Translation:I was very young, I could have eaten a horse.
Oh man. Where shall I begin...? :D We've been lying to you all this time. Grammatically speaking, accusative is totally fine for indefinite objects. I hope you won't sue us. ;p
The thing is, it happens quite rarely. The nuance it adds to the sentence is sort of similar to adding the adjective "given" or "any given" in English. It may or may not be translated that way, but it's good to know that whatever meaning is added by this accusative can also be achieved in English, whether you choose to do it or not. This kind of accusative is generally used in explanatory statements, encyclopediae etc. Observe the following sentences:
-- Bir yıldızı gözlemlemek için teleskop gerekir. - It's necessary to have a telescope in order to observe a (given) star.
-- Bir belgeyi kaydetmek için kontrol-S komutu kullanılabilir. - The ctrl-S command can be used to save a (given) document.
Sometimes, the accusative following a "bir" indicates that we're talking about a specific item from a group:
-- Bir kitabı kaybettim. = I've lost a specific book. / There is a book that I've lost. / I've lost one of the books. (Compare with: Bir kitap kaybettim. = I've lost a book.)
So an indefinite accusative can be translated as: "a(ny) given" or "a specific". As these are somewhat infrequent constructions, and the overuse of "indefinite accusative" really starts to sound weird at some point, we opted for banning it for the beginners in this course. :-]
Ektor, when you said you had been lying to us I started to get mad but when I read the rest I realized that there was no such lie, because you're saying that the horse, or star, were really definite for some reason that I will probably get when I grow up as a Turkish speaker. For now that will have to do (from my perspective).
This is really one of the most quirky features of Turkish and I actually haven't realized it until now. I think in the middle of definiteness and indefiniteness we have a third category and it can be called semi-definite. (I just made it up.)
So normally when the listener hears about something for the first-time we use an indefinite object.
I saw a cat. - Bir kedi gördüm. (The listener hears about the cat for the first time.)
In Turkish we don't only consider the listener but also the subject of the sentence. I mean we also have to take into account whether the subject knows about that object for the first time or not.
I forgot a person. - Bir insanı unuttum.
Here we cannot say Bir insan unuttum. because the subject already knows about that person (in order to forget someone you must already know them) and this is why we use the accusative. However since the listener hears about that person for the first time we use bir.
If we return to this example you could also say Çok gençtim, bir at yiyebilirdim. However when we make some exaggeration we tend to use this semi-definite form (I don't know why). It sounds as if the subject already has a horse available and he states that he will eat it up.
why is the statement "I was young, i could have eaten a horse"
would "çok gençken, bir atı yiyebilirim" be more concise? its a far more common everyday used sayıng in English. we always say "when I was young...." do they say it lıke that in turkey?
There again if people haven't got as far as "when & whıle" yet, they would not know "ken". Sorry, I'm on re-strengthening duties.
In that case would "ne zaman(ım) Cok gençtim..." also mean the same?
Imagine you are telling a story about your eating habits now as an old person as compared to when you were old (old people use this construction a lot in English). You example is definitely not the only thing said in English.
(Back in those days) I was very young, I could have eaten a horse. (Now I eat very little).
The last thing you wrote makes no sense. You could say "çok genç olduğum zaman" instead of "çok gençken."