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Relativity and Renormalization

Explanation of the Meta Model M Notation

The Four Layer Architecture adopted by the OMG names the abstraction levels M0, M1, M2 and M3.  The M in M[n] stands for meta and the [n] simply indicates which meta level.

The notation follows the “power to” rule.  The highest abstraction level is at M3, Model Compilers exist at M2, Analysts work at M1 and finally M0 is the lowest level and represents actual things in the Real World as investigated by the analyst or, alternatively, objects which are tracked and manipulated by the application.

The table below shows the powers of meta and their uses:

Renormalization Relativity in Modeling

The metamodel levels exist relative to each other.  They are also mobile since the levels can shuffle up abstraction levels to align with the Real World.  It should not be thought that by assigning numbers to meta levels they are fixed.

In fact, meta levels beyond both M0 & M3 may exist.  They are created by the development of Model Compilers.

When required, renormalization is used to shift silos (vertical columns) in the Matrix to the left causing M[n] to become M[n+1] and so on.  This usually happens when a new Model Compiler becomes operational and creates a M[-1] meta level.  Renormalization is based on M0 and its correspondence to the Real World, so M[-1] is reassigned as M0 and all the other levels are incremented as a result.  Therefore, M0 stands out as the constant in the modeling business, not M3.

Sometimes, it’s appropriate to promote domains to a higher or lower meta level.  This usually occurs when certain functionality in the domain is included in the Model Compiler from the application or the other way around.