“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!” 
Through the Looking Glass, Lewis Caroll
A Red Queen’s race is any conflict situation where any absolute advances are equal on all sides such that the relative advantages stay constant despite significant changes from the initial state.
In other words … Much Ado/efforts and pains About Nothing; all for naught.
Learn more @ http://rationalwiki.org
A cat may look at a king.
It certainly can and it most probably may, why not? But if you are not a native speaker and/or you are reading the magnificent “Through the looking glass” there is a good chance that you miss the figurative meaning of the phrase.
‘Who are you talking to?’ said the King, going up to Alice, and looking at the Cat’s head with great curiosity.
‘It’s a friend of mine — a Cheshire Cat,’ said Alice: ‘allow me to introduce it.’
‘I don’t like the look of it at all,’ said the King: ‘however, it may kiss my hand if it likes.’
‘I’d rather not,’ the Cat remarked.
‘Don’t be impertinent,’ said the King, ‘and don’t look at me like that!’ He got behind Alice as he spoke.
‘A cat may look at a king,’ said Alice. ‘I’ve read that in some book, but I don’t remember where.‘
‘Well, it must be removed,’ said the King very decidedly, and he called the Queen, who was passing at the moment, ‘My dear! I wish you would have this cat removed!’
What it actually means is “An inferior isn’t completely restricted in what they may do in the presence of a superior. “,
or the proverb in simpler words: “even a person of low status or importance has rights.”
A little bit but now you know it 🙂
Wandering through Englishland,