The first time you hear the song of the summer, you know what the summer is going to be like. Other hits will land over the next few weeks, but the weirdly titled “#Beautiful,” Mariah Carey’s duet with the silk-voiced R&B singer Miguel, will make an impact you may not be prepared for. I wasn’t. The music critics I follow on Twitter all took notice within hours of its arrival—I was at work and didn’t hear it until a little later. When I did, I knew what they meant.

I had to listen again.

And again.

After 10 or 15 plays, I wondered what it would be like to live in the song a while. After 30 plays I decided I had to take drastic action to get it out of my system.

I have 99.5 days of music in my iTunes library. I am a paying Spotify subscriber and can hear pretty much anything I want within seconds.

I decided to listen only to “#Beautiful” for a week.

To restrict my choice to one song felt perversely old-fashioned—infantilizing, even, as if I had just come back from a birthday party or bar mitzvah with a 45 as a party favor and wouldn’t get my allowance for a week. [...]