Size of least monad sets

We just said that the least monad sets (i.e., of the objects of the monad granularity) need not be singletons. So you may be wondering...

What's this about non-singleton monad sets?

Well, objects of the monad granularity object type should have the smallest monad sets. But even though the smallest monad set is a singleton (e.g., {1}, {2}, {3}), you need not use singletons for your monad granularity objects.

You could assign contiguous segments of monads, e.g., {1-100}, {101-200}, {201-300}.

How can this help?

An advantage of this is that you can then later split the objects without moving monads around. You would split them by first deleting the object, then recreating new objects in the same monad range as the original object, but split between the new objects.

For example, say you have an object A at monads {201-300}. You want to split it into two objects, B and C, which occupy the same monads, but which share the monads of the original A.

You then drop A, and in its place create objects B and C, where B has monad set {201-250}, and C has monad set {251-300}. If you later need to split object C, you have ample room to do so.

A general rule of thumb is that if you ever need to split an object up into m distinct objects n times, then you need to make sure that the monad set is larger than m to the power of n (m^n). Put another way, n should be less than the logarithm of the size of the monad set to base m.