Okay, this character is just weird. But in a cool way, right?
Baby is the weird, fat infant who lies in his bassinet for most of the novel. Heck, he doesn't even get a proper name. He's basically just an information tool, but since he's part of the gestalt, he's also a main character.
Baby is a super-computer, able to figure out pretty much anything the gestalt needs to know. He invents the basis for the anti-gravity generator, answering Lone's questions. Baby's knowledge would advance Unified Field Theory so far that scientists would understand psionics (psychic or mental energy). Baby's super-thoughts, if widely known, would turn the world upside down.
For the most part, Baby just lies in his bassinet, gurgling. He can receive input from anyone, but his output goes through the twins and Janie. He first sends messages strictly telepathically, but once the twins and Janie age too much to hear him that way, he signals complete thoughts to Janie by semaphoring, a fancy word for waving your arms and legs. He also stores the pictures she paints and other memories for the gestalt.
It's unclear whether Baby feels any of the loneliness most of the other members of the gestalt do. He's definitely unique and unwanted by the Prodds and Miss Kew, but he doesn't seem to feel anything.
Toward the close of the novel, he reveals to Hip that the gestalt is immortal, giving Hip the knowledge he needs to see that Gerry's life form could help the entire species. After all, the gestalt won't have to worry so much about self-preservation, being immortal.
Baby is a super-computer. He seems able to answer any question once he knows the basic facts involved.
Part 1 includes a humorous description of his psionic power in action before he knows many facts or has much experience communicating with the rest of the gestalt. Answering Lone's questions about how to unstick Mr. Prodd's truck:
Baby was matching every fact [Janie] fed him with every other fact he had been fed previously and was giving correct but unsolicited answers to situational sums of tires plus weight plus soup plus bird's nests, and babies plus soft dirt plus wheel diameters plus straw. (1.28.34)
And here we were just learning to clap at that age. Way to show us up, Baby.