President Trump’s substantive defense against the ongoing impeachment inquiry has crumbled entirely—not just eroded or weakened, but been flattened like a sandcastle hit with a large wave.

It was never a strong defense. After all, Trump himself released the smoking gun early in L’Affaire Ukrainienne when the White House published its memo of Trump’s call with Ukrainian President Volodymyr Zelensky. That document erased any question as to whether Trump had asked a foreign head of state to “investigate”—a euphemism for digging up dirt on—his political opponents. There was no longer any doubt that he had asked a foreign country to violate the civil liberties of American citizens by way of interfering in the coming presidential campaign. That much we have known for certain for weeks.

The clarity of the evidence did not stop the president’s allies from trying to fashion some semblance of defense. But the past few days of damaging testimony have stripped away the remaining fig leaves. There was no quid pro quo, we were told—except that it’s now clear that there was one. If there was a quid pro quo, we were told, it was the good kind of quid pro quo that happens all the time in foreign relations—except that, we now learn, it wasn’t that kind at all but the very corrupt kind instead. The Ukrainians didn’t even know that the president was holding up their military aid, we were told—except that, it turns out, they did know. And, the president said, it was all about anti-corruption. This was the most Orwellian inversion; describing such a corrupt demand as a request for an investigation of corruption is a bit like describing a speakeasy as an alcoholism treatment facility.

As this tawdry fact pattern has become increasingly exposed, the only defense that remains to the president is that it does not amount to an impeachment-worthy offense—an argument difficult to square with either the history of impeachment or its purpose in our constitutional system.

Yet the president’s public support has not collapsed alongside the substance of his defense. The president’s approval rating, even as support for impeachment has ballooned, has moved only modestly. In the FiveThirtyEight average of presidential approval polls, Trump has dropped about two percentage points over the past month—which is not nothing, given the narrow range in which his approval numbers fluctuate. But it shows considerable resilience under the circumstances.

Most people know Federalist 65, if they know it at all, for its famous characterization of the impeachable offense: “those offenses which proceed from the misconduct of public men, or, in other words, from the abuse or violation of some public trust. They are of a nature which may with peculiar propriety be denominated POLITICAL, as they relate chiefly to injuries done immediately to the society itself.”

But it is in the sentences that immediately follow these words that Alexander Hamilton peered through the ages and commented on the current Republican failure to abandon Donald Trump:

The prosecution of [impeachments], for this reason, will seldom fail to agitate the passions of the whole community, and to divide it into parties more or less friendly or inimical to the accused. In many cases it will connect itself with the pre-existing factions, and will enlist all their animosities, partialities, influences, and interests on one side or on the other; and in such cases there will always be the greatest danger that the decision will be regulated more by the comparative strength of the parties than by the real demonstrations of innocence or guilt.

Nailed it.

Yes, Trump’s approval numbers show there are cracks in the wall, as every pundit is busily pointing out. But the larger point, it seems to me, is that there is still a wall. And as Hamilton argued, it is the comparative strength of that wall, not any demonstration of Trump’s innocence or guilt, that will regulate the decision as to the president’s fate. The president’s defense, in other words, has been reduced to raw political power; it is not a genuine examination of facts but rather a numbers game to assemble enough elected officials aligned with the president’s faction to refuse to look reality in the eye and thus to ensure Trump’s acquittal.

Of course, no senators or members of the House of Representatives can say this outright. Despite this era of shredded norms and broken taboos, it is still verboten to state what is so obviously true: “I refuse to support Trump’s impeachment because, however merited it may be, I am a Republican and he is a Republican and the advantage of my party would be ill-served by his removal—which might also threaten my own prospects of reelection, which depend on voters who like the president more than they like me.” Perhaps such a defense—so overtly unprincipled and open in embrace of Federalist 65—is impossible because Americans still have some shame about seeking power for its own sake. I’ll leave the reason for its impossibility to others. Suffice it for now to observe that it is impossible, which means that even those making obvious political calculations have to hide behind arguments, however implausible, that sound in some kind of principle or public good.

The problem is that it’s pretty hard to mask the reality of cold political calculus when the president’s defenses have collapsed as they have here. There are no plausibly exculpatory facts to hide behind. Each new witness makes matters worse for the president; even his own chief of staff can’t manage to talk about the matter without piling on more damning admissions. There just isn’t any good argument for Trump at this stage. So what is a poor Republican member of Congress or senator, animated by Federalist 65 but unable to admit it, to do?

Their answer is to make noise. Indeed, the more the president’s defense crumbles, the louder the noise gets: Republicans have gone after Peter Strzok. Trump has tweeted, once again, about “insurance policies.” He and his allies in Congress have complained about House Intelligence Committee Chairman Adam Schiff and about the supposed deficiencies in the “process” and the legitimacy of the House’s impeachment inquiry. They have yelled about outing the whistleblower and the procedural protections available to the president in a process he does not recognize.

But the problem with a strategy of making noise is that, if you do it long enough, the ear grows accustomed to a certain ambient level of it and the public collectively tunes it out. In order to sustain distracted attention, one has to constantly increase the volume and vary the sound. It’s not enough to quote the same text messages over and over again. Distraction has to be distracting, which means it has to be at least a little bit novel. And you always have to escalate.

And so the president and his allies have graduated from the propagation of conspiracy theories to “Storming the SCIF,” an effort by House Republicans to simply barge into the space in which the Intelligence Committee is conducting depositions and refuse to leave. The president brands career public servants and lawyers who have the temerity to represent their clients as “human scum.” They seek to censure Schiff. And, of course, they clamor for investigation of the investigators, as though if John Durham could only discredit John Brennan or James Comey or some career official no one has ever heard of, that would somehow discredit Robert Mueller, which would somehow mean that it was okay for the president to lean on Zelensky for political favors in a totally different election cycle.

It all could change, of course. Polls are unmovable until they move. Cracks in the wall are mere cracks until the wall comes down and we realize the bricks were actually just the spaces between the cracks. Senators are a fickle lot, and when the winds shift, they can shift suddenly.

Hamilton’s point was that guilt or innocence might be not be dispositive in impeachment trials. It was not that guilt or innocence doesn’t matter in the face of political power. There’s a temptation to conflate these two points. If the president’s defense has crumbled but that fact will not trigger his removal, does it even matter? In fact, the crumbling of the president’s defense matters a great deal—even if the wall ultimately holds, even if a large segment of the public refuses to engage that reality and even if a large cadre of elected officials chooses to keep escalating the noise instead of either accepting Trump’s guilt or mounting a substantive defense of his actions.

The collapse matters—even if it does not prove dispositive politically—because persuasion matters and thus persuasiveness matters. The last line of defense against a lawless, oathless president is the electoral process, and clarifying Trump’s conduct before the electorate is thus crucial to voters’ ability to make informed decisions. The process of evaluation itself also plays an important role here. The definition in the minds of members of Congress of what is unacceptable helps to articulate and reinforce norms of behavior. In a period in which we are fighting to defend norms, that articulation and reinforcement is a critical exercise.

It’s a little harder to violate a particular norm of behavior once you have publicly voted to impeach someone for it—not impossible, to be sure, but harder. Conversely, argue that conduct is acceptable or tolerable in a president, and it becomes a little easier to do it yourself. It is a notable fact that Democrats have not, by and large, argued for Trump’s impeachment based on his conduct—very likely criminal—in the Stormy Daniels and Karen McDougal matters. Having argued during Bill Clinton’s tenure that crimes undertaken to cover up mere sexual misconduct are not impeachable, Democrats are staying away from that one.

We can hope that something of the opposite effect is happening here: If the only consequence of going through this process is to make it a little harder for some Democratic president in the future to emulate Trump’s ongoing abuses of foreign policy and law enforcement in the service of political ends—because essentially all Democrats will have labeled the conduct as impeachment-worthy—that alone will be worth the process the country is going through now.

Because the adjudication matters, the record Congress builds matters too. It is important to build it rigorously, to be able to defend it as amply justifying whatever action Congress takes. And it is also important, even while tuning out the noise and not jumping in response to every frivolous process grievance Republicans may raise, to run a process that a reasonable Republican would regard as fair. The goal has to be to create a record that would speak to marginal, open-minded Republican members—even if one worries that the species is close to extinct. Every Mitt Romney, every Justin Amash, every Adam Kinzinger is important. So being persuasive—even if there are very few people to persuade—is important too. I’m less concerned here with the process points that Republicans are raising, most of which are trivial, than I am with the creation of an evidentiary record that will stand up well in the Senate, through whatever trial happens, and in the press and over time.

Because while Hamilton was surely correct that impeachments will “agitate the passions of the whole community, and ... divide it into parties more or less friendly or inimical to the accused,” while he was surely correct as well that it “will connect itself with the pre-existing factions and ... enlist all their animosities, partialities, influences, and interests on one side or on the other,” and while he was no doubt prescient in his warning that such concerns will overwhelm “real demonstrations of innocence or guilt,” democracy at the end of the day is government by persuasion.

We shouldn’t be quick to give up on persuading marginal legislators—much less marginal voters. Eventually, if only in historical retrospect, people do hear the signal through the noise.