Monday, March 6, 2017

Central planning, on the fly with the master of linear programming

COSMA SHALIZI has a great post about some novel and the father of linear programming. Linear programming is a problem of intersecting linear surfaces. The problem is finding the most lucrative spot to be in that space when you have some cost function. So our mathematician fund the least number of steps to bounce through the corners of linear spaces, always getting closer to your objective point, never turning back.

The story was that he was kidnapped by a German retail outfit, needed to get yhe best assortment of goods to purchase on a truck somewhere.  So they held this guy in a room for weeks, colder than jesus, until he produced.

Anyway, his algorithm has been reduced by elliptical programming where we better price ur way around the bend, and made irrelevant by self adapting statistics that requantize rather than compound.

Anyway, our kidnapped Russian, being pissed, set out to prove the impossibility of central planning. I show that in the aggregate, local planning works just fine.

How to central plan:

I. We need a quantity to maximize. This objective function has to be a function of the quantities of all the different goods (and services) produced by our economic system.

We got that. We recognize the distribution is stable when the queues are optimally stable. We go deja vu when Poisson is short and peaked.

IIA. We need complete and accurate knowledge of all the physical constraints on the economy, the resources available to it.
IIB. We need complete and accurate knowledge of the productive capacities of the economy, the ways in which it can convert inputs to outputs.

Not true, we need an almost complete knowlede up to the acceptable uncertainty defined in I.

II. For Kantorovich, the objective function from (I) and the constraints and production technology from (II) must be linear.

No, we need a locally smooth elliptical surface to turn the bend in his linear programming model. This was proved in the 80s sometime, we can bend the indexing and sufficiently approximate the constraints embedded in his model of linear binding surfaces.

IV. Computing time must be not just too cheap to meter, but genuinely immense.

No, it is measurably free in the finite, elliptical model. The difference is lattice and fermion spin rules both change, we get a re-quant
He then counts up operations, order of solutions. I do that someimes, count up the order of transaction until liquidity stabilizes after a queuing disturbance to government. The large number comes from single color option pricing, it compounds. In reality, we requantize the elliptical curves, they are finite. It is self adapting statistics. So we do not hit the hard problem, the aggregate actually finds the lowest order problem, changes the theory to fit the available moves. It is like cheating, but it is ok, it is done at the local level.

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