Space being continuous or discrete

Is there any proof of space being continous or discrete?

>>13
How is that a reason for spacetime not to be discrete?

Also, if spacetime were continuous, it cannot be computed by a Turing machine. Yet within the universe, it seems it is not possible to perform hypercomputation. If it is in fact not possible (this cannot be proved, but all signs point to it), then it seems inexplicably wasteful for the universe itself to not be computable.