We were just discussing things like "loop" and "spin" with regards to the quantum, then, in mathematical physics one account since the '80's makes for the account of the metric, which you'll known that in mechanism its establishment is central as for the metric and norm for length and distance, there's the "zollfrei metric", as an account of for something like geometry: that Euclid, and, Poincare, make for two distinct perspectives on the plane, Euclid's _smooth_ plane, and Poincare's _rough_ plane.
Now, Poincare was a man, and furthermore a geometer, and "Euclid" is generally considered a panel, of a man.
So, much like the considerations of Dirichlet, about the continuous vis-a-vis the differential, where Dirichlet is another giant of a man, in mathematics and thus all of mathematical science, Poincare's "rough plane" then for the zollfrei (or, equivalently enough, "freizoll"), helps then when thinking about something like "Dirac's positronic sea", about something like "Einstein's Poincare's zoll-frei white-hole sea", effecting for a continuous smooth manifold of space-time and its contents, why it's as well a continuous reticulation, nowhere smooth, manifold of space-time.
Dirac's function: the Dirac delta, is not-a-real-function, yet it has a particular real analytical character, and it's used everywhere throughout analysis and is deeply embedded in all the usual formalisms of physics.
It's often enough said that physics "the real theory" is at least these things: a gauge theory.
Here that's simply enough after tendencies and propensities of oscillation and restitution and attenuation and dissipation with least-action least-gradient in a sum-of-histories sum-of-potentials: a potentialistic "the mechanics".
It's a continuum mechanics, ....