Operation: Is it just a name or is there a metaphor behind it?
A function of the form 
A binary operation is a special case of n-ary operation for any natural number 
It is useful at times to consider multisorted algebra, where a binary operation can be a function 
Calling a function a multisorted unary operation suggest a different way of thinking about it, but as far as I can tell the difference is only that the author is thinking of algebraic operations as examples. This does not seem to be a different metaphor the way “function as map” and “function as transformation” are different metaphors. Am I missing something?
In the 1960’s some mathematicians (not algebraists) were taken aback by the idea that addition of real numbers (for example) is a function. I observed this personally. I don’t think any mathematician would react this way today.
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“In the 1960′s some mathematicians (not algebraists) were taken aback by the idea that addition of real numbers (for example) is a function.”
As opposed to what? (An algorithm? Surely not.)
Dignus est operarius mercede sua…
An ill-founded suspicion, born of idle generalization; just as a *computer*, up untill shortly after Turing described his machines, used to be a person, so an *operator* often was (and often still is) a person; and the particular sorts of work done by a computer to give her the title were rather laborious *operations* indeed! That is, it took real work, supported by food calories, to get them done. Most of us were required to develop some proficiency at these computers’ operations in grade school, although they didn’t teach me how to extract square roots. I’ll have to check when my tutorees learned long division, next time…
I can’t mind read fifty years into the past, but I suspect that to many mathematicians back then a binary operation was a way of combining two elements of a set to give a third. (There were textbooks that said things like that.) If you brought to their consciousness the fact that that means it is a function of two variables, at least some of them were startled and said things like, yes, but I never think of a binary operation that way.