Mindaugas braught this topic to light and described this one new field of Science - Philosophy of Mind. This field is a sort of combination of philosophy and neurobiology. I do not want to convince you of anything, I just wanted to talk about the first ideas that came to my mind while thinking about this duality of body and consciousness.
First of all, let me say how I imagine the machinery behind the process of thinking (my ideas are actually based on books of Kandel, Koch, Martynas Ycas, etc.). We all know that all types of signals that come from our senses are converted into trains of electrical impulses (spikes), they travel through our body with a limited speed and are processed inside our brain. You might think, that when we are thinking these external senses are unimportant, but you are mistaken. Every word/sight is encoded into the brain as a pattern of some sort, for example when we smell fish the pattern is of one type, when we smell carrot it is different. These patterns are just some average electrical activity in brain regions (or if we look at it even more closely - synaptic connections and their relative strength and activity). Patterns are not constant and they change - merge, move or dissolve when time flows. The first idea comes to our mind is when external impulses manage to resemble some pattern which is stored inside our brain. When this pattern is activated - it has connections to all other different kinds of patterns, for example, when we think of carrot, the next idea could be the visualization of it, orange color, rabbit or any other idea which is personal to every individual's experience. So it may seem to you that you "yourself" started thinking about some sort of music, when actually the electrical activity of your body sparked this idea. This is the way we think and there is no divine intervention, just pure simple correlation of electrical impulses and their resemblance to a pattern of some sort.
Shortly, I disagree with this duality of body and consciousness, because there is no such thing as "thinking without the body", as there is no such thing as electrical current without the voltage difference. Thoughts, ideas and feelings are just properties of your body, when brain dies - these die with it. The biggest mistake people make is when they say that an idea of "seven headed monster with lizard's tail and bat's wings" comes out of nowhere - it's not true, this one is just a product of different patterns of your brain.
If you take a look at evolution of science - it's all the same: people are just trying to break down complex laws of nature into small understandable and "thinkable" blocks. The biggest genius (Einstein, Newton, etc.) is this who can produce a wide array of patterns (or, in other words, associations) - by using different patterns he manages to simplify complex laws and produce these comprehensive blocks, which can be understood by everyone.