Are there two of you.. one thinking and one watching yourself think?

When I was at yoga a couple of days ago, we were doing some relaxation exercises to wind us down after our stretches. "Just watch as your thoughts go by", said yoga teacher lady, intending this to be a calming exercise. And somehow we know how to do this, to watch your thoughts go by without getting too involved with them. See them, but don't get into them, watch them float past your mind.

But if you think about it, if you can watch your thoughts, then there has to be two of you right? One of you thinking the thoughts, and another watching you thinking them. The more I thought about this the more interesting it became, probably not the effect the yoga teacher had intended...