Although our cat does not sit on my desk, I nevertheless liked this piece by Muriel Spark:
If you want to concentrate deeply on some problem, and especially some piece of writing or paper-work, you should acquire a cat. Alone with the cat in the room where you work … the cat will invariably get up on your desk and settle placidly under the desk lamp. The light from a desk lamp … gives a cat great satisfaction. The cat will settle down and be serene, with a serenity that passes all understanding. And the tranquility of the cat will gradually come to affect you, sitting there at your desk, so that all the excitable qualities that impede your concentration compose themselves and give your mind back the self-command it has lost. You need not watch the cat all the time. Its presence alone is enough. The effect of a cat on your concentration is remarkable, very mysterious.