Accept, for a moment, Joe Biden’s contention that he is as mentally as sharp as ever. Then try to explain some revelations of the books beginning to appear about his presidency: that he never held a formal meeting to discuss whether to run for a second term; that he never heard directly from his own pollsters about his dismal public standing, or anything else; that by 2024 most of his own cabinet secretaries had no contact with him; that, when he was in Washington, he would often eat dinner at 4.30pm and vanish into his private quarters by 5.15; that when he travelled, he often skipped briefings while keeping a morning appointment with a makeup artist to cover his wrinkles and liver spots. You might think that Mr Biden—that anyone—would welcome as a rationale that he had lost a step or two. It is a kinder explanation than the alternatives: vanity, hubris, incompetence.