Saturday, December 25, 2010

Everybody gets a calculus in economics

Stiglitz get his, stochastic calculus, and we quantums have ours, a Borel calculus.  I can produce a rule of thumb about the both.  Ours is a bounded functional calculus, and I am not the one to give the theory, but I can give the shorthand.

Here is our working definition.  Given rank N, say 8, we can use binary logarithms on any data series from 0 to 255, provided the round off error is less than 15%.  When rounding error exceeds 15%, our calculus is not working, and rank is reduced.  So, take a data series, and map the Y axis into a precisions of say, 6,7 or 8; the largest data value should match the largest fixed precision value supported [2 exp(N-1)].  Increase the precision while all the data is within 15% of an integer exponent of 2.

We can contrast this with stochastic calculus which uses the natural log and fixes the precision enough to maintain the statistics within some specified bound.  Stochastics assume necessary precision is available.

In the real world of quantum deliveries what does this mean?  If a truck holds eight pallets, then the calculus won't work if store outlets generally take need five. The inventory workers will notice a cyclic excess and eventually one of them will leave and start a new outlet. So coherence in supply chains is equivalent to finding a proper bounded functional calculus, that is what we agents do.

No comments: