More on Fibonnacci

When I want a finite set of quants to work with I select a Fibonacci series as a set of transaction rates, scaled such that the fastest rate is .5, like this: g = 0.015 0.029 0.044 0.074 0.118 0.191 0.309 0.500
Scaling my quants put
Taken from this: f = 1 2 3 5 8 13 21 34 by dividing by 68.

The plot of log(g) is uniform in the plot. Within an integer, the spread of log(g) is even across the series.
I cal the series log(g) the quants of a maximum entropy distribution which are delivered at rate g, so that:
 -g*log(g)  is the entropy measured over the whole network at rate g. It is also the total quantity of -log(g) delivered over the network.

This simple model  would result from perfect encoding out of my Huffman encoder, and the distribution of quantity sizes would be uniform, hence this sequence defines a maximum entropy distribution network of rank 8, the number of quants in my series.

Looking at -g*log(g): 0.029 0.050 0.069 0.100 0.139 0.191 0.252 0.316 0.363 0.347
where I have increased the rank by two.  The values are all within an integer of being equal.
 round(-g*log(g)+.5), rounding g to the nearest integer, yields 1 1 1 1 1 1 1 1 1 1.

When I talk about maximum entropy, I also mean minimum redundancy, which is more intituitive in economics.  It would be natural from the sense of Hayek that we would find sustainable patterns of trade by looking to remove redundancy. Integer soltions arrise naturally because of transaction costs, for us to entertain an infinite variety of transaction sizes would imply that there is no cost in a trip to the store for even the smallest item.

How do we find the proper price of an item? On the micro level we generally know only -log(g), not g itself. But we get an estimate of g by looking at the number of people in line to buy a -log(g).  Computing the price of items over the whole economy involves estimating the yield curve of money with a discount rate.

 Comparing the variance of money to the variaince of a good, in the minimum vaiance world, is equivalent to finding the mutual entropy between money and a good in the minimum redundancy world.  Hidalgo and Hausmann compute conditional variance in the product space of final demand. But I suspect the entire economics profession will eventually adopt minimum redundancy.

Anyway,  the result here is that the generalized yield curve can have either -g*log(g) in the numerator, or -log(g) in the numerator depending upon when one is working on the macro or micro level.  The effort is always to find the approximate measure of the yield curve in some local space that is a mix of macro and micro, because that is the measure of heteroskedacity entrepreneurs look for, heteroskedacity is a measure of excess redundancy.