Maybe a better analogy would be: If you know the complete state of the universe at one moment in time, you know the state at all moments in time, because you ca

Maybe a better analogy would be: If you know the complete state of the universe at one moment in time, you know the state at all moments in time, because you can run the laws of physics (forward or backward) and compute the state at some other time without adding information. (In physics, this arises from a property called "unitarity"). The holographic principle says you can do the same thing, but by knowing the state of the universe on a boundary that encompasses the whole system (when you parameterize spacetime in a convenient way), as opposed to by knowing the state everywhere at one moment.