In case of a relation, we connect two arbitrary objects with keys that represent the common features of the these objects. Further development requires re-definition of these objects and their features. In case of a graph, we have this arbitrary relations. We can represent relations using graphs and the contrary. In case of a tree, the data structure is confined to the well-ordered sequences of relations, whereas only certain elements are allowed to be related. In case of a graph, all elements are connected, these relations may be one- or two-directional.

A relation may be modelled with a prime. An object may be represented as a single number, a geometrical notion of number has been depicted in my earlier posts. A relation is the common divisor, also a multi-dimensional geometrical object. The maximum change, i.e. in the Newtonian physics modelled with the notion of an infinitesimal, in the GTR represented with the c velocity, would be represented by the highest prime number for a given perceived. For the objective case, there is an infinite amount of primes, and such is the maximum change, but perceivable for the objects capable of perceiving the objective. To perceive the objective an object would have to be itself the objective, having all prime numbers as divisors, therefore would have to be infinite itself.

When geometry of the perceived p1..pn changes, for finite n, the perceived status of objects within changes. The max change is defined by pn, as stated before. In our case that would be somehow tantamount to c velocity, still understood in terms of the geometry of the objects.

Time would not exist in such a model and would be just an effect of the change in the geometry. Two notions p1..pn and p(n-1)pn…pk would be able to interact due to a common divisor, i.e. p(n-1)pn. Due to interactions of objects we observe passing of the time.

Goedel referred to the passage of time as an illusion, because he explained that space-time is the notion that goes beyond time and time is just an element of it, the perceived one, but not enough to explain the phenomenon. This is still not enough, because time itself does not exist and is a secondary parameter, an implicit one, and only the changes in space define the change. Still, the space itself could be presented in a generic way using a notion of graphs. A generic one: with arbitrary nodes and relations.

As for the notion of graph, a graph may be represented with primes. Each element would be connected to another with a geometrical object defined by the GCD. A change within a connection changes the values of the nodes. A constant change means that object change and therefore we perceive the passage of time. The time was not enough due to its implicit value only, the space-time had a time param redundant, whereas the space graph with a relatively generic notion of space, based on the notion of a prime number, may be used for the description of everything at most that generic.

The clue of the recommended idea used to resolve the structure boils down to the density of connections between the elements of the graph and a referential type of an interconnection (change for one object results in a change for the connected objects). Also, the infinite number of primes could be used for the modelling of the potentially infinite.

A side note to that: the incompleteness theorem could be modelled using the fact that you cannot describe the p(n+1)p(n+5) object using p1..pn, because it is just outside the range.