At a time when the tone of American politics seems to be at rock bottom, something happens to remind everyone it can go lower still. Case in point: the latest schoolyard exchange between the president of the United States and the former vice president of the United States over who is the tougher tough guy.

Did former vice president Joe Biden really say if he and President Trump were still in high school, “I’d take him behind the gym and beat the hell out of him” for the way he has treated women? Did he really compare Trump to the “fattest, ugliest SOB” in the locker room? Did the president really tweet in response that Biden is “weak, both mentally and physically”? Did he call him “Crazy Joe”? Did he write, “He doesn’t know me, but he would go down fast and hard, crying all the way.”?

That is what passes for political discourse these days, two grown men acting like macho little boys. It would be easy to dismiss it all as so much catnip for the cable networks, which of course it is. It also is a reminder of what has happened since Trump came onto the political scene, the extent to which he has defined politics down and the degree to which others seem unable to resist playing at that level.

There are any number of unsavory aspects to the exchange. One obviously is the sheer idiocy of this kind of talk between politicians at the level of Trump and Biden.

People do expect more of their leaders. Another is the apparent glorification of violence, reveling in the equivalent of a political Fight Club.

Biden said what he said in the context of Trump’s treatment of women, the infamous “grab ‘em by the” you-know-what from the infamous “Access Hollywood” video. Michelle Obama once said, “When they go low, we go high.” So much for that admonition. Apparently, it is now, “When they go low, we go there, too.” Who would have guessed that is where things would be today?

This is the trap the president has laid for his opponents. The question for so long, when he was a candidate and then when he was the nominee and then when he took the oath of office, was whether he would become more presidential as the weight of the responsibility settled on his shoulders. After all, he once bragged that, with the exception of Abraham Lincoln, he could be “more presidential than any president who’s ever held this office.”

That is not what suits him, and he knows it. Being presidential in the traditional definition of the term is not what helped him win the Republican nomination or the presidency. Instead it was his willingness to operate with a cruder style and at a baser level than what is customarily assumed as appropriate or effective. He rewrote the rules. He understood something about the nature of politics today and of at least a portion of the electorate that others did not.

No one likes his most outrageous tweets. Yet he continues to use the platform to communicate all manner of thoughts, whether commentary on policy or events or to attack and denigrate his opponents. He breaks through partly because he continues to go places no other president has gone and in a vernacular uncommon to political speak, one that does find an audience. If congressional leaders cringe at his worst, they still refuse to stand up to him.

The Trumpian style has flummoxed political opponents. His Republican rivals tried different ways of countering him. Some tried to be “manly,” demanding indignantly that he apologize for things he had said or done. They fell by the wayside. Sen. Marco Rubio (R-Fla.) tried to play Trump’s game and ended up as “Little Marco,” diminished by a rival he could not best in the how-low-can-they-go game of tit for tat.

For Democrats contemplating a 2020 campaign against the president, there are lessons but no clear answers as to how best to counter him. Hillary Clinton tried a combination of approaches. She preferred to ignore him. She wanted to avoid getting showered by the chaff of his campaign style. She also systematically tried to declare him unfit to be president, to disqualify him in the eyes of the voters.

Many voters bought the argument. More than half the electorate on Election Day said he was not qualified to be president. Some of them still voted for him, which is why he now is president. Other factors had greater salience when people cast their ballots. Clinton had her own baggage, which other Democrats thinking of running in 2020 assume they would not have. Still, they will be dealing with an uncommon foe.

This was not the first time Biden has used some brio and bravado to talk about Trump. After all, he likes to operate in his own distinctive style. He is Bidenesque to the president’s Trumpian style. He plays the folksy neighbor, the nonelite, blue-collar kid who projects he cannot quite believe he made it to the highest echelons of American politics (though he has harbored dreams of being president as long as he has been in elective office). Had he been the Democratic nominee in 2016, might he have been president? He must believe in his heart he could have won against Trump.

Still, the question is, what possessed him to do what he did in Miami? Does he really believe fighting at that level is either becoming or effective? Is that the kind of campaign he or other Democrats who seriously seek the presidency really want to run? That is the dilemma for all of them as they get ready for 2020. Can they beat Trump at his own game? Or better, can they beat Trump by playing another game?

The Biden-Trump exchange should be mostly a throwaway. It is meaningless. Everyone can laugh it off. Except for what it says about politics today. That is where the smiling stops.