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In the same way that a holographic projection is physically two-dimensional, but contains enough data to appear three-dimensional from many different angles? (I'm guessing here, I don't really get holograms.)

A regular photograph captures the intensity pattern of light at a particular location at a particular time.

Holograms recreate the interference pattern of light in a volume of space. By interfering two coherent sources using a film that has the interference pattern captured, you recreate the interference pattern. Hence it exists in 3-D.

Thank you for that description, now I understand it at least on a basic conceptual level.

That sounds like Stokes' Theorem!