Singularities define/determine the end of definability of a system.
The singularity is the boundary of the boundary of the system; where the system ends.
This applies to the level of definition of any system; and to our system of definitions.
In the Singularity the System ‘ends’, and the UniVerse (as a whole) ‘begins’.

In a singularity, the uniVerse turns outside-in on itself; forming its inVerse.
In the singularity, a system turns itself inside-out, turning back into the uniVerse.
The dynamic of a singularity, is that of a Boundary Transition.
It is specified by the geometry of a system/boundary turning inside-out on itself: a Vortex.

The process of system inversion is a dynamic logic of dimensional changes.
Therein 4 phases of the inversion process can be explicitly described.
In science, in Systems Theory, this is formulated as the four aspects of a system.
Traditionally, this same understanding was called the Four Elements of Alchemy.

System, Boundary, Transformation, Integration.
Classical, Relativistic, Probabilistic, Unified,
Matter, Molecules, Atoms, Phase/information
Solid, Liquid, Gas, Plasma