zero article - Why use "at" in this way?

I always see signs such as

Men at work

or

Children at play

I was wondering why we use "at" in this way. Is it just a formal way of saying Men Working / Children Playing?

Saying "At Lunch" seems sensible, yet even so I would only use this if I were out of the office etc, I wouldnt say "I'm at lunch" if I weren't changing location. If I were to say "I'm At Work" I would use this to inform someone I am at my workplace, not that I am actually working, and no one I know would say their children are "At Play" rather than "Playing".

At to me has always seemed more a word used with a location rather than an action.

Answer

The answer is "because that is how we use it". It sounds circular, but constructions like these are arbitrary. It seems that your main difficulty with this construction comes with the assumption you make in your last sentence:

At to me has always seemed more a word used with a location rather than an action.

Other uses of at that are not locative:

• I am mad at you.


• He was at peace with his decision.


• The effort was amateur at best.


• See you at 5 o'clock.

There are actually lots and lots of non-locative uses for at. From these examples, I am sure you can think of many more.

Maybe we should actually ask why at is ever used as a locative, since we have in, on, by and to? :)