Maximum disorder

Consider N^N N to the Nth power, and N is the number of things you have that have a unique ordering, their ordering is relatively prime.

N^N are the maximum number of ordering I can make.  The N are my cardinals, i need N +1 to make any more orderings otherwise they are indistinguishable.

N^N is the maximum disorder possible for a set of N ordered things.

If I have a tool can measures at 16 different levels, then this can measure cab order a system with four levels of ordering.     The three prime maximum disorder being 1^1*2^2*3^3 .  Beyond that, counting requires state change, hoping around the 3 tuples.

To maximize disorder is to take order and get work from it.  That is also minimize redundancy.  The things disordered are transactions, in the econom,  exchanges. Maximizing dirorder is also hedging, betting the predictable  will releases redundant resources.