Holographic principle, mathematical universe & dimensional reduction

[tobiasnas]

If the holographic principle says that the the observable universe could be represented as a two dimensional surface, and we accept the idea that the universe is itself a mathematical object, and cantor showed that we could in some cases represent higher dimensional sets within lower dimensional sets, then could we say that the universe is a one dimensional string, and could we also say that if it were a finite random string of arbitrarily large size then within it there would be apparently nonrandom strings of arbitrary length?

 

[Chalnoth]

Holography isn't always possible. There are some specific physical three-dimensional systems whose behavior can be captured by instead describing them as a different two-dimensional system.

At a bare minimum, for holography to function there needs to be a boundary. For example, the event horizon of a black hole acts as a sort of boundary separating the interior of the black hole from the exterior. It may be the case that with quantum gravity, we can fully and completely describe the interior of the black hole simply by talking about the state of its event horizon.

But that event horizon doesn't itself have a boundary: if it did, it couldn't fully-enclose the black hole. So there is no one-dimensional surface that can possibly represent the behavior of the event horizon.

You need more than just a boundary for the holographic principle to apply, but this shows that it fails even the simplest test.