The Ying and Yang of Joseph R. Biden being President at 80 years of age….

The New York Times does a piece playing out the natural age slowing of things and the experience and sharpness still there….And a sense of humor….

The portrait that emerges from months of interviews with dozens of current and former officials and others who have spent time with him lies somewhere between the partisan cartoon of an addled and easily manipulated fogy promoted by Republicans and the image spread by his staff of a president in aviator shades commanding the world stage and governing with vigor.

It is one of a man who has slowed with age in ways that are more pronounced than just the graying hair common to most recent presidents during their time in office. Mr. Biden sometimes mangles his words and looks older than he used to because of his stiff gait and thinning voice.

Yet people who deal with him regularly, including some of his adversaries, say he remains sharp and commanding in private meetings. Diplomats share stories of trips to places like Ukraine, Japan, Egypt, Cambodia and Indonesia in which he often outlasts younger colleagues. Democratic lawmakers point to a long list of accomplishments as proof that he still gets the job done.

His verbal miscues are nothing new, friends note; he has struggled throughout his life with a stutter and was a “gaffe machine,” to use his own term, long before he entered Social Security years. Advisers said his judgment is as good as ever. So many of them use the phrase “sharp as a tack” to describe him that it has become something of a mantra.

Mr. Biden says age is a legitimate issue but maintains that his longevity is an asset, not a liability. “You say I’m ancient?” he said at the White House Correspondents’ Association dinner in April. “I say I’m wise.”…

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The question of Mr. Biden’s age does not come in isolation, of course. Mr. Trump, his likeliest Republican challenger, is just four years younger and was the oldest president in history until Mr. Biden succeeded him. If Mr. Trump were to win next year, he would be 82 at the end of his term, older than Mr. Biden will be at the end of this one.

While in office, Mr. Trump generated concerns about his mental acuity and physical condition. He did not exercise, his diet leaned heavily on cheeseburgers and steak and he officially tipped the scales at 244 pounds, a weight formally deemed obese for his height.

After complaining that he was overscheduled with morning meetings, Mr. Trump stopped showing up at the Oval Office until 11 or 11:30 a.m. each day, staying in the residence to watch television, make phone calls or send out incendiary tweets. During an appearance at the U.S. Military Academy at West Point, he had trouble lifting a glass of water and seemed to have trouble making his way down a modest ramp.

Most striking was Mr. Trump’s cognitive performance. He was erratic and tended to ramble; experts found that he had grown less articulate and that his vocabulary had shrunk since his younger days. Aides said privately that Mr. Trump had trouble processing information and distinguishing fact from fiction….

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