I am a jazz fusion drummer and I often use both sides of my brain.
The right side is always arguing with the left.
Your comment reminds me of the tale of two-headed birds. It is the legend told along Silk road. There were a bird with two heads. They share the same body. If one tries to kill the other, both would die. However, two heads hate each other so much that they fought all the time. In the end, one killed the other, killing them both:
The painting of two-headed birds
