P=TC0?

Once upon a time, mathematicians orbiting PSR 1257+12 were studying the P=TC0? question. In their dauntless pursuit of knowledge they explored many worlds until they chanced upon a bluish planet in the Local Group. There they found bipeds who appeared to be able to carry out computation, at least on finite inputs. This incarnation of P puzzled the mathematicians, though they didn’t know what to make of it. Until one day a biped slid and their skull split open. The mathematicians were astonished at the sight of the biped’s brain, the source of the biped’s computational ability. It was arranged as a network of neurons, much wider than deep, rather like TC0.