I would not have considered my post lengthy by any stretch. Sean Carroll offered nothing in that short video other than an assertion that the mind is the brain, and then some consequences that follow from that raw assertion. I have done no worse than him.

As for what the mind might be if it is not the brain, that is not a short discussion. As a pointer, take a look at various substance or property dualist views, or monist views such as that of George Berkeley.