My use of symbols is intentionally simplified. I use P as a synonymy. My points are not in any space in advance. The may have properties. They are not geometric. The may have membership in classification (Index, Database, Manifold, ...).
In addition these three P class I need Adjacency A. It is tool for telling if objects are connected by adjacency). Adjacency can define a connectome where some points belong to connectome by a rule Points in connectome chare a Path or another Polytope.
The I Introduce hypegraphic generating model for everything as sum of all possible partitions (sub sets of points if you will. I define generating functional of all form (that have connected forma or order) by very simple but in principle infinite object. This is my "Lagrangian", but because it is space and theory independent before using constraining rules on differential actions (symmetry) of the model elements, I call it Leonardo.
The short hand notation for Leonardo is L=P+PQP+ P(Q,P), where P is Point, PQP is Path and P(Q,P) is any higher order polytope. Imaging terms like PQPQP, PQPQPQP; .... as portioned sum here in the formula of L.
Now I paint my structures with properties. I have for instance P=P(S), P=P(T), P=P(C) and P=PQP=P(S)Q(C)P(T) and so forth. S define the starting (set), T defines Terminal (set) and C define the connectome Q by connected Points P(C).
The new idea I will write more in my blog (Theory of completely everything) is that I ad for S,T,C free variables that do not yet define the membership in Stare, Terminal or in connectome. These are the seed of evolution I need to make modelling dynamic.
I do replacement P=P(S,s), P=P(T,t) and P=P(C,c) and I add configuration structure for lower case parameters as deltafuntion family (type D(S-s)). This way I generate new points in connectome or new paths or Polytopes. That is I generate new state of Leonardo from the previous one.
As one example think my previous article about holography. I can first make Leonardo for 3D space and parametric it by new points on horizon (by paths from pixel to pixel true voxel). These objects are Points in my Leonardo.
I write also more how this type of Leonardo’s can be used to model brain network ant the action of Filabods to create new connection. Actually I can enrich my Finsler geometric model of brains to become defined on evaluative hyperconnectome.
See my idea ModellingBrains as Finsler Manifold with Fractal Action induced by observations.
Actually it is very easy to enrich model by P=P(S,s), P=P(T,t) and P=P(C,c) and the lagrangian of the model by generating delta function or other type of distribution. This way:
L:=P+PQP+ D(s,t,c)*P(Q,P) where P=P(S,s), P=P(T,t) and P=P(C,c) and Q(P(C,c))
This has interesting consequences for the plasticity of modelling.
