Summary: When baby sitters first started baby-sitting, we had no way to talk about what they were doing. That's because at first, all we had was a noun – there was no verb to speak of. According to the Oxford English Dictionary, the noun "baby sitter" was first recorded in 1937. The verb "baby-sit" didn’t come along until 1946. Linguists call this a back-formation. A back-formation is when a new word is formed by removing "actual or supposed affixes." In this case, the "er" suffix is removed from the
