Carry that Wait

Language Log: Wait, wait, don't tell me

In Prague last month, the Association for Computational Linguistics honored Lauri Karttunen with its Lifetime Achievement Reward for his contributions to the field...he left the audience with a little conundrum to puzzle over...

The construction didn't wait to is ambiguous. Here are a couple of examples from Google to to illustrate the ambiguity.

(21)  a. Deena did not wait to talk to anyone. Instead, she ran home.
        b. It hurt like hell, but I'm glad she didn't wait to tell me.

(21a) implies Deena did not talk to anyone.  But (21b) implies She told me something right away.

How does it come about that X didn't wait to do Y means either that X did Y right away or that X didn't do Y at all?
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