No - if it's mutually, it must obviously be "ourselves" if the subject is "we". Note that the English sentence is fine without an explicit "ourselves" - the "each other" in combination with the subject "we" unambiguously identifies the object as well.
Esperanto needs the "nin", yes, but you can't say that it does so because of some logical necessity.
It is not because a speaker of languages where the object wouldn't be needed doesn't understand the sentence. It is needed because "helpi" is a transitive verb and requires an object.
English also is totally fine with saying "The door closed".
Native speakers of eg. Esperanto or any Scandinavian language would sit there waiting for the rest of the sentence: The door closed... what? The door closed the locker, the car, the book?
So to speakers of other languages "nin" might be a logical necessity here.
But the course is titled Esperanto for speakers of English.... so you can't blame someone wondering why "nin" is required.
I wanted to ask the same question.
I don't know that that is true. How about "We helped them reciprocally"? Of course, with "each other" it is implicit, but Esperanto doesn't have "each other"; what it has is more closely equivalent to "reciprocally". Even in English, when you use that, you still need the object.
Ne, "Ni helpis ilin reciproke"
We can reciprocate help between more than just ourselves.
Ni * helpis * nin *.
All those * are acceptable places put reciproke. I think you can even put it at the beggining, before 'ni' in this sentence.
If you were to just say "Ni helpis nin" it could be translated as "We helped ourselves" which could just mean that everyone just helped their own selves. Adding "reciproke" makes it unambiguous: "We helped each other."
I feel that 'Ni helpis reciproke' would be clear and not incorrect Esperanto. A transitive verb doesn't necessarily need to take an object, nor, as in this special case, does a reflexive verb, but only because the adverb 'reciproke' states the reflexive nature of the action.
"We helped mutually"?
In both languages, it feels to me as if something is missing.
Interesting point, Mizinamo. I agree that 'We helped mutually', which is your translation, not mine, is not conventional English but also not incorrect, and I would say rather elevated stylistically. It does have a degree of ambiguity in that it could also be used when two people take turns in helping a third. And I imagine the same could be said for the Esperanto 'Ni helpis reciproke.' Whereas 'Ni helpis nin reciproke' allows no ambiguity.
Why is "We helped ourselves" not a correct translation? While English is not my first language, it feels equivalent to "We helped each other"
ourselves is reflexive while each other is reciprocal.
If you have Peter, Paul, and Mary, and they all help themselves, then Peter helps Peter, Paul helps Paul, and Mary helps Mary.
But if Peter, Paul, and Mary all help each other, then Peter helps Paul, Paul helps Mary, and Mary helps Peter (for example).