Generally, to start a conversation on Twitter requires seeing a tweet in more or less real-time. Tweets are found by either following the person tweeting or through a search for keyword. If too much time passes then the tweet slips down the list of latest postings to be unnoticed. Granted, if it's a particularly obscure keyword then a reply may be some days/weeks after the original tweet was posted, but in the main I would say conversations are instigated within 24 hours of posting.
Schank suggested that intelligence is intimately connected with story knowledge. Conversation is the exchange of stories. The more stories you know, the better you can select an appropriate story to tell next.
Schank says;
We are satisfied, as observers of actions, when the stories we hear match our own stories. When the match is very similar, we tell our version of the story. When the match is hardly a match at all, when we have a contradictory story, we tell it. Actually, the middle cases are the most interesting - when we have no story to tell. What do we do then? We look for one.How does this translate to Twitter? Well, I'm not sure. But my own experience of Twitter conversations suggests that for the middle cases Schank suggests I simply do not tweet back.
Unlike real-life conversations, which require some form of mutual acknowledgement and interaction to maintain, Tweets are easy to ignore. A reply is not expected from each tweet. And I think this is what happens in the middle cases.
However, for dissimilar or similar matches, I think Twitter conforms quite closely to Schank's observations on conversation.