Fictional event from Lewis Carroll's Through the Looking-Glass
The Red Queen's race is an incident that appears in Lewis Carroll's "Through the Looking-Glass" and involves both the Red Queen, a representation of a Queen in chess, and Alice constantly running but remaining in the same spot.
"Well, in our country," said Alice, still panting a little, "you'd generally get to somewhere else—if you run very fast for a long time, as we've been doing."
"A slow sort of country!" said the Queen. "Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!" 
The Red Queen's race is often used to illustrate similar situations:
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