Q: Why do so many people say “I can’t get my head around” a problem? I always thought the expression was “I can’t get my arms around” it. You’d have to be a Hydra to get your head around a problem.
A: For dozens of years, people have been trying to get or wrap their heads, minds, brains, or arms around problems (often unsuccessfully, as in the example you mention).
The oldest of these expressions appears to be to “get one’s head around” something, a usage that the Oxford English Dictionary has been tracking since the 1920s.
The OED defines the expression and its variants as “to master or fully comprehend (a subject or fact), esp. despite initial difficulty or reluctance” or “to come to terms with (a situation).”
The dictionary’s earliest example of the usage is from the July 15, 1922, issue of Gem: “Wait a minute, my boy. Let me get my head round it.”
The most recent citation is from a July 26, 2010, post on the Spitalfields Life blog: “So many have pegged out. I can’t get my head round it. I suppose I’m next for the chop.”
The Cambridge Idioms Dictionary (2d ed.) describes the “get your head” version of the expression as informal and defines it as “to be able to understand something (usually negative).”
Cambridge gives this example of the usage: “He’s tried to explain the rules of the game dozens of times but I just can’t get my head around them.”
The OED doesn’t have separate entries for the other versions of the expression, but Cambridge defines “get your mind around something” as “to succeed in understanding something difficult or strange (usually negative).”
Here’s the example in Cambridge: “I still can’t get my mind around the strange things she said that night.”
The Cambridge Idioms Dictionary doesn’t have an entry for “get your arms around something,” but the Cambridge Dictionary of American Idioms says it means “to feel confident that you have a good understanding of something that is complicated.”
The dictionary gives this example of what its editors apparently consider an American idiom: “There are so many different aspects of the energy situation that it’s hard to get your arms around it.”
The use of “wrap” instead of “get” in the expression seems to be a relatively recent phenomenon. In a search of Google Books, we found this example in Wild Harvest, a 1987 novel by Eleanor Gustafson: “I can’t wrap my mind around the stuff I should believe.”
As for the hydra-headed business, relax. Idioms don’t have to make literal sense. So don’t worry your head about them.
[Update, Jan. 6, 2015. A reader of the blog sent in this interesting comment: “Given the 1920s early citation of ‘get one’s head around’ something, I’m wondering if it’s a humorous inversion of getting something into one’s head, parallel to P. G. Wodehouse’s frequent use of ‘getting outside’ something (or similar words) to mean consuming food or drink. For instance, ‘The Oldest Member, who had been meditatively putting himself outside a cup of tea and a slice of seed-cake, raised his white eyebrows.’ (From a short story, ‘The Long Hole,’ published in The Strand, August 1921.) And this even earlier example: ‘You were in bed. Remember? You got outside your breakfast, while I sat on the chest of drawers and asked you questions.’ (From ‘How Kid Brady Joined the Press,’ published in Pearsons, May 1906.)”]