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In the British show Call The Midwife, which is a show about midwifery, a lot of the dialogue is about babies. Whenever someone refers to a specific baby, they never use the definite article. So "That's not good for baby" rather than "That's not good for the baby". "I'll ask the doctor to listen to baby's heartbeat" rather than "I'll ask the doctor to listen to the baby's heartbeat". I notice they use the definitive article for everything else ("the doctor", "the children", "the hospital", "the midwife") but never for "baby".
What is the reasoning for this? Is this an archaic thing (the show is set in the 50's-60's), a British thing, a medical thing?