The singer-songwriter, now age 40, is a thousand miles, emotionally and artistically, from where she was when she wrote her piano pop song “A Thousand Miles” as a teenage ballet student. And while the debut single was the biggest hit of her career — earning Grammy nominations for Record and Song of the Year and placing at No. 6 on Billboard’s overall year-end chart for 2002 — she admits to me that she hated it for years. And it is still associated with some painful memories of her early days in the music business.