Can we "think" with our heart or gut?

You may be thinking of the enteric nervous system of the intestine, which Michael Gershon (a well known gut neuroscientist) has termed, "the second brain," and which is also the title of a recent popular science book he wrote on the subject. Gershon (I think he's still Chairman of the Cell Biology & Anatomy Dept. at Columbia University Med School) is not just any popular science writer, he's an M.D. himself, and has been an active researcher at the top of the field of gut physiology, particularly the enteric nervous system, for decades. He has called it that because if you cut the nerves that connect the brain and gut, the gut can still function fairly well, independently of its connection to the central nervous system--it can still "think," though not in the sense our brains think--but its ability to move food down its length is only slightly impaired, its ability to digest and absorb nutrients are little affected, and it pretty much can function very well without that connection to the CNS. It can do this because in its wall, and unique among all the organ systems, it has a rich network of its own neurons and ganglia which serve to locally control its movement and other activities.