If you split the connection between the left and right brain hemispheres as has been done to some people suffering from seizures you can then by using clever methods interview each side separate from the other and discover that they do not agree about most things.

What’s ever more interesting is that you can give tasks to one side and let the other side observe you do these tasks and when questioned it will come up with lies about why it did this despite this not being the actual reason.

Split brain experiments if you want to google more info.