Pink's new single "So What," debuted on New York City's Z100 Thursday morning - and it may provide insight into her relationship with estranged husband Carey Hart.

Though Hart told PEOPLE last month that he misses "everything about" Pink - and even hopes for a future with her - Pink's new song may tell a different tale, as evidenced in her lyrics:

"And I don't need you/And guess what/I'm having more fun/And now that we're done/I'm gonna show you tonight/I'm all right, I'm just fine/And you're a tool/So so what?"

Still, on the singer's Myspace blog, she wrote about the new song: "Glad you likey's. And don't worry - Carey likey's too. We are insane."

Meanwhile, Pink has also been keeping busy filming the video for "So What," which included a ride down a Los Angeles street on a lawnmower. "This video was too much fun," she writes on her blog. "If you ever get a chance to drive a lawnmower down Sunset Blvd. - I highly suggest it."

Photo: Frank Micelotta / Getty