my6senseMy6sense, the maker of mobile applications that help users find the most personally relevant content, is expanding beyond smartphones today with a service that offers a new view on Twitter.

The product is an extension for Google’s Web browser. After you’ve installed it, when you visit Twitter.com you’ll see a new “my6sense” tab to the right of the timeline, retweets, and all the other standard features. If you click on the tab, you’ll get a rearranged view of all the tweets in your timeline, a view that prioritizes the content that’s relevant to you.

So for Twitter users who follow thousands or tens of thousands of other people and have an overwhelming amount of information flowing through their tweet stream, this could become the default way to view Twitter. But even if your Twitter usage is less intense, this could be a nice supplement or catch-up tool. For example, if you’ve been stuck in meetings for hours and want to see what happened on Twitter, rather than trying to skim through an entire day of tweets, you could just view the most relevant ones in My6sense.

One of the coolest things about the extension, and about the company’s approach in general, is that users don’t manually enter their preferences. Instead of explicitly telling My6sense that you’re interested in tweets about the iPhone and Facebook that come from a specific subset of the people you follow, you just behave on Twitter as you normally would, clicking on and responding to the tweets and links that you think are interesting.

The extension starts out with a basic understanding of your interests based on what you’ve tweeted already. When I installed My6sense last week, it was already doing a decent job of highlighting tweets I found interesting from people whose opinions I care about. Vice president of marketing Louis Gray said that the longer the extension is installed, the better it understands your behavior and the better its recommendations become.

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You can let My7sense cull your entire tweet stream or just focus on tweets with links. (It’s harder to figure out your preferences for tweets without links, so you may read and like a tweet without interacting with it in any way.) The extension also tailors its recommendations to the time of day. If (like me) you’re mostly interested in tech and business news during the day but prefer to click on politics- and culture-related links in the evening, My6sense’s recommendations should start to reflect that.

For now, the extension only affects your Twitter experience, but the broader vision, according to founder and chief executive Barak Hachamov, is to eventually tailor any website to your interests. The mission sounds similar to Gravity, a startup founded by former Myspace executives.

After playing with the Twitter service for a week and finding that, yes, interesting tweets keep floating to the top, I think that vision looks believable.