The announcements all started at the same time but some went on longer than others, the imams and the pope segueing into prayers. The president and other secular leaders, having finished their remarks, stood there uncomfortably for a minute or two, then began to shuffle away toward aides who enveloped them in big warm coats. Doob and the other scientists, as much a part of the backdrop as Crater Lake, were obliged to remain in place until the last prayers ended.