Dave Surgenor works as one of twelve crewmen on board a survey ship that visits and maps planets in an ever expanding bubble from Earth. The book is a series of short stories about their more interesting forays. 1) They meet a "Gray Man" that is left over from a civilization 7000 years ago and can change shape at will in its efforts to take over the space ship. The battle is won when the Gray Man does not realize, until it's too late, that Captain Aesop is a computer and thus not subject to mind control. 2) Some of the ship's crew try out Trance-Port tapes that give you a dream girlfriend that users of the tapes believe are real. The end results are unsettling when two crewmembers end up with the same girl. 3) The crew has a run-in with automated homing torpedoes from a centuries ago civilization. The theme of this story is chances and odds as they need to hit the exact same torpedo twice out of a swarm of 362 and they have 26 shots left. 4) They run into a civilization that travels in time as casually as we do in three-dimensional space. A military ship comes along and believes they can kidnap one of the time travelers but everyone gets hit by a "time bomb" and dropped millions of years into the past along with a portal that will allow two people to go back to normal time. Surgenor ends up being one of the two. 5) In the last story they run into a "Dwindlestar" where they end up shrinking into nothingness. But, it turns out they are now larger than the universe and by adjusting the ship's center of gravity they are able to steer themselves back into their spot in the normal universe and Surgenor then retires after 20 years in the Cartographical Service.