On Wednesday morning, in Britain’s House of Commons, Jeremy Corbyn, the Labour Party leader, rose to ask Prime Minister Theresa May a question. The night before, Parliament had passed an amendment expressing approval for the Brexit withdrawal agreement that May had painstakingly negotiated with the European Union, on one condition: that she renegotiate it. The amendment had been proposed by one of May’s fellow Tories, Sir Graham Brady, and passed with her government’s support. It demanded that she go straight to Brussels and tell the Europeans to ditch the part of the agreement dealing with the border between Northern Ireland, which is part of Britain, and the Republic of Ireland, which is a member of the E.U.—the most vexed aspect of Brexit. Those provisions would be replaced with what the Brady amendment, mysteriously and Britishly, refers to only as “alternative arrangements.” Could May, Corbyn wondered, “set out today what these alternative arrangements might be?”

“Well, absolutely!” May replied briskly, and then proceeded to envelop herself in vagueness. “There are a number of proposals for how that could be done.” She reeled off references to several, including the musings of Jacob Rees-Mogg, a particularly impractical Brexiteer, and catchphrases such as “unilateral exit mechanism” and “trusted-trader schemes.” She said that her government was “engaging positively” with a slew of proposals; she didn’t say which she wanted, or which would help, since some contradict one another. Nor did she acknowledge that both Ireland and the E.U. have already ruled them out. (She did point out that Corbyn has not been a model of clarity himself, which is very true, but the Brexit moment demands more than an I-know-you-are-but-what-am-I retort.)

And yet May seemed determined to project an air of victory. Two weeks ago, Parliament rejected her deal by a margin of two hundred and thirty votes; there is no record of a P.M. being defeated so badly in all of British Parliamentary history. That loss increased the risk that the U.K., which is scheduled to leave the E.U., willy-nilly, on March 29th, might simply crash out, with no divorce agreement in place, promising chaos all around. (Parliament has to approve any deal, but a no-deal Brexit can happen all by itself.) The Brady amendment passed 317–301. That was good enough, May told the M.P.s, for her to go back to Brussels with something that “crucially showed what it would take” to get a deal through Parliament.

Except that it really won’t. “Yesterday, we found out what the UK doesn’t want. But we still don’t know what the UK does want,” Donald Tusk, the president of the European Council, tweeted. President Emmanuel Macron, of France, said that there would be no renegotiation, a position that other European leaders took, as well. A European diplomat told the BBC that the only reason there wasn’t panic in Brussels about the U.K. careening to a no-deal Brexit was that officials there “still have the popcorn out”—meaning that they are fascinated by the self-destructive pyrotechnics on display in Parliament.

Brexit, which hardens the border between Britain and the rest of the E.U., is fundamentally at odds with the Good Friday Agreement, signed in 1998, a peace accord which relies on a mostly open border between the Republic of Ireland and Northern Ireland. May’s government has said that it does not want to harden that border. (The Brady amendment seconded that desire.) But it does want Brexit, which promises independently negotiated trade deals and an end to free movement. A sensible alternative—some special status for Northern Ireland—has been angrily rejected by the Northern Irish Democratic Unionists, on whom May relies for her majority. One of those things has to give.

The withdrawal agreement that May negotiated would have pushed off the problem by including a transition period that would run until the end of next year. But the agreement says that if, when the time expired, the whole thing still hadn’t been figured out, all of the U.K. would remain in a customs union with the E.U. until it was. This is called the “backstop,” and it’s what the Brady amendment rejected. By supporting the amendment, in other words, May was deciding to renounce her own deal. (Confused? This quick Brexit-for-Americans quiz might help.)

Europeans regard the backstop as essential—an insurance policy to protect Ireland and the peace process. (On Tuesday night, minutes after the Brady amendment passed, Ian Blackford, a Scottish National Party M.P., said that the Tories had “effectively ripped apart the Good Friday Agreement.”) The Brexiteers regard it as a conniving measure to keep the U.K. in the E.U. against its will.

The Brexiteers claim that they have been very clear about what they want instead. Some of them, including Rees-Mogg and Boris Johnson (whose enthusiasm is always a bad sign), have signed on to what is being called the Malthouse compromise, after May’s Housing Minister, Kit Malthouse, who was involved in its planning. The name sounds like the title of a thriller, but is a work of science fiction—unabashedly so. The basic plan is to add a year on to the transition period and, in that time, wait for “technology” to develop that will allow people to sit in warehouses distant from the actual Irish border and fill out digital forms that will then, after some process involving algorithms, allow goods to be controlled without actually going through any physical border controls. Perhaps there would even be electronic eyes and vehicle-recognizing artificial-intelligence systems.

And what about bad actors—say, smugglers submitting forms that claim a truck is carrying one cargo when it actually contains another? No problem, according to the Malthouse crew: this is where the “trusted traders” come in, along with more algorithms—or profiling mechanisms, or maybe just psychic powers—and a dose of “spot checks.” Here the plan can be said to have moved from speculative science to pseudoscience. And the backstop that it envisions, in the absence of laboratory breakthroughs, is a slightly modified no-deal Brexit.

Even May’s government admits that the technology is fanciful. When John Penrose, the state minister for Northern Ireland, was asked about the options on Wednesday morning, he said, “After examination, there are no currently available off-the-shelf solutions.” Sabine Weyand, one of the E.U.’s negotiators, was more blunt, saying, according to the Guardian, “We looked at every border on this earth, every border E.U. has with a third country—there’s simply no way you can do away with checks and controls.” She added, with regard to such proposals that had been put forward in earlier talks, “The negotiators have not been able to explain them to us and that’s not their fault; it’s because they don’t exist.”

And yet many Tory M.P.s act as though they are entranced by the idea, which they apparently mooted in their WhatsApp group chat. According to the Guardian, after Boris Johnson told the group that he thought it was a “breakthrough,” others chimed in, and Thérèse Coffey, the Parliamentary Undersecretary of State for the Environment, “also sent some enthusiastic emojis.”

Trade is not the only problem. The Brexiteers, along with many in the larger British political establishment, seem to be in a bubble of denial about what will happen to the movement of people across the Irish border after Brexit. The Republic of Ireland and the U.K. are now part of a Common Travel Area (C.T.A.) that predates and, in some respects, could theoretically survive Brexit. Currently, it allows British citizens to enter Ireland and vice versa. But it doesn’t give them the right to do so without document checks, although many in Britain think that it does.