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The interview aired today and Silicon Alley Insider posted a clip from the show to YouTube. In the clip Stone describes his first experience with Twitter to Stewart, and says he knew "this is IT, because this is making me laugh...the world always needs humor."
And that was it. Stone decided to "double down" efforts on Twitter in lieu of other projects, and the rest is history. Of course Twitter has gone on to become so much more than a platform for laughter, but to this day it does still make us laugh.