I'm not sure that you can just turn around and move in the opposite direction through time.
Even though time is a dimension, the arrow of time is a consequence of thermodynamics. Since entropy must always increase,
there is an entropy gradient from 'past' to 'future' across the time dimension. Any information-processing device (such as your brain) is subject to the same physical laws as every other object, and increases the total entropy of the universe every time it it performs an operation. So any information-processor must perceive a total increase in entropy through time in one direction only.
This does not preclude the possibility of closed timelike curves.