable-seeming boundaries at the edge of chaos?

### Indices of the world, unite!

I'd like to suggest an idea.  Within a short number of years, thanks to Amazon and Google Books, we'll soon be in a position to have available to us in textual format virtually all of the indices of all of the books which have ever been written.  Clearly this is somewhat of an exaggeration, but not too much, especially in the realm of non-fiction.  Imagine a research project which applied the techniques of computational linguistics to automatically link all these indices together, to provide a search and browsing resource between parts of books.  Something like this is already just beginning to happen with citations - but in a sense these are external (but still related) to the content.  Indices get you right in to a particular page.  Once in place, the Big Index, as I'd like to name it, then becomes an intellectual super-highway, a novel way to read (parts of) books, of seeing connections, of hopping, of surfing, of delving freely into the history of a concept, of tracing influence.  On top of this super-highway, us travellers can then leave notes, attach personal commentary (rather like the Amazon kindle shared notes).  In time, we'll be able to follow the paths of great thinkers themselves, what they read and thought about, which connections inspired them.  How they felt about it at the time.  Pieces of text will become cultural monuments, with many transit routes in and out, and with a wealth of personal commentary.  Indices, after all, capture a lot of intelligence and work in abstracting a book - why not put it to use.  Also, it side-steps the famous Borges taxonomy probem, and always remains fully open.   The internet in general, and sites like Wikipedia do some of this for you, but it isn't the same idea.  With my idea we're exploiting a probably well-crafted index designed around the time the book was written, probably with the involvement and approval of the author, which captures some of the structure and flow of the book.

Soon we'll have an additional option to read through a book, moving at speed.  The idea remains indifferent to one's position on copyright, and of course there'll be nay-sayers who'll decry the already too-disposable approach to reading we have moved to.    I disagree and see it as an enhanced mode of reading, which treat concepts not individual books as the core nuggets you're seeking.  Indices of the world, unite, you have nothing to lose except your identity.