Another Practical Application For Singularities

When there is a change in concavity, there is a change in the second derivative.  When there is a change in the second or more derivative of a curvature that has enough spatial dimensions so that the Laplacian-based mapping of the traversal of the said curvature is not spurious (the curve is smooth thru out the mapping), then, the curve is said to be hermitian.  This means that, if you have a two-dimensional plane, and there is a change in both the first and the second derivative, the curve can possibly be smooth.  Yet, if there are more changes in derivative than the number of dimensions that one is considering in a given mapping of a given curvature, then, it is impossible for the said mapping to be hermitian.  When there is a change in the second derivative, then, the limit does not exist from one side to the next of the related locus where the change happens to be specifically at.

So, whenever there is a change in concavity -- or more of a change in a derivative (relating to a jointal condition here) -- there is what is known of as a singularity.  

Singularities imply the existence of infinity, yet, as an entity -- infinity is nothing that is physical or tangible.Yet, infinity must exist in order to sustain the existence of the stuff that is tangible.

My belief is that both the physical and the metaphysical are both subtended in the vastness of infinity.

The infinitesimal must be able to exist in order for motion to not jump around sporadically.

If motion jumped around sporadically, then, there would be no smooth motion.

If there was no smooth motion, then, there would be no hermicity.

Without hermicity, the motion of the Fujikawa motion would snap at the attempt to form a photon, and thus, light would have never been produced.  Yet, obviously, light exists.  Therefore, it is obvious to me that gauge-metrics go down to the infinitesimal -- way smaller than a discrete unit of time.

Consider allegorically, a cartoon (please bear with me, I have a major point).  

After many frames, the cartoon forms an animation.

Consider that during the BRST portion of each instanton, superstrings are basically at a standstill.

In-Between the durations of each individual instanton, the substringular goes through Ultimon Flow.

The integration of the successive series of instantons forms the motion that interacts as energy.

Please read some of my other related posts.

I will continue with the suspense later!

Sincerely

Samuel David Roach.