いくほどの年を経たものか
I know the basic uses of ものか like strong negation etc, but I do not understand this use. Does it have the same meaning here as ことか? Is the speaker wondering about the present or the past?
Is it related to this 日本語文法辞典 entry that appear in this topic: What does the ~たものか mean in どうやって彼らを誤魔化したものか??
What are the possible meanings of 過去形＋ものか？
As for the sentence in question, 過去形 is simple past.
In the same I wonder sense of 過去形+ものか, a past tense can be used for something that hasn't happened yet, as in the following question and the linked one.
(A little superficial, but) It can be considered something like subjunctive in English.
To some extent, this is ambiguous. That is, 過去形＋ものか can mean a thing that happened or haven't happened. For example, どう言い訳したものか in some contexts can mean I wonder how (someone else) explained (in the past).
(added)
At the bottom, ものか makes the question rhetoric. A J-E dictionary has the following:
1〔思案〕
行ったものかどうか
I wonder whether I should go (or not).2〔強い反問〕
二度とあそこに行くものか
I will never go there again.／《俗》 I'll be damned if I go there again!
そんなこと知るものか
How would I know (such a thing)?
I agree that 現在形＋ものか tends to mean 2, but it still depends on context.
is #1 above and 'I wonder if it will work; I can't tell unless I actually try'.
is 'How can this work = Never!' and means #2.
