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A Twitter user asked the other day if her followers preferred purely "on topic" tweets or if they liked some personal tweets that help you get to know the tweeter. Her replies all said the same thing: they liked a mix of business and personal tweets so they could get to know the tweeter a little. And several people mentioned that Twitter is about building relationships.
Public speaking is the same way (in fact, I might argue that you're public speaking every time you post a tweet!). If you stand up in front of an audience and recite facts, figures and data, your audience will learn a few things, but they won't connect with you personally.
The personal connection is what makes them want to know more, want to follow up with you, want to tell their friends and colleagues about you. When they can relate to you as a person and feel like they know you a little, they're more likely to recommend you to others.
People like to have relationships. They like to feel connected. Remember this when you tweet and when you speak.
Hey, are we Twitter friends yet? Here's my profile!