Great cities are not static—they constantly change, and they take the world along with them. When New York and Chicago and Paris experienced great spurts of creativity and growth, they reshaped themselves to provide new structures that could house new talent and new ideas. Cities can’t force change with new buildings—as the Rust Belt’s experience clearly shows. But if change is already happening, new building can speed the process along. Yet many of the world’s old and new cities have increasingly arrayed rules that prevent construction that would accommodate higher densities.