One thing I've wanted to see tried with Twitter is the idea that you have your typical stream of tweets (vertical), but that any tweet can have depth (by swiping horizontally). Your "my thoughts" example would indicate "1/8" automatically, updating as it was created.

Means that someone can read as usual, or delve for the full series of tweets. They could provide an indication to the writer of what percentage of people read to which depth, for example.

It could work well for presenting news articles (sentence or paragraph at a time), photo galleries/essays, slidedecks, stories, advertising, etc. Using a news article as an example, some people will be interested in just the headline, others in the first three bits, a few in the full story to its end.