By analogy, computers don't write software programs. Programs 'run' in a physical environment, but I'll assert that higher levels of their 'behavior' when they interact with the outside world (for non-trivial programs) are non-transparent to someone who can only observe the physical computing elements.

The individual mind is far more complex than any existing programs. We are certainly not aware of all of the aspects of the world it is responding to. Furthermore, the diversity of those responses across the population is staggering. 'Irreducible' seems like the right adjective at present.