A model of a model is called a meta-model. Meta-models are made to increase the efficiency of the software-development process. You can go on with the creation of models-of-models (a meta-meta-model).
If there is nothing to stop you to model the model there is something wrong with the modeling approach.
When you are modeling you are compressing data. When you compress data the amount of data is reduced. A compression of a compression amounts to less data so there must be an end to the process of meta-modeling.
The counterpart of Compression is Expansion. When you have used a valid meta-modeling approach the meta-model has to expand to the original model without losing data.
When you want to make a meta-model you can model a static (a database) or a dynamic model (a process). Most of the meta-models of dynamic models are static models. They are stored in a database (dictionary, repository). The process of meta-modeling has the tendency to freeze the dynamics of a dynamic model.
A database is a combination of a storage-system and a software-program that stores and retrieves the data at the right place. A storage-system is also a software-program connected to a rotating device, a disk-drive, which is also managed by a software-program.
In reality every thing moves. Meta-Modeling splits a Dynamic System in a Database (a Datamodel) and Software (a Process) to Apply the Meta-Model. The Software is used to Expand the Compression of the Dynamic Model.
If you want to evaluate the efficiency of a meta-modeling approach you have look at the efficiency of the compression and the expansion of the data and the process.
When everything is a process, a method is a dynamic meta-model of a process. The meta-model of a method, a meta-meta-process, is a summary of the method. If you are not able to use the summary something is wrong with the method. If the summary is sufficient the real method is too complex.
The only way to create an efficient and reliable meta-model of a process is to find the self-similarity of the process. A self-reference, a fractal, of a process always contains less data and it is possible to enfold the fractal to a lower level without losing data.
If you use the fractal approach meta-meta-meta-….modeling is not needed because a fractal meta-model contains two parts, the fractal and the program to expand or compress the fractal to a lower or higher level.
Fractal compression and expansion is very successful in the area of image processing and textual summaries.
Is it possible to find the meta-model fractal?
The big problem is language. We express our reality in language and our current language is heavily distorted. It contains many interrelated overlapping layers.
If we use the language that is produced to describe processes we will perhaps be able to summarize, find the essence of the text, but we are never sure the text contains the real processes.
The solution to this problem is to observe processes and make a picture. If we Observe processes, look with the Eyes, we are producing Images. Fractal compression is able to compress these images.
How about the Ancient Scientists?
The ancient scientists were aware of the divine fractal. In my blog “About the Whole and the Parts” I use the Ternary Numbers or the Trinity to define a Meta-Model. The model starts with the Dynamic Whole and is expanded until it has replicated itself.
Interesting enough the theory behind fractal compression uses iterated functions based on the so called Sierpinski Gasket to detect fractals. The Sierpinski Gasket is an expansion of Triangles in Triangles. It is used to simulate DNA, a Biological Meta-Model and other “natural” structures
The first expansion: Ø → 0. The Void, the Infinite Potential, transformed into the Nothing.
The second expansion: 0 →(-1,0,1). The nothing expanded in a negative and a positive part. The sum of the expansion is still zero. This is the principle of voiding. Every part that is created needs a counter-part that is it’s opposite (Part ∩ Counterpart = Ø). Every Expansion is compensated with the same Compression. When we divide a Whole we always have to make a “clear” cut (no overlap).
The third expansion: (-1,0,1) → (-2,-1,0),(0), (0,1,2). This is the creation of the Four Forces with the Void, the Zero (now the Fifth, Quintessence), in the Middle. Two of the Four Forces are the Same Forces that were formed in the Second Expansion. They could be called Expanding Expansion (Desire) and Compressing Compression (Control). The other two combinations are Expanding Compression and Compressing Expansion. Most of the time they are called Spirit (Creating) and Soul (Connecting). In the third expansion the Divine Fractal has expanded in Itself. That’s why we, the Humans, are created in the Image of God, the Creator.
Is it possible to transform the “divine” metamodel into a “normal” metamodel?
The whole problem comes down to language again. Are we able to translate the numbers into the Right Words? Let’s have a try.
0 or 5 are mostly called consciousness or the observer. In the terminology of IT 0 or 5 could be called a Monitor. The Monitor has to take care that every part has a counter-part.
1 and -1 are called Control and Desire. In terms of IT they could be called Rules and Sensors. The Sensors and the Rules are opposites. The Facts of the Sensors always fight the Structures (Methods, Systems, Programs) of the Rule-System. The conflict between Facts and Rules (Testing the Model) is the basic conflict behind every Scientific Approach.
-2 and +2 are called the Creator, the Imagination (Ideas) and the Emotions (Social Relationships). They represent the Possibility (in terms of new combinations of the existing Parts) to Enfold the model to a New level and the Role of the Human, the Actor, in the Game (defined by the Rules) that the Controller is playing with the Sensors. The Creator and the Emotions are also opposites. The Creator Splits and the Emotions Merge.
What is the fractal?
The Fractal is a Spiraling Spiral that moves Three Cycles Up and Three Cycles Down and rests in the Middle (the Seventh Day).
In the Cycle the Controller, the Sensors, Spirit and Soul are connected in Twelve possible ways.
Sometimes Spirit & Soul and Control & Desire void each other. It this case the Spiral moves back to the Void.
When Soul, Spirit and Desire (The Mother), the Female Trinity, are connected the Spiral Expands.
When Soul, Spirit and Control (The Father), the Male Trinity are connected the Spiral Compresses.
Spirit moves the Spiral Up and starts a new Level of Awareness.
Soul moves the Spiral Down to an existing Level of Communion.
The Divine Rule, the Golden Mean, the principle of Harmony, controls the Trinities of the Golden Spiral, to make sure that the spiraling spiral always voids itself in the end and returns to the Beginning.
A website about Fractal Compression of Images