The ongoing crisis in Egypt, prima facie, is a case of irresistible force (the army) meeting an immovable object (the Muslim Brotherhood, MB). The officers have declared that “the clock cannot be turned back” (i.e. Morsi will not be reinstated), while the deposed president’s supporters aver that they will settle for nothing less than the “reestablishment of democratic rule” (one man, one vote, once). The metaphor is misleading, however. The army is firmly in charge, and the MB has lost this battle. Who will win the war remains unknown.

European Union’s foreign policy chief Catherine Ashton’s visit to Morsi on Monday provided an implicit testimony to the generals’ firmness. She was driven around Cairo at night to an army base, put on board a helicopter, and driven again to the compound where the deposed president is held. “He had been told about half an hour before I arrived that I was coming. He was, I think, pleased to see me,” Ashton said. After having a two-hour “frank, in-depth” conversation with Morsi—who “had access to news and followed developments”—she declared that he was “well,” but that she did not know where he was being held. “He is there with two advisers,” she went on. “They are there together. It is a military place. The people around him do care for him. I looked at the facilities.” She added that EU officials in Cairo would continue pursuing “a number of elements,” and she was ready to come back to Egypt if that would help.

Treating the EU chief diplomat to a James Bond-style nocturnal voyage of this kind (at least she was apparently not blindfolded) is remarkable. It would be interesting to find out whether her security detail were told of her itinerary; I guess not. “We are taking over from here,” was the likely scenario, “and we’ll bring her back some time after midnight.” In extremis the EU can dispense with the “Baroness,” of course, but the implicit significance of the episode—unnoticed by the mainstream media—is breathtaking. It is hard to imagine John Kerry or Sergei Lavrov agreeing to that kind of arrangement, which is eccentric to the point of outright disrespect.

According to the BBC Middle East correspondent Jim Muir, “the EU is one of the few outside parties capable of stepping in and trying to help the alienated and mutually suspicious Egyptian parties move away from confrontation and towards a political solution.” This is not so: the EU may try to “step in,” but it can help nothing in resolving the crisis. Both camps in Egypt know that Brussels is grandstanding, but that the signals to watch are those from Washington. Judging by Ashton’s ordeal, the generals have decided that EU is not a serious player.

The signals from Washington are confused. The Obama Administration faces the impossible task of standing up for “democracy” (i.e. bringing in the MB into the transition process, with the objective of reinstating Morsi), maintaining strong relations with Egypt’s military (which means no MB comeback on the latter’s intransigent terms, and no funding cut-off), keeping the pretense of a “peace process” between Israel and the Arabs (which means supporting Egypt’s generals for the sake of security in the Sinai, which is Netanyahu’s sine qua non), placating Turkey (which means telling Erdogan that the U.S. would help restore the MB-dominant status quo ante), and reassuring Saudi Arabia and the Emirates that the desired outcome does not mean giving power back to the MB.

This is a veritable Rubik’s Cube with no solution, and neither Obama nor Kerry are up to solving it. On Monday the White House said that it would hold Egypt’s military-backed government to its “moral and legal obligations,” which is meaningless in substance and potentially destabilizing in practice. The generals sense that the U.S. administration is out of its depth. No balancing act can reconcile mutually exclusive outcomes that the interested parties desire. According to The New York Times, Defense Secretary Chuck Hagel has repeatedly asked the head of the Egyptian armed forces, General Abdul-Fattah el-Sisi, to soften his hard-line course. Snce at the same time administration lawyers had found a legal loophole to avoid cutting off $1.5 billion a year in military aid, Sisi knows that he can proceed as he deems fit.

The U.S. dilemma between upholding “democracy” and maintaining the relationship with the Egyptian military is false. The generals are in charge, and they will pay no heed to the pleading from Washington to give the MB a break. Their perfectly plausible defense is that the MB does not want a deal, short of the impossible scenario of reinstating Morsi. They are also well aware that if the American aid were to be cut off, it would have immediate repercussions on the security of Israel’s western border in the Sinai—which Israel would inevitably present as an existential threat to its friends on the Hill.

The U.S. should stop this ambiguity and let the generals run the show. They can control the violence. Tahrir is safe. The bloodshed has not shaken up the regime. The number of victims—seventy-plus Morsi supporters were killed over the weekend—does not represent an unacceptable level of violence in Egypt. The Muslim Brotherhood members, like their Islamic brethren everywhere, subscribe to a culture of death, aka “martyrdom.” To a fervent Muslim, being killed by the Egyptian army (or by Assad’s forces in Syria, or by U.S. soldiers in Afghanistan) in what is perceived as a righteous cause is an eschatological shortcut to a blissful and eminently sensual afterlife, as promised by Muhammad in the Kuran. To many a semiliterate Morsi backer, legitimately entering the eternal world of houris is a pleasing alternative to the meaningless, miserable life, on a dollar or two a day, in the stinking slums of greater Cairo. Even if a thousand were to die in the days and weeks to come, there will be no civil war and no Morsi comeback.

The U.S. policy should follow the American interest: stability and predictability, keeping the Suez Canal open and keeping the Sinai peaceful. The military-backed government is the only party capable of providing it. Morsi is history, the EU is irrelevant, and Washington should act accordingly. Erdogan will not like it, but he has outlived his shelf-life anyway.