What's worse than being ignored or capturing someone's attention only to watch them yank it away? Getting silenced while you're still faving and retweeting into the void (emphasis mine):
In the same way you can turn on device notifications so you never miss a Tweet from your favorite users, you can now mute users you'd like to hear from less. Muting a user on Twitter means their Tweets and Retweets will no longer be visible in your home timeline, and you will no longer receive push or SMS notifications from that user. The muted user will still be able to fave, reply to, and retweet your Tweets; you just won't see any of that activity in your timeline. The muted user will not know that you've muted them, and of course you can unmute at any time.
Brutal stuff, Brutus.
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