So, I was thinking recently about the entire Universe. If the Universe has a finite volume, then there must be a maximum amount of information that can fit in the space, right? Let's say that you have this massive hard drive. Even it has to have a maximum amount of data that can be inserted and preserved within the hard drive. If there is an informational maximum to the universe, then what would happen if you went over it?
How would though the hard drive have more information than the Universe , since the Universe is where all your information comes from ?
If the physical universe contains a finite amount of energy, then it has a finite amount of computational capacity. That means, among other things, that there could be theorems of standard ZFC set theory that are true, yet can not possibly be proved by any human: because the smallest proof exceeds the computational capacity of the universe That's sort of a computational analog of Godel's incompleteness theorem. In a given axiom system, there is always something that's true but that can't be proven. I believe that Chaitin has actually re-proven the full esults of Godel, not just the physical computation version I outlined. Algorithmic information theory is really interesting. There are some things we simply cannot compute ... simply because the algorithm is too complex for the universe to express. So in theory there are algorithms that "God" could know but man could not ... if you define God as an entity having infinite computational capacity. A definition for our modern times!
The Universe stores information as a physical manifestation, just as hard drives do. Hard drives crash through a physical malfunction in reading/writing the data, however. For this analogy to hold in the Universe we would have to have a mechanism for "reading/writing the physical manifestations" that was liable to fail; we don't have that, we simply have data accessing and interacting with itself. The data IS the read/write head. Also, adding "more" data to a finite Universe simply means adding more of this physical manifestation that represents the data (e.g. more quantum states, more energy, etc); ignoring the feasibility of this, the act would simply expand the definition of the Universe.
