I've thought of this in my recent existential crisis. It would actually not be very absurd if your clone was an exact clone of you as you are now, both mind and body. Why? Because there is a clone of us all, in our own minds. We have a separate person inside us all, that we bounce ideas off of , and that we often hold conversations with (It's not actually a separate person, I'm just using that for illustrative purposes. Its still you.). Ancient people mistook this "voice in our head" for a spirit, a separate entity that lives within our mind. There is actually a sociologist who put forth the theory recently that they mistook this entity for a god! It planted the seed for religion! But I digress, so back to our main branch of thought. If you had an exact clone, it would be like this VIOH jumped out of your mind, and suddenly materialized in front of you! Now, your thoughts and feelings would be vocalized in the world outside of your mind, instead of just inside of it. In effect, you would literally be taking to yourself, except a separate yourself, as paradoxical as that might be!
However, very soon, life would begin to separate you, and you would begin to grow apart, into separate individuals. This leads into my next thought experiment, with the non-constant variables changed (those being the clone's age at materialization, and the amount of time before you meet your clone)
Now, if the clone was an infant clone that grew up in a separate environment, the person that grew up would be VERY different from you. Personality is a combination of both nature and nurture, and this new person would be very different, like a twin almost; same base, different structure built on that base. You would be looking at a you that, while having the same starting structure, would have its variables different, its personality variables morphed by its environment.
Doing your exact clone would probably be like masturbation, except taken to a whole new level! Would that be creepy? Probably! Masturbation 2.0. Imagine watching yourself!
Could you use your gaze to psychoanalyze yourself? Wouldn't it be weird to actually know almost EXACTLY what another person is thinking? Or maybe, it would be incredibly comforting? Food for thought..
I've been watching Blade Runner and doing a transhumanism paper recently, I've been thinking about this question ( and similar ones) a lot. This is actually something that I haven't heard before , and would really like some feedback.