Friday, October 8, 2010

Ergodic hypothesis

Moral: Wherein we start the slow trek toward a defensible position in regard to that which stinks and, thereby, honor Adam Smith and other thinkers.


Ah, did we ever say that we have the answers?

Last time, we were looking at a constructive basis for capitalism; that goal is still there. However, a couple of concepts ought to be introduced into the argument. These are the ergodic hypothesis and fixed point issues.
  • Ergodic hypothesis -- We mentioned this as a comment earlier, while talking about the problems brought on by misuse of mathematics by the 'quants' view. As the article said, Samuelson noted that bringing in this principle was needed to make economics more scientific. That is, we can solve the game of risk, it is thought.
  • Fixed point -- Deep with the thinking that would apply the ergodic principle is some notion about convergence that may be stronger than warranted. In the large, we do not see much that is really divergent. The sun rises. The car runs down the road that is usually passable, without overly large potholes, and so forth. But, in the small, convergence relies on equivalence.
Now, given that we mentioned equivalence, please note that this is not an easy problem. And, I'm not talking about what 'is' is. You see, any equivalence decision will have been set up within a predefined framework supported by axioms, and other assumptions, in an operational sense. Yet, in order to attain an equivalent choice, all sorts of, supposedly, unimportant properties are thrown out or trivialized into a type of norm.

What do I mean when I say that 'equivalence' is hard. Firstly, the problem is NP of some sort. We looked at that earlier. Secondly, there are undecidable issues involved related to the context.


The basic problem that needs attention is that concepts, like Arrow-Debreu equilibrium, furthers the delusions brought on by mathematization via computation. But, perhaps, that was inevitable; the latter progresses so the former would try to make use of the new facilities.

In short, though, not only do we not have 20-20 foresight (and hindsight) due to undecidability (and more), some things cannot be computed which begs the question of the Church hypothesis which will have to be addressed, to boot.


02/02/2012 -- This post's subject motivated the Ideology series.

04/02/2011 -- Weierstrass did not banish the motivations behind Berkeley's concerns.

10/14/2010 -- Capitalism, as known now, requires an endless supply of suckers.

10/13/2010 -- We'll get back to our itemization, soon. But, cannot resist mentioning that the foreclosure mess is indicative of the types of problems that 'capitalism' will face, especially as it facilitates movement of money from the pockets of the hapless to that of the fat cats. As well, analysis of Paulson, and how he benefited Goldman Sachs - who were rolling in the dough while others lost their livelihoods -- with his actions, and inactions, pertains to the next Remark.

10/07/2010 -- You know what is funny? Those who tend to ca-pital-sino laugh about State planning, to wit the failure of the USSR, etc. You see, these people claim, models, like the Input-output model, are touted as the means for that type of planning. Who can think of handling all that is necessary? But, then these same people see 'the market' as the means (look at the Arrow-Debreu view) based upon what (as in, what the hell is that? the money-sucking methods of Wall Street?)? The invisible hand?

Wait! What's the answer? Well we're getting there, albeit without any compunction about when.

Modified: 02/02/2012

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