I have recently read about the information paradox of black holes and how it lead eventually to the formulation of the holographic principle. Quoting Wikipedia: "the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region — preferably a light-like boundary like a gravitational horizon."
There is a branch of classical physics, where a very similar sounding principle is nowadays almost trivially well-known, namely the field of linear wave propagation (in the language of mathematics, linear hyperbolic PDEs of second order). Huygens' principle, as it was later encoded in Kirchhoff's integral theorem, states roughly that in order to "understand" (i.e. predict, calculate) the wave propagation in a volume, you just need boundary values on the surface of the volume.
Is there any deeper mathematical connection between the holographic and Huygens' principle, or is this pure coincidence?