Am I Just A Thought?

The eye sees the world
Then comes a thought which says -'I see the world'
A thought appears in the mind

And another thought immediately comes in to say - 'I am thinking'
This 'I' seems to always come in after the event is over
Is it possible that this 'I' has no real existence at all?

Is it possible that this 'I' has never done or thought anything?
Is it possible that everything happens by itself and that 'I' is just a thought, an idea in the mind?