It was a pretty amusing dream. It reminded me when I woke up with "Oracles" in the theoretical computer science sense (where you can ask an oracle a query and get the answer the next second). Actually the explanation for this is that the time the oracle takes is in a second time dimension, that is orthogonal to ours. It can take forever in its dimension, but we only feel our own orthogonal time dimension.
This also makes sense that given for instance L^P, means that the original time dimension is logarithmic (allowed to have only logarithmic number of steps in the size of the input) while the "orthogonal" time for the oracle "P" is polynomial in the size of the input. So having an oracle is just extending 1 dimensional time to 2 dimensional time.
Having several oracles can also generalize this idea to n-dimensional time. For instance L^P^EXP, you'd have 3D time. The order of which oracle has access to which is implied by the exponentiation, but that is only an artificial restriction because if it was a real 3D time then L would have access to EXP as well. Talk about Inception ....
Man, I love my dreams :D