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Thursday, December 2, 2010

very strange dream: time is 2D

I've had a very strange dream yesterday night. That time goes on orthogonally to our own time. That is, you can think about a problem, forever, but in the next second you find the solution. No contradiction here, you felt that "forever" has passed in a second.

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

3 comments:

ضياء الدين said...

tesada2 inception fe3lan kan keda !!!

Omar said...

hmmmm well inception argues that brains work faster inside ur dreams cause ur brain simulates another brain that is supposed to be working really fast in the simulated time.

Inception is more about being recursive than orthogonal

Actually if it was orthogonal, it shouldn't take 1 second. it should take 0 seconds. Its like moving in one dimension doesn't change the other one.

but yea, nice dream!!

ضياء الدين said...

@Omar
Think about it as multi-dimension :D
He created one more dimension for every new dream