They also communicate by touch and smell, and by sound at frequencies we can't hear. No amount of human attention can entirely replace the company of another rat. Rats with company live more full and active lives than those kept alone. There are many experiences open to them which the single rat simply cannot have. And no matter how much attention a person gives a single rat, she will not be available 24 hours a day and willing to play in the middle of the night when rats are at their most active.
Rats are just too intelligent and easily bored to be left alone when they want to play.
Occasionally a rat will be too aggressive to live with another. Males who are often used for stud or who weren't introduced to a companion when young, may fall into this category. In some cases there is little alternative to keeping them alone. But in many cases, all that's required is a more gradual introduction process or neutering. Because it's not natural for rats to be alone, single rats sometimes develop neurotic tendencies or behavioral problems.