Consciousness Understanding Consciousness - For Computer Scientists!

I've always mused at the idea that perhaps we will never understand our own conciousness. Perhaps there are different levels of conciousness, and only higher levels of conciousness can understand a lower level. For example, maybe a plant (or a computer!?) has a "conciousness" of some sort, and we can understand how a plant functions because we are at the higher level of animal "conciousness," and a being at a higher level of "conciousness" than us can fully understand how we function (What if even inanimate objects have some form of "conciousness," what ever that may be?). Well, I won't get into discussions about this here, since I know very little about conciousness and I don't really have any way to argue for any side.

I recently came across some interesting computer science problems that reminded me of this view - but applied completely to computers! If you are unfamiliar with computer science, it may be a good idea to look up Turing Machines and the Halting Problem before reading the next part.

There is a fundamental problem, called the Halting Problem on Turing Machines that are not solvable by Turing Machines, which can solve all computable problems (read: anything a computer can do). A Zeno version of the Turing Machine, a Turing Machine that doubles its speed of computation at each step, can perform an infinite amount of Turing Machine steps in just two steps due to series convergence. Thus, a Zeno Turing Machine can actually solve the Halting Problem of a regular Turing Machine! However, it is unable to solve the Halting Problem for itself or other Zeno Turing Machines. From what I can tell, this chain seems to go on forever - a Zeno Zeno Turing Machine can solve the Halting Problem for a Zeno Machine, but not itself and so on. This seems to create classes of computation problems (under the umbrella term "hypercomputation") that can't "understand" itself or anything higher, but can "understand" problem classes below it (the use of the term "understand" is even more applicable when one considers Rice's Theorem about Turing Machines being to determine some property of other Turing Machines). I don't know where the boundaries of the classes are, but the Zeno extension seems to create some pretty intuitive examples.

Of course, this has nothing to do with consciousness, but it just reminded me of it, as it seemed to be such a perfect analogy! So I hope pseudo-scientists don't take this the wrong way and get a way overblown idea of how important this "connection" between computers and conciousness is. , anyone?