It changes that we can prove it. In as much as you can do experiments where you "hide" actions from one half, mess with it (e.g. totally change "choices" suppos

It changes that we can prove it. In as much as you can do experiments where you "hide" actions from one half, mess with it (e.g. totally change "choices" supposedly made by the brain) and ask the other half to explain why "it" made the choice, and it will do so, unaware that the choice was made by the experimenters. It won't go "sorry, but I don't know" or similar.