The 7-level standard size of the key hierarchies has always been puzzling. It suggested some underlying unifying principle but its nature was unknown for many years. While the focus was on Primary Hierarchies, it was evident that the other architectural forms were derived from these and this derivation forced a similar number of levels. However, it was not clear why the Primary Hierarchies all had 7 levels, and whether there were other similar hierarchies as yet undiscovered.
Two important discoveries led to crucial conjectures.
Subsequent work to be posted in detail here in the Architecture Room suggested that the Root Hierarchy is «projected» into all the main architectural forms. This is probably why they possess 7 levels: or at least in pushes the question backwards: because it is still not clear why the Root Hierarchy itself has 7 levels and not more or fewer.
The (re-)ordering of Root Levels is unique and different in every case of projection.
It is assumed that the numbers of possible re-orderings will be limited, but that is not something about which any confident statement can be made at this early stage.
Combinatorially, there are over 5000 possible orderings of 7 levels (i.e. 7! or factorial 7). Yet less than a dozen have been hypothesized so far.
The first projection to be explored is the last to be identified. It is the projection on to the Primary Hierarchy.
Other Projections that will be examined will include:
The present conjectured re-orderings are presented in advance of a full exposition which may take many years. Differences and similarities between the orderings are immediately apparent and some initial thoughts will be provided. You are welcome to make suggestions and conduct your own investigations.
Last amended: 14-Jul-2013