grammar - Is there a relationship between ~たところで and するところだっ た?

I am studying an JLPT book on listening, and in two questions very close to each other, the grammatical forms ~たところで and するところだった came up.

My book defines ~たところで as giving an impression of giving up because something is perceived to be impossible. An example they give is:

走{はし}ったところで...

My rough translation is, "(we won't make it) even if we run."

My book defines するところだった as meaning something was intended, but it did not happen. An example they provide is:

危{あや}うく、だまされるところだった。

My approximate translation is, "that was close - we were almost tricked."

Both mean something won't happen in spite of intention...?

This sentence came up in a question:

お伝{つた}えするのを忘{わす}れるところでした。

And apparently it means that the speaker did not forget to tell someone something.

First, I got a little confused about which of the above two variations on ところ was being used, but either way, it seems like it's saying the person did not forget in spite of intending to. Intending to forget something seems a little weird, though, so I think something isn't adding up.

Am I right that ~たところで and するところだった are similar in meaning? Do they have anything to do with intention? And does 忘{わす}れるところでした have anything to do with intending to forget?

Answer

I understand ~たところで as "even if you try ... it's not possible that...". As such, I don't think it's really about intention, it's more about an impossible situation (though maybe it can be argued that the impossible outcome is the intention).

Your sentence might be finished with 「もう間に合わない」- making it on time is not possible despite the effort:

走ったところで、もう間に合わない。 (Even if we run, we won't make it on time).

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As for するところだった, I understand it as "something almost happen/didn't happen, it was close". It's often used with phrases like 「もうちょっとで」,「もう少しで」,「[危]{あや}うく([危]{あぶ}なく)」 to show that it was really close to something happening or not happening. There may be intention involved but it's not the focus of this structure and sometimes the intention may be less clear. Examples might be:

もう少しで乗り遅れるところだった。
I almost missed the train. (It was my intention to board that train.)

もう少しで階段から落ちるところだった。

I almost fell down the stairs. (Here the intention is less clear. People generally don't want to fall down the stairs but it's a rather "passive" intention.)

In the case of your sentence, I understand it as:

お伝えするのを忘れるところでした。
I almost forgot to pass the message. (I wanted to do it. I almost forgot but I just remembered.)