Conceptual Science 
Concepts are Containers
Imagine you had four identical carrier bags. How many ways are there arranging them within each other? Well within the parameters I am speaking of there are exactly nine possible arrangements:
For any number of such containers their are a set number of patterns in which they can be arranged. For example five containers may be arranged in a maximum of twenty such patterns.
These "Container Numbers" are related to Rooted Trees (Graph Theory).
Related:
sci.tech-archive.net...
combinatorics.org...
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Conceptual Science