Twitter is testing a new feature that undermines the most basic principle of its platform, namely that all tweets are public. Now, for the first time, non-public tweets can be shared using a new trial feature allowing users to make tweets visible only to select people. “Some tweets are for everyone and others are just for people you’ve picked,” Twitter said on Tuesday, announcing the new feature, called Circle. Twitter says its new Circle feature allows you to have semi-private conversations on Twitter and build closer connections with a smaller group of people. Up to 150 users can be added to…