I know there's an urban legend that women can multi task, but even if it's true then it's only multi threading, not real multitasking.
Though what about true multitasking, where you can divide attention to two or more things at the same point of time?

While the subconscious mind does do a whole lot of stuff at parallel, is it possible to be consciously aware of doing two separate things at once, without getting confused? (For example writing a letter to your grandma with your left hand and writing a review of the movie Saw with the right one. Wouldn't want to mix up those now, would you?)

So what do you think? Is such an idea feasible?

I agree with your suggestion that there seems to be limits on parallel conscious thinking, or on consciously following multiple disparate thought streams simultaneously. Perhaps consciousness requires that items be held in working memory in the prefrontal cortex, and there's only enough room in working memory for the contents from one thought stream.

Just a note; simultaneous multithreading (as opposed to temporal multithreading) involves executing multiple instructions across multiple pipelines simultaneously, so anyone employing simultaneous multithreading should be multitasking.

As a juggler, I'd say that yes, true multitasking is very possible. Some tasks can become truly autonomous and independent tasks from the 'focused' stream of thought.

Also, I'd say the corpus callosum cases, where people physically have their brains cut in two argues that this is at least possible. It's just not the way we're organized to solving tasks.

Ryan Fenton

plus we could consider the idea of a quantum brain...infinite tasks all in a single timeless moment

OR

a higher dimensional brain, capable of different realities in the same instant. one reality chooses one option, the other reality a different option

Wow that's a pretty interesting idea!

In our time passed awake, our conscious thoughts might flow in such a way that one moment of thought closely resembles the next, and so exists a logical changing over time. Consciousness becomes a melody, where all the notes of the song are in the same key. (Maybe that's why we are attracted to music so much!)

Dreams, our unconscious thoughts, would flow in a more disordered way. There would be a lesser resemblance between consecutive instances. It would be experience none the less, but would be a less melodic song.

Has there ever existed a split-brain patient who maintained consciousness in both hemispheres, thus having two separate consciousnesses?

This would seem to suggest epiphenomenalism, where all processes are physical, including mental processes, and that thoughts do not have any momental affect on the physical body. The physics involved however, as Bryce seems to be suggesting are much more complicated than we understand, and the brain creating the mental processes functions on a quantum or higher dimensional level.

In the case of a dual-minded split-brain patient, each hemisphere would be able to perform the same physics as the full brain does, and two consciousnesses would exist.