Tuesday, December 18, 2012

Markov’s Inequality and Distributed Cultural Output Options

commentary by Roger Erickson

Lars Syll waxes misty-eyed over the beauty of one of Andre Markov’s probability theories.

If X is a non-negative stochastic variable (X ≥ 0) with a finite expectation value E(X), then for every a > 0:

the probability that {X ≥ a} is ≤ the (Expectation of X)/a.

In other words, the rate of divergence from a definable expectation is a function of the accuracy of the expectation itself. Production engineers love this function since it's useful in controllable situations.  Curiously, even people in economics get excited about it's supposed implications.

Yet how useful is that particular mathematical truism, if the boundary conditions are not met? This particular Markov axiom only helps in situations where the expectation value is known within some bounds.

Since no real-life, distributed operations functions come with accurate error propagation, the primary lesson for economic policy is that no "organized" system can scale up without adequately scaling distributed feedback-parsing-selection-testing. I think we knew that, say 5000 years ago? At least by the time people were organizing large construction projects.  Unlike orthodox economics, cultural expectation functions are highly distributed, and rapidly changing.

That, in turn, only means that the scale of auto-catalysis tracks discovery of newly distributed new methods. Duh!

It's the return-on-[total]coordination, silly ... but we always shy away from that simple fact. Minus total-system feedback, there's always the temptation to think that the probability of some local projection is different this time. Some economists even have the expectation that their expectations are probable!

What could possibly diverge from the expected probability of such expectations? :)  Oh, let's see. Reality?  Perhaps we should inform the universe what orthodox economics expects from it.  That should make a difference, if we really expect hard enough.




2 comments:

Edmund Kar said...

I'm sorry, I just can't take any more coordination, group awareness, adaptation, etc., etc., etc.

Roger Erickson said...

Edmund,
Try getting your mind some more exercise. Here's one of many places to start.

http://longnow.org/seminars/02012/apr/20/social-conquest-earth/