In the days since Erik ten Hag’s unveiling as Manchester United’s next manager the talk has turned, hungrily, to the scale of the task. There is a kind of relish in this. How many years are we talking now? What’s the current bid? I hear five. I hear six. How about ten years. How about a hundred years. How about infinite years.

It is of course a pointless discussion. Partly because it has no content, nothing but numbers plucked out of the air. Let’s face it, if you’re walking in the wrong direction you’re not going to get there at all. But there is also something deeply facile about hiring a first-team manager as a kind of balm. Fix us. Give us “a culture”. Make us like Ajax, while having none of the structures that make Ajax into Ajax. In many ways bolting Ten Hag on to this ailing machine is up there with buying a replica shirt in the hope it might turn you into Johan Cruyff.

And yet as Arsenal extracted from this fun, slightly delirious game a potentially season-defining result, led by the reliably excellent Bukayo Saka; as United thrashed away without any luck at all, it was tempting to wonder. The hundred-year plan, the doom-scenario talk is rooted in an obsession with moral decay, physical cowardice, all the things people love to pick out of the theatre of sport. Is it really this complex?

Moments of theatre. Scorelines. The last thing you’ve seen. All of this has a powerful intoxicant effect. But this is basically a game of talent and money. And the world’s fifth richest football club still has a large helping of both. On a breezy day in north London United might have scored six by the hour mark. They kept hitting bar, post and goalkeeper. They offered, even in an error-strewn 3-1 defeat, evidence of the low-hanging fruit a coach as organised and as focused as Ten Hag might yet be able to scoop up.

At this level so much rests on clarity and fine margins. Most telling here was the start, a moment that seemed to capture something of the hysteria around this team. Never mind Total Football. This was Total Non-Football. Total entropy. Total collapse.

United had started slowly. Eventually Diogo Dalot gave Granit Xhaka space to hang a cross into the area – not whip or ping, just doodle one in. It was too much for the defenders of Manchester United, as first Raphaël Varane and then Alex Telles produced synchronised air clearances, a kind of folie bergéres matinee, all high-kicking grace, as the ball trundled through to Saka.

Saka cut inside. This is of course a tautology. Saka always cuts inside. But then, knowing he’s going to do it isn’t the same as having the balance, the twitch in your feet to get near him. Saka shot for the far corner. David de Gea saved. The ball fell to Nuno Tavares, unbothered by Dalot, who watched as Arsenal’s left back tapped it into the net.

Ralf Rangnick had looked relatively chipper at kick off, with that air of the demob happy boarding house master looking forward to spending more time with his jazz records. As the goal went in he turned and just frowned, a man caught in the wrong movie.

Bukayo Saka is congratulated by teammates after scoring from the spot.
Bukayo Saka is congratulated by teammates after scoring from the spot. Photograph: Charlotte Wilson/Offside/Getty Images

This has turned out to be a startlingly bad appointment: a process manager at a club with no process whatsoever. Not to mention a manager who is so clearly out of step with this kind of player, this kind of environment. United’s director of football of football John Murtough was responsible for this farcical interim appointment. At a sensible club he might be answering for it – the lost millions, the dead end to the season – with his own job.

With 28 minutes gone it was time for episode two, another helping of defending-style product from the Manchester United Entertainment Company. A series of mistakes led to Victor Lindelöf fouling Saka as Eddie Nketiah scored from an offside positions, providing a consolation penalty. It arrived via a strange VAR check, Mikel Arteta doing a kind of celebrity Goggle-Box alongside Craig Pawson. Saka scored to make it 2-0.

The odd thing was either side of this United had been tearing Arsenal to shreds. Yes, really. Jadon Sancho began taking big hungry chunks out of Cedric. Cristiano Ronaldo – who was excellent all game – eventually scored. United continued to miss chances, but to play with genuine vigour and enterprise. Bruno Fernandes missed a penalty and then lost the ball for Granit Xhaka’s brilliantly struck third Arsenal goal.

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Such is the Manchester United noise it is easy to lose sight of the fact this was of course Arsenal’s afternoon by a mile. Victory is a huge result. Performances can wait. This is about outcomes. Arteta’s team has reached that point of crisis. Either the slow steps, the weeding out, the bad days have all been part of an overarching plan, or that many-sided die falls the other way and the Arteta mini-era will be deemed another dead end, another false illumination.

It is a perfect measure of how delicate those margins are, how arbitrary some elements of this race. The Manchester United Industrial complex would do well to remember that fact. This sport offers plenty of agony, but also the chance for endless renewal. Even in the midst of a 90 minute wake for United’s league season, there was evidence of life here. The trick for Ten Hag will be to capture that, to seal it off, to make it bloom.