North Carolina and the federal government are suing each other over whether the state's new transgender bathroom regulation violates federal civil rights laws. The cultural stakes are clear: the two governments have sharply different ideas about the acceptance of transgender people. But what about the legal stakes?

The legal problem in the case is whether the North Carolina law, which bars transgender people from restrooms, locker rooms and changing rooms, violates the provision of the Civil Rights Act of 1964 that prohibits discrimination on the basis of sex.

That question may sound simple, but it's actually profound. It will require a court to decide whether gender is the same thing as sex, and if so, for what purposes.