On November 4th — exactly six months from Alice's May 4th birthday, making it her 'un-birthday' — Alice steps through the looking glass above the fireplace into a mirror-world where chess pieces are alive, advertisements precede the shops, and the Red Queen advises running as fast as possible just to stay in place. Carroll embedded the date as a private note: the mathematical precision of the half-birthday is exactly the kind of joke he savored.