Someone was telling me about the holographic principle, basically he said that the state of a system is determined entirely by the values of various physical quantities on its boundary. This is not exactly what it says on Wikipedia's Holographic Principle article - "The holographic principle is a principle of string theories ... that states that 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".
I think Wikipedia's definition is a bit confusing to a beginner, since string theories have maybe 10 dimensions, so it's not clear what "lower-dimensional" means (9 dimensions?), and also since it requires one to understand the concept of a "light-like" geodesic and how this concept can be extended to define a "light-like boundary" surface.
I am wondering if the same principle can be stated in a more elementary form without invoking string theory. For example, is it the case that knowing the electric and magnetic field on the surface of a sphere will tell me the spatial distribution and velocities of charges within the sphere? If so, does this simpler idea have a name? (Would it be incorrect to refer to it as the holographic principle?)