There is no unmoving mover behind the movement. It is only movement. It is not correct to say that life is moving, but life is movement itself. Life and movement are not two different things. In other words, there is no thinker behind the thought. Thought itself is the thinker. If you remove the thought, there is no thinker to be found.
According to the Buddha's teaching the beginning of the life-stream of living beings is unthinkable. THe believer in the creation of life by God may be astonished at this reply. But if you were to ask him 'What is the beginning of God?' he would answer without hesitation 'God has no beginning', and he is not astonished at his own reply.