I was inside the new David Geffen Galleries at the Los Angeles County Museum of Art for all of 20 minutes before I realized I had absolutely no idea where I was. Fully open to the public on May 4, the galleries twist and expand and narrow and open again, and before long I'd lost the thread of any logical sequence. But I found myself not caring—that disorientation is entirely the point.

An installation view at the David Geffen Galleries, featuring El Anatsui's Fading Scroll. Museum Associates/LACMA

LACMA's long-awaited new building—designed by Pritzker Prize-winning Swiss architect Peter Zumthor in collaboration with Skidmore, Owings & Merrill —is one of the most radical projects a major American art museum has attempted in decades.…