The New York Times was recently the target of a protest by a group protesting its “sanewashing” of Trump, that is, publishing stories that made his incoherent speeches sound normal when they were not. Critics have complained that the Times published many stories about Biden’s age and his gaffes and misstatements, but overlooked Trump’s gaffes and persistent lying.

With this story by Peter Baker and Dylan Freedman, with the assistance of two journalists who excerpted relevant videos, the Times may have mollified the critics. The story contains excellent video clips that show Trump making incoherent statements. Unfortunately, I was unable to copy them. Each of them shows Trump saying what is quoted in the article.

The story begins:

Former President Donald J. Trump vividly recounted how the audience at his climactic debate with Vice President Kamala Harris was on his side. Except that there was no audience. The debate was held in an empty hall. No one “went crazy,” as Mr. Trump put it, because no one was there.

Anyone can misremember, of course. But the debate had been just a week earlier and a fairly memorable moment. And it was hardly the only time Mr. Trump has seemed confused, forgetful, incoherent or disconnected from reality lately. In fact, it happens so often these days that it no longer even generates much attention.

He rambles, he repeats himself, he roams from thought to thought — some of them hard to understand, some of them unfinished, some of them factually fantastical. He voices outlandish claims that seem to be made up out of whole cloth. He digresses into bizarre tangents about golf, about sharks, about his own “beautiful” body. He relishes “a great day in Louisiana” after spending the day in Georgia. He expresses fear that North Korea is “trying to kill me” when he presumably means Iran. As late as last month, Mr. Trump was still speaking as if he were running against President Biden, five weeks after his withdrawal from the race.

With Mr. Biden out, Mr. Trump, at 78, is now the oldest major party nominee for president in history and would be the oldest president ever if he wins and finishes another term at 82. A review of Mr. Trump’s rallies, interviews, statements and social media posts finds signs of change since he first took the political stage in 2015. He has always been discursive and has often been untethered to truth, but with the passage of time his speeches have grown darker, harsher, longer, angrier, less focused, more profane and increasingly fixated on the past.

According to a computer analysis by The New York Times, Mr. Trump’s rally speeches now last an average of 82 minutes, compared with 45 minutes in 2016. Proportionately, he uses 13 percent more all-or-nothing terms like “always” and “never” than he did eight years ago, which some experts consider a sign of advancing age.

Similarly, he uses 32 percent more negative words than positive words now, compared with 21 percent in 2016, which can be another indicator of cognitive change. And he uses swearwords 69 percent more often than he did when he first ran, a trend that could reflect what experts call disinhibition. (A study by Stat, a health care news outlet, produced similar findings.)

Mr. Trump frequently reaches to the past for his frame of reference, often to the 1980s and 1990s, when he was in his tabloid-fueled heyday. He cites fictional characters from that era like Hannibal Lecter from “Silence of the Lip” (he meant “Silence of the Lambs”), asks “where’s Johnny Carson, bring back Johnny” (who died in 2005) and ruminates on how attractive Cary Grant was (“the most handsome man”). He asks supporters whether they remember the landing in New York of Charles Lindbergh, who actually landed in Paris and long before Mr. Trump was born.

He seems confused about modern technology, suggesting that “most people don’t have any idea what the hell a phone app is” in a country where 96 percent of people own a smartphone. If sometimes he seems stuck in the 1990s, there are moments when he pines for the 1890s, holding out that decade as the halcyon period of American history and William McKinley as his model president because of his support for tariffs.

And he heads off into rhetorical cul-de-sacs. “So we built a thing called the Panama Canal,” he told the conservative host Tucker Carlson last year. “We lost 35,000 people to the mosquito, you know, malaria. We lost 35,000 people building — we lost 35,000 people because of the mosquito. Vicious. They had to build under nets. It was one of the true great wonders of the world. As he said, ‘One of the nine wonders of the world.’ No, no, it was one of the seven. It just happened a little while ago. You know, he says, ‘Nine wonders of the world.’ You could make nine wonders. He would’ve been better off if he stuck with the nine and just said, ‘Yeah, I think it’s nine….’”

Mr. Trump dismisses any concerns and insists that he has passed cognitive tests. “I go for two hours without teleprompters, and if I say one word slightly out, they say, ‘He’s cognitively impaired,’” he complained at a recent rally. He calls his meandering style “the weave” and asserts that it is an intentional and “brilliant” communication strategy….

How much his rambling discourse — what some experts call tangentiality — can be attributed to age is the subject of some debate. Mr. Trump has always had a distinctive speaking style that entertained and captivated supporters even as critics called him detached from reality. Indeed, questions have been raised about Mr. Trump’s mental fitness for years.

John F. Kelly, his second White House chief of staff, was so convinced that Mr. Trump was psychologically unbalanced that he bought a book called “The Dangerous Case of Donald Trump,” written by 27 mental health professionals, to try to understand his boss better. As it was, Mr. Kelly came to refer to Mr. Trump’s White House as “Crazytown….”

He does not stick to a single train of thought for long. During one 10-minute stretch in Mosinee, Wis., last month, for instance, he ping-ponged from topic to topic: Ms. Harris’s record; the virtues of the merit system; Robert F. Kennedy Jr.’s endorsement; supposed corruption at the F.D.A., the C.D.C. and the W.H.O.; the Covid-19 pandemic; immigration; back to the W.H.O.; China; Mr. Biden’s age; Ms. Harris again; Mr. Biden again; chronic health problems and childhood diseases; back to Mr. Kennedy; the “Biden crime family”; the president’s State of the Union address; Franklin D. Roosevelt; the 25th Amendment; the “parasitic political class”; Election Day; back to immigration; Senator Tammy Baldwin; back to immigration; energy production; back to immigration; and Ms. Baldwin again.

Some of what he says is inexplicable except to those who listen to him regularly and understand the shorthand. And he throws out assertions without any apparent regard for whether they are true or not. Lately, he has claimed that crowds Ms. Harris has drawn were not real but the creation of artificial intelligence, never mind the reporters and cameras on hand to record them.

He mispronounces names and places with some regularity — “Charlottestown” instead of “Charlottesville,” “Minnianapolis” instead of “Minneapolis,” the website “Snoops”instead of “Snopes,” “Leon” Musk instead of “Elon.”

In Rome, Ga., he went on an extended riff about Mr. Biden in swim trunks on a beach. “Look, at 81 — do you remember Cary Grant? How good was Cary Grant, right? I don’t think Cary Grant, he was good. I don’t know what happened to movie stars today. We used to have Cary Grant and Clark Gable and all these people. Today we have — I won’t say names because I don’t need enemies. I don’t need enemies. I got enough enemies. But Cary Grant was like, Michael Jackson once told me, ‘The most handsome man, Trump, in the world.’ Who? ‘Cary Grant.’ Well, we don’t have that anymore. But Cary Grant at 81 or 82 — going on 100, this guy, he’s 81 going on 100 — Cary Grant wouldn’t look too good in a bathing suit either, and he was pretty good-looking, right?…”

He considers himself the master of nearly every subject. He said Venezuelan gangs were armed “with MK-47s,” evidently meaning AK-47s, and then added, “I know that gun very well” because “I’ve become an expert on guns.” He claims to have been named “man of the year” in Michigan, although no such prize exists.

He is easily distracted. He halted in the middle of another extended monologue when he noticed a buzzing insect. “Oh, there’s a fly,” he said. “Oh. I wonder where the fly came from. See? Two years ago, I wouldn’t have had a fly up here. You’re changing rapidly. But we can’t take it any longer.”

But like some people approaching the end of their eighth decade, he is not open to correction. “Trump is never wrong,” he said recently in Wisconsin. “I am never, ever wrong.”